diff options
| author | dos-reis <gdr@axiomatics.org> | 2008-09-21 05:21:05 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2008-09-21 05:21:05 +0000 |
| commit | 70462ce64473329cbb0108e4bde18bb797196f99 (patch) | |
| tree | 19cc4b8b23f8428b5574c9c6968c968f1b87d619 | |
| parent | efd27489ffb3778032742b14697166bc9bdef365 (diff) | |
| download | open-axiom-70462ce64473329cbb0108e4bde18bb797196f99.tar.gz | |
* algebra/boolean.spad.pamphlet (Boolean): Now belong to
OrderedFinite.
| -rw-r--r-- | src/ChangeLog | 5 | ||||
| -rw-r--r-- | src/algebra/boolean.spad.pamphlet | 4 | ||||
| -rw-r--r-- | src/algebra/strap/BOOLEAN.lsp | 19 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 748 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1128 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1304 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8586 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 25502 |
8 files changed, 18652 insertions, 18644 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index ef3796f0..9c24e981 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,3 +1,8 @@ +2008-09-21 Gabriel Dos Reis <gdr@cs.tamu.edu> + + * algebra/boolean.spad.pamphlet (Boolean): Now belong to + OrderedFinite. + 2008-09-20 Gabriel Dos Reis <gdr@cs.tamu.edu> * interp/sys-macros.lisp (|byteEqual|): New. diff --git a/src/algebra/boolean.spad.pamphlet b/src/algebra/boolean.spad.pamphlet index b9cb64cb..735c7fcf 100644 --- a/src/algebra/boolean.spad.pamphlet +++ b/src/algebra/boolean.spad.pamphlet @@ -353,14 +353,14 @@ Logic: Category == BasicType with )abbrev domain BOOLEAN Boolean ++ Author: Stephen M. Watt ++ Date Created: -++ Change History: +++ Date Last Changed: September 20, 2008 ++ Basic Operations: true, false, not, and, or, xor, nand, nor, implies ++ Related Constructors: ++ Keywords: boolean ++ Description: \spadtype{Boolean} is the elementary logic with 2 values: ++ true and false -Boolean(): Join(OrderedSet, Finite, Logic, PropositionalLogic, ConvertibleTo InputForm) with +Boolean(): Join(OrderedFinite, Logic, PropositionalLogic, ConvertibleTo InputForm) with true: % ++ true is a logical constant. false: % diff --git a/src/algebra/strap/BOOLEAN.lsp b/src/algebra/strap/BOOLEAN.lsp index ebdb87c8..39b700a3 100644 --- a/src/algebra/strap/BOOLEAN.lsp +++ b/src/algebra/strap/BOOLEAN.lsp @@ -128,12 +128,13 @@ |false| 115 |equiv| 119 |convert| 125 |coerce| 130 |and| 135 |\\/| 141 >= 147 > 153 = 159 <= 165 < 171 |/\\| 177) 'NIL - (CONS (|makeByteWordVec2| 1 '(0 0 0 0 0 0 0 0)) - (CONS '#(|OrderedSet&| NIL |Logic&| |SetCategory&| NIL - NIL |BasicType&| NIL) - (CONS '#((|OrderedSet|) (|Finite|) (|Logic|) - (|SetCategory|) (|ConvertibleTo| 34) - (|PropositionalLogic|) (|BasicType|) + (CONS (|makeByteWordVec2| 1 '(0 0 0 0 0 0 0 0 0)) + (CONS '#(NIL |OrderedSet&| NIL NIL |Logic&| + |SetCategory&| NIL |BasicType&| NIL) + (CONS '#((|OrderedFinite|) (|OrderedSet|) + (|PropositionalLogic|) (|Finite|) + (|Logic|) (|SetCategory|) + (|ConvertibleTo| 34) (|BasicType|) (|CoercibleTo| 37)) (|makeByteWordVec2| 40 '(1 25 18 0 26 1 32 0 31 33 1 34 0 32 @@ -181,7 +182,7 @@ ((= ((|Boolean|) $ $)) T (ELT $ 19)) ((~= ((|Boolean|) $ $)) T (ELT $ NIL))) (|addModemap| '|Boolean| '(|Boolean|) - '((|Join| (|OrderedSet|) (|Finite|) (|Logic|) + '((|Join| (|OrderedFinite|) (|Logic|) (|PropositionalLogic|) (|ConvertibleTo| (|InputForm|)) (CATEGORY |domain| @@ -194,8 +195,8 @@ T '|Boolean| (|put| '|Boolean| '|mode| '(|Mapping| - (|Join| (|OrderedSet|) (|Finite|) - (|Logic|) (|PropositionalLogic|) + (|Join| (|OrderedFinite|) (|Logic|) + (|PropositionalLogic|) (|ConvertibleTo| (|InputForm|)) (CATEGORY |domain| (SIGNATURE |true| ($) |constant|) diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index ceff1afe..b5166231 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2255670 . 3430960042) +(2255670 . 3430962939) (-18 A S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) NIL NIL (-19 S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) -((-4329 . T) (-4328 . T) (-2608 . T)) +((-4329 . T) (-4328 . T) (-2609 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (* (($ (|Integer|) $) "\\spad{n*x} is the product of \\spad{x} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}."))) @@ -46,7 +46,7 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4325 . T) (-4323 . T) (-4322 . T) ((-4330 "*") . T) (-4321 . T) (-4326 . T) (-4320 . T) (-2608 . T)) +((-4325 . T) (-4323 . T) (-4322 . T) ((-4330 "*") . T) (-4321 . T) (-4326 . T) (-4320 . T) (-2609 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,{}x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,{}x,{}y,{}a..b,{}c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b,{} c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,{}x,{}y,{}xMin..xMax,{}yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) @@ -56,7 +56,7 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|Syntax|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|Syntax|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -1409) +(-32 R -1410) ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p,{} n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p,{} x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) NIL ((|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) @@ -66,7 +66,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4328))) (-34) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) -((-2608 . T)) +((-2609 . T)) NIL (-35) ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\spad{acosh(x)} returns the hyperbolic arc-cosine of \\spad{x}."))) @@ -74,7 +74,7 @@ NIL NIL (-36 |Key| |Entry|) ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4328 . T) (-4329 . T) (-2608 . T)) +((-4328 . T) (-4329 . T) (-2609 . T)) NIL (-37 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#2|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) @@ -88,11 +88,11 @@ NIL ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{} [a1,{}...,{}an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-40 -1409 UP UPUP -3148) +(-40 -1410 UP UPUP -1830) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4321 |has| (-398 |#2|) (-354)) (-4326 |has| (-398 |#2|) (-354)) (-4320 |has| (-398 |#2|) (-354)) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| (-398 |#2|) (QUOTE (-143))) (|HasCategory| (-398 |#2|) (QUOTE (-145))) (|HasCategory| (-398 |#2|) (QUOTE (-340))) (-1524 (|HasCategory| (-398 |#2|) (QUOTE (-354))) (|HasCategory| (-398 |#2|) (QUOTE (-340)))) (|HasCategory| (-398 |#2|) (QUOTE (-354))) (|HasCategory| (-398 |#2|) (QUOTE (-359))) (-1524 (-12 (|HasCategory| (-398 |#2|) (QUOTE (-225))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (|HasCategory| (-398 |#2|) (QUOTE (-340)))) (-1524 (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-398 |#2|) (QUOTE (-340))))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-359))) (-1524 (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (QUOTE (-225))) (|HasCategory| (-398 |#2|) (QUOTE (-354))))) -(-41 R -1409) +((|HasCategory| (-398 |#2|) (QUOTE (-143))) (|HasCategory| (-398 |#2|) (QUOTE (-145))) (|HasCategory| (-398 |#2|) (QUOTE (-340))) (-1525 (|HasCategory| (-398 |#2|) (QUOTE (-354))) (|HasCategory| (-398 |#2|) (QUOTE (-340)))) (|HasCategory| (-398 |#2|) (QUOTE (-354))) (|HasCategory| (-398 |#2|) (QUOTE (-359))) (-1525 (-12 (|HasCategory| (-398 |#2|) (QUOTE (-225))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (|HasCategory| (-398 |#2|) (QUOTE (-340)))) (-1525 (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-398 |#2|) (QUOTE (-340))))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-359))) (-1525 (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (QUOTE (-225))) (|HasCategory| (-398 |#2|) (QUOTE (-354))))) +(-41 R -1410) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,{}f,{}n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f,{} a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -421) (|devaluate| |#1|))))) @@ -111,7 +111,7 @@ NIL (-45 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) ((-4328 . T) (-4329 . T)) -((-1524 (-12 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-821))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3326) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1777) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3326) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1777) (|devaluate| |#2|))))))) (-1524 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-821))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (-1524 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-821))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (-1524 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1524 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (-12 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3326) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1777) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) +((-1525 (-12 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-821))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1778) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1778) (|devaluate| |#2|))))))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-821))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-821))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (-12 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1778) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -1409) +(-54 |Base| R -1410) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -154,7 +154,7 @@ NIL NIL (-56 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}a)} assign \\spad{a(i,{}j)} to \\spad{f(a(i,{}j))} for all \\spad{i,{} j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,{}a,{}b,{}r)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} when both \\spad{a(i,{}j)} and \\spad{b(i,{}j)} exist; else \\spad{c(i,{}j) = f(r,{} b(i,{}j))} when \\spad{a(i,{}j)} does not exist; else \\spad{c(i,{}j) = f(a(i,{}j),{}r)} when \\spad{b(i,{}j)} does not exist; otherwise \\spad{c(i,{}j) = f(r,{}r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i,{} j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = f(a(i,{}j))} for all \\spad{i,{} j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,{}j,{}v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,{}i,{}v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,{}r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,{}n,{}r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-4328 . T) (-4329 . T) (-2608 . T)) +((-4328 . T) (-4329 . T) (-2609 . T)) NIL (-57 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}."))) @@ -163,64 +163,64 @@ NIL (-58 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) ((-4329 . T) (-4328 . T)) -((-1524 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1524 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-1525 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-59 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) -(-60 -2464) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +(-60 -2465) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-61 -2464) +(-61 -2465) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-62 -2464) +(-62 -2465) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-63 -2464) +(-63 -2465) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-64 -2464) +(-64 -2465) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct|) (|construct| (QUOTE X) (QUOTE HESS)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-65 -2464) +(-65 -2465) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-66 -2464) +(-66 -2465) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-67 -2464) +(-67 -2465) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-68 -2464) +(-68 -2465) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-69 -2464) +(-69 -2465) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-70 -2464) +(-70 -2465) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-71 -2464) +(-71 -2465) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-72 -2464) +(-72 -2465) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-73 -2464) +(-73 -2465) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -232,55 +232,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-76 -2464) +(-76 -2465) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-77 -2464) +(-77 -2465) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-78 -2464) +(-78 -2465) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-79 -2464) +(-79 -2465) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -2464) +(-80 -2465) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -2464) +(-81 -2465) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-82 -2464) +(-82 -2465) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -2464) +(-83 -2465) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -2464) +(-84 -2465) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -2464) +(-85 -2465) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -2464) +(-86 -2465) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -2464) +(-87 -2465) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-88 -2464) +(-88 -2465) ((|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 @@ -291,7 +291,7 @@ NIL (-90 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,{}y,{}...,{}z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-91 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -339,7 +339,7 @@ NIL (-102 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}t1,{}f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t,{} ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-103 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,{}q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,{}q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,{}q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL @@ -354,12 +354,12 @@ NIL NIL (-106 S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) -((-4329 . T) (-2608 . T)) +((-4329 . T) (-2609 . T)) NIL (-107) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion.")) (|coerce| (((|RadixExpansion| 2) $) "\\spad{coerce(b)} converts a binary expansion to a radix expansion with base 2.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(b)} converts a binary expansion to a rational number."))) ((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| (-547) (QUOTE (-878))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| (-547) (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-145))) (|HasCategory| (-547) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-547) (QUOTE (-991))) (|HasCategory| (-547) (QUOTE (-794))) (-1524 (|HasCategory| (-547) (QUOTE (-794))) (|HasCategory| (-547) (QUOTE (-821)))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-1111))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-547) (QUOTE (-225))) (|HasCategory| (-547) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-547) (LIST (QUOTE -503) (QUOTE (-1135)) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -300) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -277) (QUOTE (-547)) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-298))) (|HasCategory| (-547) (QUOTE (-532))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-547) (LIST (QUOTE -615) (QUOTE (-547)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (-1524 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (|HasCategory| (-547) (QUOTE (-143))))) +((|HasCategory| (-547) (QUOTE (-878))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| (-547) (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-145))) (|HasCategory| (-547) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-547) (QUOTE (-991))) (|HasCategory| (-547) (QUOTE (-794))) (-1525 (|HasCategory| (-547) (QUOTE (-794))) (|HasCategory| (-547) (QUOTE (-821)))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-1111))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-547) (QUOTE (-225))) (|HasCategory| (-547) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-547) (LIST (QUOTE -503) (QUOTE (-1135)) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -300) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -277) (QUOTE (-547)) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-298))) (|HasCategory| (-547) (QUOTE (-532))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-547) (LIST (QUOTE -615) (QUOTE (-547)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (|HasCategory| (-547) (QUOTE (-143))))) (-108) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Symbol|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -388,7 +388,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) NIL NIL -(-115 -1409 UP) +(-115 -1410 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 @@ -399,14 +399,14 @@ NIL (-117 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) ((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-878))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| (-116 |#1|) (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-116 |#1|) (QUOTE (-991))) (|HasCategory| (-116 |#1|) (QUOTE (-794))) (-1524 (|HasCategory| (-116 |#1|) (QUOTE (-794))) (|HasCategory| (-116 |#1|) (QUOTE (-821)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-116 |#1|) (QUOTE (-1111))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| (-116 |#1|) (QUOTE (-225))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -503) (QUOTE (-1135)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -300) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -277) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-298))) (|HasCategory| (-116 |#1|) (QUOTE (-532))) (|HasCategory| (-116 |#1|) (QUOTE (-821))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-878)))) (-1524 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-878)))) (|HasCategory| (-116 |#1|) (QUOTE (-143))))) +((|HasCategory| (-116 |#1|) (QUOTE (-878))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| (-116 |#1|) (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-116 |#1|) (QUOTE (-991))) (|HasCategory| (-116 |#1|) (QUOTE (-794))) (-1525 (|HasCategory| (-116 |#1|) (QUOTE (-794))) (|HasCategory| (-116 |#1|) (QUOTE (-821)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-116 |#1|) (QUOTE (-1111))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| (-116 |#1|) (QUOTE (-225))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -503) (QUOTE (-1135)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -300) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -277) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-298))) (|HasCategory| (-116 |#1|) (QUOTE (-532))) (|HasCategory| (-116 |#1|) (QUOTE (-821))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-878)))) (|HasCategory| (-116 |#1|) (QUOTE (-143))))) (-118 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL ((|HasAttribute| |#1| (QUOTE -4329))) (-119 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) -((-2608 . T)) +((-2609 . T)) NIL (-120 UP) ((|constructor| (NIL "\\indented{1}{Author: Frederic Lehobey,{} James \\spad{H}. Davenport} Date Created: 28 June 1994 Date Last Updated: 11 July 1997 Basic Operations: brillhartIrreducible? Related Domains: Also See: AMS Classifications: Keywords: factorization Examples: References: [1] John Brillhart,{} Note on Irreducibility Testing,{} Mathematics of Computation,{} vol. 35,{} num. 35,{} Oct. 1980,{} 1379-1381 [2] James Davenport,{} On Brillhart Irreducibility. To appear. [3] John Brillhart,{} On the Euler and Bernoulli polynomials,{} \\spad{J}. Reine Angew. Math.,{} \\spad{v}. 234,{} (1969),{} \\spad{pp}. 45-64")) (|noLinearFactor?| (((|Boolean|) |#1|) "\\spad{noLinearFactor?(p)} returns \\spad{true} if \\spad{p} can be shown to have no linear factor by a theorem of Lehmer,{} \\spad{false} else. \\spad{I} insist on the fact that \\spad{false} does not mean that \\spad{p} has a linear factor.")) (|brillhartTrials| (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{brillhartTrials(n)} sets to \\spad{n} the number of tests in \\spadfun{brillhartIrreducible?} and returns the previous value.") (((|NonNegativeInteger|)) "\\spad{brillhartTrials()} returns the number of tests in \\spadfun{brillhartIrreducible?}.")) (|brillhartIrreducible?| (((|Boolean|) |#1| (|Boolean|)) "\\spad{brillhartIrreducible?(p,{}noLinears)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} else. If \\spad{noLinears} is \\spad{true},{} we are being told \\spad{p} has no linear factors \\spad{false} does not mean that \\spad{p} is reducible.") (((|Boolean|) |#1|) "\\spad{brillhartIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} is inconclusive."))) @@ -415,14 +415,14 @@ NIL (-121 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,{}b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,{}b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-123) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4329 . T) (-4328 . T) (-2608 . T)) +((-4329 . T) (-4328 . T) (-2609 . T)) NIL (-124 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -430,20 +430,20 @@ NIL NIL (-125 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4328 . T) (-4329 . T) (-2608 . T)) +((-4328 . T) (-4329 . T) (-2609 . T)) NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,{}v,{}r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-128) ((|constructor| (NIL "ByteArray provides datatype for fix-sized buffer of bytes."))) ((-4329 . T) (-4328 . T)) -((-1524 (-12 (|HasCategory| (-129) (QUOTE (-821))) (|HasCategory| (-129) (LIST (QUOTE -300) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1063))) (|HasCategory| (-129) (LIST (QUOTE -300) (QUOTE (-129)))))) (-1524 (-12 (|HasCategory| (-129) (QUOTE (-1063))) (|HasCategory| (-129) (LIST (QUOTE -300) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-129) (LIST (QUOTE -592) (QUOTE (-523)))) (-1524 (|HasCategory| (-129) (QUOTE (-821))) (|HasCategory| (-129) (QUOTE (-1063)))) (|HasCategory| (-129) (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-129) (QUOTE (-1063))) (-12 (|HasCategory| (-129) (QUOTE (-1063))) (|HasCategory| (-129) (LIST (QUOTE -300) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -591) (QUOTE (-832))))) +((-1525 (-12 (|HasCategory| (-129) (QUOTE (-821))) (|HasCategory| (-129) (LIST (QUOTE -300) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1063))) (|HasCategory| (-129) (LIST (QUOTE -300) (QUOTE (-129)))))) (-1525 (-12 (|HasCategory| (-129) (QUOTE (-1063))) (|HasCategory| (-129) (LIST (QUOTE -300) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-129) (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| (-129) (QUOTE (-821))) (|HasCategory| (-129) (QUOTE (-1063)))) (|HasCategory| (-129) (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-129) (QUOTE (-1063))) (-12 (|HasCategory| (-129) (QUOTE (-1063))) (|HasCategory| (-129) (LIST (QUOTE -300) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -591) (QUOTE (-832))))) (-129) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|coerce| (($ (|NonNegativeInteger|)) "\\spad{coerce(x)} has the same effect as byte(\\spad{x}).")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -464,11 +464,11 @@ NIL ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0,{} 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,{}1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4330 "*") . T)) NIL -(-134 |minix| -2712 S T$) +(-134 |minix| -2713 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-135 |minix| -2712 R) +(-135 |minix| -2713 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 @@ -487,7 +487,7 @@ NIL (-139) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) ((-4328 . T) (-4318 . T) (-4329 . T)) -((-1524 (-12 (|HasCategory| (-142) (QUOTE (-359))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-142) (QUOTE (-359))) (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-142) (QUOTE (-1063))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -591) (QUOTE (-832))))) +((-1525 (-12 (|HasCategory| (-142) (QUOTE (-359))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-142) (QUOTE (-359))) (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-142) (QUOTE (-1063))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -591) (QUOTE (-832))))) (-140 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -512,7 +512,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4325 . T)) NIL -(-146 -1409 UP UPUP) +(-146 -1410 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 @@ -526,7 +526,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasAttribute| |#1| (QUOTE -4328))) (-149 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) -((-2608 . T)) +((-2609 . T)) NIL (-150 |n| K Q) ((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,{}[i1,{}i2,{}...,{}iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,{}[i1,{}i2,{}...,{}iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element."))) @@ -548,7 +548,7 @@ NIL ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) NIL NIL -(-155 R -1409) +(-155 R -1410) ((|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 @@ -582,7 +582,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-878))) (|HasCategory| |#2| (QUOTE (-532))) (|HasCategory| |#2| (QUOTE (-971))) (|HasCategory| |#2| (QUOTE (-1157))) (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (QUOTE (-991))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-354))) (|HasAttribute| |#2| (QUOTE -4324)) (|HasAttribute| |#2| (QUOTE -4327)) (|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-821)))) (-163 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4321 -1524 (|has| |#1| (-539)) (-12 (|has| |#1| (-298)) (|has| |#1| (-878)))) (-4326 |has| |#1| (-354)) (-4320 |has| |#1| (-354)) (-4324 |has| |#1| (-6 -4324)) (-4327 |has| |#1| (-6 -4327)) (-3397 . T) (-2608 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4321 -1525 (|has| |#1| (-539)) (-12 (|has| |#1| (-298)) (|has| |#1| (-878)))) (-4326 |has| |#1| (-354)) (-4320 |has| |#1| (-354)) (-4324 |has| |#1| (-6 -4324)) (-4327 |has| |#1| (-6 -4327)) (-3398 . T) (-2609 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) NIL (-164 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -594,8 +594,8 @@ NIL NIL (-166 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4321 -1524 (|has| |#1| (-539)) (-12 (|has| |#1| (-298)) (|has| |#1| (-878)))) (-4326 |has| |#1| (-354)) (-4320 |has| |#1| (-354)) (-4324 |has| |#1| (-6 -4324)) (-4327 |has| |#1| (-6 -4327)) (-3397 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-340))) (-1524 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-340)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-359))) (-1524 (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#1| (QUOTE (-340)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-340)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1135)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-340)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-340)))) (-12 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-340)))) (-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-340)))) (|HasCategory| |#1| (QUOTE (-225))) (-12 (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-340)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-340)))) (-12 (|HasCategory| |#1| (QUOTE (-340))) (|HasCategory| |#1| (LIST (QUOTE -277) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-340))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547))))) (-12 (|HasCategory| |#1| (QUOTE (-340))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135))))) (-12 (|HasCategory| |#1| (QUOTE (-340))) (|HasCategory| |#1| (QUOTE (-359)))) (-12 (|HasCategory| |#1| (QUOTE (-340))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| |#1| (QUOTE (-340))) (|HasCategory| |#1| (QUOTE (-802)))) (-12 (|HasCategory| |#1| (QUOTE (-340))) (|HasCategory| |#1| (QUOTE (-821)))) (-12 (|HasCategory| |#1| (QUOTE (-340))) (|HasCategory| |#1| (QUOTE (-991)))) (-12 (|HasCategory| |#1| (QUOTE (-340))) (|HasCategory| |#1| (QUOTE (-1157)))) (-12 (|HasCategory| |#1| (QUOTE (-340))) (|HasCategory| |#1| (LIST (QUOTE -592) 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(-12 (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135))))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-340))))) (-167 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -648,7 +648,7 @@ NIL ((|constructor| (NIL "This domains represents a syntax object that designates a category,{} domain,{} or a package. See Also: Syntax,{} Domain")) (|arguments| (((|List| (|Syntax|)) $) "\\spad{arguments returns} the list of syntax objects for the arguments used to invoke the constructor.")) (|constructorName| (((|Symbol|) $) "\\spad{constructorName c} returns the name of the constructor"))) NIL NIL -(-180 R -1409) +(-180 R -1410) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -756,23 +756,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} makes a database out of a list")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,{}start,{}end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,{}s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,{}q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,{}s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-207 -1409 UP UPUP R) +(-207 -1410 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f,{} ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-208 -1409 FP) +(-208 -1410 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,{}k,{}v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,{}k,{}v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,{}k,{}v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,{}sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-209) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion.")) (|coerce| (((|RadixExpansion| 10) $) "\\spad{coerce(d)} converts a decimal expansion to a radix expansion with base 10.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(d)} converts a decimal expansion to a rational number."))) ((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| (-547) (QUOTE (-878))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| (-547) (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-145))) (|HasCategory| (-547) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-547) (QUOTE (-991))) (|HasCategory| (-547) (QUOTE (-794))) (-1524 (|HasCategory| (-547) (QUOTE (-794))) (|HasCategory| (-547) (QUOTE (-821)))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-1111))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-547) (QUOTE (-225))) (|HasCategory| (-547) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-547) (LIST (QUOTE -503) (QUOTE (-1135)) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -300) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -277) (QUOTE (-547)) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-298))) (|HasCategory| (-547) (QUOTE (-532))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-547) (LIST (QUOTE -615) (QUOTE (-547)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (-1524 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (|HasCategory| (-547) (QUOTE (-143))))) +((|HasCategory| (-547) (QUOTE (-878))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| (-547) (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-145))) (|HasCategory| (-547) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-547) (QUOTE (-991))) (|HasCategory| (-547) (QUOTE (-794))) (-1525 (|HasCategory| (-547) (QUOTE (-794))) (|HasCategory| (-547) (QUOTE (-821)))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-1111))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-547) (QUOTE (-225))) (|HasCategory| (-547) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-547) (LIST (QUOTE -503) (QUOTE (-1135)) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -300) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -277) (QUOTE (-547)) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-298))) (|HasCategory| (-547) (QUOTE (-532))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-547) (LIST (QUOTE -615) (QUOTE (-547)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (|HasCategory| (-547) (QUOTE (-143))))) (-210) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|Syntax|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|List| (|Identifier|)) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-211 R -1409) +(-211 R -1410) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -787,18 +787,18 @@ NIL (-214 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-215 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,{}df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,{}u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) ((-4325 . T)) NIL -(-216 R -1409) +(-216 R -1410) ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p,{} a,{} b,{} incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p,{} x,{} a,{} b,{} incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x,{} g,{} a,{} b,{} eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) NIL NIL (-217) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-2645 . T) (-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-2646 . T) (-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) NIL (-218) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}"))) @@ -807,14 +807,14 @@ NIL (-219 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,{}Y,{}Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,{}sy,{}sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-539))) (|HasAttribute| |#1| (QUOTE (-4330 "*"))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-539))) (|HasAttribute| |#1| (QUOTE (-4330 "*"))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-220 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL NIL (-221 S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) -((-4329 . T) (-2608 . T)) +((-4329 . T) (-2609 . T)) NIL (-222 S R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) @@ -838,28 +838,28 @@ NIL ((|HasAttribute| |#1| (QUOTE -4328))) (-227 S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,{}d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#1| $) "\\spad{remove!(x,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#1|)) "\\spad{dictionary([x,{}y,{}...,{}z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) -((-4329 . T) (-2608 . T)) +((-4329 . T) (-2609 . T)) NIL (-228) ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-229 S -2712 R) +(-229 S -2713 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL ((|HasCategory| |#3| (QUOTE (-354))) (|HasCategory| |#3| (QUOTE (-767))) (|HasCategory| |#3| (QUOTE (-819))) (|HasAttribute| |#3| (QUOTE -4325)) (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (QUOTE (-359))) (|HasCategory| |#3| (QUOTE (-701))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (QUOTE (-1063)))) -(-230 -2712 R) +(-230 -2713 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) -((-4322 |has| |#2| (-1016)) (-4323 |has| |#2| (-1016)) (-4325 |has| |#2| (-6 -4325)) ((-4330 "*") |has| |#2| (-169)) (-4328 . T) (-2608 . T)) +((-4322 |has| |#2| (-1016)) (-4323 |has| |#2| (-1016)) (-4325 |has| |#2| (-6 -4325)) ((-4330 "*") |has| |#2| (-169)) (-4328 . T) (-2609 . T)) NIL -(-231 -2712 A B) +(-231 -2713 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-232 -2712 R) +(-232 -2713 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."))) ((-4322 |has| |#2| (-1016)) (-4323 |has| |#2| (-1016)) (-4325 |has| |#2| (-6 -4325)) ((-4330 "*") |has| |#2| (-169)) (-4328 . 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(-547))))) (-12 (|HasCategory| |#2| (QUOTE (-225))) (|HasCategory| |#2| (QUOTE (-1016)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135))))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547))))) (-1525 (|HasCategory| |#2| (QUOTE (-1016))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (QUOTE (-1063)))) (|HasAttribute| |#2| (QUOTE -4325)) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (-233) ((|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 @@ -874,12 +874,12 @@ NIL NIL (-236 S) ((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,{}v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,{}v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) -((-2608 . T)) +((-2609 . T)) NIL (-237 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}")) (|coerce| (((|List| |#1|) $) "\\spad{coerce(x)} returns the list of elements in \\spad{x}") (($ (|List| |#1|)) "\\spad{coerce(l)} creates a datalist from \\spad{l}"))) ((-4329 . T) (-4328 . T)) -((-1524 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1524 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-1525 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-238 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL @@ -887,19 +887,19 @@ NIL (-239 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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Date Last Updated: January 19,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall")) (|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall|)) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall|) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}."))) 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(-547))))) (-12 (|HasCategory| |#3| (QUOTE (-354))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-359))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-701))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-767))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-819))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547)))))) (|HasCategory| (-547) (QUOTE (-821))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -615) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -869) (QUOTE (-1135))))) (-12 (|HasCategory| |#3| (QUOTE (-225))) (|HasCategory| |#3| (QUOTE (-1016)))) (-1525 (-12 (|HasCategory| |#3| (QUOTE (-225))) (|HasCategory| |#3| (QUOTE (-1016)))) (|HasCategory| |#3| (QUOTE (-701))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -615) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -869) (QUOTE (-1135)))))) (-1525 (|HasCategory| |#3| (QUOTE (-1016))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547)))))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#3| (QUOTE (-1063)))) (-1525 (|HasAttribute| |#3| (QUOTE -4325)) (-12 (|HasCategory| |#3| (QUOTE (-225))) (|HasCategory| |#3| (QUOTE (-1016)))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -615) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -869) (QUOTE (-1135)))))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -300) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -591) (QUOTE (-832))))) (-243 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL @@ -910,7 +910,7 @@ NIL NIL (-245 S) ((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) -((-4328 . T) (-4329 . T) (-2608 . T)) +((-4328 . T) (-4329 . T) (-2609 . T)) NIL (-246) ((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d,{}l)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g),{}a..b)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) @@ -951,7 +951,7 @@ NIL (-255 R S V) ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) (((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-878))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1524 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1524 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#3| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#3| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#3| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#3| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#3| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#1| (QUOTE (-354))) (-1524 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4326)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1524 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) +((|HasCategory| |#1| (QUOTE (-878))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#3| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#3| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#3| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#3| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#3| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#1| (QUOTE (-354))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4326)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) (-256 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -996,11 +996,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-267 R -1409) +(-267 R -1410) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,{}l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{\\spad{pi}()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-268 R -1409) +(-268 R -1410) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,{}a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f,{} k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,{}...,{}kn],{}f,{}x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,{}x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f,{} x)} returns \\spad{[g,{} [k1,{}...,{}kn],{} [h1,{}...,{}hn]]} such that \\spad{g = normalize(f,{} x)} and each \\spad{\\spad{ki}} was rewritten as \\spad{\\spad{hi}} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f,{} x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1022,7 +1022,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063)))) (-273 S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,{}i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,{}i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) -((-4329 . T) (-2608 . T)) +((-4329 . T) (-2609 . T)) NIL (-274 S) ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) @@ -1048,7 +1048,7 @@ NIL ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,{}x,{}y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,{}x,{}y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u,{} x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u,{} x,{} y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-280 S R |Mod| -2112 -1294 |exactQuo|) +(-280 S R |Mod| -2129 -2037 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) ((-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) NIL @@ -1070,21 +1070,21 @@ NIL NIL (-285 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3326) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1777) (|devaluate| |#2|)))))) (-1524 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1524 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063))) (-1524 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1778) (|devaluate| |#2|)))))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) (-287) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",{}\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,{}lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,{}msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-288 -1409 S) +(-288 -1410 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f,{} p,{} k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-289 E -1409) +(-289 E -1410) ((|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 @@ -1132,7 +1132,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f,{} [x1 = v1,{}...,{}xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,{}x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-301 -1409) +(-301 -1410) ((|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 @@ -1147,7 +1147,7 @@ NIL (-304 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,{}f(var))}."))) ((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-878))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-143))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-991))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-794))) (-1524 (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-794))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-821)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-1111))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-225))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -503) (QUOTE (-1135)) (LIST (QUOTE -1204) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -300) (LIST (QUOTE -1204) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -277) (LIST (QUOTE -1204) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1204) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-298))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-532))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-821))) (-12 (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-878))) (|HasCategory| $ (QUOTE (-143)))) (-1524 (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-143))) (-12 (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-878))) (|HasCategory| $ (QUOTE (-143)))))) +((|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-878))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-143))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-991))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-794))) (-1525 (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-794))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-821)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-1111))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-225))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -503) (QUOTE (-1135)) (LIST (QUOTE -1204) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -300) (LIST (QUOTE -1204) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -277) (LIST (QUOTE -1204) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1204) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-298))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-532))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-821))) (-12 (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-878))) (|HasCategory| $ (QUOTE (-143)))) (-1525 (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-143))) (-12 (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-878))) (|HasCategory| $ (QUOTE (-143)))))) (-305 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f,{} e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL @@ -1158,9 +1158,9 @@ NIL NIL (-307 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4325 -1524 (-1806 (|has| |#1| (-1016)) (|has| |#1| (-615 (-547)))) (-12 (|has| |#1| (-539)) (-1524 (-1806 (|has| |#1| (-1016)) (|has| |#1| (-615 (-547)))) (|has| |#1| (-1016)) (|has| |#1| (-463)))) (|has| |#1| (-1016)) (|has| |#1| (-463))) (-4323 |has| |#1| (-169)) (-4322 |has| |#1| (-169)) ((-4330 "*") |has| |#1| (-539)) (-4321 |has| |#1| (-539)) (-4326 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(|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))))) (-1525 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-1016)))) (-1525 (-12 (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1075))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| $ (QUOTE (-1016))) (|HasCategory| $ (LIST (QUOTE -1007) (QUOTE (-547))))) +(-308 R -1410) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) NIL NIL @@ -1171,7 +1171,7 @@ NIL (-310 FE |var| |cen|) ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) (((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-354)) (-4320 |has| |#1| (-354)) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|)))) (|HasCategory| (-398 (-547)) (QUOTE (-1075))) (|HasCategory| |#1| (QUOTE (-354))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-1524 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasSignature| |#1| (LIST (QUOTE -3834) (LIST (|devaluate| |#1|) (QUOTE (-1135)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (-1524 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -2069) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1135))))) (|HasSignature| |#1| (LIST (QUOTE -2259) (LIST (LIST (QUOTE -619) (QUOTE (-1135))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|)))) (|HasCategory| (-398 (-547)) (QUOTE (-1075))) (|HasCategory| |#1| (QUOTE (-354))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-1525 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasSignature| |#1| (LIST (QUOTE -3835) (LIST (|devaluate| |#1|) (QUOTE (-1135)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (-1525 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -2963) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1135))))) (|HasSignature| |#1| (LIST (QUOTE -2259) (LIST (LIST (QUOTE -619) (QUOTE (-1135))) (|devaluate| |#1|))))))) (-311 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 @@ -1203,12 +1203,12 @@ NIL (-318 S) ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) ((-4329 . T) (-4328 . T)) -((-1524 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1524 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) -(-319 S -1409) +((-1525 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +(-319 S -1410) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-359)))) -(-320 -1409) +(-320 -1410) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) ((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) NIL @@ -1228,15 +1228,15 @@ 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 -(-325 S -1409 UP UPUP R) +(-325 S -1410 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-326 -1409 UP UPUP R) +(-326 -1410 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-327 -1409 UP UPUP R) +(-327 -1410 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 @@ -1256,26 +1256,26 @@ NIL ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{} p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL NIL -(-332 S -1409 UP UPUP) +(-332 S -1410 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-354)))) -(-333 -1409 UP UPUP) +(-333 -1410 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) ((-4321 |has| (-398 |#2|) (-354)) (-4326 |has| (-398 |#2|) (-354)) (-4320 |has| (-398 |#2|) (-354)) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) NIL (-334 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((-1524 (|HasCategory| (-879 |#1|) (QUOTE (-143))) (|HasCategory| (-879 |#1|) (QUOTE (-359)))) (|HasCategory| (-879 |#1|) (QUOTE (-145))) (|HasCategory| (-879 |#1|) (QUOTE (-359))) (|HasCategory| (-879 |#1|) (QUOTE (-143)))) +((-1525 (|HasCategory| (-879 |#1|) (QUOTE (-143))) (|HasCategory| (-879 |#1|) (QUOTE (-359)))) (|HasCategory| (-879 |#1|) (QUOTE (-145))) (|HasCategory| (-879 |#1|) (QUOTE (-359))) (|HasCategory| (-879 |#1|) (QUOTE (-143)))) (-335 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) ((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((-1524 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) +((-1525 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) (-336 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((-1524 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) +((-1525 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) (-337 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1292,31 +1292,31 @@ NIL ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) ((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) NIL -(-341 R UP -1409) +(-341 R UP -1410) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-342 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((-1524 (|HasCategory| (-879 |#1|) (QUOTE (-143))) (|HasCategory| (-879 |#1|) (QUOTE (-359)))) (|HasCategory| (-879 |#1|) (QUOTE (-145))) (|HasCategory| (-879 |#1|) (QUOTE (-359))) (|HasCategory| (-879 |#1|) (QUOTE (-143)))) +((-1525 (|HasCategory| (-879 |#1|) (QUOTE (-143))) (|HasCategory| (-879 |#1|) (QUOTE (-359)))) (|HasCategory| (-879 |#1|) (QUOTE (-145))) (|HasCategory| (-879 |#1|) (QUOTE (-359))) (|HasCategory| (-879 |#1|) (QUOTE (-143)))) (-343 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((-1524 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) +((-1525 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) (-344 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((-1524 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) +((-1525 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) (-345 |p| |n|) ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) ((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((-1524 (|HasCategory| (-879 |#1|) (QUOTE (-143))) (|HasCategory| (-879 |#1|) (QUOTE (-359)))) (|HasCategory| (-879 |#1|) (QUOTE (-145))) (|HasCategory| (-879 |#1|) (QUOTE (-359))) (|HasCategory| (-879 |#1|) (QUOTE (-143)))) +((-1525 (|HasCategory| (-879 |#1|) (QUOTE (-143))) (|HasCategory| (-879 |#1|) (QUOTE (-359)))) (|HasCategory| (-879 |#1|) (QUOTE (-145))) (|HasCategory| (-879 |#1|) (QUOTE (-359))) (|HasCategory| (-879 |#1|) (QUOTE (-143)))) (-346 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) ((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((-1524 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) -(-347 -1409 GF) +((-1525 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) +(-347 -1410 GF) ((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL @@ -1324,14 +1324,14 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,{}x**q,{}x**(q**2),{}...,{}x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,{}n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-349 -1409 FP FPP) +(-349 -1410 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-350 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) ((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((-1524 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) +((-1525 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) (-351 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL @@ -1386,7 +1386,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4329)) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063)))) (-364 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4328 . T) (-2608 . T)) +((-4328 . T) (-2609 . T)) NIL (-365 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) @@ -1410,7 +1410,7 @@ NIL NIL (-370) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|convert| (($ (|DoubleFloat|)) "\\spad{convert(x)} converts a \\spadtype{DoubleFloat} \\spad{x} to a \\spadtype{Float}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4311 . T) (-4319 . T) (-2645 . T) (-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4311 . T) (-4319 . T) (-2646 . T) (-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) NIL (-371 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf,{} eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,{}lv,{}eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,{}eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,{}eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,{}eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,{}eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -1426,11 +1426,11 @@ NIL NIL (-374) ((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) -((-2608 . T)) +((-2609 . T)) NIL (-375) ((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-2608 . T)) +((-2609 . T)) NIL (-376 R S) ((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) @@ -1460,7 +1460,7 @@ NIL ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-383 -1409 UP UPUP R) +(-383 -1410 UP UPUP R) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) NIL NIL @@ -1474,27 +1474,27 @@ NIL NIL (-386) ((|constructor| (NIL "\\axiomType{FortranProgramCategory} provides various models of FORTRAN subprograms. These can be transformed into actual FORTRAN code.")) (|outputAsFortran| (((|Void|) $) "\\axiom{outputAsFortran(\\spad{u})} translates \\axiom{\\spad{u}} into a legal FORTRAN subprogram."))) -((-2608 . T)) +((-2609 . T)) NIL (-387) ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-2608 . T)) +((-2609 . T)) NIL (-388) ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}t,{}lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,{}l,{}ll,{}lv,{}t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}ll,{}lv)} \\undocumented{}"))) NIL NIL -(-389 -2464 |returnType| -2856 |symbols|) +(-389 -2465 |returnType| -2857 |symbols|) ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) NIL NIL -(-390 -1409 UP) +(-390 -1410 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p,{} [[j,{} Dj,{} Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,{}Dj,{}Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL (-391 R) ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) -((-2608 . T)) +((-2609 . T)) NIL (-392 S) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,{}s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,{}a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) @@ -1510,7 +1510,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4311)) (|HasAttribute| |#1| (QUOTE -4319))) (-395) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-2645 . T) (-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-2646 . T) (-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) NIL (-396 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,{}u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) @@ -1523,7 +1523,7 @@ NIL (-398 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) ((-4315 -12 (|has| |#1| (-6 -4326)) (|has| |#1| (-442)) (|has| |#1| (-6 -4315))) (-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-878))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-991))) (|HasCategory| |#1| (QUOTE (-794))) (-1524 (|HasCategory| |#1| (QUOTE (-794))) (|HasCategory| |#1| (QUOTE (-821)))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-1111))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (-1524 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802))))) (-1524 (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1135)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -277) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802)))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-532))) (-12 (|HasAttribute| |#1| (QUOTE -4326)) (|HasAttribute| |#1| (QUOTE -4315)) (|HasCategory| |#1| (QUOTE (-442)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1524 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) +((|HasCategory| |#1| (QUOTE (-878))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-991))) (|HasCategory| |#1| (QUOTE (-794))) (-1525 (|HasCategory| |#1| (QUOTE (-794))) (|HasCategory| |#1| (QUOTE (-821)))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-1111))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802))))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1135)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -277) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802)))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-532))) (-12 (|HasAttribute| |#1| (QUOTE -4326)) (|HasAttribute| |#1| (QUOTE -4315)) (|HasCategory| |#1| (QUOTE (-442)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) (-399 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1544,11 +1544,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-404 R -1409 UP A) +(-404 R -1410 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\spad{minimize(I)} returns a reduced set of generators for \\spad{I}.")) (|denom| ((|#1| $) "\\spad{denom(1/d * (f1,{}...,{}fn))} returns \\spad{d}.")) (|numer| (((|Vector| |#4|) $) "\\spad{numer(1/d * (f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}.")) (|norm| ((|#2| $) "\\spad{norm(I)} returns the norm of the ideal \\spad{I}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,{}...,{}fn))} returns the vector \\spad{[f1,{}...,{}fn]}.")) (|ideal| (($ (|Vector| |#4|)) "\\spad{ideal([f1,{}...,{}fn])} returns the ideal \\spad{(f1,{}...,{}fn)}."))) ((-4325 . T)) NIL -(-405 R -1409 UP A |ibasis|) +(-405 R -1410 UP A |ibasis|) ((|constructor| (NIL "Module representation of fractional ideals.")) (|module| (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{module(I)} returns \\spad{I} viewed has a module over \\spad{R}.") (($ (|Vector| |#4|)) "\\spad{module([f1,{}...,{}fn])} = the module generated by \\spad{(f1,{}...,{}fn)} over \\spad{R}.")) (|norm| ((|#2| $) "\\spad{norm(f)} returns the norm of the module \\spad{f}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1007) (|devaluate| |#2|)))) @@ -1567,7 +1567,7 @@ NIL (-409 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,{}n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,{}n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,{}n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,{}exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,{}listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) ((-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1135)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -300) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -277) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-1176))) (-1524 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-1176)))) (|HasCategory| |#1| (QUOTE (-991))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1135)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -277) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-442)))) +((|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1135)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -300) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -277) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-1176))) (-1525 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-1176)))) (|HasCategory| |#1| (QUOTE (-991))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1135)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -277) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-442)))) (-410 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,{}v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,{}fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,{}2)} then \\spad{refine(u,{}factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,{}2) * primeFactor(5,{}2)}."))) NIL @@ -1594,9 +1594,9 @@ NIL ((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-359)))) (-416 S) ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4328 . T) (-4318 . T) (-4329 . T) (-2608 . T)) +((-4328 . T) (-4318 . T) (-4329 . T) (-2609 . T)) NIL -(-417 R -1409) +(-417 R -1410) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1604,7 +1604,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,{}r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,{}r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) ((-4315 -12 (|has| |#1| (-6 -4315)) (|has| |#2| (-6 -4315))) (-4322 . T) (-4323 . T) (-4325 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4315)) (|HasAttribute| |#2| (QUOTE -4315)))) -(-419 R -1409) +(-419 R -1410) ((|constructor| (NIL "\\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) NIL NIL @@ -1614,17 +1614,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-1075))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523))))) (-421 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4325 -1524 (|has| |#1| (-1016)) (|has| |#1| (-463))) (-4323 |has| |#1| (-169)) (-4322 |has| |#1| (-169)) ((-4330 "*") |has| |#1| (-539)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-539)) (-4320 |has| |#1| (-539)) (-2608 . T)) +((-4325 -1525 (|has| |#1| (-1016)) (|has| |#1| (-463))) (-4323 |has| |#1| (-169)) (-4322 |has| |#1| (-169)) ((-4330 "*") |has| |#1| (-539)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-539)) (-4320 |has| |#1| (-539)) (-2609 . T)) NIL -(-422 R -1409) +(-422 R -1410) ((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,{}y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,{}y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,{}y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,{}y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,{}y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,{}y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,{}x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) NIL NIL -(-423 R -1409) +(-423 R -1410) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1,{} a2)} returns \\spad{[a,{} q1,{} q2,{} q]} such that \\spad{k(a1,{} a2) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,{}...,{}an])} returns \\spad{[a,{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-424 R -1409) +(-424 R -1410) ((|constructor| (NIL "This package provides function which replaces transcendental kernels in a function space by random integers. The correspondence between the kernels and the integers is fixed between calls to new().")) (|newReduc| (((|Void|)) "\\spad{newReduc()} \\undocumented")) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) "\\spad{bringDown(f,{}k)} \\undocumented") (((|Fraction| (|Integer|)) |#2|) "\\spad{bringDown(f)} \\undocumented"))) NIL NIL @@ -1632,7 +1632,7 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-426 R -1409 UP) +(-426 R -1410 UP) ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) NIL ((|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-48))))) @@ -1650,17 +1650,17 @@ NIL NIL (-430) ((|constructor| (NIL "\\axiomType{FortranVectorCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Vector} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Vector| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) -((-2608 . T)) +((-2609 . T)) NIL (-431) ((|constructor| (NIL "\\axiomType{FortranVectorFunctionCategory} is the catagory of arguments to NAG Library routines which return the values of vectors of functions.")) (|retractIfCan| (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-2608 . T)) +((-2609 . T)) NIL (-432 UP) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,{}sqf,{}pd,{}r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,{}sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r,{}sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,{}p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-433 R UP -1409) +(-433 R UP -1410) ((|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 @@ -1707,7 +1707,7 @@ NIL (-444 |vl| R E) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4330 "*") |has| |#2| (-169)) (-4321 |has| |#2| (-539)) (-4326 |has| |#2| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#2| (QUOTE (-878))) (-1524 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-878)))) (-1524 (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-878)))) (-1524 (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-169))) (-1524 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-539)))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (QUOTE (-354))) (-1524 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#2| (QUOTE -4326)) (|HasCategory| |#2| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (-1524 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-143))))) +((|HasCategory| |#2| (QUOTE (-878))) (-1525 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-878)))) (-1525 (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-878)))) (-1525 (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-169))) (-1525 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-539)))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (QUOTE (-354))) (-1525 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#2| (QUOTE -4326)) (|HasCategory| |#2| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-143))))) (-445 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,{}lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,{}table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,{}prime,{}lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,{}lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,{}prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1772,7 +1772,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-461 |lv| -1409 R) +(-461 |lv| -1410 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 @@ -1787,11 +1787,11 @@ NIL (-464 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) (((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-354)) (-4320 |has| |#1| (-354)) (-4322 . T) (-4323 . T) (-4325 . 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T)) -((-12 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3326) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1777) (|devaluate| |#2|)))))) (-1524 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1524 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-821))) (-1524 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1778) (|devaluate| |#2|)))))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-821))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) (-466 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) ((-4329 . T) (-4328 . T)) @@ -1807,7 +1807,7 @@ NIL (-469 |Key| |Entry| |hashfn|) ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3326) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1777) (|devaluate| |#2|)))))) (-1524 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1524 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063))) (-1524 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1778) (|devaluate| |#2|)))))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) (-470) ((|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 @@ -1815,11 +1815,11 @@ NIL (-471 |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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(|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|Identifier|))) "\\spad{headAst(f,{}[x1,{}..,{}xn])} constructs a function definition header."))) NIL @@ -1827,8 +1827,8 @@ NIL (-474 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) ((-4328 . T) (-4329 . 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In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL ((|HasAttribute| |#1| (QUOTE -4328)) (|HasAttribute| |#1| (QUOTE -4329)) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (-479 S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) -((-2608 . T)) +((-2609 . T)) NIL (-480) ((|constructor| (NIL "This domain represents hostnames on computer network.")) (|host| (($ (|String|)) "\\spad{host(n)} constructs a Hostname from the name \\spad{`n'}."))) @@ -1860,7 +1860,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-483 -1409 UP |AlExt| |AlPol|) +(-483 -1410 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 @@ -1871,16 +1871,16 @@ NIL (-485 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4329 . T) (-4328 . T)) -((-1524 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1524 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-1525 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-486 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-487 K R UP) ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,{}lr,{}n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,{}q,{}n)} returns the list \\spad{[bas,{}bas^Frob,{}bas^(Frob^2),{}...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,{}n,{}m,{}j)} \\undocumented"))) NIL NIL -(-488 R UP -1409) +(-488 R UP -1410) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1900,7 +1900,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-493 -1409 |Expon| |VarSet| |DPoly|) +(-493 -1410 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,{}f,{}lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,{}f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,{}lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,{}listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,{}listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,{}f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,{}J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,{}J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,{}lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,{}I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,{}J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,{}I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -592) (QUOTE (-1135))))) @@ -1951,7 +1951,7 @@ NIL (-505 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,{}n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) ((-4329 . T) (-4328 . T)) -((-1524 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1524 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-1525 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-506) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|Syntax|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|Syntax|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|Syntax|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL @@ -1959,15 +1959,15 @@ NIL (-507 |p| |n|) ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) ((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((-1524 (|HasCategory| (-561 |#1|) (QUOTE (-143))) (|HasCategory| (-561 |#1|) (QUOTE (-359)))) (|HasCategory| (-561 |#1|) (QUOTE (-145))) (|HasCategory| (-561 |#1|) (QUOTE (-359))) (|HasCategory| (-561 |#1|) (QUOTE (-143)))) +((-1525 (|HasCategory| (-561 |#1|) (QUOTE (-143))) (|HasCategory| (-561 |#1|) (QUOTE (-359)))) (|HasCategory| (-561 |#1|) (QUOTE (-145))) (|HasCategory| (-561 |#1|) (QUOTE (-359))) (|HasCategory| (-561 |#1|) (QUOTE (-143)))) (-508 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-509 S |mn|) ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,{}mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) ((-4329 . T) (-4328 . T)) -((-1524 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1524 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-1525 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-510 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL @@ -1979,7 +1979,7 @@ NIL (-512 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-539))) (|HasAttribute| |#1| (QUOTE (-4330 "*"))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-539))) (|HasAttribute| |#1| (QUOTE (-4330 "*"))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-513) ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) NIL @@ -2008,7 +2008,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL NIL -(-520 K -1409 |Par|) +(-520 K -1410 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,{}eps,{}factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol,{} eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL @@ -2028,7 +2028,7 @@ NIL ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),{}a,{}d)} computes \\spad{product(n=a,{}a+d,{}a+2*d,{}...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,{}3,{}5...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,{}4,{}6...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,{}2,{}3...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-525 K -1409 |Par|) +(-525 K -1410 |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 @@ -2063,12 +2063,12 @@ NIL (-533 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3326) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1777) (|devaluate| |#2|)))))) (-1524 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1524 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063))) (-1524 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) -(-534 R -1409) +((-12 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1778) (|devaluate| |#2|)))))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) +(-534 R -1410) ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f,{} x,{} y,{} d)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) NIL NIL -(-535 R0 -1409 UP UPUP R) +(-535 R0 -1410 UP UPUP R) ((|constructor| (NIL "This package provides functions for integrating a function on an algebraic curve.")) (|palginfieldint| (((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)) "\\spad{palginfieldint(f,{} d)} returns an algebraic function \\spad{g} such that \\spad{dg = f} if such a \\spad{g} exists,{} \"failed\" otherwise. Argument \\spad{f} must be a pure algebraic function.")) (|palgintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{palgintegrate(f,{} d)} integrates \\spad{f} with respect to the derivation \\spad{d}. Argument \\spad{f} must be a pure algebraic function.")) (|algintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{algintegrate(f,{} d)} integrates \\spad{f} with respect to the derivation \\spad{d}."))) NIL NIL @@ -2078,7 +2078,7 @@ NIL NIL (-537 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,{}f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,{}sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,{}sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-2645 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-2646 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) NIL (-538 S) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) @@ -2088,7 +2088,7 @@ NIL ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) ((-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) NIL -(-540 R -1409) +(-540 R -1410) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,{}x,{}k,{}[k1,{}...,{}kn])} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f,{} x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f,{} x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,{}x,{}[g1,{}...,{}gn])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{gi})))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f,{} x,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2100,7 +2100,7 @@ NIL ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-543 R -1409 L) +(-543 R -1410 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x,{} y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,{}g,{}x,{}y,{}z,{}t,{}c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op,{} g,{} x,{} y,{} d,{} p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,{}k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,{}k,{}f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,{}k,{}k,{}p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} t,{} c)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} d,{} p)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} z,{} t,{} c)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} d,{} p)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f,{} x,{} y,{} g,{} z,{} t,{} c)} returns functions \\spad{[h,{} d]} such that \\spad{dh/dx = f(x,{}y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f,{} x,{} y,{} g,{} d,{} p)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f,{} x,{} y,{} z,{} t,{} c)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f,{} x,{} y,{} d,{} p)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -630) (|devaluate| |#2|)))) @@ -2108,11 +2108,11 @@ NIL ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,{}k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,{}p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,{}p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,{}b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,{}b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,{}k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,{}1/2)},{} where \\spad{E(n,{}x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,{}m1,{}x2,{}m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,{}0)},{} where \\spad{B(n,{}x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-545 -1409 UP UPUP R) +(-545 -1410 UP UPUP R) ((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f,{} ')} returns \\spad{[g,{}h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) NIL NIL -(-546 -1409 UP) +(-546 -1410 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 @@ -2124,15 +2124,15 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp,{} x = a..b,{} numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp,{} x = a..b,{} \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel,{} routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp,{} a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsabs,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} a..b,{} epsrel,{} routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-549 R -1409 L) +(-549 R -1410 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op,{} g,{} kx,{} y,{} x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp,{} f,{} g,{} x,{} y,{} foo)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a,{} b,{} x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f,{} x,{} y,{} [u1,{}...,{}un])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f,{} x,{} y,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f,{} x,{} y)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -630) (|devaluate| |#2|)))) -(-550 R -1409) +(-550 R -1410) ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f,{} x)} returns \\spad{[c,{} g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1099)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-605))))) -(-551 -1409 UP) +(-551 -1410 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{gi})))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2140,27 +2140,27 @@ NIL ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-553 -1409) +(-553 -1410) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f,{} x,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f,{} x,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{gi})))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f,{} x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-554 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) -((-2645 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-2646 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) NIL (-555) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-556 R -1409) +(-556 R -1410) ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f,{} x,{} int,{} pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f,{} x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f,{} x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,{}...,{}fn],{}x)} returns the set-theoretic union of \\spad{(varselect(f1,{}x),{}...,{}varselect(fn,{}x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1,{} l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k,{} [k1,{}...,{}kn],{} x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,{}...,{}kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,{}...,{}kn],{} x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-275))) (|HasCategory| |#2| (QUOTE (-605))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-1135))))) (-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-275)))) (|HasCategory| |#1| (QUOTE (-539)))) -(-557 -1409 UP) +(-557 -1410 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p,{} ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f,{} ')} returns \\spad{[ir,{} s,{} p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p,{} foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p,{} ',{} t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f,{} ',{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[\\spad{ci} * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f,{} ',{} g)} returns \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-558 R -1409) +(-558 R -1410) ((|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 @@ -2180,15 +2180,15 @@ NIL ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-563 R -1409) +(-563 R -1410) ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,{}x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,{}x) + ... + sum_{Pn(a)=0} Q(a,{}x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) NIL NIL -(-564 E -1409) +(-564 E -1410) ((|constructor| (NIL "\\indented{1}{Internally used by the integration packages} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 12 August 1992 Keywords: integration.")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,{}ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,{}ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,{}ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,{}ire)} \\undocumented"))) NIL NIL -(-565 -1409) +(-565 -1410) ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,{}x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,{}D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,{}l,{}ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) ((-4323 . T) (-4322 . T)) ((|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-1135))))) @@ -2219,7 +2219,7 @@ NIL (-572 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) ((-4329 . T) (-4328 . T)) -((-1524 (-12 (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142)))))) (-1524 (|HasCategory| (-142) (LIST (QUOTE -591) (QUOTE (-832)))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -592) (QUOTE (-523)))) (-1524 (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-142) (QUOTE (-1063)))) (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-142) (QUOTE (-1063))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -591) (QUOTE (-832))))) +((-1525 (-12 (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142)))))) (-1525 (|HasCategory| (-142) (LIST (QUOTE -591) (QUOTE (-832)))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-142) (QUOTE (-1063)))) (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-142) (QUOTE (-1063))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -591) (QUOTE (-832))))) (-573 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n),{} n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n),{} n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL @@ -2227,7 +2227,7 @@ NIL (-574 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,{}r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,{}r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,{}refer,{}var,{}cen,{}r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,{}g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,{}g,{}taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,{}f)} returns the series \\spad{sum(fn(n) * an * x^n,{}n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,{}n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,{}str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) (((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-547)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-547)) (|devaluate| |#1|)))) (|HasCategory| (-547) (QUOTE (-1075))) (|HasCategory| |#1| (QUOTE (-354))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -3834) (LIST (|devaluate| |#1|) (QUOTE (-1135)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-547)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-547)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-547)) (|devaluate| |#1|)))) (|HasCategory| (-547) (QUOTE (-1075))) (|HasCategory| |#1| (QUOTE (-354))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -3835) (LIST (|devaluate| |#1|) (QUOTE (-1135)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-547)))))) (-575 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,{}n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) ((-4323 |has| |#1| (-539)) (-4322 |has| |#1| (-539)) ((-4330 "*") |has| |#1| (-539)) (-4321 |has| |#1| (-539)) (-4325 . T)) @@ -2240,7 +2240,7 @@ NIL ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented"))) NIL NIL -(-578 R -1409 FG) +(-578 R -1410 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 @@ -2251,14 +2251,14 @@ NIL (-580 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4329 . T) (-4328 . T)) -((-1524 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1524 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-701))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-971))) (|HasCategory| |#1| (QUOTE (-1016)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-1525 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-701))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-971))) (|HasCategory| |#1| (QUOTE (-1016)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-581 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL ((|HasAttribute| |#1| (QUOTE -4329)) (|HasCategory| |#2| (QUOTE (-821))) (|HasAttribute| |#1| (QUOTE -4328)) (|HasCategory| |#3| (QUOTE (-1063)))) (-582 |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) -((-2608 . T)) +((-2609 . T)) NIL (-583) ((|constructor| (NIL "\\indented{1}{This domain defines the datatype for the Java} Virtual Machine byte codes.")) (|coerce| (($ (|Byte|)) "\\spad{coerce(x)} the numerical byte value into a \\spad{JVM} bytecode."))) @@ -2270,19 +2270,19 @@ NIL NIL (-585 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,{}b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) -((-4325 -1524 (-1806 (|has| |#2| (-358 |#1|)) (|has| |#1| (-539))) (-12 (|has| |#2| (-408 |#1|)) (|has| |#1| (-539)))) (-4323 . T) (-4322 . T)) -((-1524 (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|)))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|)))) +((-4325 -1525 (-1807 (|has| |#2| (-358 |#1|)) (|has| |#1| (-539))) (-12 (|has| |#2| (-408 |#1|)) (|has| |#1| (-539)))) (-4323 . T) (-4322 . T)) +((-1525 (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|)))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|)))) (-586 |Entry|) ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3326) (QUOTE (-1118))) (LIST (QUOTE |:|) (QUOTE -1777) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| (-1118) (QUOTE (-821))) (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|)) (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|)) (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (QUOTE (-1118))) (LIST (QUOTE |:|) (QUOTE -1778) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| (-1118) (QUOTE (-821))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (LIST (QUOTE -591) (QUOTE (-832))))) (-587 S |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}."))) NIL NIL (-588 |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#2| "failed") |#1| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#2| "failed") |#1| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#1|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#1| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}."))) -((-4329 . T) (-2608 . T)) +((-4329 . T) (-2609 . T)) NIL (-589 R S) ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) @@ -2300,7 +2300,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-593 -1409 UP) +(-593 -1410 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2320,7 +2320,7 @@ NIL ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) ((-4322 . T) (-4323 . T) (-4325 . T)) ((|HasCategory| |#1| (QUOTE (-819)))) -(-598 R -1409) +(-598 R -1410) ((|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 @@ -2352,18 +2352,18 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-606 R -1409) +(-606 R -1410) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,{}x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,{}x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\spad{Ei}(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL -(-607 |lv| -1409) +(-607 |lv| -1410) ((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) NIL NIL (-608) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) ((-4329 . T)) -((-12 (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 (-52))) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3326) (QUOTE (-1118))) (LIST (QUOTE |:|) (QUOTE -1777) (QUOTE (-52))))))) (-1524 (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 (-52))) (QUOTE (-1063))) (|HasCategory| (-52) (QUOTE (-1063)))) (-1524 (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 (-52))) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -300) (QUOTE (-52))))) (|HasCategory| (-1118) (QUOTE (-821))) (-1524 (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 (-52))) (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 (-52))) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (QUOTE (-1118))) (LIST (QUOTE |:|) (QUOTE -1778) (QUOTE (-52))))))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-52) (QUOTE (-1063)))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 (-52))) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -300) (QUOTE (-52))))) (|HasCategory| (-1118) (QUOTE (-821))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 (-52))) (LIST (QUOTE -591) (QUOTE (-832))))) (-609 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2374,8 +2374,8 @@ NIL NIL (-611 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,{}b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) -((-4325 -1524 (-1806 (|has| |#2| (-358 |#1|)) (|has| |#1| (-539))) (-12 (|has| |#2| (-408 |#1|)) (|has| |#1| (-539)))) (-4323 . T) (-4322 . T)) -((-1524 (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|)))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|)))) +((-4325 -1525 (-1807 (|has| |#2| (-358 |#1|)) (|has| |#1| (-539))) (-12 (|has| |#2| (-408 |#1|)) (|has| |#1| (-539)))) (-4323 . T) (-4322 . T)) +((-1525 (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|)))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|)))) (-612 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit \\spad{lim(x -> a,{}f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),{}x=a,{}\"left\")} computes the left hand real limit \\spad{lim(x -> a-,{}f(x))}; \\spad{limit(f(x),{}x=a,{}\"right\")} computes the right hand real limit \\spad{lim(x -> a+,{}f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),{}x = a)} computes the real limit \\spad{lim(x -> a,{}f(x))}."))) NIL @@ -2407,7 +2407,7 @@ NIL (-619 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list."))) ((-4329 . T) (-4328 . T)) -((-1524 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1524 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-802))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-1525 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-802))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-620 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2415,7 +2415,7 @@ NIL (-621 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-622 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2430,9 +2430,9 @@ NIL ((|HasAttribute| |#1| (QUOTE -4329))) (-625 S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) -((-2608 . T)) +((-2609 . T)) NIL -(-626 R -1409 L) +(-626 R -1410 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 @@ -2452,11 +2452,11 @@ NIL ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) ((-4322 . T) (-4323 . T) (-4325 . T)) NIL -(-631 -1409 UP) +(-631 -1410 UP) ((|constructor| (NIL "\\spadtype{LinearOrdinaryDifferentialOperatorFactorizer} provides a factorizer for linear ordinary differential operators whose coefficients are rational functions.")) (|factor1| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor1(a)} returns the factorisation of a,{} assuming that a has no first-order right factor.")) (|factor| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor(a)} returns the factorisation of a.") (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{factor(a,{} zeros)} returns the factorisation of a. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-632 A -2926) +(-632 A -1341) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator} defines a ring of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) ((-4322 . T) (-4323 . T) (-4325 . T)) ((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-354)))) @@ -2490,13 +2490,13 @@ NIL NIL (-640 S) ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) -((-4329 . T) (-4328 . T) (-2608 . T)) +((-4329 . T) (-4328 . T) (-2609 . T)) NIL -(-641 -1409) +(-641 -1410) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-642 -1409 |Row| |Col| M) +(-642 -1410 |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 @@ -2507,7 +2507,7 @@ NIL (-644 |n| R) ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,{}R) b - b *\\$SQMATRIX(n,{}R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) ((-4325 . T) (-4328 . T) (-4322 . T) (-4323 . T)) -((|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#2| (QUOTE (-225))) (|HasAttribute| |#2| (QUOTE (-4330 "*"))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (-1524 (-12 (|HasCategory| |#2| (QUOTE (-225))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))))) (|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-539))) (-1524 (|HasAttribute| |#2| (QUOTE (-4330 "*"))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#2| (QUOTE (-225)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-169)))) +((|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#2| (QUOTE (-225))) (|HasAttribute| |#2| (QUOTE (-4330 "*"))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (-1525 (-12 (|HasCategory| |#2| (QUOTE (-225))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))))) (|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-539))) (-1525 (|HasAttribute| |#2| (QUOTE (-4330 "*"))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#2| (QUOTE (-225)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-169)))) (-645) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|Syntax|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL @@ -2522,12 +2522,12 @@ NIL NIL (-648 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,{}n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least \\spad{'n'} explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length \\spad{<=} \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,{}st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,{}st) = [x for x in st | not f(x)]}."))) -((-2608 . T)) +((-2609 . T)) NIL (-649 R) ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,{}x,{}y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,{}i,{}j,{}k,{}s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,{}i,{}j,{}k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,{}y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,{}j,{}k)} create a matrix with all zero terms"))) NIL -((-1524 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1063))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-1525 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-650) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|Syntax|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|List| (|Identifier|)) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2574,7 +2574,7 @@ NIL ((|HasAttribute| |#2| (QUOTE (-4330 "*"))) (|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-539)))) (-661 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then \\spad{x(i<k>,{}j<l>)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i<k>,{}j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) -((-4328 . T) (-4329 . T) (-2608 . T)) +((-4328 . T) (-4329 . T) (-2609 . T)) NIL (-662 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that \\spad{m*n} = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,{}a,{}i,{}j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,{}a,{}i,{}j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,{}i,{}j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square."))) @@ -2583,7 +2583,7 @@ NIL (-663 R) ((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal."))) ((-4328 . T) (-4329 . T)) -((-1524 (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1063))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-539))) (|HasAttribute| |#1| (QUOTE (-4330 "*"))) (|HasCategory| |#1| (QUOTE (-354))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-1525 (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-539))) (|HasAttribute| |#1| (QUOTE (-4330 "*"))) (|HasCategory| |#1| (QUOTE (-354))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-664 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,{}b,{}c,{}m,{}n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,{}a,{}b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,{}a,{}r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,{}r,{}a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,{}a,{}b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,{}a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,{}a,{}b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,{}a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -2592,7 +2592,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional vallue,{} where a computation may fail to produce expected value.")) (|nothing| (($) "represents failure.")) (|autoCoerce| ((|#1| $) "same as above but implicitly called by the compiler.")) (|coerce| ((|#1| $) "x::T tries to extract the value of \\spad{T} from the computation \\spad{x}. Produces a runtime error when the computation fails.") (($ |#1|) "x::T injects the value \\spad{x} into \\%.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} evaluates \\spad{true} if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}."))) NIL NIL -(-666 S -1409 FLAF FLAS) +(-666 S -1410 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,{}xlist,{}kl,{}ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,{}xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,{}xlist,{}k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,{}xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,{}xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,{}xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,{}xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2602,11 +2602,11 @@ NIL NIL (-668) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4321 . T) (-4326 |has| (-673) (-354)) (-4320 |has| (-673) (-354)) (-3397 . T) (-4327 |has| (-673) (-6 -4327)) (-4324 |has| (-673) (-6 -4324)) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . 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As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,{}d,{}n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) -((-4329 . T) (-2608 . T)) +((-4329 . T) (-2609 . T)) NIL (-670 U) ((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,{}n,{}g,{}p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl,{} p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,{}p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,{}p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,{}p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,{}f2,{}p)} computes the \\spad{gcd} of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) @@ -2616,13 +2616,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,{}b,{}c,{}d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,{}t,{}u,{}f,{}s1,{}l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,{}g,{}s1,{}s2,{}l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,{}f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented"))) NIL NIL -(-672 OV E -1409 PG) +(-672 OV E -1410 PG) ((|constructor| (NIL "Package for factorization of multivariate polynomials over finite fields.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field. \\spad{p} is represented as a univariate polynomial with multivariate coefficients over a finite field.") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field."))) NIL NIL (-673) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,{}man,{}base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-2645 . T) (-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-2646 . T) (-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) NIL (-674 R) ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m,{} d,{} p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,{}p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m,{} d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) @@ -2672,14 +2672,14 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) 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(-1045) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-340))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasAttribute| |#1| (QUOTE -4326)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) (-688 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|coerce| (((|Record| (|:| |index| |#1|) (|:| |exponent| |#2|)) $) "\\spad{coerce(x)} \\undocumented") (($ (|Record| (|:| |index| |#1|) (|:| |exponent| |#2|))) "\\spad{coerce(x)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2688,7 +2688,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,{}f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f,{} u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4323 |has| |#1| (-169)) (-4322 |has| |#1| (-169)) (-4325 . T)) ((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145)))) -(-690 R |Mod| -2112 -1294 |exactQuo|) +(-690 R |Mod| -2129 -2037 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) ((-4325 . T)) NIL @@ -2700,7 +2700,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4323 . T) (-4322 . T)) NIL -(-693 -1409) +(-693 -1410) ((|constructor| (NIL "\\indented{1}{MoebiusTransform(\\spad{F}) is the domain of fractional linear (Moebius)} transformations over \\spad{F}.")) (|eval| (((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|)) "\\spad{eval(m,{}x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,{}b,{}c,{}d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).") ((|#1| $ |#1|) "\\spad{eval(m,{}x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,{}b,{}c,{}d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).")) (|recip| (($ $) "\\spad{recip(m)} = recip() * \\spad{m}") (($) "\\spad{recip()} returns \\spad{matrix [[0,{}1],{}[1,{}0]]} representing the map \\spad{x -> 1 / x}.")) (|scale| (($ $ |#1|) "\\spad{scale(m,{}h)} returns \\spad{scale(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{scale(k)} returns \\spad{matrix [[k,{}0],{}[0,{}1]]} representing the map \\spad{x -> k * x}.")) (|shift| (($ $ |#1|) "\\spad{shift(m,{}h)} returns \\spad{shift(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{shift(k)} returns \\spad{matrix [[1,{}k],{}[0,{}1]]} representing the map \\spad{x -> x + k}.")) (|moebius| (($ |#1| |#1| |#1| |#1|) "\\spad{moebius(a,{}b,{}c,{}d)} returns \\spad{matrix [[a,{}b],{}[c,{}d]]}."))) ((-4325 . T)) NIL @@ -2736,7 +2736,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-702 -1409 UP) +(-702 -1410 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 @@ -2755,7 +2755,7 @@ NIL (-706 |vl| R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) (((-4330 "*") |has| |#2| (-169)) (-4321 |has| |#2| (-539)) (-4326 |has| |#2| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#2| (QUOTE (-878))) (-1524 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-878)))) (-1524 (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-878)))) (-1524 (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-169))) (-1524 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-539)))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (QUOTE (-354))) (-1524 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#2| (QUOTE -4326)) (|HasCategory| |#2| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (-1524 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-143))))) +((|HasCategory| |#2| (QUOTE (-878))) (-1525 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-878)))) (-1525 (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-878)))) (-1525 (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-169))) (-1525 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-539)))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (QUOTE (-354))) (-1525 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#2| (QUOTE -4326)) (|HasCategory| |#2| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-143))))) (-707 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,{}var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,{}var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,{}var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2774,7 +2774,7 @@ NIL ((-12 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-821)))) (-711 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4318 . T) (-4329 . T) (-2608 . T)) +((-4318 . T) (-4329 . T) (-2609 . T)) NIL (-712 S) ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,{}ms,{}number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,{}ms,{}number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,{}ms,{}number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,{}ms,{}number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|members| (((|List| |#1|) $) "\\spad{members(ms)} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) @@ -2888,15 +2888,15 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,{}eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-740 -1409) +(-740 -1410) ((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions \\indented{2}{for converting floating point numbers to continued fractions.}")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction."))) NIL NIL -(-741 P -1409) +(-741 P -1410) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}."))) NIL NIL -(-742 UP -1409) +(-742 UP -1410) ((|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 @@ -2912,7 +2912,7 @@ NIL ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,{}b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) (((-4330 "*") . T)) NIL -(-746 R -1409) +(-746 R -1410) ((|constructor| (NIL "NonLinearFirstOrderODESolver provides a function for finding closed form first integrals of nonlinear ordinary differential equations of order 1.")) (|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(M(x,{}y),{} N(x,{}y),{} y,{} x)} returns \\spad{F(x,{}y)} such that \\spad{F(x,{}y) = c} for a constant \\spad{c} is a first integral of the equation \\spad{M(x,{}y) dx + N(x,{}y) dy = 0},{} or \"failed\" if no first-integral can be found."))) NIL NIL @@ -2932,7 +2932,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-751 -1409 |ExtF| |SUEx| |ExtP| |n|) +(-751 -1410 |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 @@ -2947,7 +2947,7 @@ NIL (-754 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) (((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . 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(LIST (QUOTE -38) (QUOTE (-547))))) (-3998 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-1135)))) (-3998 (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-547))))))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4326)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) (-755 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -2955,14 +2955,14 @@ NIL (-756 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4324 |has| |#1| (-354)) (-4326 |has| |#1| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-878))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1524 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1524 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (-1524 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasAttribute| |#1| (QUOTE -4326)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1524 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) +((|HasCategory| |#1| (QUOTE (-878))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasAttribute| |#1| (QUOTE -4326)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) (-757 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) (-758 R E V P) ((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,{}v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,{}v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,{}mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}"))) -((-4329 . T) (-4328 . T) (-2608 . T)) +((-4329 . T) (-4328 . T) (-2609 . T)) NIL (-759 S) ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) @@ -3016,23 +3016,23 @@ NIL ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4322 . T) (-4323 . T) (-4325 . T)) NIL -(-772 -1524 R OS S) +(-772 -1525 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-773 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1135)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -277) (|devaluate| |#1|) (|devaluate| |#1|))) (-1524 (|HasCategory| (-968 |#1|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (-1524 (|HasCategory| (-968 |#1|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| (-968 |#1|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-968 |#1|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) +((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1135)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -277) (|devaluate| |#1|) (|devaluate| |#1|))) (-1525 (|HasCategory| (-968 |#1|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (-1525 (|HasCategory| (-968 |#1|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| (-968 |#1|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-968 |#1|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (-774) ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-775 R -1409 L) +(-775 R -1410 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op,{} g,{} x)} returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-776 R -1409) +(-776 R -1410) ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m,{} x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m,{} v,{} x)} returns \\spad{[v_p,{} [v_1,{}...,{}v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL @@ -3040,7 +3040,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-778 R -1409) +(-778 R -1410) ((|constructor| (NIL "\\spadtype{ODEIntegration} provides an interface to the integrator. This package is intended for use by the differential equations solver but not at top-level.")) (|diff| (((|Mapping| |#2| |#2|) (|Symbol|)) "\\spad{diff(x)} returns the derivation with respect to \\spad{x}.")) (|expint| ((|#2| |#2| (|Symbol|)) "\\spad{expint(f,{} x)} returns e^{the integral of \\spad{f} with respect to \\spad{x}}.")) (|int| ((|#2| |#2| (|Symbol|)) "\\spad{int(f,{} x)} returns the integral of \\spad{f} with respect to \\spad{x}."))) NIL NIL @@ -3048,11 +3048,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}epsabs,{}epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,{}R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-780 -1409 UP UPUP R) +(-780 -1410 UP UPUP R) ((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) NIL NIL -(-781 -1409 UP L LQ) +(-781 -1410 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op,{} [g1,{}...,{}gm])} returns \\spad{op0,{} [h1,{}...,{}hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op,{} [g1,{}...,{}gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op,{} g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -3060,38 +3060,38 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-783 -1409 UP L LQ) +(-783 -1410 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} zeros,{} ezfactor)} returns \\spad{[[f1,{} L1],{} [f2,{} L2],{} ... ,{} [fk,{} Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z=0}. \\spad{zeros(C(x),{}H(x,{}y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,{}P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{} Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op,{} ric)} returns \\spad{[[a1,{} L1],{} [a2,{} L2],{} ... ,{} [ak,{} Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1,{} p1],{} [m2,{} p2],{} ... ,{} [mk,{} pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-784 -1409 UP) +(-784 -1410 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-785 -1409 L UP A LO) +(-785 -1410 L UP A LO) ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op,{} g)} returns \\spad{[m,{} v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,{}...,{}z_m) . (b_1,{}...,{}b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}."))) NIL NIL -(-786 -1409 UP) +(-786 -1410 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{}Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{\\spad{Li} z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} ezfactor)} returns \\spad{[[f1,{}L1],{} [f2,{}L2],{}...,{} [fk,{}Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-787 -1409 LO) +(-787 -1410 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m,{} v)} returns \\spad{[m_0,{} v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,{}v)} returns \\spad{A,{}[[C_1,{}g_1,{}L_1,{}h_1],{}...,{}[C_k,{}g_k,{}L_k,{}h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-788 -1409 LODO) +(-788 -1410 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) 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with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . 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(|coerce| ((|#2| $) "\\spad{coerce(p)} views \\spad{p} as a valie in the partial differential ring.") (($ |#2|) "\\spad{coerce(r)} views \\spad{r} as a value in the ordinary differential ring."))) (((-4330 "*") |has| |#2| (-354)) (-4321 |has| |#2| (-354)) (-4326 |has| |#2| (-354)) (-4320 |has| |#2| (-354)) (-4325 . T) (-4323 . T) (-4322 . T)) @@ -3146,7 +3146,7 @@ NIL NIL (-804 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4328 . T) (-4318 . T) (-4329 . T) (-2608 . T)) +((-4328 . T) (-4318 . T) (-4329 . T) (-2609 . T)) NIL (-805) ((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,{}timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,{}u)} attempts to output \\axiom{\\spad{u}} on \\aciom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object."))) @@ -3159,7 +3159,7 @@ NIL (-807 R) ((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) ((-4325 |has| |#1| (-819))) -((|HasCategory| |#1| (QUOTE (-819))) (-1524 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-532))) (-1524 (|HasCategory| |#1| (QUOTE (-819))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-819))) (-1525 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-532))) (-1525 (|HasCategory| |#1| (QUOTE (-819))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-21)))) (-808 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) ((-4323 |has| |#1| (-169)) (-4322 |has| |#1| (-169)) (-4325 . T)) @@ -3187,12 +3187,12 @@ NIL (-814 R) ((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4325 |has| |#1| (-819))) -((|HasCategory| |#1| (QUOTE (-819))) (-1524 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-532))) (-1524 (|HasCategory| |#1| (QUOTE (-819))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-819))) (-1525 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-532))) (-1525 (|HasCategory| |#1| (QUOTE (-819))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-21)))) (-815) ((|constructor| (NIL "Ordered finite sets."))) NIL NIL -(-816 -2712 S) +(-816 -2713 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 @@ -3228,11 +3228,11 @@ NIL ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p,{} c,{} m,{} sigma,{} delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p,{} q,{} sigma,{} delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) -(-825 R |sigma| -2642) +(-825 R |sigma| -2647) ((|constructor| (NIL "This is the domain of sparse univariate skew polynomials over an Ore coefficient field. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{} x)} returns the output form of \\spad{p} using \\spad{x} for the otherwise anonymous variable."))) ((-4322 . T) (-4323 . T) (-4325 . T)) ((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-354)))) -(-826 |x| R |sigma| -2642) +(-826 |x| R |sigma| -2647) ((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} returns \\spad{x} as a skew-polynomial."))) ((-4322 . T) (-4323 . T) (-4325 . T)) ((|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-354)))) @@ -3291,15 +3291,15 @@ NIL (-840 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) ((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| (-839 |#1|) (QUOTE (-878))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| (-839 |#1|) (QUOTE (-143))) (|HasCategory| (-839 |#1|) (QUOTE (-145))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-839 |#1|) (QUOTE (-991))) (|HasCategory| (-839 |#1|) (QUOTE (-794))) (-1524 (|HasCategory| (-839 |#1|) (QUOTE (-794))) (|HasCategory| (-839 |#1|) (QUOTE (-821)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-839 |#1|) (QUOTE (-1111))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| (-839 |#1|) (QUOTE (-225))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -503) (QUOTE (-1135)) (LIST (QUOTE -839) (|devaluate| |#1|)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -300) (LIST (QUOTE -839) (|devaluate| |#1|)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -277) (LIST (QUOTE -839) (|devaluate| |#1|)) (LIST (QUOTE -839) (|devaluate| |#1|)))) (|HasCategory| (-839 |#1|) (QUOTE (-298))) (|HasCategory| (-839 |#1|) (QUOTE (-532))) (|HasCategory| (-839 |#1|) (QUOTE (-821))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-839 |#1|) (QUOTE (-878)))) (-1524 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-839 |#1|) (QUOTE (-878)))) (|HasCategory| (-839 |#1|) (QUOTE (-143))))) +((|HasCategory| (-839 |#1|) (QUOTE (-878))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| (-839 |#1|) (QUOTE (-143))) (|HasCategory| (-839 |#1|) (QUOTE (-145))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-839 |#1|) (QUOTE (-991))) (|HasCategory| (-839 |#1|) (QUOTE (-794))) (-1525 (|HasCategory| (-839 |#1|) (QUOTE (-794))) (|HasCategory| (-839 |#1|) (QUOTE (-821)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-839 |#1|) (QUOTE (-1111))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| (-839 |#1|) (QUOTE (-225))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -503) (QUOTE (-1135)) (LIST (QUOTE -839) (|devaluate| |#1|)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -300) (LIST (QUOTE -839) (|devaluate| |#1|)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -277) (LIST (QUOTE -839) (|devaluate| |#1|)) (LIST (QUOTE -839) (|devaluate| |#1|)))) (|HasCategory| (-839 |#1|) (QUOTE (-298))) (|HasCategory| (-839 |#1|) (QUOTE (-532))) (|HasCategory| (-839 |#1|) (QUOTE (-821))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-839 |#1|) (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-839 |#1|) (QUOTE (-878)))) (|HasCategory| (-839 |#1|) (QUOTE (-143))))) (-841 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) ((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#2| (QUOTE (-878))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-991))) (|HasCategory| |#2| (QUOTE (-794))) (-1524 (|HasCategory| |#2| (QUOTE (-794))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-225))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#2| (LIST (QUOTE -503) (QUOTE (-1135)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -277) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (QUOTE (-532))) (|HasCategory| |#2| (QUOTE (-821))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (-1524 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-143))))) +((|HasCategory| |#2| (QUOTE (-878))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-991))) (|HasCategory| |#2| (QUOTE (-794))) (-1525 (|HasCategory| |#2| (QUOTE (-794))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-225))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#2| (LIST (QUOTE -503) (QUOTE (-1135)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -277) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (QUOTE (-532))) (|HasCategory| |#2| (QUOTE (-821))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-143))))) (-842 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,{}t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,{}t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))))) (-843) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL @@ -3388,7 +3388,7 @@ NIL ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-865 UP -1409) +(-865 UP -1410) ((|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 @@ -3411,7 +3411,7 @@ NIL (-870 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|coerce| (((|Tree| |#1|) $) "\\spad{coerce(x)} \\undocumented")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-871 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL @@ -3427,7 +3427,7 @@ NIL (-874 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,{}...,{}n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) ((-4325 . T)) -((-1524 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-821)))) +((-1525 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-821)))) (-875 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL @@ -3448,7 +3448,7 @@ NIL ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) ((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) ((|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-143))) (|HasCategory| $ (QUOTE (-359)))) -(-880 R0 -1409 UP UPUP R) +(-880 R0 -1410 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 @@ -3476,7 +3476,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,{}...,{}nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{li}} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{li}} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,{}...,{}ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,{}...,{}ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,{}...,{}nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,{}2)} with {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,{}...,{}n)} and the 2-cycle {\\em (1,{}2)}."))) NIL NIL -(-887 -1409) +(-887 -1410) ((|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 @@ -3492,11 +3492,11 @@ NIL ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) (((-4330 "*") . T)) NIL -(-891 -1409 P) +(-891 -1410 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-892 |xx| -1409) +(-892 |xx| -1410) ((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,{}lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,{}lf,{}lg)} \\undocumented"))) NIL NIL @@ -3520,7 +3520,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-898 R -1409) +(-898 R -1410) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3532,7 +3532,7 @@ NIL ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-901 S R -1409) +(-901 S R -1410) ((|constructor| (NIL "This package provides pattern matching functions on function spaces.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL @@ -3552,7 +3552,7 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -855) (|devaluate| |#1|)))) -(-906 R -1409 -1686) +(-906 R -1410 -1686) ((|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 @@ -3579,7 +3579,7 @@ NIL (-912 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4329 . T) (-4328 . T)) -((-1524 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1524 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-701))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-971))) (|HasCategory| |#1| (QUOTE (-1016)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-1525 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-701))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-971))) (|HasCategory| |#1| (QUOTE (-1016)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-913 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL @@ -3604,7 +3604,7 @@ NIL ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) (((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . T)) NIL -(-919 E V R P -1409) +(-919 E V R P -1410) ((|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 @@ -3615,8 +3615,8 @@ NIL (-921 R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,{}x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) (((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-878))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1524 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1524 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| (-1135) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-1135) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-1135) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-1135) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-1135) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-354))) (-1524 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4326)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1524 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) -(-922 E V R P -1409) +((|HasCategory| |#1| (QUOTE (-878))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| (-1135) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-1135) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-1135) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-1135) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-1135) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-354))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4326)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) +(-922 E V R P -1410) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,{}n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|coerce| (($ |#4|) "\\spad{coerce(p)} \\undocumented")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-442)))) @@ -3639,12 +3639,12 @@ NIL (-927 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4329 . T) (-4328 . T)) -((-1524 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1524 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-1525 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-928) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f,{} x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f,{} x)} returns the formal integral of \\spad{f} \\spad{dx}."))) NIL NIL -(-929 -1409) +(-929 -1410) ((|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 @@ -3659,11 +3659,11 @@ NIL (-932 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-6 -4326)) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-130)))) (-1524 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4326))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-130)))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4326))) (-933 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,{}b)} \\undocumented"))) ((-4325 -12 (|has| |#2| (-463)) (|has| |#1| (-463)))) -((-1524 (-12 (|HasCategory| |#1| (QUOTE (-767))) (|HasCategory| |#2| (QUOTE (-767)))) (-12 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(|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-821))))) (-12 (|HasCategory| |#1| (QUOTE (-767))) (|HasCategory| |#2| (QUOTE (-767)))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-767))) (|HasCategory| |#2| (QUOTE (-767))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-767))) (|HasCategory| |#2| (QUOTE (-767))))) (-12 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-463)))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-463)))) (-12 (|HasCategory| |#1| (QUOTE (-701))) (|HasCategory| |#2| (QUOTE (-701))))) (-12 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-359)))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-463)))) (-12 (|HasCategory| |#1| (QUOTE (-701))) (|HasCategory| |#2| (QUOTE (-701)))) (-12 (|HasCategory| |#1| (QUOTE (-767))) (|HasCategory| |#2| (QUOTE (-767))))) (-12 (|HasCategory| |#1| (QUOTE (-701))) (|HasCategory| |#2| (QUOTE (-701)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-821))))) (-934) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Symbol|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Symbol|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3678,7 +3678,7 @@ NIL NIL (-937 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\spad{merge(q1,{}q2)} returns combines priority queues \\spad{q1} and \\spad{q2} to return a single priority queue \\spad{q}.")) (|max| ((|#1| $) "\\spad{max(q)} returns the maximum element of priority queue \\spad{q}."))) -((-4328 . T) (-4329 . T) (-2608 . T)) +((-4328 . T) (-4329 . T) (-2609 . T)) NIL (-938 R |polR|) ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean1}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean2}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.\\spad{fr}}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{nextsousResultant2(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard2(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{coef1 * \\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) @@ -3710,7 +3710,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-539)))) (-945 R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) -((-4328 . T) (-2608 . T)) +((-4328 . T) (-2609 . T)) NIL (-946 R E V P) ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{irreducibleFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of \\spad{gcd} techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{\\spad{lp}}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp},{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(\\spad{lp})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp})} returns \\axiom{\\spad{lg}} where \\axiom{\\spad{lg}} is a list of the gcds of every pair in \\axiom{\\spad{lp}} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(\\spad{lp},{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} and \\axiom{\\spad{lp}} generate the same ideal in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{lq}} has rank not higher than the one of \\axiom{\\spad{lp}}. Moreover,{} \\axiom{\\spad{lq}} is computed by reducing \\axiom{\\spad{lp}} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{\\spad{lp}}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(\\spad{lp},{}pred?,{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and and \\axiom{\\spad{lq}} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{\\spad{lq}}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(\\spad{lp})} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{\\spad{lp}}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and \\axiom{\\spad{lq}} generate the same ideal and no polynomial in \\axiom{\\spad{lq}} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}\\spad{lf})} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}\\spad{lf},{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf},{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(\\spad{lp})} returns \\axiom{\\spad{bps},{}nbps} where \\axiom{\\spad{bps}} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(\\spad{lp})} returns \\axiom{\\spad{lps},{}nlps} where \\axiom{\\spad{lps}} is a list of the linear polynomials in \\spad{lp},{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(\\spad{lp})} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(\\spad{lp})} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{\\spad{lp}} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{\\spad{bps}} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(\\spad{lp})} returns \\spad{true} iff the number of polynomials in \\axiom{\\spad{lp}} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}\\spad{llp})} returns \\spad{true} iff for every \\axiom{\\spad{lp}} in \\axiom{\\spad{llp}} certainlySubVariety?(newlp,{}\\spad{lp}) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}\\spad{lp})} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is \\spad{gcd}-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(\\spad{lp})} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in \\spad{lp}]} if \\axiom{\\spad{R}} is \\spad{gcd}-domain else returns \\axiom{\\spad{lp}}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq},{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lq})),{}\\spad{lq})} assuming that \\axiom{remOp(\\spad{lq})} returns \\axiom{\\spad{lq}} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{removeRedundantFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}\\spad{lp}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lq}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lq} = [\\spad{q1},{}...,{}\\spad{qm}]} then the product \\axiom{p1*p2*...\\spad{*pn}} vanishes iff the product \\axiom{q1*q2*...\\spad{*qm}} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{\\spad{pj}},{} and no polynomial in \\axiom{\\spad{lq}} divides another polynomial in \\axiom{\\spad{lq}}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{\\spad{lq}} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is \\spad{gcd}-domain,{} the polynomials in \\axiom{\\spad{lq}} are pairwise without common non trivial factor."))) @@ -3726,7 +3726,7 @@ NIL NIL (-949 R) ((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,{}l,{}r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|convert| (($ (|List| |#1|)) "\\spad{convert(l)} takes a list of elements,{} \\spad{l},{} from the domain Ring and returns the form of point category.")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}."))) -((-4329 . T) (-4328 . T) (-2608 . T)) +((-4329 . T) (-4328 . T) (-2609 . T)) NIL (-950 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3744,7 +3744,7 @@ NIL ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,{}p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,{}v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,{}v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-954 K R UP -1409) +(-954 K R UP -1410) ((|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 @@ -3774,7 +3774,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-878))) (|HasCategory| |#2| (QUOTE (-532))) (|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-991))) (|HasCategory| |#2| (QUOTE (-794))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1111)))) (-961 S) ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#1| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#1| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#1| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#1| |#1|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) -((-2608 . T) (-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-2609 . T) (-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) NIL (-962 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,{}v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) @@ -3786,7 +3786,7 @@ NIL NIL (-964 S) ((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\spad{#q}}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,{}q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) -((-4328 . T) (-4329 . T) (-2608 . T)) +((-4328 . T) (-4329 . T) (-2609 . T)) NIL (-965 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) @@ -3803,11 +3803,11 @@ NIL (-968 R) ((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) ((-4321 |has| |#1| (-281)) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-354))) (-1524 (|HasCategory| |#1| (QUOTE (-281))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-281))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1135)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -277) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-532))) (-1524 (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-354))))) +((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-354))) (-1525 (|HasCategory| |#1| (QUOTE (-281))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-281))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1135)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -277) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-532))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-354))))) (-969 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,{}y,{}...,{}z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}."))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-970 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3816,14 +3816,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-972 -1409 UP UPUP |radicnd| |n|) +(-972 -1410 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4321 |has| (-398 |#2|) (-354)) (-4326 |has| (-398 |#2|) (-354)) (-4320 |has| (-398 |#2|) (-354)) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| (-398 |#2|) (QUOTE (-143))) (|HasCategory| (-398 |#2|) (QUOTE (-145))) (|HasCategory| (-398 |#2|) (QUOTE (-340))) (-1524 (|HasCategory| (-398 |#2|) (QUOTE (-354))) (|HasCategory| (-398 |#2|) (QUOTE (-340)))) (|HasCategory| (-398 |#2|) (QUOTE (-354))) (|HasCategory| (-398 |#2|) (QUOTE (-359))) (-1524 (-12 (|HasCategory| (-398 |#2|) (QUOTE (-225))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (|HasCategory| (-398 |#2|) (QUOTE (-340)))) (-1524 (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-398 |#2|) (QUOTE (-340))))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-359))) (-1524 (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (QUOTE (-225))) (|HasCategory| (-398 |#2|) (QUOTE (-354))))) +((|HasCategory| (-398 |#2|) (QUOTE (-143))) (|HasCategory| (-398 |#2|) (QUOTE (-145))) (|HasCategory| (-398 |#2|) (QUOTE (-340))) (-1525 (|HasCategory| (-398 |#2|) (QUOTE (-354))) (|HasCategory| (-398 |#2|) (QUOTE (-340)))) (|HasCategory| (-398 |#2|) (QUOTE (-354))) (|HasCategory| (-398 |#2|) (QUOTE (-359))) (-1525 (-12 (|HasCategory| (-398 |#2|) (QUOTE (-225))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (|HasCategory| (-398 |#2|) (QUOTE (-340)))) (-1525 (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-398 |#2|) (QUOTE (-340))))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-359))) (-1525 (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (QUOTE (-225))) (|HasCategory| (-398 |#2|) (QUOTE (-354))))) (-973 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,{}cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],{}[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,{}3,{}4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,{}1,{}4,{}2,{}8,{}5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,{}0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion.")) (|coerce| (((|Fraction| (|Integer|)) $) "\\spad{coerce(rx)} converts a radix expansion to a rational number."))) ((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| (-547) (QUOTE (-878))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| (-547) (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-145))) (|HasCategory| (-547) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-547) (QUOTE (-991))) (|HasCategory| (-547) (QUOTE (-794))) (-1524 (|HasCategory| (-547) (QUOTE (-794))) (|HasCategory| (-547) (QUOTE (-821)))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-1111))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-547) (QUOTE (-225))) (|HasCategory| (-547) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-547) (LIST (QUOTE -503) (QUOTE (-1135)) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -300) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -277) (QUOTE (-547)) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-298))) (|HasCategory| (-547) (QUOTE (-532))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-547) (LIST (QUOTE -615) (QUOTE (-547)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (-1524 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (|HasCategory| (-547) (QUOTE (-143))))) +((|HasCategory| (-547) (QUOTE (-878))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| (-547) (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-145))) (|HasCategory| (-547) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-547) (QUOTE (-991))) (|HasCategory| (-547) (QUOTE (-794))) (-1525 (|HasCategory| (-547) (QUOTE (-794))) (|HasCategory| (-547) (QUOTE (-821)))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-1111))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-547) (QUOTE (-225))) (|HasCategory| (-547) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-547) (LIST (QUOTE -503) (QUOTE (-1135)) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -300) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -277) (QUOTE (-547)) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-298))) (|HasCategory| (-547) (QUOTE (-532))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-547) (LIST (QUOTE -615) (QUOTE (-547)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (|HasCategory| (-547) (QUOTE (-143))))) (-974) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,{}b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL @@ -3846,7 +3846,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4329)) (|HasCategory| |#2| (QUOTE (-1063)))) (-979 S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) -((-2608 . T)) +((-2609 . T)) NIL (-980 S) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) @@ -3856,19 +3856,19 @@ NIL ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) ((-4321 . T) (-4326 . T) (-4320 . T) (-4323 . T) (-4322 . T) ((-4330 "*") . T) (-4325 . T)) NIL -(-982 R -1409) +(-982 R -1410) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 1 February 1988 Date Last Updated: 2 November 1995 Keywords: elementary,{} function,{} integration.")) (|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDE(n,{} f,{} g,{} x,{} lim,{} ext)} returns \\spad{[y,{} h,{} b]} such that \\spad{dy/dx + n df/dx y = h} and \\spad{b := h = g}. The equation \\spad{dy/dx + n df/dx y = g} has no solution if \\spad{h \\~~= g} (\\spad{y} is a partial solution in that case). Notes: \\spad{lim} is a limited integration function,{} and ext is an extended integration function."))) NIL NIL -(-983 R -1409) +(-983 R -1410) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 12 August 1992 Date Last Updated: 17 August 1992 Keywords: elementary,{} function,{} integration.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDEsys(n,{} f,{} g_1,{} g_2,{} x,{}lim,{}ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,{}dy2/dx) + ((0,{} - n df/dx),{}(n df/dx,{}0)) (y1,{}y2) = (g1,{}g2)} if \\spad{y_1,{}y_2} exist,{} \"failed\" otherwise. \\spad{lim} is a limited integration function,{} \\spad{ext} is an extended integration function."))) NIL NIL -(-984 -1409 UP) +(-984 -1410 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} transcendental case.} Author: Manuel Bronstein Date Created: Jan 1988 Date Last Updated: 2 November 1995")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a,{} B,{} C,{} n,{} D)} returns either: 1. \\spad{[Q,{} b]} such that \\spad{degree(Q) <= n} and \\indented{3}{\\spad{a Q'+ B Q = C} if \\spad{b = true},{} \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1,{} C1,{} m,{} \\alpha,{} \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A Q' + BQ = C} must be of the form} \\indented{3}{\\spad{Q = \\alpha H + \\beta} where \\spad{degree(H) <= m} and} \\indented{3}{\\spad{H} satisfies \\spad{H' + B1 H = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f,{} g)} returns a \\spad{[y,{} b]} such that \\spad{y' + fy = g} if \\spad{b = true},{} \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,{}g,{}D)} returns \\spad{[A,{} B,{} C,{} T]} such that \\spad{y' + f y = g} has a solution if and only if \\spad{y = Q / T},{} where \\spad{Q} satisfies \\spad{A Q' + B Q = C} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use."))) NIL NIL -(-985 -1409 UP) +(-985 -1410 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 @@ -3903,8 +3903,8 @@ NIL (-993 |TheField|) ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) ((-4321 . T) (-4326 . T) (-4320 . T) (-4323 . T) (-4322 . T) ((-4330 "*") . T) (-4325 . T)) -((-1524 (|HasCategory| (-398 (-547)) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-398 (-547)) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-398 (-547)) (LIST (QUOTE -1007) (QUOTE (-547))))) -(-994 -1409 L) +((-1525 (|HasCategory| (-398 (-547)) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-398 (-547)) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-398 (-547)) (LIST (QUOTE -1007) (QUOTE (-547))))) +(-994 -1410 L) ((|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 @@ -3940,14 +3940,14 @@ NIL ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-1003 -1409 |Expon| |VarSet| |FPol| |LFPol|) +(-1003 -1410 |Expon| |VarSet| |FPol| |LFPol|) ((|constructor| (NIL "ResidueRing is the quotient of a polynomial ring by an ideal. The ideal is given as a list of generators. The elements of the domain are equivalence classes expressed in terms of reduced elements")) (|lift| ((|#4| $) "\\spad{lift(x)} return the canonical representative of the equivalence class \\spad{x}")) (|coerce| (($ |#4|) "\\spad{coerce(f)} produces the equivalence class of \\spad{f} in the residue ring")) (|reduce| (($ |#4|) "\\spad{reduce(f)} produces the equivalence class of \\spad{f} in the residue ring"))) (((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) NIL (-1004) ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| (-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3326) (QUOTE (-1135))) (LIST (QUOTE |:|) (QUOTE -1777) (QUOTE (-52))))))) (-1524 (|HasCategory| (-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) (QUOTE (-1063))) (|HasCategory| (-52) (QUOTE (-1063)))) (-1524 (|HasCategory| (-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -300) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) (QUOTE (-1063))) (|HasCategory| (-1135) (QUOTE (-821))) (|HasCategory| (-52) (QUOTE (-1063))) (-1524 (|HasCategory| (-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (QUOTE (-1135))) (LIST (QUOTE |:|) (QUOTE -1778) (QUOTE (-52))))))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-52) (QUOTE (-1063)))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -300) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-1135) (QUOTE (-821))) (|HasCategory| (-52) (QUOTE (-1063))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (LIST (QUOTE -591) (QUOTE (-832))))) (-1005) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|Syntax|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -3996,7 +3996,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} converts the integer \\spad{i} to a member of the given domain.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4325 . T)) NIL -(-1017 |xx| -1409) +(-1017 |xx| -1410) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4006,12 +4006,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-298))) (|HasCategory| |#4| (QUOTE (-354))) (|HasCategory| |#4| (QUOTE (-539))) (|HasCategory| |#4| (QUOTE (-169)))) (-1019 |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#3| |#3|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = a(i,{}j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) -((-4328 . T) (-2608 . T) (-4323 . T) (-4322 . T)) +((-4328 . T) (-2609 . T) (-4323 . T) (-4322 . T)) NIL (-1020 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|coerce| (((|Matrix| |#3|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{RectangularMatrix} to a matrix of type \\spad{Matrix}.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4328 . T) (-4323 . T) (-4322 . T)) -((-1524 (-12 (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (LIST (QUOTE -300) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-354))) (|HasCategory| |#3| (LIST (QUOTE -300) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -300) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -592) (QUOTE (-523)))) (-1524 (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (QUOTE (-354)))) (|HasCategory| |#3| (QUOTE (-354))) (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (QUOTE (-298))) (|HasCategory| |#3| (QUOTE (-539))) (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (LIST (QUOTE -591) (QUOTE (-832)))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -300) (|devaluate| |#3|))))) +((-1525 (-12 (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (LIST (QUOTE -300) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-354))) (|HasCategory| |#3| (LIST (QUOTE -300) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -300) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (QUOTE (-354)))) (|HasCategory| |#3| (QUOTE (-354))) (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (QUOTE (-298))) (|HasCategory| |#3| (QUOTE (-539))) (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (LIST (QUOTE -591) (QUOTE (-832)))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -300) (|devaluate| |#3|))))) (-1021 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL @@ -4043,7 +4043,7 @@ NIL (-1028) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,{}routineName,{}ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,{}s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,{}s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,{}s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,{}s,{}newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,{}s,{}newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,{}y)} merges two tables \\spad{x} and \\spad{y}"))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| (-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3326) (QUOTE (-1135))) (LIST (QUOTE |:|) (QUOTE -1777) (QUOTE (-52))))))) (-1524 (|HasCategory| (-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) (QUOTE (-1063))) (|HasCategory| (-52) (QUOTE (-1063)))) (-1524 (|HasCategory| (-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -300) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) (QUOTE (-1063))) (|HasCategory| (-1135) (QUOTE (-821))) (|HasCategory| (-52) (QUOTE (-1063))) (-1524 (|HasCategory| (-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (QUOTE (-1135))) (LIST (QUOTE |:|) (QUOTE -1778) (QUOTE (-52))))))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-52) (QUOTE (-1063)))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -300) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-1135) (QUOTE (-821))) (|HasCategory| (-52) (QUOTE (-1063))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (LIST (QUOTE -591) (QUOTE (-832))))) (-1029 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL @@ -4074,7 +4074,7 @@ NIL NIL (-1036 R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,{}...,{}xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,{}...,{}tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,{}...,{}\\spad{ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,{}...,{}\\spad{Ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(\\spad{Ti})} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,{}...,{}Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,{}lts)} returns the same as \\spad{concat([extend(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,{}ts)} if \\spad{lp = [p]} else \\spad{extend(first lp,{} extend(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,{}lts)} returns the same as \\spad{concat([extend(p,{}ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,{}ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp,{} internalAugment(first lp,{} ts))}") (($ |#4| $) "\\spad{internalAugment(p,{}ts)} assumes that \\spad{augment(p,{}ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,{}lts)} returns the same as \\spad{concat([augment(lp,{}ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,{}ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp,{} augment(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,{}lts)} returns the same as \\spad{concat([augment(p,{}ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,{}lts)} returns the same as \\spad{intersect([p],{}lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,{}lts)} returns the same as \\spad{concat([intersect(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,{}ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,{}ts)} returns the same as \\spad{intersect([p],{}ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,{}p2,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,{}p2,{}ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,{}ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,{}lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,{}ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,{}ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,{}ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-4329 . T) (-4328 . T) (-2608 . T)) +((-4329 . T) (-4328 . T) (-2609 . T)) NIL (-1037 R E V P TS) ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts},{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) @@ -4084,11 +4084,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1039 |Base| R -1409) +(-1039 |Base| R -1410) ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r,{} [a1,{}...,{}an],{} f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,{}...,{}an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f,{} g,{} [f1,{}...,{}fn])} creates the rewrite rule \\spad{f == eval(eval(g,{} g is f),{} [f1,{}...,{}fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}\\spad{fn} are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f,{} g)} creates the rewrite rule: \\spad{f == eval(g,{} g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL -(-1040 |Base| R -1409) +(-1040 |Base| R -1410) ((|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 @@ -4103,7 +4103,7 @@ NIL (-1043 R UP M) ((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) ((-4321 |has| |#1| (-354)) (-4326 |has| |#1| (-354)) (-4320 |has| |#1| (-354)) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-340))) (-1524 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-340)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-359))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-340)))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135))))) (-12 (|HasCategory| |#1| (QUOTE (-340))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135))))) (-1524 (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (QUOTE (-354))))) +((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-340))) (-1525 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-340)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-359))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-340)))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135))))) (-12 (|HasCategory| |#1| (QUOTE (-340))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135))))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (QUOTE (-354))))) (-1044 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4135,7 +4135,7 @@ NIL (-1051 R) ((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential. \\blankline"))) (((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-878))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1524 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1524 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| (-1052 (-1135)) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-1052 (-1135)) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-1052 (-1135)) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-1052 (-1135)) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-1052 (-1135)) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#1| (QUOTE (-354))) (-1524 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4326)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1524 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) +((|HasCategory| |#1| (QUOTE (-878))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| (-1052 (-1135)) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-1052 (-1135)) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-1052 (-1135)) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-1052 (-1135)) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-1052 (-1135)) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#1| (QUOTE (-354))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4326)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) (-1052 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -4158,7 +4158,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-1063)))) (-1057 S) ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|convert| (($ |#1|) "\\spad{convert(i)} creates the segment \\spad{i..i}.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,{}j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{\\spad{hi}(s)} returns the second endpoint of \\spad{s}. Note: \\spad{\\spad{hi}(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) -((-2608 . T)) +((-2609 . T)) NIL (-1058 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) @@ -4166,7 +4166,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-819))) (|HasCategory| |#1| (QUOTE (-1063)))) (-1059 S L) ((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l),{} f(l+k),{} ...,{} f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l,{} l+k,{} ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,{}3,{}5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}."))) -((-2608 . T)) +((-2609 . T)) NIL (-1060 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) @@ -4174,7 +4174,7 @@ NIL NIL (-1061 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) -((-4318 . T) (-2608 . T)) +((-4318 . T) (-2609 . T)) NIL (-1062 S) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) @@ -4191,7 +4191,7 @@ NIL (-1065 S) ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,{}b,{}c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,{}m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{union(s,{}t)},{} \\spad{intersect(s,{}t)},{} \\spad{minus(s,{}t)},{} \\spad{symmetricDifference(s,{}t)} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{member(x,{}t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,{}t)} and \\spad{remove(x,{}t)} is \\spad{O(n)}}"))) ((-4328 . T) (-4318 . T) (-4329 . T)) -((-1524 (-12 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-821))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-1525 (-12 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-821))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-1066 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|convert| (($ |#5|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#4|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#3|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#2|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#1|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the \\spad{S}-expression \\spad{(a1,{}...,{}an)}.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL @@ -4218,7 +4218,7 @@ NIL NIL (-1072 R E V P) ((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the \\spad{gcd} of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,{}mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) -((-4329 . T) (-4328 . T) (-2608 . T)) +((-4329 . T) (-4328 . T) (-2609 . T)) NIL (-1073) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,{}0,{}0] < [0,{}3,{}0] < [0,{}0,{}3] < [2,{}1,{}0] < [2,{}0,{}1] < [0,{}2,{}1] < [1,{}2,{}0] < [1,{}0,{}2] < [0,{}1,{}2] < [1,{}1,{}1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,{}0,{}3] < [0,{}1,{}2] < [0,{}2,{}1] < [0,{}3,{}0] < [1,{}0,{}2] < [1,{}1,{}1] < [1,{}2,{}0] < [2,{}0,{}1] < [2,{}1,{}0] < [3,{}0,{}0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,{}m,{}k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,{}1,{}...,{}(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,{}...,{}(m-1)} into {\\em 0,{}...,{}(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,{}m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,{}3)} is 10,{} since {\\em [0,{}0,{}3],{} [0,{}1,{}2],{} [0,{}2,{}1],{} [0,{}3,{}0],{} [1,{}0,{}2],{} [1,{}1,{}1],{} [1,{}2,{}0],{} [2,{}0,{}1],{} [2,{}1,{}0],{} [3,{}0,{}0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,{}lattP,{}constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,{}beta,{}C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,{}1,{}0)}. Also,{} {\\em new(1,{}1,{}0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,{}gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,{}...,{}n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,{}...,{}n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,{}beta,{}C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em \\spad{pi}} in the corresponding double coset. Note: the resulting permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,{}beta,{}\\spad{pi})}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em \\spad{pi}} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha,{} beta,{} \\spad{pi}}. Note: The permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em \\spad{pi}} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) @@ -4235,12 +4235,12 @@ NIL (-1076 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. 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(QUOTE (-169))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-225))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-354))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-359))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-701))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-767))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-819))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547)))))) (|HasCategory| (-547) (QUOTE (-821))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -615) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-225))) (|HasCategory| |#3| (QUOTE (-1016)))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -869) (QUOTE (-1135))))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-1525 (|HasCategory| |#3| (QUOTE (-1016))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#3| (QUOTE (-1063)))) (|HasAttribute| |#3| (QUOTE -4325)) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -300) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -591) (QUOTE (-832))))) (-1077 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL ((|HasCategory| |#1| (QUOTE (-442)))) -(-1078 R -1409) +(-1078 R -1410) ((|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 @@ -4262,7 +4262,7 @@ NIL NIL (-1083 S) ((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\spad{#s}}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4328 . T) (-4329 . T) (-2608 . T)) +((-4328 . T) (-4329 . T) (-2609 . T)) NIL (-1084 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) @@ -4270,7 +4270,7 @@ NIL ((|HasCategory| |#3| (QUOTE (-354))) (|HasAttribute| |#3| (QUOTE (-4330 "*"))) (|HasCategory| |#3| (QUOTE (-169)))) (-1085 |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) -((-2608 . T) (-4328 . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-2609 . T) (-4328 . T) (-4322 . T) (-4323 . T) (-4325 . T)) NIL (-1086 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,{}B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}."))) @@ -4279,16 +4279,16 @@ NIL (-1087 R |VarSet|) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) (((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-878))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1524 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1524 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-354))) (-1524 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4326)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1524 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) +((|HasCategory| |#1| (QUOTE (-878))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-354))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4326)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) (-1088 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,{}b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) (((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-354)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-354)))) (-1089 R E V P) ((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}"))) -((-4329 . T) (-4328 . T) (-2608 . T)) +((-4329 . T) (-4328 . T) (-2609 . T)) NIL -(-1090 UP -1409) +(-1090 UP -1410) ((|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 @@ -4335,18 +4335,18 @@ NIL (-1101 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| (-1100 |#1| |#2|) (LIST (QUOTE -300) (LIST (QUOTE -1100) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1100 |#1| |#2|) (QUOTE (-1063)))) (|HasCategory| (-1100 |#1| |#2|) (QUOTE (-1063))) (-1524 (|HasCategory| (-1100 |#1| |#2|) (LIST (QUOTE -591) (QUOTE (-832)))) (-12 (|HasCategory| (-1100 |#1| |#2|) (LIST (QUOTE -300) (LIST (QUOTE -1100) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1100 |#1| |#2|) (QUOTE (-1063))))) (|HasCategory| (-1100 |#1| |#2|) (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| (-1100 |#1| |#2|) (LIST (QUOTE -300) (LIST (QUOTE -1100) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1100 |#1| |#2|) (QUOTE (-1063)))) (|HasCategory| (-1100 |#1| |#2|) (QUOTE (-1063))) (-1525 (|HasCategory| (-1100 |#1| |#2|) (LIST (QUOTE -591) (QUOTE (-832)))) (-12 (|HasCategory| (-1100 |#1| |#2|) (LIST (QUOTE -300) (LIST (QUOTE -1100) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1100 |#1| |#2|) (QUOTE (-1063))))) (|HasCategory| (-1100 |#1| |#2|) (LIST (QUOTE -591) (QUOTE (-832))))) (-1102 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|coerce| (((|Matrix| |#2|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{SquareMatrix} to a matrix of type \\spadtype{Matrix}.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}."))) ((-4325 . T) (-4317 |has| |#2| (-6 (-4330 "*"))) (-4328 . T) (-4322 . T) (-4323 . T)) -((|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#2| (QUOTE (-225))) (|HasAttribute| |#2| (QUOTE (-4330 "*"))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (-1524 (-12 (|HasCategory| |#2| (QUOTE (-225))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-354))) (-1524 (|HasAttribute| |#2| (QUOTE (-4330 "*"))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#2| (QUOTE (-225)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-169)))) +((|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#2| (QUOTE (-225))) (|HasAttribute| |#2| (QUOTE (-4330 "*"))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (-1525 (-12 (|HasCategory| |#2| (QUOTE (-225))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-354))) (-1525 (|HasAttribute| |#2| (QUOTE (-4330 "*"))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#2| (QUOTE (-225)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-169)))) (-1103 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1104) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-4329 . T) (-4328 . T) (-2608 . T)) +((-4329 . T) (-4328 . T) (-2609 . T)) NIL (-1105 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,{}E,{}V,{}P,{}TS)} and \\spad{RSETGCD(R,{}E,{}V,{}P,{}TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) @@ -4359,19 +4359,19 @@ NIL (-1107 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,{}y,{}...,{}z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-1108 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL (-1109 S) ((|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})}."))) -((-2608 . T)) +((-2609 . T)) NIL (-1110 |Key| |Ent| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4329 . T)) -((-12 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3326) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1777) (|devaluate| |#2|)))))) (-1524 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1524 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-821))) (-1524 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1778) (|devaluate| |#2|)))))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-821))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) (-1111) ((|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 @@ -4395,19 +4395,19 @@ NIL (-1116 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n-1)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,{}x) = [x,{}f(x),{}f(f(x)),{}...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),{}f(),{}f(),{}...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,{}n,{}y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,{}st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,{}s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,{}s) = concat(a,{}s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,{}st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,{}s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} converts a list \\spad{l} to a stream.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) ((-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-1117) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4329 . T) (-4328 . T) (-2608 . T)) +((-4329 . T) (-4328 . T) (-2609 . T)) NIL (-1118) NIL ((-4329 . T) (-4328 . T)) -((-1524 (-12 (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-142) (QUOTE (-1063))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -591) (QUOTE (-832))))) +((-1525 (-12 (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-142) (QUOTE (-1063))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -591) (QUOTE (-832))))) (-1119 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3326) (QUOTE (-1118))) (LIST (QUOTE |:|) (QUOTE -1777) (|devaluate| |#1|)))))) (-1524 (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|)) (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-1063)))) (-1524 (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|)) (QUOTE (-1063))) (|HasCategory| (-1118) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-1524 (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|)) (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (QUOTE (-1118))) (LIST (QUOTE |:|) (QUOTE -1778) (|devaluate| |#1|)))))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-1063)))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (QUOTE (-1063))) (|HasCategory| (-1118) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (LIST (QUOTE -591) (QUOTE (-832))))) (-1120 A) ((|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 @@ -4434,9 +4434,9 @@ NIL NIL (-1126 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-745)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-745)) (|devaluate| |#1|)))) (|HasCategory| (-745) (QUOTE (-1075))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-745))))) (|HasSignature| |#1| (LIST (QUOTE -3834) (LIST (|devaluate| |#1|) (QUOTE (-1135)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-745))))) (|HasCategory| |#1| (QUOTE (-354))) (-1524 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -2069) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1135))))) (|HasSignature| |#1| (LIST (QUOTE -2259) (LIST (LIST (QUOTE -619) (QUOTE (-1135))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-745)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-745)) (|devaluate| |#1|)))) (|HasCategory| (-745) (QUOTE (-1075))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-745))))) (|HasSignature| |#1| (LIST (QUOTE -3835) (LIST (|devaluate| |#1|) (QUOTE (-1135)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-745))))) (|HasCategory| |#1| (QUOTE (-354))) (-1525 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -2963) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1135))))) (|HasSignature| |#1| (LIST (QUOTE -2259) (LIST (LIST (QUOTE -619) (QUOTE (-1135))) (|devaluate| |#1|))))))) (-1134) ((|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 @@ -4479,7 +4479,7 @@ NIL (-1137 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-6 -4326)) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| (-940) (QUOTE (-130))) (|HasCategory| |#1| (QUOTE (-539)))) (-1524 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4326))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| (-940) (QUOTE (-130))) (|HasCategory| |#1| (QUOTE (-539)))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4326))) (-1138) ((|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 @@ -4511,7 +4511,7 @@ NIL (-1145 |Key| |Entry|) ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) ((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3326) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1777) (|devaluate| |#2|)))))) (-1524 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1524 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063))) (-1524 (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1778) (|devaluate| |#2|)))))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) (-1146 R) ((|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 @@ -4522,7 +4522,7 @@ NIL NIL (-1148 |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(fn,{}t1,{}t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) "\\spad{table([x,{}y,{}...,{}z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(t,{}k,{}e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) -((-4329 . T) (-2608 . T)) +((-4329 . T) (-2609 . T)) NIL (-1149 |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."))) @@ -4563,7 +4563,7 @@ NIL (-1158 S) ((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1,{} t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4329 . T) (-4328 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-1159 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4572,7 +4572,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1161 R -1409) +(-1161 R -1410) ((|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 @@ -4580,7 +4580,7 @@ NIL ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1163 R -1409) +(-1163 R -1410) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -855) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -855) (|devaluate| |#1|))))) @@ -4590,12 +4590,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-359)))) (-1165 R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#4|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4329 . T) (-4328 . T) (-2608 . T)) +((-4329 . T) (-4328 . T) (-2609 . T)) NIL (-1166 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) (((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-354)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-354)))) (-1167 |Curve|) ((|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 @@ -4608,7 +4608,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,{}n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based")) (|coerce| (($ (|PrimitiveArray| |#1|)) "\\spad{coerce(a)} makes a tuple from primitive array a"))) NIL ((|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) -(-1170 -1409) +(-1170 -1410) ((|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 @@ -4618,7 +4618,7 @@ NIL NIL (-1172) ((|constructor| (NIL "The fundamental Type."))) -((-2608 . T)) +((-2609 . T)) NIL (-1173 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}.}"))) @@ -4650,16 +4650,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-354)))) (-1180 |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)]}.")) 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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 @@ -4695,7 +4695,7 @@ NIL (-1191 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. 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T)) -((|HasCategory| |#2| (QUOTE (-878))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-169))) (-1524 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-539)))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (-1524 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-878)))) (-1524 (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-878)))) (-1524 (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))) (-1524 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasCategory| |#2| (QUOTE (-225))) (|HasAttribute| |#2| (QUOTE -4326)) (|HasCategory| |#2| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (-1524 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-143))))) +((|HasCategory| |#2| (QUOTE (-878))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-169))) (-1525 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-539)))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (-1525 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-878)))) (-1525 (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-878)))) (-1525 (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))) (-1525 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasCategory| |#2| (QUOTE (-225))) (|HasAttribute| |#2| (QUOTE -4326)) (|HasCategory| |#2| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-143))))) (-1192 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 @@ -4711,7 +4711,7 @@ NIL (-1195 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1075))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3834) (LIST (|devaluate| |#2|) (QUOTE (-1135)))))) +((|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1075))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3835) (LIST (|devaluate| |#2|) (QUOTE (-1135)))))) (-1196 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) (((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4322 . T) (-4323 . T) (-4325 . T)) @@ -4739,22 +4739,22 @@ NIL (-1202 |Coef| ULS) ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. Univariate Puiseux series are represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}."))) (((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-354)) (-4320 |has| |#1| (-354)) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|)))) (|HasCategory| (-398 (-547)) (QUOTE (-1075))) (|HasCategory| |#1| (QUOTE (-354))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-1524 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasSignature| |#1| (LIST (QUOTE -3834) (LIST (|devaluate| |#1|) (QUOTE (-1135)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (-1524 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -2069) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1135))))) (|HasSignature| |#1| (LIST (QUOTE -2259) (LIST (LIST (QUOTE -619) (QUOTE (-1135))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) +((|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|)))) (|HasCategory| (-398 (-547)) (QUOTE (-1075))) (|HasCategory| |#1| (QUOTE (-354))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-1525 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasSignature| |#1| (LIST (QUOTE -3835) (LIST (|devaluate| |#1|) (QUOTE (-1135)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (-1525 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -2963) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1135))))) (|HasSignature| |#1| (LIST (QUOTE -2259) (LIST (LIST (QUOTE -619) (QUOTE (-1135))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) (-1203 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) (((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-354)) (-4320 |has| |#1| (-354)) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|)))) (|HasCategory| (-398 (-547)) (QUOTE (-1075))) (|HasCategory| |#1| (QUOTE (-354))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-1524 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasSignature| |#1| (LIST (QUOTE -3834) (LIST (|devaluate| |#1|) (QUOTE (-1135)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (-1524 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -2069) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1135))))) (|HasSignature| |#1| (LIST (QUOTE -2259) (LIST (LIST (QUOTE -619) (QUOTE (-1135))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|)))) (|HasCategory| (-398 (-547)) (QUOTE (-1075))) (|HasCategory| |#1| (QUOTE (-354))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-1525 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasSignature| |#1| (LIST (QUOTE -3835) (LIST (|devaluate| |#1|) (QUOTE (-1135)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (-1525 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -2963) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1135))))) (|HasSignature| |#1| (LIST (QUOTE -2259) (LIST (LIST (QUOTE -619) (QUOTE (-1135))) (|devaluate| |#1|))))))) (-1204 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,{}f(var))}."))) (((-4330 "*") |has| (-1203 |#2| |#3| |#4|) (-169)) (-4321 |has| (-1203 |#2| |#3| |#4|) (-539)) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| (-1203 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-1203 |#2| |#3| |#4|) (QUOTE (-143))) (|HasCategory| (-1203 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1203 |#2| |#3| |#4|) (QUOTE (-169))) (|HasCategory| (-1203 |#2| |#3| |#4|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-1203 |#2| |#3| |#4|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-1203 |#2| |#3| |#4|) (QUOTE (-354))) (|HasCategory| (-1203 |#2| |#3| |#4|) (QUOTE (-442))) (-1524 (|HasCategory| (-1203 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-1203 |#2| |#3| |#4|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasCategory| (-1203 |#2| |#3| |#4|) (QUOTE (-539)))) +((|HasCategory| (-1203 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-1203 |#2| |#3| |#4|) (QUOTE (-143))) (|HasCategory| (-1203 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1203 |#2| |#3| |#4|) (QUOTE (-169))) (|HasCategory| (-1203 |#2| |#3| |#4|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-1203 |#2| |#3| |#4|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-1203 |#2| |#3| |#4|) (QUOTE (-354))) (|HasCategory| (-1203 |#2| |#3| |#4|) (QUOTE (-442))) (-1525 (|HasCategory| (-1203 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-1203 |#2| |#3| |#4|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasCategory| (-1203 |#2| |#3| |#4|) (QUOTE (-539)))) (-1205 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL ((|HasAttribute| |#1| (QUOTE -4329))) (-1206 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) -((-2608 . T)) +((-2609 . T)) NIL (-1207 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) @@ -4763,7 +4763,7 @@ NIL (-1208 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (QUOTE (-1157))) (|HasSignature| |#2| (LIST (QUOTE -2259) (LIST (LIST (QUOTE -619) (QUOTE (-1135))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2069) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1135))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (QUOTE (-354)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (QUOTE (-1157))) (|HasSignature| |#2| (LIST (QUOTE -2259) (LIST (LIST (QUOTE -619) (QUOTE (-1135))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2963) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1135))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (QUOTE (-354)))) (-1209 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#1|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) (((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4322 . T) (-4323 . T) (-4325 . T)) @@ -4771,18 +4771,18 @@ NIL (-1210 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (-1524 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-745)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-745)) (|devaluate| |#1|)))) (|HasCategory| (-745) (QUOTE (-1075))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-745))))) (|HasSignature| |#1| (LIST (QUOTE -3834) (LIST (|devaluate| |#1|) (QUOTE (-1135)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-745))))) (|HasCategory| |#1| (QUOTE (-354))) (-1524 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -2069) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1135))))) (|HasSignature| |#1| (LIST (QUOTE -2259) (LIST (LIST (QUOTE -619) (QUOTE (-1135))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-745)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-745)) (|devaluate| |#1|)))) (|HasCategory| (-745) (QUOTE (-1075))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-745))))) (|HasSignature| |#1| (LIST (QUOTE -3835) (LIST (|devaluate| |#1|) (QUOTE (-1135)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-745))))) (|HasCategory| |#1| (QUOTE (-354))) (-1525 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -2963) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1135))))) (|HasSignature| |#1| (LIST (QUOTE -2259) (LIST (LIST (QUOTE -619) (QUOTE (-1135))) (|devaluate| |#1|))))))) (-1211 |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,{}f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,{}y[1],{}y[2],{}...,{}y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,{}cl)} is the solution to \\spad{y<n>=f(y,{}y',{}..,{}y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,{}c0,{}c1)} is the solution to \\spad{y'' = f(y,{}y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,{}c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,{}g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1212 -1409 UP L UTS) +(-1212 -1410 UP L UTS) ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s,{} n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) NIL ((|HasCategory| |#1| (QUOTE (-539)))) (-1213) ((|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."))) -((-2608 . T)) +((-2609 . T)) NIL (-1214 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) @@ -4794,7 +4794,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-971))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-701))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1216 R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,{}v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,{}y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4329 . T) (-4328 . T) (-2608 . T)) +((-4329 . T) (-4328 . T) (-2609 . T)) NIL (-1217 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -4803,7 +4803,7 @@ NIL (-1218 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) ((-4329 . T) (-4328 . T)) -((-1524 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1524 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1524 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-701))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-971))) (|HasCategory| |#1| (QUOTE (-1016)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-1525 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-701))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-971))) (|HasCategory| |#1| (QUOTE (-1016)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-1219) ((|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 @@ -4836,7 +4836,7 @@ NIL ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,{}s,{}st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,{}ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,{}s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1227 K R UP -1409) +(-1227 K R UP -1410) ((|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 @@ -4872,11 +4872,11 @@ NIL ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,{}n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,{}y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,{}r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,{}y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,{}w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,{}v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,{}y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,{}w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,{}v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,{}y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,{}w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4321 |has| |#2| (-6 -4321)) (-4323 . T) (-4322 . T) (-4325 . T)) NIL -(-1236 S -1409) +(-1236 S -1410) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,{}s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145)))) -(-1237 -1409) +(-1237 -1410) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,{}s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 016cb9e0..116a5f48 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,14 +1,14 @@ -(144748 . 3430960048) -(((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) ((#0=(-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) #0#) |has| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (-300 (-2 (|:| -3326 |#1|) (|:| -1777 |#2|))))) +(144748 . 3430962944) +(((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) ((#0=(-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) #0#) |has| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (-300 (-2 (|:| -3327 |#1|) (|:| -1778 |#2|))))) (((|#2| |#2|) . T)) ((((-547)) . T)) -((($ $) -1524 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) ((|#2| |#2|) . T) ((#0=(-398 (-547)) #0#) |has| |#2| (-38 (-398 (-547))))) +((($ $) -1525 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) ((|#2| |#2|) . T) ((#0=(-398 (-547)) #0#) |has| |#2| (-38 (-398 (-547))))) ((($) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) (((|#2|) . T)) -((($) -1524 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) ((|#2|) . T) (((-398 (-547))) |has| |#2| (-38 (-398 (-547))))) +((($) -1525 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) ((|#2|) . T) (((-398 (-547))) |has| |#2| (-38 (-398 (-547))))) (|has| |#1| (-878)) ((((-832)) . T)) ((((-832)) . T)) @@ -23,29 +23,29 @@ ((((-217)) . T) (((-832)) . T)) (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) (((|#1|) . T)) -(-1524 (|has| |#1| (-21)) (|has| |#1| (-819))) -((($ $) . T) ((#0=(-398 (-547)) #0#) -1524 (|has| |#1| (-354)) (|has| |#1| (-340))) ((|#1| |#1|) . T)) -(-1524 (|has| |#1| (-794)) (|has| |#1| (-821))) +(-1525 (|has| |#1| (-21)) (|has| |#1| (-819))) +((($ $) . T) ((#0=(-398 (-547)) #0#) -1525 (|has| |#1| (-354)) (|has| |#1| (-340))) ((|#1| |#1|) . T)) +(-1525 (|has| |#1| (-794)) (|has| |#1| (-821))) ((((-398 (-547))) |has| |#1| (-1007 (-398 (-547)))) (((-547)) |has| |#1| (-1007 (-547))) ((|#1|) . T)) ((((-832)) . T)) ((((-832)) . T)) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) (|has| |#1| (-819)) (((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) (((|#1| |#2| |#3|) . T)) (((|#4|) . T)) -((($) . T) (((-398 (-547))) -1524 (|has| |#1| (-354)) (|has| |#1| (-340))) ((|#1|) . T)) +((($) . T) (((-398 (-547))) -1525 (|has| |#1| (-354)) (|has| |#1| (-340))) ((|#1|) . T)) ((((-832)) . T)) ((((-832)) |has| |#1| (-1063))) ((((-832)) . T) (((-1140)) . T)) (((|#1|) . T) ((|#2|) . T)) (((|#1|) . T) (((-547)) |has| |#1| (-1007 (-547))) (((-398 (-547))) |has| |#1| (-1007 (-398 (-547))))) -(-1524 (|has| |#2| (-169)) (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) -(-1524 (|has| |#1| (-169)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) -(((|#2| (-472 (-3763 |#1|) (-745))) . T)) +(-1525 (|has| |#2| (-169)) (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) +(-1525 (|has| |#1| (-169)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(((|#2| (-472 (-3764 |#1|) (-745))) . T)) (((|#1| (-519 (-1135))) . T)) (((#0=(-839 |#1|) #0#) . T) ((#1=(-398 (-547)) #1#) . T) (($ $) . T)) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) (|has| |#4| (-359)) (|has| |#3| (-359)) (((|#1|) . T)) @@ -55,10 +55,10 @@ (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-539)) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-539))) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) ((($) . T)) -((((-832)) -1524 (|has| |#1| (-591 (-832))) (|has| |#1| (-821)) (|has| |#1| (-1063)))) +((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-821)) (|has| |#1| (-1063)))) ((((-523)) |has| |#1| (-592 (-523)))) ((($) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547)))) ((|#1|) . T)) ((($) . T)) @@ -67,59 +67,59 @@ ((((-832)) . T)) ((((-832)) . T)) ((((-398 (-547))) . T) (($) . T)) -((((-398 (-547))) -1524 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (((-1210 |#1| |#2| |#3|)) |has| |#1| (-354)) (($) . T) ((|#1|) . T)) +((((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (((-1210 |#1| |#2| |#3|)) |has| |#1| (-354)) (($) . T) ((|#1|) . T)) ((((-832)) . 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T)) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-340))) -(-1524 (|has| |#4| (-767)) (|has| |#4| (-819))) -(-1524 (|has| |#4| (-767)) (|has| |#4| (-819))) -(-1524 (|has| |#3| (-767)) (|has| |#3| (-819))) -(-1524 (|has| |#3| (-767)) (|has| |#3| (-819))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-340))) +(-1525 (|has| |#4| (-767)) (|has| |#4| (-819))) +(-1525 (|has| |#4| (-767)) (|has| |#4| (-819))) +(-1525 (|has| |#3| (-767)) (|has| |#3| (-819))) +(-1525 (|has| |#3| (-767)) (|has| |#3| (-819))) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-1063)) @@ -133,21 +133,21 @@ ((((-547)) . T)) ((((-547)) . T)) (((|#1|) . T)) -(-1524 (|has| |#2| (-169)) (|has| |#2| (-701)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +(-1525 (|has| |#2| (-169)) (|has| |#2| (-701)) (|has| |#2| (-819)) (|has| |#2| (-1016))) (((|#1| (-745)) . T)) (|has| |#2| (-767)) -(-1524 (|has| |#2| (-767)) (|has| |#2| (-819))) +(-1525 (|has| |#2| (-767)) (|has| |#2| (-819))) (|has| |#2| (-819)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) ((((-1118) |#1|) . T)) -((((-832)) -1524 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) (((|#1|) . T)) (((|#3| (-745)) . T)) (|has| |#1| (-145)) (|has| |#1| (-143)) -(-1524 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) -(-1524 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) (|has| |#1| (-1063)) ((((-398 (-547))) . T) (((-547)) . T)) ((((-1135) |#2|) |has| |#2| (-503 (-1135) |#2|)) ((|#2| |#2|) |has| |#2| (-300 |#2|))) @@ -155,7 +155,7 @@ (((|#1|) . T) (($) . T)) ((((-547)) . T)) ((((-547)) . T)) -((($) -1524 (|has| |#1| (-354)) (|has| |#1| (-539))) (((-398 (-547))) -1524 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) ((|#1|) |has| |#1| (-169))) +((($) -1525 (|has| |#1| (-354)) (|has| |#1| (-539))) (((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) ((|#1|) |has| |#1| (-169))) ((((-547)) . T)) ((((-547)) . T)) (((#0=(-673) (-1131 #0#)) . T)) @@ -174,12 +174,12 @@ ((((-832)) . T)) ((((-832)) . T)) (((|#1| |#1|) . T)) -(((#0=(-398 (-547)) #0#) |has| |#1| (-38 (-398 (-547)))) ((|#1| |#1|) . T) (($ $) -1524 (|has| |#1| (-169)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878)))) -((($ $) -1524 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1| |#1|) . T) ((#0=(-398 (-547)) #0#) |has| |#1| (-38 (-398 (-547))))) +(((#0=(-398 (-547)) #0#) |has| |#1| (-38 (-398 (-547)))) ((|#1| |#1|) . T) (($ $) -1525 (|has| |#1| (-169)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878)))) +((($ $) -1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1| |#1|) . T) ((#0=(-398 (-547)) #0#) |has| |#1| (-38 (-398 (-547))))) (((|#1|) . T)) -((((-398 (-547))) |has| |#1| (-38 (-398 (-547)))) ((|#1|) . T) (($) -1524 (|has| |#1| (-169)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878)))) -((($) -1524 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) -((($) -1524 (|has| |#2| (-169)) (|has| |#2| (-819)) (|has| |#2| (-1016))) ((|#2|) -1524 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-1016)))) +((((-398 (-547))) |has| |#1| (-38 (-398 (-547)))) ((|#1|) . T) (($) -1525 (|has| |#1| (-169)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878)))) +((($) -1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +((($) -1525 (|has| |#2| (-169)) (|has| |#2| (-819)) (|has| |#2| (-1016))) ((|#2|) -1525 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-1016)))) ((((-832)) . T)) ((((-832)) . T)) ((((-832)) . T)) @@ -190,27 +190,27 @@ ((((-166 (-217))) |has| |#1| (-991)) (((-166 (-370))) |has| |#1| (-991)) (((-523)) |has| |#1| (-592 (-523))) (((-1131 |#1|)) . T) (((-861 (-547))) |has| |#1| (-592 (-861 (-547)))) (((-861 (-370))) |has| |#1| (-592 (-861 (-370))))) (((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) (((|#1|) . T)) -(-1524 (|has| |#1| (-21)) (|has| |#1| (-819))) -(-1524 (|has| |#1| (-21)) (|has| |#1| (-819))) -((((-398 (-547))) -1524 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) -1524 (|has| |#1| (-354)) (|has| |#1| (-539))) ((|#2|) |has| |#1| (-354)) ((|#1|) |has| |#1| (-169))) -(((|#1|) |has| |#1| (-169)) (((-398 (-547))) -1524 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) -1524 (|has| |#1| (-354)) (|has| |#1| (-539)))) +(-1525 (|has| |#1| (-21)) (|has| |#1| (-819))) +(-1525 (|has| |#1| (-21)) (|has| |#1| (-819))) +((((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) -1525 (|has| |#1| (-354)) (|has| |#1| (-539))) ((|#2|) |has| |#1| (-354)) ((|#1|) |has| |#1| (-169))) +(((|#1|) |has| |#1| (-169)) (((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) -1525 (|has| |#1| (-354)) (|has| |#1| (-539)))) (|has| |#1| (-354)) (-12 (|has| |#4| (-225)) (|has| |#4| (-1016))) (-12 (|has| |#3| (-225)) (|has| |#3| (-1016))) -(-1524 (|has| |#4| (-169)) (|has| |#4| (-819)) (|has| |#4| (-1016))) -(-1524 (|has| |#3| (-169)) (|has| |#3| (-819)) (|has| |#3| (-1016))) +(-1525 (|has| |#4| (-169)) (|has| |#4| (-819)) (|has| |#4| (-1016))) +(-1525 (|has| |#3| (-169)) (|has| |#3| (-819)) (|has| |#3| (-1016))) ((((-832)) . T) (((-1140)) . T)) ((((-832)) . T) (((-1140)) . T)) ((((-832)) . T)) (((|#1|) . T)) ((((-398 (-547))) |has| |#1| (-1007 (-398 (-547)))) (((-547)) |has| |#1| (-1007 (-547))) ((|#1|) . T)) (((|#1|) . T) (((-547)) |has| |#1| (-615 (-547)))) -(((|#2|) . T) (((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -3326 (-1118)) (|:| -1777 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) . T)) (|has| |#1| (-539)) (|has| |#1| (-539)) (((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) -(-1524 (|has| |#1| (-821)) (|has| |#1| (-1063))) +(-1525 (|has| |#1| (-821)) (|has| |#1| (-1063))) (((|#1|) . T)) (|has| |#1| (-539)) (|has| |#1| (-539)) @@ -221,11 +221,11 @@ (((|#2|) . T) (($) . T) (((-398 (-547))) . T)) (-12 (|has| |#1| (-1063)) (|has| |#2| (-1063))) ((($) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547)))) ((|#1|) . T)) -((((-398 (-547))) -1524 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (((-1133 |#1| |#2| |#3|)) |has| |#1| (-354)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-398 (-547))) -1524 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) . T)) +((((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (((-1133 |#1| |#2| |#3|)) |has| |#1| (-354)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) . T)) (((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547)))) (($) . T)) -(((|#4| |#4|) -1524 (|has| |#4| (-169)) (|has| |#4| (-354)) (|has| |#4| (-1016))) (($ $) |has| |#4| (-169))) -(((|#3| |#3|) -1524 (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-1016))) (($ $) |has| |#3| (-169))) +(((|#4| |#4|) -1525 (|has| |#4| (-169)) (|has| |#4| (-354)) (|has| |#4| (-1016))) (($ $) |has| |#4| (-169))) +(((|#3| |#3|) -1525 (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-1016))) (($ $) |has| |#3| (-169))) (((|#1|) . T)) (((|#2|) . T)) ((((-523)) |has| |#2| (-592 (-523))) (((-861 (-370))) |has| |#2| (-592 (-861 (-370)))) (((-861 (-547))) |has| |#2| (-592 (-861 (-547))))) @@ -233,22 +233,22 @@ (((|#1| |#2| |#3| |#4|) . T)) ((((-832)) . T)) ((((-523)) |has| |#1| (-592 (-523))) (((-861 (-370))) |has| |#1| (-592 (-861 (-370)))) (((-861 (-547))) |has| |#1| (-592 (-861 (-547))))) -(((|#4|) -1524 (|has| |#4| (-169)) (|has| |#4| (-354)) (|has| |#4| (-1016))) (($) |has| |#4| (-169))) -(((|#3|) -1524 (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-1016))) (($) |has| |#3| (-169))) +(((|#4|) -1525 (|has| |#4| (-169)) (|has| |#4| (-354)) (|has| |#4| (-1016))) (($) |has| |#4| (-169))) +(((|#3|) -1525 (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-1016))) (($) |has| |#3| (-169))) ((((-832)) . T)) ((((-832)) . T)) ((((-523)) . T) (((-547)) . T) (((-861 (-547))) . T) (((-370)) . T) (((-217)) . T)) (((|#1|) . T) (((-547)) |has| |#1| (-1007 (-547))) (((-398 (-547))) |has| |#1| (-1007 (-398 (-547))))) ((($) . T) (((-398 (-547))) |has| |#2| (-38 (-398 (-547)))) ((|#2|) . T)) ((((-398 $) (-398 $)) |has| |#2| (-539)) (($ $) . T) ((|#2| |#2|) . T)) -((((-2 (|:| -3326 (-1118)) (|:| -1777 (-52)))) . T)) +((((-2 (|:| -3327 (-1118)) (|:| -1778 (-52)))) . T)) (((|#1|) . T)) (|has| |#2| (-878)) ((((-1118) (-52)) . T)) ((((-547)) |has| #0=(-398 |#2|) (-615 (-547))) ((#0#) . T)) ((((-523)) . T) (((-217)) . T) (((-370)) . T) (((-861 (-370))) . T)) ((((-832)) . T)) -(-1524 (|has| |#1| (-21)) (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016))) +(-1525 (|has| |#1| (-21)) (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016))) (((|#1|) |has| |#1| (-169))) (((|#1| $) |has| |#1| (-277 |#1| |#1|))) ((((-832)) . T)) @@ -259,15 +259,15 @@ (|has| |#1| (-821)) (|has| |#1| (-1063)) (((|#1|) . T)) -((((-832)) -1524 (|has| |#1| (-591 (-832))) (|has| |#1| (-821)) (|has| |#1| (-1063)))) +((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-821)) (|has| |#1| (-1063)))) ((((-523)) |has| |#1| (-592 (-523)))) ((((-129)) . T)) -((((-398 (-547))) |has| |#2| (-38 (-398 (-547)))) ((|#2|) |has| |#2| (-169)) (($) -1524 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878)))) +((((-398 (-547))) |has| |#2| (-38 (-398 (-547)))) ((|#2|) |has| |#2| (-169)) (($) -1525 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878)))) ((((-129)) . T)) -((($) -1524 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) -((($) -1524 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +((($) -1525 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +((($) -1525 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) (|has| |#1| (-225)) -((($) -1524 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +((($) -1525 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) (((|#1| (-519 (-792 (-1135)))) . T)) (((|#1| (-940)) . T)) (((#0=(-839 |#1|) $) |has| #0# (-277 #0# #0#))) @@ -276,7 +276,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1111)) -((((-2 (|:| -3326 (-1118)) (|:| -1777 |#1|))) . T)) +((((-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) . T)) (|has| (-1204 |#1| |#2| |#3| |#4|) (-143)) (|has| (-1204 |#1| |#2| |#3| |#4|) (-145)) (|has| |#1| (-143)) @@ -293,20 +293,20 @@ ((($) . T) ((|#1|) . T)) (((|#2|) |has| |#2| (-1016))) ((((-832)) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) ((#0=(-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) #0#) |has| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (-300 (-2 (|:| -3326 |#1|) (|:| -1777 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) ((#0=(-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) #0#) |has| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (-300 (-2 (|:| -3327 |#1|) (|:| -1778 |#2|))))) (((|#1|) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063))) ((#0=(-2 (|:| -3326 (-1118)) (|:| -1777 |#1|)) #0#) |has| (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|)) (-300 (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|))))) +(((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063))) ((#0=(-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) #0#) |has| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (-300 (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))))) ((((-547) |#1|) . T)) ((((-832)) . T)) ((((-523)) -12 (|has| |#1| (-592 (-523))) (|has| |#2| (-592 (-523)))) (((-861 (-370))) -12 (|has| |#1| (-592 (-861 (-370)))) (|has| |#2| (-592 (-861 (-370))))) (((-861 (-547))) -12 (|has| |#1| (-592 (-861 (-547)))) (|has| |#2| (-592 (-861 (-547)))))) ((((-832)) . T)) ((($) . T)) ((((-832)) . T)) -((($ $) -1524 (|has| |#1| (-169)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1| |#1|) . T) ((#0=(-398 (-547)) #0#) |has| |#1| (-38 (-398 (-547))))) +((($ $) -1525 (|has| |#1| (-169)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1| |#1|) . T) ((#0=(-398 (-547)) #0#) |has| |#1| (-38 (-398 (-547))))) ((($) . T)) ((($) . T)) ((($) . T)) -((($) -1524 (|has| |#1| (-169)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +((($) -1525 (|has| |#1| (-169)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) ((((-832)) . T)) ((((-832)) . T)) (|has| (-1203 |#2| |#3| |#4|) (-145)) @@ -317,16 +317,16 @@ ((((-832)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-1524 (|has| |#1| (-21)) (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016))) +(-1525 (|has| |#1| (-21)) (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016))) (((|#1|) . T)) ((((-547) |#1|) . T)) (((|#2|) |has| |#2| (-169))) (((|#1|) |has| |#1| (-169))) (((|#1|) . T)) -(-1524 (|has| |#1| (-21)) (|has| |#1| (-819))) +(-1525 (|has| |#1| (-21)) (|has| |#1| (-819))) ((((-832)) |has| |#1| (-1063))) -(-1524 (|has| |#1| (-463)) (|has| |#1| (-701)) (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016)) (|has| |#1| (-1075))) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-340))) +(-1525 (|has| |#1| (-463)) (|has| |#1| (-701)) (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016)) (|has| |#1| (-1075))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-340))) ((((-879 |#1|)) . T)) ((((-398 |#2|) |#3|) . T)) (|has| |#1| (-15 * (|#1| (-547) |#1|))) @@ -338,7 +338,7 @@ (((|#1|) . T)) ((((-398 (-547))) |has| |#1| (-38 (-398 (-547)))) ((|#1|) |has| |#1| (-169)) (($) |has| |#1| (-539))) (|has| |#1| (-354)) -(-1524 (-12 (|has| (-1210 |#1| |#2| |#3|) (-225)) (|has| |#1| (-354))) (|has| |#1| (-15 * (|#1| (-547) |#1|)))) +(-1525 (-12 (|has| (-1210 |#1| |#2| |#3|) (-225)) (|has| |#1| (-354))) (|has| |#1| (-15 * (|#1| (-547) |#1|)))) (|has| |#1| (-15 * (|#1| (-398 (-547)) |#1|))) (|has| |#1| (-354)) ((((-547)) . T)) @@ -350,31 +350,31 @@ (((|#1|) . T)) ((((-547) |#1|) . T)) (((|#2|) . T)) -(-1524 (|has| |#2| (-354)) (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) -(-1524 (|has| |#2| (-767)) (|has| |#2| (-819))) -(-1524 (|has| |#2| (-767)) (|has| |#2| (-819))) +(-1525 (|has| |#2| (-354)) (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) +(-1525 (|has| |#2| (-767)) (|has| |#2| (-819))) +(-1525 (|has| |#2| (-767)) (|has| |#2| (-819))) (((|#1|) . 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T) (($) -1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) (((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354)))) (((|#3|) |has| |#3| (-1016))) -((($) -1524 (|has| |#1| (-169)) (|has| |#1| (-539))) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +((($) -1525 (|has| |#1| (-169)) (|has| |#1| (-539))) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) (|has| |#1| (-1063)) (((|#2| (-793 |#1|)) . T)) (((|#1|) . T)) @@ -386,37 +386,37 @@ ((((-142)) . T)) (((|#3|) |has| |#3| (-1063)) (((-547)) -12 (|has| |#3| (-1007 (-547))) (|has| |#3| (-1063))) (((-398 (-547))) -12 (|has| |#3| (-1007 (-398 (-547)))) (|has| |#3| (-1063)))) ((((-832)) . T)) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) (((|#1|) . 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T)) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) (|has| |#1| (-359)) (|has| |#1| (-359)) (|has| |#1| (-359)) ((((-832)) . T)) (((|#1|) . T)) -(-1524 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) +(-1525 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) (|has| |#1| (-359)) -(-1524 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(-1525 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((((-547)) . T)) ((((-547)) . T)) -(-1524 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) +(-1525 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) ((((-832)) . T)) ((((-832)) . T)) (-12 (|has| |#2| (-225)) (|has| |#2| (-1016))) @@ -425,10 +425,10 @@ ((((-547) |#4|) . T)) ((((-547) |#3|) . T)) (((|#1|) . T) (((-547)) |has| |#1| (-615 (-547)))) -(-1524 (|has| |#2| (-169)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +(-1525 (|has| |#2| (-169)) (|has| |#2| (-819)) (|has| |#2| (-1016))) ((((-1204 |#1| |#2| |#3| |#4|)) . T)) ((((-398 (-547))) . T) (((-547)) . T)) -((((-832)) -1524 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) @@ -457,38 +457,38 @@ ((($) . T)) ((($ $) . T) ((#0=(-1135) $) . T) ((#0# |#1|) . 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T)) (|has| (-398 |#2|) (-145)) (|has| (-398 |#2|) (-143)) @@ -693,26 +693,26 @@ (|has| |#1| (-539)) (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) ((((-832)) . T)) -((((-2 (|:| -3326 (-1118)) (|:| -1777 |#1|))) . T)) +((((-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) . T)) (|has| |#1| (-38 (-398 (-547)))) -((((-379) (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|))) . T)) +((((-379) (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) . T)) (|has| |#1| (-38 (-398 (-547)))) (|has| |#2| (-1111)) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) ((((-832)) . T) (((-1140)) . T)) ((((-832)) . T) (((-1140)) . T)) ((((-832)) . T) (((-1140)) . T)) ((((-1171)) . T) (((-832)) . T) (((-1140)) . T)) (((|#1|) . T)) ((((-379) (-1118)) . T)) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) (|has| |#1| (-539)) ((((-116 |#1|)) . T)) ((((-129)) . T)) ((((-547) |#1|) . T)) -(-1524 (|has| |#1| (-169)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(-1525 (|has| |#1| (-169)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) (((|#2|) . T)) ((((-832)) . T)) ((((-793 |#1|)) . T)) @@ -725,7 +725,7 @@ (((|#1|) |has| |#1| (-169))) ((((-832)) . T)) ((((-523)) |has| |#1| (-592 (-523)))) -(-1524 (|has| |#1| (-821)) (|has| |#1| (-1063))) +(-1525 (|has| |#1| (-821)) (|has| |#1| (-1063))) (((|#2|) |has| |#2| (-300 |#2|))) (((#0=(-547) #0#) . T) ((#1=(-398 (-547)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -735,7 +735,7 @@ (((#0=(-547) #0#) . T) ((#1=(-398 (-547)) #1#) . T) (($ $) . T)) ((($) . T) (((-547)) . T) (((-398 (-547))) . T)) (|has| |#2| (-359)) -(-1524 (|has| |#1| (-821)) (|has| |#1| (-1063))) +(-1525 (|has| |#1| (-821)) (|has| |#1| (-1063))) (((|#1|) . T) (((-398 (-547))) . T) (($) . T)) (((|#1|) . T) (((-398 (-547))) . T) (($) . T)) (((|#1|) . T) (((-398 (-547))) . T) (($) . T)) @@ -746,9 +746,9 @@ ((((-1133 |#1| |#2| |#3|) $) -12 (|has| (-1133 |#1| |#2| |#3|) (-277 (-1133 |#1| |#2| |#3|) (-1133 |#1| |#2| |#3|))) (|has| |#1| (-354))) (($ $) . T)) ((((-832)) . T)) ((((-832)) . T)) -((($) . T) (((-398 (-547))) -1524 (|has| |#1| (-354)) (|has| |#1| (-340))) ((|#1|) . T)) +((($) . T) (((-398 (-547))) -1525 (|has| |#1| (-354)) (|has| |#1| (-340))) ((|#1|) . T)) ((((-523)) |has| |#1| (-592 (-523)))) -((((-832)) -1524 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) ((($ $) . T)) ((($ $) . T)) ((((-832)) . T)) @@ -758,12 +758,12 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((($) -1524 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +((($) -1525 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) ((((-398 (-547))) . T) (((-547)) . T)) ((((-547) (-142)) . T)) ((((-142)) . T)) (((|#1|) . T)) -(-1524 (|has| |#1| (-21)) (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-539)) (|has| |#1| (-1016))) +(-1525 (|has| |#1| (-21)) (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-539)) (|has| |#1| (-1016))) ((((-112)) . T)) (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) ((((-112)) . T)) @@ -771,38 +771,38 @@ ((((-523)) |has| |#1| (-592 (-523))) (((-217)) . #0=(|has| |#1| (-991))) (((-370)) . #0#)) ((((-832)) . T)) (|has| |#1| (-794)) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) (|has| |#1| (-821)) -(-1524 (|has| |#1| (-169)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-169)) (|has| |#1| (-539))) (|has| |#1| (-539)) (|has| |#1| (-878)) (((|#1|) . T)) (|has| |#1| (-1063)) ((((-832)) . T)) -(-1524 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) -(-1524 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) -(-1524 (|has| |#1| (-169)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-169)) (|has| |#1| (-539))) ((((-832)) . T)) ((((-832)) . T)) ((((-832)) . T)) (((|#1| (-1218 |#1|) (-1218 |#1|)) . T)) ((((-547) (-142)) . T)) ((($) . T)) -(-1524 (|has| |#4| (-169)) (|has| |#4| (-819)) (|has| |#4| (-1016))) -(-1524 (|has| |#3| (-169)) (|has| |#3| (-819)) (|has| |#3| (-1016))) +(-1525 (|has| |#4| (-169)) (|has| |#4| (-819)) (|has| |#4| (-1016))) +(-1525 (|has| |#3| (-169)) (|has| |#3| (-819)) (|has| |#3| (-1016))) ((((-832)) . T)) (|has| |#1| (-1063)) (((|#1| (-940)) . T)) (((|#1| |#1|) . T)) ((($) . T)) -(-1524 (|has| |#2| (-767)) (|has| |#2| (-819))) -(-1524 (|has| |#2| (-767)) (|has| |#2| (-819))) +(-1525 (|has| |#2| (-767)) (|has| |#2| (-819))) +(-1525 (|has| |#2| (-767)) (|has| |#2| (-819))) (-12 (|has| |#1| (-463)) (|has| |#2| (-463))) -(-1524 (|has| |#2| (-169)) (|has| |#2| (-701)) (|has| |#2| (-819)) (|has| |#2| (-1016))) -(-1524 (-12 (|has| |#1| (-463)) (|has| |#2| (-463))) (-12 (|has| |#1| (-701)) (|has| |#2| (-701)))) +(-1525 (|has| |#2| (-169)) (|has| |#2| (-701)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +(-1525 (-12 (|has| |#1| (-463)) (|has| |#2| (-463))) (-12 (|has| |#1| (-701)) (|has| |#2| (-701)))) (((|#1|) . T)) (|has| |#2| (-767)) -(-1524 (|has| |#2| (-767)) (|has| |#2| (-819))) +(-1525 (|has| |#2| (-767)) (|has| |#2| (-819))) (((|#1| |#2|) . T)) (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) (|has| |#2| (-819)) @@ -817,7 +817,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-398 (-547))) . T) (($) . T)) -((($) . T) (((-398 (-547))) -1524 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) ((|#1|) . T)) +((($) . T) (((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) ((|#1|) . T)) (|has| |#1| (-802)) ((((-398 (-547))) |has| |#1| (-1007 (-398 (-547)))) (((-547)) |has| |#1| (-1007 (-547))) ((|#1|) . T)) (|has| |#1| (-1063)) @@ -828,10 +828,10 @@ (((|#3|) |has| |#3| (-1063))) (|has| |#3| (-359)) (((|#1|) . T) (((-832)) . T)) -((((-398 (-547))) -1524 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) -1524 (|has| |#1| (-354)) (|has| |#1| (-539))) (((-1210 |#1| |#2| |#3|)) |has| |#1| (-354)) ((|#1|) |has| |#1| (-169))) +((((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) -1525 (|has| |#1| (-354)) (|has| |#1| (-539))) (((-1210 |#1| |#2| |#3|)) |has| |#1| (-354)) ((|#1|) |has| |#1| (-169))) ((((-832)) . T)) (((|#2|) . T)) -(((|#1|) |has| |#1| (-169)) (((-398 (-547))) -1524 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) -1524 (|has| |#1| (-354)) (|has| |#1| (-539)))) +(((|#1|) |has| |#1| (-169)) (((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) -1525 (|has| |#1| (-354)) (|has| |#1| (-539)))) ((($) |has| |#1| (-539)) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) (((|#1| |#1|) |has| |#1| (-169))) (((|#1| |#2|) . T)) @@ -839,30 +839,30 @@ (((|#1|) . T)) (((|#1|) |has| |#1| (-169))) ((((-398 (-547))) . T) (((-547)) . T)) -((($ $) -1524 (|has| |#1| (-169)) (|has| |#1| (-539))) ((|#1| |#1|) . T) ((#0=(-398 (-547)) #0#) |has| |#1| (-38 (-398 (-547))))) -((($) -1524 (|has| |#1| (-169)) (|has| |#1| (-539))) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +((($ $) -1525 (|has| |#1| (-169)) (|has| |#1| (-539))) ((|#1| |#1|) . T) ((#0=(-398 (-547)) #0#) |has| |#1| (-38 (-398 (-547))))) +((($) -1525 (|has| |#1| (-169)) (|has| |#1| (-539))) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) (((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) ((((-142)) . T)) (((|#1|) . T)) ((((-142)) . T)) -((($) -1524 (|has| |#2| (-169)) (|has| |#2| (-819)) (|has| |#2| (-1016))) ((|#2|) -1524 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-1016)))) +((($) -1525 (|has| |#2| (-169)) (|has| |#2| (-819)) (|has| |#2| (-1016))) ((|#2|) -1525 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-1016)))) ((((-142)) . T)) (((|#1| |#2| |#3|) . T)) -(-1524 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-539)) (|has| |#1| (-1016))) +(-1525 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-539)) (|has| |#1| (-1016))) (|has| $ (-145)) (|has| $ (-145)) (|has| |#1| (-1063)) ((((-832)) . T)) (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) -(-1524 (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-463)) (|has| |#1| (-539)) (|has| |#1| (-1016)) (|has| |#1| (-1075))) +(-1525 (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-463)) (|has| |#1| (-539)) (|has| |#1| (-1016)) (|has| |#1| (-1075))) ((($ $) |has| |#1| (-277 $ $)) ((|#1| $) |has| |#1| (-277 |#1| |#1|))) (((|#1| (-398 (-547))) . T)) (((|#1|) . T)) ((((-1135)) . T)) (|has| |#1| (-539)) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-539))) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) (|has| |#1| (-539)) (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) @@ -873,7 +873,7 @@ (|has| |#1| (-145)) (|has| |#1| (-143)) (|has| |#4| (-819)) -(((|#2| (-232 (-3763 |#1|) (-745)) (-834 |#1|)) . T)) +(((|#2| (-232 (-3764 |#1|) (-745)) (-834 |#1|)) . T)) (|has| |#3| (-819)) (((|#1| (-519 |#3|) |#3|) . T)) (|has| |#1| (-145)) @@ -887,21 +887,21 @@ (|has| |#1| (-143)) ((((-398 (-547))) |has| |#2| (-354)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) -(-1524 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) -(-1524 (|has| |#1| (-340)) (|has| |#1| (-359))) +(-1525 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) +(-1525 (|has| |#1| (-340)) (|has| |#1| (-359))) ((((-1102 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-169)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-225)) (|has| |#2| (-1016))) -(((|#2|) . T) (((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) -(-1524 (|has| |#3| (-767)) (|has| |#3| (-819))) -(-1524 (|has| |#3| (-767)) (|has| |#3| (-819))) +(((|#2|) . T) (((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) +(-1525 (|has| |#3| (-767)) (|has| |#3| (-819))) +(-1525 (|has| |#3| (-767)) (|has| |#3| (-819))) ((((-832)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) (((|#1|) . T) (($) . T)) ((((-673)) . T)) -(-1524 (|has| |#2| (-169)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +(-1525 (|has| |#2| (-169)) (|has| |#2| (-819)) (|has| |#2| (-1016))) (|has| |#1| (-539)) (((|#1|) . T)) (((|#1|) . T)) @@ -923,10 +923,10 @@ (((|#1| (-398 (-547))) . T)) (((|#3|) . T) (((-590 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) ((($ $) . T) ((|#2| $) . T)) (((|#1|) . T) (((-398 (-547))) . T) (($) . T)) (((#0=(-1133 |#1| |#2| |#3|) #0#) -12 (|has| (-1133 |#1| |#2| |#3|) (-300 (-1133 |#1| |#2| |#3|))) (|has| |#1| (-354))) (((-1135) #0#) -12 (|has| (-1133 |#1| |#2| |#3|) (-503 (-1135) (-1133 |#1| |#2| |#3|))) (|has| |#1| (-354)))) @@ -934,8 +934,8 @@ ((((-832)) . T)) ((((-832)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) (((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) |has| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (-300 (-2 (|:| -3326 |#1|) (|:| -1777 |#2|))))) -(((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063))) (((-2 (|:| -3326 (-1118)) (|:| -1777 |#1|))) |has| (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|)) (-300 (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|))))) +(((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) (((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) |has| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (-300 (-2 (|:| -3327 |#1|) (|:| -1778 |#2|))))) +(((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063))) (((-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) |has| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (-300 (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))))) ((((-832)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -946,10 +946,10 @@ ((($ $) . T) ((#0=(-834 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-802)) (|has| |#1| (-1063)) -(((|#2| |#2|) -1524 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-1016))) (($ $) |has| |#2| (-169))) -(((|#2|) -1524 (|has| |#2| (-169)) (|has| |#2| (-354)))) -((((-547) (-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -1524 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-1016))) (($) |has| |#2| (-169))) +(((|#2| |#2|) -1525 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-1016))) (($ $) |has| |#2| (-169))) +(((|#2|) -1525 (|has| |#2| (-169)) (|has| |#2| (-354)))) +((((-547) (-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -1525 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-1016))) (($) |has| |#2| (-169))) ((((-745)) . T)) ((((-547)) . T)) (|has| |#1| (-539)) @@ -962,30 +962,30 @@ ((((-116 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-145)) -(-1524 (|has| |#1| (-169)) (|has| |#1| (-539))) -(-1524 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) -(-1524 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) -(-1524 (|has| |#1| (-169)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-169)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-169)) (|has| |#1| (-539))) ((((-861 (-547))) . T) (((-861 (-370))) . T) (((-523)) . T) (((-1135)) . T)) ((((-832)) . T)) -(-1524 (|has| |#1| (-821)) (|has| |#1| (-1063))) +(-1525 (|has| |#1| (-821)) (|has| |#1| (-1063))) ((((-832)) . T) (((-1140)) . T)) ((($) . T)) ((((-832)) . 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T)) -((($) -1524 (|has| |#1| (-298)) (|has| |#1| (-354)) (|has| |#1| (-340)) (|has| |#1| (-539))) (((-398 (-547))) -1524 (|has| |#1| (-354)) (|has| |#1| (-340))) ((|#1|) . T)) +((($) -1525 (|has| |#1| (-298)) (|has| |#1| (-354)) (|has| |#1| (-340)) (|has| |#1| (-539))) (((-398 (-547))) -1525 (|has| |#1| (-354)) (|has| |#1| (-340))) ((|#1|) . T)) ((((-547) |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) @@ -993,37 +993,37 @@ (-12 (|has| |#1| (-359)) (|has| |#2| (-359))) ((((-832)) . T)) ((((-1135) |#1|) |has| |#1| (-503 (-1135) |#1|)) ((|#1| |#1|) |has| |#1| (-300 |#1|))) -(-1524 (|has| |#1| (-143)) (|has| |#1| (-359))) -(-1524 (|has| |#1| (-143)) (|has| |#1| (-359))) -(-1524 (|has| |#1| (-143)) (|has| |#1| (-359))) +(-1525 (|has| |#1| (-143)) (|has| |#1| (-359))) +(-1525 (|has| |#1| (-143)) (|has| |#1| (-359))) +(-1525 (|has| |#1| (-143)) (|has| |#1| (-359))) (((|#1|) . 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T)) (((|#1|) |has| |#1| (-300 |#1|))) (|has| |#1| (-359)) @@ -1031,32 +1031,32 @@ (|has| |#1| (-359)) ((((-1135) $) |has| |#1| (-503 (-1135) $)) (($ $) |has| |#1| (-300 $)) ((|#1| |#1|) |has| |#1| (-300 |#1|)) (((-1135) |#1|) |has| |#1| (-503 (-1135) |#1|))) ((((-1135)) |has| |#1| (-869 (-1135)))) -(-1524 (-12 (|has| |#1| (-225)) (|has| |#1| (-354))) (|has| |#1| (-340))) +(-1525 (-12 (|has| |#1| (-225)) (|has| |#1| (-354))) (|has| |#1| (-340))) ((((-379) (-1082)) . T)) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-379) |#1|) . T)) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-340))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-340))) (|has| |#1| (-1063)) ((((-832)) . T)) ((((-832)) . T)) ((((-879 |#1|)) . T)) ((((-832)) . T) (((-1140)) . 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T)) ((((-832)) . T)) ((((-832)) . T)) @@ -1083,14 +1083,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-819)) (|has| |#1| (-819)) -((($) . T) (((-398 (-547))) -1524 (|has| |#1| (-354)) (|has| |#1| (-340))) ((|#1|) . T)) -(-1524 (|has| |#1| (-169)) (|has| |#1| (-539))) -(((#0=(-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) #0#) |has| (-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) (-300 (-2 (|:| -3326 (-1135)) (|:| -1777 (-52)))))) +((($) . T) (((-398 (-547))) -1525 (|has| |#1| (-354)) (|has| |#1| (-340))) ((|#1|) . T)) +(-1525 (|has| |#1| (-169)) (|has| |#1| (-539))) +(((#0=(-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) #0#) |has| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (-300 (-2 (|:| -3327 (-1135)) (|:| -1778 (-52)))))) ((($) . T)) (|has| |#2| (-821)) ((($) . 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T)) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) ((((-832)) . T)) ((((-879 |#1|)) . T)) (|has| |#1| (-354)) @@ -1126,32 +1126,32 @@ ((((-832)) . T)) ((($) . T)) (((|#2|) . T) (($) . T)) -((((-547) (-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T) ((|#1| |#2|) . T)) +((((-547) (-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-169))) ((($) |has| |#1| (-539)) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) (((|#3|) . 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T)) ((((-547)) |has| |#1| (-855 (-547))) (((-370)) |has| |#1| (-855 (-370)))) -((((-398 (-547))) -1524 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) -1524 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) ((|#1|) . T)) +((((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) -1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) ((|#1|) . T)) (((|#1|) . T)) ((((-619 |#4|)) . T) (((-832)) . T)) ((((-523)) |has| |#4| (-592 (-523)))) @@ -1164,17 +1164,17 @@ (((|#1|) . T)) (((|#2|) . T)) ((((-1135)) |has| (-398 |#2|) (-869 (-1135)))) -(((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) ((#0=(-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) #0#) |has| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (-300 (-2 (|:| -3326 |#1|) (|:| -1777 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) ((#0=(-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) #0#) |has| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (-300 (-2 (|:| -3327 |#1|) (|:| -1778 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) -((((-832)) -1524 (|has| |#3| (-25)) (|has| |#3| (-130)) (|has| |#3| (-591 (-832))) (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-359)) (|has| |#3| (-701)) (|has| |#3| (-767)) (|has| |#3| (-819)) (|has| |#3| (-1016)) (|has| |#3| (-1063))) (((-1218 |#3|)) . T)) +((((-832)) -1525 (|has| |#3| (-25)) (|has| |#3| (-130)) (|has| |#3| (-591 (-832))) (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-359)) (|has| |#3| (-701)) (|has| |#3| (-767)) (|has| |#3| (-819)) (|has| |#3| (-1016)) (|has| |#3| (-1063))) (((-1218 |#3|)) . T)) ((((-547) |#2|) . T)) -(-1524 (|has| |#1| (-821)) (|has| |#1| (-1063))) -(((|#2| |#2|) -1524 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-1016))) (($ $) |has| |#2| (-169))) +(-1525 (|has| |#1| (-821)) (|has| |#1| (-1063))) +(((|#2| |#2|) -1525 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-1016))) (($ $) |has| |#2| (-169))) ((((-832)) . T)) ((((-832)) . T)) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T) ((|#2|) . T)) ((((-832)) . T)) ((((-832)) . T)) ((((-1118) (-1135) (-547) (-217) (-832)) . T)) @@ -1209,8 +1209,8 @@ (|has| |#1| (-38 (-398 (-547)))) ((((-832)) . T)) ((((-523)) |has| |#1| (-592 (-523)))) -((((-832)) -1524 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) -(((|#2|) -1524 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-1016))) (($) |has| |#2| (-169))) +((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +(((|#2|) -1525 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-1016))) (($) |has| |#2| (-169))) (|has| $ (-145)) ((((-398 |#2|)) . T)) ((((-398 (-547))) |has| #0=(-398 |#2|) (-1007 (-398 (-547)))) (((-547)) |has| #0# (-1007 (-547))) ((#0#) . T)) @@ -1221,11 +1221,11 @@ (((|#3|) |has| |#3| (-169))) (|has| |#1| (-145)) (|has| |#1| (-143)) -(-1524 (|has| |#1| (-143)) (|has| |#1| (-359))) +(-1525 (|has| |#1| (-143)) (|has| |#1| (-359))) (|has| |#1| (-145)) -(-1524 (|has| |#1| (-143)) (|has| |#1| (-359))) +(-1525 (|has| |#1| (-143)) (|has| |#1| (-359))) (|has| |#1| (-145)) -(-1524 (|has| |#1| (-143)) (|has| |#1| (-359))) +(-1525 (|has| |#1| (-143)) (|has| |#1| (-359))) (|has| |#1| (-145)) (((|#1|) . T)) (((|#2|) . T)) @@ -1257,7 +1257,7 @@ ((((-968 |#1|)) . T) ((|#1|) . T)) ((((-832)) . T)) ((((-832)) . T)) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) ((((-398 (-547))) . T) (((-398 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1131 |#1|)) . T)) ((((-547)) . T) (($) . T) (((-398 (-547))) . T)) @@ -1265,9 +1265,9 @@ (|has| |#1| (-821)) (((|#2|) . T)) ((((-547)) . T) (($) . T) (((-398 (-547))) . T)) -((((-2 (|:| -3326 (-1118)) (|:| -1777 |#1|))) . T)) +((((-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) . T)) ((((-547) |#2|) . T)) -((((-832)) -1524 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) (((|#2|) . T)) ((((-547) |#3|) . T)) (((|#2|) . T)) @@ -1282,7 +1282,7 @@ (|has| |#1| (-38 (-398 (-547)))) (((|#2|) . T)) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) ((#0=(-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) #0#) |has| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (-300 (-2 (|:| -3326 |#1|) (|:| -1777 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) ((#0=(-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) #0#) |has| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (-300 (-2 (|:| -3327 |#1|) (|:| -1778 |#2|))))) (((|#2| |#2|) . T)) (|has| |#2| (-354)) (((|#2|) . T) (((-547)) |has| |#2| (-1007 (-547))) (((-398 (-547))) |has| |#2| (-1007 (-398 (-547))))) @@ -1312,19 +1312,19 @@ (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) (((|#1| |#2|) . T)) ((((-547) (-142)) . T)) -(((#0=(-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) #0#) |has| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (-300 (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) -((($) -1524 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +(((#0=(-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) #0#) |has| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (-300 (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) +((($) -1525 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) (|has| |#1| (-821)) (((|#2| (-745) (-1045)) . T)) (((|#1| |#2|) . T)) -(-1524 (|has| |#1| (-169)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-169)) (|has| |#1| (-539))) (|has| |#1| (-765)) (((|#1|) |has| |#1| (-169))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-1524 (|has| |#1| (-145)) (-12 (|has| |#1| (-354)) (|has| |#2| (-145)))) -(-1524 (|has| |#1| (-143)) (-12 (|has| |#1| (-354)) (|has| |#2| (-143)))) +(-1525 (|has| |#1| (-145)) (-12 (|has| |#1| (-354)) (|has| |#2| (-145)))) +(-1525 (|has| |#1| (-143)) (-12 (|has| |#1| (-354)) (|has| |#2| (-143)))) (((|#4|) . T)) (|has| |#1| (-143)) ((((-1118) |#1|) . T)) @@ -1337,10 +1337,10 @@ (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) (((|#3|) . T)) ((((-1210 |#1| |#2| |#3|)) |has| |#1| (-354))) -(-1524 (|has| |#1| (-821)) (|has| |#1| (-1063))) +(-1525 (|has| |#1| (-821)) (|has| |#1| (-1063))) (((|#1|) . T)) -((((-832)) -1524 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) -((((-832)) -1524 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063))) (((-927 |#1|)) . T)) +((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063))) (((-927 |#1|)) . T)) (|has| |#1| (-819)) (|has| |#1| (-819)) (((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) @@ -1353,8 +1353,8 @@ ((($) . T)) ((((-379) (-1118)) . T)) ((($) |has| |#1| (-539)) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) -((((-832)) -1524 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-591 (-832))) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-359)) (|has| |#2| (-701)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016)) (|has| |#2| (-1063))) (((-1218 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -3326 (-1118)) (|:| -1777 #0#))) . T)) +((((-832)) -1525 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-591 (-832))) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-359)) (|has| |#2| (-701)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016)) (|has| |#2| (-1063))) (((-1218 |#2|)) . T)) +(((#0=(-52)) . T) (((-2 (|:| -3327 (-1118)) (|:| -1778 #0#))) . T)) (((|#1|) . T)) ((((-832)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) @@ -1362,7 +1362,7 @@ (|has| |#2| (-143)) (|has| |#2| (-145)) (|has| |#1| (-463)) -(-1524 (|has| |#1| (-463)) (|has| |#1| (-701)) (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016))) +(-1525 (|has| |#1| (-463)) (|has| |#1| (-701)) (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016))) (|has| |#1| (-354)) ((((-832)) . T)) (|has| |#1| (-38 (-398 (-547)))) @@ -1371,8 +1371,8 @@ (|has| |#1| (-819)) (|has| |#1| (-819)) ((((-832)) . T)) -((((-398 (-547))) -1524 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) -1524 (|has| |#1| (-354)) (|has| |#1| (-539))) (((-1210 |#1| |#2| |#3|)) |has| |#1| (-354)) ((|#1|) |has| |#1| (-169))) -(((|#1|) |has| |#1| (-169)) (((-398 (-547))) -1524 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) -1524 (|has| |#1| (-354)) (|has| |#1| (-539)))) +((((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) -1525 (|has| |#1| (-354)) (|has| |#1| (-539))) (((-1210 |#1| |#2| |#3|)) |has| |#1| (-354)) ((|#1|) |has| |#1| (-169))) +(((|#1|) |has| |#1| (-169)) (((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) -1525 (|has| |#1| (-354)) (|has| |#1| (-539)))) ((($) |has| |#1| (-539)) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) (((|#1| |#2|) . T)) ((((-1135)) |has| |#1| (-869 (-1135)))) @@ -1380,7 +1380,7 @@ ((((-832)) . T)) ((((-832)) . T)) (|has| |#1| (-1063)) -(((|#2| (-472 (-3763 |#1|) (-745)) (-834 |#1|)) . T)) +(((|#2| (-472 (-3764 |#1|) (-745)) (-834 |#1|)) . T)) ((((-398 (-547))) . #0=(|has| |#2| (-354))) (($) . #0#)) (((|#1| (-519 (-1135)) (-1135)) . T)) (((|#1|) . T)) @@ -1400,16 +1400,16 @@ (|has| |#1| (-145)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -3326 (-1118)) (|:| -1777 |#1|))) . T)) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) -((((-2 (|:| -3326 (-1135)) (|:| -1777 (-52)))) . T)) +(((|#1|) . T) (((-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) +((((-2 (|:| -3327 (-1135)) (|:| -1778 (-52)))) . T)) ((((-1133 |#1| |#2| |#3|)) |has| |#1| (-354))) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) ((((-1135) (-52)) . T)) ((($ $) . T)) (((|#1| (-547)) . T)) ((((-879 |#1|)) . T)) -(((|#1|) -1524 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-1016))) (($) -1524 (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016)))) +(((|#1|) -1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-1016))) (($) -1525 (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016)))) (((|#1|) . T) (((-547)) |has| |#1| (-1007 (-547))) (((-398 (-547))) |has| |#1| (-1007 (-398 (-547))))) (|has| |#1| (-821)) (|has| |#1| (-821)) @@ -1424,13 +1424,13 @@ (((|#4| |#4|) -12 (|has| |#4| (-300 |#4|)) (|has| |#4| (-1063)))) (((|#1|) |has| |#1| (-169))) (((|#4| |#4|) -12 (|has| |#4| (-300 |#4|)) (|has| |#4| (-1063)))) -(((|#3|) -1524 (|has| |#3| (-169)) (|has| |#3| (-354)))) +(((|#3|) -1525 (|has| |#3| (-169)) (|has| |#3| (-354)))) (|has| |#2| (-821)) (|has| |#1| (-821)) -(-1524 (|has| |#2| (-354)) (|has| |#2| (-442)) (|has| |#2| (-878))) +(-1525 (|has| |#2| (-354)) (|has| |#2| (-442)) (|has| |#2| (-878))) ((($ $) . T) ((#0=(-398 (-547)) #0#) . T)) ((((-547) |#2|) . T)) -(((|#2|) -1524 (|has| |#2| (-169)) (|has| |#2| (-354)))) +(((|#2|) -1525 (|has| |#2| (-169)) (|has| |#2| (-354)))) (|has| |#1| (-340)) (((|#3| |#3|) -12 (|has| |#3| (-300 |#3|)) (|has| |#3| (-1063)))) ((($) . T) (((-398 (-547))) . T)) @@ -1438,7 +1438,7 @@ (|has| |#1| (-794)) (|has| |#1| (-794)) (((|#1|) . T)) -(-1524 (|has| |#1| (-298)) (|has| |#1| (-354)) (|has| |#1| (-340))) +(-1525 (|has| |#1| (-298)) (|has| |#1| (-354)) (|has| |#1| (-340))) (|has| |#1| (-819)) (|has| |#1| (-819)) (|has| |#1| (-819)) @@ -1447,13 +1447,13 @@ ((((-547)) . T) (($) . T) (((-398 (-547))) . T)) (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-340))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-340))) (|has| |#1| (-38 (-398 (-547)))) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) ((((-1135)) |has| |#1| (-869 (-1135))) (((-1045)) . T)) (((|#1|) . T)) (|has| |#1| (-819)) -(((#0=(-2 (|:| -3326 (-1118)) (|:| -1777 (-52))) #0#) |has| (-2 (|:| -3326 (-1118)) (|:| -1777 (-52))) (-300 (-2 (|:| -3326 (-1118)) (|:| -1777 (-52)))))) +(((#0=(-2 (|:| -3327 (-1118)) (|:| -1778 (-52))) #0#) |has| (-2 (|:| -3327 (-1118)) (|:| -1778 (-52))) (-300 (-2 (|:| -3327 (-1118)) (|:| -1778 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) (|has| |#1| (-1063)) ((((-832)) . T) (((-1140)) . T)) @@ -1473,7 +1473,7 @@ (((|#1|) . T)) ((((-142)) . T)) (((|#2|) |has| |#2| (-169))) -(-1524 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-359)) (|has| |#2| (-701)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016)) (|has| |#2| (-1063))) +(-1525 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-359)) (|has| |#2| (-701)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016)) (|has| |#2| (-1063))) (((|#1|) . T)) (|has| |#1| (-143)) (|has| |#1| (-145)) @@ -1495,32 +1495,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) (((|#1|) . T)) (((|#1| |#2|) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063))) ((#0=(-2 (|:| -3326 (-1118)) (|:| -1777 |#1|)) #0#) |has| (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|)) (-300 (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|))))) -(-1524 (|has| |#2| (-442)) (|has| |#2| (-878))) -(-1524 (|has| |#1| (-442)) (|has| |#1| (-878))) +(((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063))) ((#0=(-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) #0#) |has| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (-300 (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))))) +(-1525 (|has| |#2| (-442)) (|has| |#2| (-878))) +(-1525 (|has| |#1| (-442)) (|has| |#1| (-878))) (((|#1|) . T) (($) . T)) (((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) (((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(((|#3|) -1524 (|has| |#3| (-169)) (|has| |#3| (-354)))) +(((|#3|) -1525 (|has| |#3| (-169)) (|has| |#3| (-354)))) (|has| |#1| (-821)) (|has| |#1| (-539)) ((((-561 |#1|)) . T)) ((($) . T)) (((|#2|) . T)) -(-1524 (-12 (|has| |#1| (-354)) (|has| |#2| (-794))) (-12 (|has| |#1| (-354)) (|has| |#2| (-821)))) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (-12 (|has| |#1| (-354)) (|has| |#2| (-794))) (-12 (|has| |#1| (-354)) (|has| |#2| (-821)))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) ((((-879 |#1|)) . T)) (((|#1| (-485 |#1| |#3|) (-485 |#1| |#2|)) . T)) (((|#1| |#4| |#5|) . T)) (((|#1| (-745)) . T)) ((((-398 (-547))) |has| |#1| (-38 (-398 (-547)))) ((|#1|) |has| |#1| (-169)) (($) |has| |#1| (-539))) -((((-398 (-547))) -1524 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) -1524 (|has| |#1| (-354)) (|has| |#1| (-539))) (((-1133 |#1| |#2| |#3|)) |has| |#1| (-354)) ((|#1|) |has| |#1| (-169))) -(((|#1|) |has| |#1| (-169)) (((-398 (-547))) -1524 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) -1524 (|has| |#1| (-354)) (|has| |#1| (-539)))) +((((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) -1525 (|has| |#1| (-354)) (|has| |#1| (-539))) (((-1133 |#1| |#2| |#3|)) |has| |#1| (-354)) ((|#1|) |has| |#1| (-169))) +(((|#1|) |has| |#1| (-169)) (((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) -1525 (|has| |#1| (-354)) (|has| |#1| (-539)))) ((($) |has| |#1| (-539)) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) -((((-2 (|:| -3326 (-1135)) (|:| -1777 (-52)))) . T)) +((((-2 (|:| -3327 (-1135)) (|:| -1778 (-52)))) . T)) ((((-398 |#2|)) . T) (((-398 (-547))) . T) (($) . T)) ((((-646 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1529,17 +1529,17 @@ ((((-832)) . T)) (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) ((((-832)) . T)) -((((-398 (-547))) |has| |#2| (-38 (-398 (-547)))) ((|#2|) |has| |#2| (-169)) (($) -1524 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878)))) +((((-398 (-547))) |has| |#2| (-38 (-398 (-547)))) ((|#2|) |has| |#2| (-169)) (($) -1525 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878)))) ((((-832)) . T)) ((((-832)) . T)) ((((-832)) . T)) (((|#2|) . T)) -(-1524 (|has| |#3| (-25)) (|has| |#3| (-130)) (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-359)) (|has| |#3| (-701)) (|has| |#3| (-767)) (|has| |#3| (-819)) (|has| |#3| (-1016)) (|has| |#3| (-1063))) -(-1524 (|has| |#2| (-169)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +(-1525 (|has| |#3| (-25)) (|has| |#3| (-130)) (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-359)) (|has| |#3| (-701)) (|has| |#3| (-767)) (|has| |#3| (-819)) (|has| |#3| (-1016)) (|has| |#3| (-1063))) +(-1525 (|has| |#2| (-169)) (|has| |#2| (-819)) (|has| |#2| (-1016))) ((((-398 (-547))) |has| |#1| (-1007 (-398 (-547)))) (((-547)) |has| |#1| (-1007 (-547))) ((|#1|) . T)) (|has| |#1| (-1157)) (|has| |#1| (-1157)) -(-1524 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-359)) (|has| |#2| (-701)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016)) (|has| |#2| (-1063))) +(-1525 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-359)) (|has| |#2| (-701)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016)) (|has| |#2| (-1063))) (|has| |#1| (-1157)) (|has| |#1| (-1157)) (((|#3| |#3|) . T)) @@ -1552,43 +1552,43 @@ (((|#1|) . T) (((-398 (-547))) . T) (($) . T)) ((((-1118) (-52)) . T)) (|has| |#1| (-1063)) -(-1524 (|has| |#2| (-794)) (|has| |#2| (-821))) +(-1525 (|has| |#2| (-794)) (|has| |#2| (-821))) (((|#1|) . T)) (((|#1|) |has| |#1| (-169)) (($) . T)) -((($) -1524 (|has| |#1| (-354)) (|has| |#1| (-340))) (((-398 (-547))) -1524 (|has| |#1| (-354)) (|has| |#1| (-340))) ((|#1|) . T)) +((($) -1525 (|has| |#1| (-354)) (|has| |#1| (-340))) (((-398 (-547))) -1525 (|has| |#1| (-354)) (|has| |#1| (-340))) ((|#1|) . T)) ((($) . T)) ((((-1133 |#1| |#2| |#3|)) -12 (|has| (-1133 |#1| |#2| |#3|) (-300 (-1133 |#1| |#2| |#3|))) (|has| |#1| (-354)))) ((((-832)) . T)) -(-1524 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) +(-1525 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) ((($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) -(-1524 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(-1525 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((((-832)) . T)) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) (|has| |#2| (-878)) (|has| |#1| (-354)) (((|#2|) |has| |#2| (-1063))) -(-1524 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) -(-1524 (|has| |#1| (-442)) (|has| |#1| (-878))) +(-1525 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(-1525 (|has| |#1| (-442)) (|has| |#1| (-878))) ((($) . T) ((|#2|) . T)) ((((-523)) . T) (((-398 (-1131 (-547)))) . T) (((-217)) . T) (((-370)) . T)) ((((-370)) . T) (((-217)) . T) (((-832)) . T)) (|has| |#1| (-878)) (|has| |#1| (-878)) (|has| |#1| (-878)) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-878))) -(-1524 (|has| |#1| (-821)) (|has| |#1| (-1063))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-878))) +(-1525 (|has| |#1| (-821)) (|has| |#1| (-1063))) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) ((($ $) . T)) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) ((($ $) . T)) ((((-547) (-112)) . T)) ((($) . T)) (((|#1|) . T)) ((((-547)) . T)) ((((-112)) . T)) -(-1524 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) (|has| |#1| (-38 (-398 (-547)))) (((|#1| (-547)) . T)) ((($) . T)) @@ -1610,7 +1610,7 @@ (((|#1| (-1182 |#1| |#2| |#3|)) . T)) (((|#1| (-745)) . T)) (((|#1|) . T)) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) ((((-832)) . T)) (|has| |#1| (-1063)) ((((-1118) |#1|) . T)) @@ -1630,18 +1630,18 @@ (((|#1|) . T)) ((((-547)) . T)) ((((-832)) . T)) -(-1524 (|has| |#1| (-143)) (|has| |#1| (-340))) +(-1525 (|has| |#1| (-143)) (|has| |#1| (-340))) (|has| |#1| (-145)) ((((-832)) . T)) (((|#3|) . T)) -(-1524 (|has| |#3| (-169)) (|has| |#3| (-819)) (|has| |#3| (-1016))) +(-1525 (|has| |#3| (-169)) (|has| |#3| (-819)) (|has| |#3| (-1016))) ((((-832)) . T)) ((((-1203 |#2| |#3| |#4|)) . T) (((-1204 |#1| |#2| |#3| |#4|)) . T)) ((((-832)) . T)) -((((-48)) -12 (|has| |#1| (-539)) (|has| |#1| (-1007 (-547)))) (((-590 $)) . T) ((|#1|) . T) (((-547)) |has| |#1| (-1007 (-547))) (((-398 (-547))) -1524 (-12 (|has| |#1| (-539)) (|has| |#1| (-1007 (-547)))) (|has| |#1| (-1007 (-398 (-547))))) (((-398 (-921 |#1|))) |has| |#1| (-539)) (((-921 |#1|)) |has| |#1| (-1016)) (((-1135)) . T)) +((((-48)) -12 (|has| |#1| (-539)) (|has| |#1| (-1007 (-547)))) (((-590 $)) . T) ((|#1|) . T) (((-547)) |has| |#1| (-1007 (-547))) (((-398 (-547))) -1525 (-12 (|has| |#1| (-539)) (|has| |#1| (-1007 (-547)))) (|has| |#1| (-1007 (-398 (-547))))) (((-398 (-921 |#1|))) |has| |#1| (-539)) (((-921 |#1|)) |has| |#1| (-1016)) (((-1135)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-745)) . T)) -((($) -1524 (|has| |#1| (-354)) (|has| |#1| (-539))) (((-398 (-547))) -1524 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) ((|#1|) |has| |#1| (-169))) +((($) -1525 (|has| |#1| (-354)) (|has| |#1| (-539))) (((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) ((|#1|) |has| |#1| (-169))) (((|#1|) |has| |#1| (-300 |#1|))) ((((-1204 |#1| |#2| |#3| |#4|)) . T)) ((((-547)) |has| |#1| (-855 (-547))) (((-370)) |has| |#1| (-855 (-370)))) @@ -1649,14 +1649,14 @@ (|has| |#1| (-539)) (((|#1|) . T)) ((((-832)) . T)) -(((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) (((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) |has| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (-300 (-2 (|:| -3326 |#1|) (|:| -1777 |#2|))))) +(((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) (((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) |has| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (-300 (-2 (|:| -3327 |#1|) (|:| -1778 |#2|))))) (((|#1|) |has| |#1| (-169))) ((($) |has| |#1| (-539)) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) (((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) (((|#1|) . T)) (((|#3|) |has| |#3| (-1063))) -(((|#2|) -1524 (|has| |#2| (-169)) (|has| |#2| (-354)))) +(((|#2|) -1525 (|has| |#2| (-169)) (|has| |#2| (-354)))) ((((-1203 |#2| |#3| |#4|)) . T)) ((((-112)) . T)) (|has| |#1| (-794)) @@ -1666,8 +1666,8 @@ (|has| |#1| (-819)) (|has| |#1| (-819)) (((|#1| (-547) (-1045)) . T)) -(-1524 (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016))) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +(-1525 (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016))) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) (((|#1| (-398 (-547)) (-1045)) . T)) (((|#1| (-745) (-1045)) . T)) (|has| |#1| (-821)) @@ -1683,28 +1683,28 @@ (((|#1|) . T)) (|has| |#1| (-1063)) ((((-547)) -12 (|has| |#1| (-354)) (|has| |#2| (-615 (-547)))) ((|#2|) |has| |#1| (-354))) -(-1524 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-359)) (|has| |#2| (-701)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016)) (|has| |#2| (-1063))) +(-1525 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-359)) (|has| |#2| (-701)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016)) (|has| |#2| (-1063))) (((|#2|) |has| |#2| (-169))) (((|#1|) |has| |#1| (-169))) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) -((((-2 (|:| -3326 (-1118)) (|:| -1777 |#1|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) +((((-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) . T)) ((((-832)) . T)) (|has| |#3| (-819)) ((((-832)) . T)) ((((-1203 |#2| |#3| |#4|) (-310 |#2| |#3| |#4|)) . T)) ((((-832)) . T)) -(((|#1| |#1|) -1524 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-1016)))) +(((|#1| |#1|) -1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-1016)))) (((|#1|) . T)) ((((-547)) . T)) ((((-547)) . T)) -(((|#1|) -1524 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-1016)))) +(((|#1|) -1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-1016)))) (((|#2|) |has| |#2| (-354))) ((($) . T) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-354))) (|has| |#1| (-821)) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -3326 (-1135)) (|:| -1777 (-52)))) |has| (-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) (-300 (-2 (|:| -3326 (-1135)) (|:| -1777 (-52)))))) -(-1524 (|has| |#1| (-442)) (|has| |#1| (-878))) +((((-2 (|:| -3327 (-1135)) (|:| -1778 (-52)))) |has| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (-300 (-2 (|:| -3327 (-1135)) (|:| -1778 (-52)))))) +(-1525 (|has| |#1| (-442)) (|has| |#1| (-878))) (((|#2|) . T) (((-547)) |has| |#2| (-615 (-547)))) ((((-832)) . T)) ((((-832)) . T)) @@ -1740,18 +1740,18 @@ (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) (((|#1|) . T)) -(-1524 (|has| |#2| (-169)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +(-1525 (|has| |#2| (-169)) (|has| |#2| (-819)) (|has| |#2| (-1016))) (((|#1| |#1|) . T) ((#0=(-398 (-547)) #0#) . T) (($ $) . T)) ((((-832)) . T)) (((|#1|) . T) (((-398 (-547))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) -((((-832)) -1524 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) (|has| |#1| (-354)) (|has| |#1| (-354)) (|has| (-398 |#2|) (-225)) (|has| |#1| (-878)) (((|#2|) |has| |#2| (-1016))) -(((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) (((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) |has| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (-300 (-2 (|:| -3326 |#1|) (|:| -1777 |#2|))))) +(((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) (((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) |has| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (-300 (-2 (|:| -3327 |#1|) (|:| -1778 |#2|))))) (|has| |#1| (-354)) (((|#1|) |has| |#1| (-169))) (((|#1| |#1|) . T)) @@ -1776,7 +1776,7 @@ (((|#1| (-398 (-547)) (-1045)) . T)) (((|#1| (-745) (-1045)) . T)) (((#0=(-398 |#2|) #0#) . T) ((#1=(-398 (-547)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-547)) -1524 (|has| (-398 (-547)) (-1007 (-547))) (|has| |#1| (-1007 (-547)))) (((-398 (-547))) . T)) +(((|#1|) . T) (((-547)) -1525 (|has| (-398 (-547)) (-1007 (-547))) (|has| |#1| (-1007 (-547)))) (((-398 (-547))) . T)) (((|#1| (-580 |#1| |#3|) (-580 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-169))) (((|#1|) . T)) @@ -1795,24 +1795,24 @@ ((((-673)) . T)) (((|#2|) |has| |#2| (-169))) (|has| |#2| (-819)) -((((-112)) |has| |#1| (-1063)) (((-832)) -1524 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-463)) (|has| |#1| (-701)) (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016)) (|has| |#1| (-1075)) (|has| |#1| (-1063)))) +((((-112)) |has| |#1| (-1063)) (((-832)) -1525 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-463)) (|has| |#1| (-701)) (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016)) (|has| |#1| (-1075)) (|has| |#1| (-1063)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3326 (-1118)) (|:| -1777 (-52)))) . T)) +((((-2 (|:| -3327 (-1118)) (|:| -1778 (-52)))) . T)) ((((-832)) . T)) ((((-547) |#1|) . T)) ((((-673)) . T) (((-398 (-547))) . T) (((-547)) . T)) (((|#1| |#1|) |has| |#1| (-169))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) (((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) |has| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (-300 (-2 (|:| -3326 |#1|) (|:| -1777 |#2|))))) +(((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) (((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) |has| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (-300 (-2 (|:| -3327 |#1|) (|:| -1778 |#2|))))) ((((-370)) . T)) ((((-673)) . T)) ((((-398 (-547))) . #0=(|has| |#2| (-354))) (($) . #0#)) (((|#1|) |has| |#1| (-169))) ((((-398 (-921 |#1|))) . T)) (((|#2| |#2|) . T)) -(-1524 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) -(-1524 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(-1525 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) +(-1525 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) (((|#2|) . T)) (|has| |#2| (-821)) (((|#3|) |has| |#3| (-1016))) @@ -1822,14 +1822,14 @@ (|has| |#1| (-821)) ((((-1135)) |has| |#2| (-869 (-1135)))) ((((-832)) . T)) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) ((((-398 (-547))) . T) (($) . T)) (|has| |#1| (-463)) (|has| |#1| (-359)) (|has| |#1| (-359)) (|has| |#1| (-359)) (|has| |#1| (-354)) -(-1524 (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-463)) (|has| |#1| (-539)) (|has| |#1| (-1016)) (|has| |#1| (-1075))) +(-1525 (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-463)) (|has| |#1| (-539)) (|has| |#1| (-1016)) (|has| |#1| (-1075))) (|has| |#1| (-38 (-398 (-547)))) ((((-116 |#1|)) . T)) ((((-116 |#1|)) . T)) @@ -1850,11 +1850,11 @@ (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-821)) -((((-2 (|:| -3326 (-1118)) (|:| -1777 |#1|))) . T)) +((((-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-145)) (|has| |#1| (-143)) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) |has| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (-300 (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)))) ((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) |has| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (-300 (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)))) ((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) (((|#2|) . T)) (((|#3|) . T)) ((((-116 |#1|)) . T)) @@ -1872,11 +1872,11 @@ ((((-523)) |has| |#1| (-592 (-523))) (((-861 (-547))) |has| |#1| (-592 (-861 (-547)))) (((-861 (-370))) |has| |#1| (-592 (-861 (-370)))) (((-370)) . #0=(|has| |#1| (-991))) (((-217)) . #0#)) (((|#1|) |has| |#1| (-354))) ((((-832)) . T)) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) ((($ $) . T) (((-590 $) $) . T)) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) ((($) . T) (((-1204 |#1| |#2| |#3| |#4|)) . T) (((-398 (-547))) . T)) -((($) -1524 (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-539)) (|has| |#1| (-1016))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-539))) +((($) -1525 (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-539)) (|has| |#1| (-1016))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-539))) (|has| |#1| (-354)) (|has| |#1| (-354)) (|has| |#1| (-354)) @@ -1887,11 +1887,11 @@ ((((-370)) . T)) (((|#3|) -12 (|has| |#3| (-300 |#3|)) (|has| |#3| (-1063)))) ((((-832)) . T)) -(-1524 (|has| |#2| (-442)) (|has| |#2| (-878))) +(-1525 (|has| |#2| (-442)) (|has| |#2| (-878))) (((|#1|) . T)) (|has| |#1| (-821)) (|has| |#1| (-821)) -((((-832)) -1524 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) ((((-523)) |has| |#1| (-592 (-523)))) (((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) (|has| |#1| (-1063)) @@ -1901,13 +1901,13 @@ (|has| |#1| (-143)) (|has| |#1| (-145)) ((((-547)) . T)) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-539))) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) (((#0=(-1203 |#2| |#3| |#4|)) . T) (((-398 (-547))) |has| #0# (-38 (-398 (-547)))) (($) . T)) ((((-547)) . T)) (|has| |#1| (-354)) -(-1524 (-12 (|has| (-1210 |#1| |#2| |#3|) (-145)) (|has| |#1| (-354))) (|has| |#1| (-145))) -(-1524 (-12 (|has| (-1210 |#1| |#2| |#3|) (-143)) (|has| |#1| (-354))) (|has| |#1| (-143))) +(-1525 (-12 (|has| (-1210 |#1| |#2| |#3|) (-145)) (|has| |#1| (-354))) (|has| |#1| (-145))) +(-1525 (-12 (|has| (-1210 |#1| |#2| |#3|) (-143)) (|has| |#1| (-354))) (|has| |#1| (-143))) (|has| |#1| (-354)) (|has| |#1| (-143)) (|has| |#1| (-145)) @@ -1924,19 +1924,19 @@ (((|#1| |#2|) . T)) (((|#1|) . T) (((-547)) |has| |#1| (-615 (-547)))) (((|#3|) |has| |#3| (-169))) -(-1524 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-359)) (|has| |#2| (-701)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016)) (|has| |#2| (-1063))) +(-1525 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-359)) (|has| |#2| (-701)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016)) (|has| |#2| (-1063))) ((((-832)) . T)) ((((-547)) . T)) (((|#1| $) |has| |#1| (-277 |#1| |#1|))) ((((-398 (-547))) . T) (($) . T) (((-398 |#1|)) . T) ((|#1|) . T)) ((((-832)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -1524 (|has| |#1| (-281)) (|has| |#1| (-354))) ((#0=(-398 (-547)) #0#) |has| |#1| (-354))) -((((-2 (|:| -3326 (-1135)) (|:| -1777 (-52)))) . T)) +(((|#1| |#1|) . T) (($ $) -1525 (|has| |#1| (-281)) (|has| |#1| (-354))) ((#0=(-398 (-547)) #0#) |has| |#1| (-354))) +((((-2 (|:| -3327 (-1135)) (|:| -1778 (-52)))) . T)) ((($) . T)) ((((-547) |#1|) . T)) ((((-1135)) |has| (-398 |#2|) (-869 (-1135)))) -(((|#1|) . T) (($) -1524 (|has| |#1| (-281)) (|has| |#1| (-354))) (((-398 (-547))) |has| |#1| (-354))) +(((|#1|) . T) (($) -1525 (|has| |#1| (-281)) (|has| |#1| (-354))) (((-398 (-547))) |has| |#1| (-354))) ((((-523)) |has| |#2| (-592 (-523)))) ((((-663 |#2|)) . T) (((-832)) . T)) (((|#1|) . T)) @@ -1944,8 +1944,8 @@ (((|#4|) -12 (|has| |#4| (-300 |#4|)) (|has| |#4| (-1063)))) ((((-839 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) -(-1524 (|has| |#4| (-767)) (|has| |#4| (-819))) -(-1524 (|has| |#3| (-767)) (|has| |#3| (-819))) +(-1525 (|has| |#4| (-767)) (|has| |#4| (-819))) +(-1525 (|has| |#3| (-767)) (|has| |#3| (-819))) ((((-832)) . T)) ((((-832)) . T)) (((|#4|) -12 (|has| |#4| (-300 |#4|)) (|has| |#4| (-1063)))) @@ -1961,17 +1961,17 @@ ((((-398 (-547))) . T) (($) . T)) ((((-398 (-547))) . T) (($) . T)) ((((-398 (-547))) . T) (($) . T)) -(-1524 (|has| |#1| (-442)) (|has| |#1| (-1176))) +(-1525 (|has| |#1| (-442)) (|has| |#1| (-1176))) ((($) . T)) ((((-398 (-547))) |has| #0=(-398 |#2|) (-1007 (-398 (-547)))) (((-547)) |has| #0# (-1007 (-547))) ((#0#) . T)) (((|#2|) . T) (((-547)) |has| |#2| (-615 (-547)))) (((|#1| (-745)) . T)) (|has| |#1| (-821)) (((|#1|) . T) (((-547)) |has| |#1| (-615 (-547)))) -((($) -1524 (|has| |#1| (-354)) (|has| |#1| (-340))) (((-398 (-547))) -1524 (|has| |#1| (-354)) (|has| |#1| (-340))) ((|#1|) . T)) +((($) -1525 (|has| |#1| (-354)) (|has| |#1| (-340))) (((-398 (-547))) -1525 (|has| |#1| (-354)) (|has| |#1| (-340))) ((|#1|) . T)) ((((-547)) . T)) (|has| |#1| (-38 (-398 (-547)))) -((((-2 (|:| -3326 (-1118)) (|:| -1777 (-52)))) |has| (-2 (|:| -3326 (-1118)) (|:| -1777 (-52))) (-300 (-2 (|:| -3326 (-1118)) (|:| -1777 (-52)))))) +((((-2 (|:| -3327 (-1118)) (|:| -1778 (-52)))) |has| (-2 (|:| -3327 (-1118)) (|:| -1778 (-52))) (-300 (-2 (|:| -3327 (-1118)) (|:| -1778 (-52)))))) (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) (|has| |#1| (-819)) (|has| |#1| (-38 (-398 (-547)))) @@ -1996,24 +1996,24 @@ (((|#1| |#2|) . T)) ((((-142)) . T)) ((((-754 |#1| (-834 |#2|))) . T)) -((((-832)) -1524 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) (|has| |#1| (-1157)) (((|#1|) . T)) -(-1524 (|has| |#3| (-25)) (|has| |#3| (-130)) (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-359)) (|has| |#3| (-701)) (|has| |#3| (-767)) (|has| |#3| (-819)) (|has| |#3| (-1016)) (|has| |#3| (-1063))) +(-1525 (|has| |#3| (-25)) (|has| |#3| (-130)) (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-359)) (|has| |#3| (-701)) (|has| |#3| (-767)) (|has| |#3| (-819)) (|has| |#3| (-1016)) (|has| |#3| (-1063))) ((((-1135) |#1|) |has| |#1| (-503 (-1135) |#1|))) (((|#2|) . T)) -((($ $) -1524 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1| |#1|) . T) ((#0=(-398 (-547)) #0#) |has| |#1| (-38 (-398 (-547))))) -((($) -1524 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +((($ $) -1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1| |#1|) . T) ((#0=(-398 (-547)) #0#) |has| |#1| (-38 (-398 (-547))))) +((($) -1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) ((((-879 |#1|)) . T)) ((($) . T)) ((((-398 (-921 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) ((((-523)) |has| |#4| (-592 (-523)))) ((((-832)) . T) (((-619 |#4|)) . T)) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-819)) -(((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063))) (((-2 (|:| -3326 (-1118)) (|:| -1777 |#1|))) |has| (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|)) (-300 (-2 (|:| -3326 (-1118)) (|:| -1777 |#1|))))) +(((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063))) (((-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) |has| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (-300 (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))))) (|has| |#1| (-1063)) (|has| |#1| (-354)) (|has| |#1| (-821)) @@ -2021,16 +2021,16 @@ (((|#1|) . T)) (((|#1|) . T)) ((($) . T) (((-398 (-547))) . T)) -((($) -1524 (|has| |#1| (-354)) (|has| |#1| (-539))) (((-398 (-547))) -1524 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) ((|#1|) |has| |#1| (-169))) +((($) -1525 (|has| |#1| (-354)) (|has| |#1| (-539))) (((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) ((|#1|) |has| |#1| (-169))) (|has| |#1| (-143)) (|has| |#1| (-145)) -(-1524 (-12 (|has| (-1133 |#1| |#2| |#3|) (-145)) (|has| |#1| (-354))) (|has| |#1| (-145))) -(-1524 (-12 (|has| (-1133 |#1| |#2| |#3|) (-143)) (|has| |#1| (-354))) (|has| |#1| (-143))) +(-1525 (-12 (|has| (-1133 |#1| |#2| |#3|) (-145)) (|has| |#1| (-354))) (|has| |#1| (-145))) +(-1525 (-12 (|has| (-1133 |#1| |#2| |#3|) (-143)) (|has| |#1| (-354))) (|has| |#1| (-143))) (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-145)) (|has| |#1| (-143)) -((((-832)) -1524 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) ((((-1210 |#1| |#2| |#3|)) |has| |#1| (-354))) (|has| |#1| (-819)) (((|#1| |#2|) . T)) @@ -2053,9 +2053,9 @@ ((((-832)) . T)) ((((-832)) . T)) ((((-523)) |has| |#1| (-592 (-523)))) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) ((((-1135) |#1|) |has| |#1| (-503 (-1135) |#1|)) ((|#1| |#1|) |has| |#1| (-300 |#1|))) -(((|#1|) -1524 (|has| |#1| (-169)) (|has| |#1| (-354)))) +(((|#1|) -1525 (|has| |#1| (-169)) (|has| |#1| (-354)))) ((((-307 |#1|)) . T)) (((|#2|) |has| |#2| (-354))) (((|#2|) . T)) @@ -2076,13 +2076,13 @@ (|has| |#1| (-143)) (|has| |#1| (-145)) ((($ $) . T)) -(-1524 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-463)) (|has| |#1| (-701)) (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016)) (|has| |#1| (-1075)) (|has| |#1| (-1063))) +(-1525 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-463)) (|has| |#1| (-701)) (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016)) (|has| |#1| (-1075)) (|has| |#1| (-1063))) (|has| |#1| (-539)) (((|#2|) . T)) ((((-547)) . T)) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) (((|#1|) . T)) -(-1524 (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-539)) (|has| |#1| (-1016))) +(-1525 (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-539)) (|has| |#1| (-1016))) ((((-561 |#1|)) . T)) ((($) . T)) (((|#1| (-58 |#1|) (-58 |#1|)) . T)) @@ -2108,12 +2108,12 @@ (((|#1| |#2|) . T)) ((((-1135) |#1|) . T)) (((|#4|) . T)) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-340))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-340))) ((((-1135) (-52)) . T)) ((((-1203 |#2| |#3| |#4|) (-310 |#2| |#3| |#4|)) . T)) ((((-398 (-547))) |has| |#1| (-1007 (-398 (-547)))) (((-547)) |has| |#1| (-1007 (-547))) ((|#1|) . T)) ((((-832)) . T)) -(-1524 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-359)) (|has| |#2| (-701)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016)) (|has| |#2| (-1063))) +(-1525 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-359)) (|has| |#2| (-701)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016)) (|has| |#2| (-1063))) (((#0=(-1204 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-398 (-547)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-169)) ((#0=(-398 (-547)) #0#) |has| |#1| (-539)) (($ $) |has| |#1| (-539))) (((|#1|) . T) (($) . T) (((-398 (-547))) . T)) @@ -2132,14 +2132,14 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) (((|#2| |#3|) . T)) -(-1524 (|has| |#2| (-354)) (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) +(-1525 (|has| |#2| (-354)) (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) (((|#1| (-519 |#2|)) . T)) (((|#1| (-745)) . T)) (((|#1| (-519 (-1052 (-1135)))) . T)) (((|#1|) |has| |#1| (-169))) (((|#1|) . T)) (|has| |#2| (-878)) -(-1524 (|has| |#2| (-767)) (|has| |#2| (-819))) +(-1525 (|has| |#2| (-767)) (|has| |#2| (-819))) ((((-832)) . T)) ((($ $) . T) ((#0=(-1203 |#2| |#3| |#4|) #0#) . T) ((#1=(-398 (-547)) #1#) |has| #0# (-38 (-398 (-547))))) ((((-879 |#1|)) . T)) @@ -2148,13 +2148,13 @@ ((($) . T)) ((($) . T)) (|has| |#1| (-354)) -(-1524 (|has| |#1| (-298)) (|has| |#1| (-354)) (|has| |#1| (-340)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-298)) (|has| |#1| (-354)) (|has| |#1| (-340)) (|has| |#1| (-539))) (|has| |#1| (-354)) ((($) . T) ((#0=(-1203 |#2| |#3| |#4|)) . T) (((-398 (-547))) |has| #0# (-38 (-398 (-547))))) (((|#1| |#2|) . T)) ((((-1133 |#1| |#2| |#3|)) |has| |#1| (-354))) -(-1524 (-12 (|has| |#1| (-298)) (|has| |#1| (-878))) (|has| |#1| (-354)) (|has| |#1| (-340))) -(-1524 (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016))) +(-1525 (-12 (|has| |#1| (-298)) (|has| |#1| (-878))) (|has| |#1| (-354)) (|has| |#1| (-340))) +(-1525 (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016))) ((((-547)) |has| |#1| (-615 (-547))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-832)) . T)) @@ -2186,27 +2186,27 @@ (((|#1|) |has| |#1| (-169))) ((((-832)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-300 |#4|)) (|has| |#4| (-1063)))) -(((|#2|) -1524 (|has| |#2| (-6 (-4330 "*"))) (|has| |#2| (-169)))) -(-1524 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) -(-1524 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(((|#2|) -1525 (|has| |#2| (-6 (-4330 "*"))) (|has| |#2| (-169)))) +(-1525 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) +(-1525 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) (|has| |#2| (-821)) (|has| |#2| (-878)) (|has| |#1| (-878)) (((|#2|) |has| |#2| (-169))) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) ((((-1210 |#1| |#2| |#3|)) |has| |#1| (-354))) ((((-832)) . T)) ((((-832)) . T)) ((((-523)) . T) (((-547)) . T) (((-861 (-547))) . T) (((-370)) . T) (((-217)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) -((((-2 (|:| -3326 (-1118)) (|:| -1777 (-52)))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) +((((-2 (|:| -3327 (-1118)) (|:| -1778 (-52)))) . T)) (((|#1|) . T)) ((((-832)) . T)) (((|#1| |#2|) . T)) (((|#1| (-398 (-547))) . T)) (((|#1|) . T)) -(-1524 (|has| |#1| (-281)) (|has| |#1| (-354))) +(-1525 (|has| |#1| (-281)) (|has| |#1| (-354))) ((((-142)) . T)) ((((-398 |#2|)) . T) (((-398 (-547))) . T) (($) . T)) (|has| |#1| (-819)) @@ -2221,7 +2221,7 @@ ((((-398 (-547))) . T) (($) . T)) ((((-832)) . T)) ((((-832)) . T)) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-832)) . T)) ((((-832)) . T)) @@ -2232,7 +2232,7 @@ (((|#1|) . T)) ((((-832)) . T)) ((((-619 (-142))) . T) (((-1118)) . T)) -((((-2 (|:| -3326 (-1118)) (|:| -1777 |#1|))) . T)) +((((-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) . T)) ((((-1135) |#1|) |has| |#1| (-503 (-1135) |#1|)) ((|#1| |#1|) |has| |#1| (-300 |#1|))) (|has| |#1| (-821)) ((((-832)) . T)) @@ -2244,16 +2244,16 @@ ((((-832)) . T) (((-619 |#4|)) . T)) (((|#2|) . T)) ((((-879 |#1|)) . T) (((-398 (-547))) . T) (($) . T)) -(-1524 (|has| |#4| (-169)) (|has| |#4| (-701)) (|has| |#4| (-819)) (|has| |#4| (-1016))) -(-1524 (|has| |#3| (-169)) (|has| |#3| (-701)) (|has| |#3| (-819)) (|has| |#3| (-1016))) +(-1525 (|has| |#4| (-169)) (|has| |#4| (-701)) (|has| |#4| (-819)) (|has| |#4| (-1016))) +(-1525 (|has| |#3| (-169)) (|has| |#3| (-701)) (|has| |#3| (-819)) (|has| |#3| (-1016))) ((((-1135) (-52)) . T)) -(-1524 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(-1525 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-1524 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016))) -(-1524 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +(-1525 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +(-1525 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-819)) (|has| |#2| (-1016))) (|has| |#1| (-878)) (|has| |#1| (-878)) (((|#2|) . T)) @@ -2268,12 +2268,12 @@ (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) (|has| |#1| (-794)) (((#0=(-879 |#1|) #0#) . T) (($ $) . T) ((#1=(-398 (-547)) #1#) . T)) ((((-398 |#2|)) . T)) (|has| |#1| (-819)) -((((-832)) -1524 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) (((|#1| |#1|) . T) ((#0=(-398 (-547)) #0#) . T) ((#1=(-547) #1#) . T) (($ $) . T)) ((((-879 |#1|)) . T) (($) . T) (((-398 (-547))) . T)) (((|#2|) |has| |#2| (-1016)) (((-547)) -12 (|has| |#2| (-615 (-547))) (|has| |#2| (-1016)))) @@ -2283,25 +2283,25 @@ (|has| |#1| (-143)) (((|#2|) . T)) ((((-832)) . T)) -(-1524 (|has| |#1| (-143)) (|has| |#1| (-359))) -(-1524 (|has| |#1| (-143)) (|has| |#1| (-359))) -(-1524 (|has| |#1| (-143)) (|has| |#1| (-359))) -((((-2 (|:| -3326 (-1135)) (|:| -1777 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -3326 (-1135)) (|:| -1777 #0#))) . T)) +(-1525 (|has| |#1| (-143)) (|has| |#1| (-359))) +(-1525 (|has| |#1| (-143)) (|has| |#1| (-359))) +(-1525 (|has| |#1| (-143)) (|has| |#1| (-359))) +((((-2 (|:| -3327 (-1135)) (|:| -1778 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -3327 (-1135)) (|:| -1778 #0#))) . T)) (|has| |#1| (-340)) ((((-547)) . T)) ((((-832)) . T)) (((#0=(-1204 |#1| |#2| |#3| |#4|) $) |has| #0# (-277 #0# #0#))) (|has| |#1| (-354)) (((#0=(-1045) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-340))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-340))) (((#0=(-398 (-547)) #0#) . T) ((#1=(-673) #1#) . T) (($ $) . T)) ((((-307 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-398 (-547))) |has| |#1| (-354))) (|has| |#1| (-1063)) (((|#1|) . T)) -(((|#1|) -1524 (|has| |#2| (-358 |#1|)) (|has| |#2| (-408 |#1|)))) -(((|#1|) -1524 (|has| |#2| (-358 |#1|)) (|has| |#2| (-408 |#1|)))) +(((|#1|) -1525 (|has| |#2| (-358 |#1|)) (|has| |#2| (-408 |#1|)))) +(((|#1|) -1525 (|has| |#2| (-358 |#1|)) (|has| |#2| (-408 |#1|)))) (((|#2|) . T)) ((((-398 (-547))) . T) (((-673)) . T) (($) . T)) (((|#3| |#3|) . T)) @@ -2320,7 +2320,7 @@ (((|#2|) . T)) (((|#1|) . T)) ((((-547)) . T)) -(-1524 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(-1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) (((|#2|) . T) (((-547)) |has| |#2| (-615 (-547)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2357,7 +2357,7 @@ (|has| |#2| (-991)) ((($) . T)) (|has| |#1| (-878)) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2365,24 +2365,24 @@ ((($) . T)) (|has| |#1| (-354)) ((((-879 |#1|)) . T)) -((($) -1524 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +((($) -1525 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) ((($ $) . T) ((#0=(-398 (-547)) #0#) . T)) -(-1524 (|has| |#1| (-359)) (|has| |#1| (-821))) +(-1525 (|has| |#1| (-359)) (|has| |#1| (-821))) (((|#1|) . T)) ((((-832)) . T)) ((((-1135)) -12 (|has| |#1| (-15 * (|#1| (-398 (-547)) |#1|))) (|has| |#1| (-869 (-1135))))) ((((-398 |#2|) |#3|) . T)) ((($) . T) (((-398 (-547))) . T)) ((((-745) |#1|) . T)) -(((|#2| (-232 (-3763 |#1|) (-745))) . T)) +(((|#2| (-232 (-3764 |#1|) (-745))) . T)) (((|#1| (-519 |#3|)) . T)) ((((-398 (-547))) . T)) -(-1524 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(-1525 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((((-832)) . T)) -(((#0=(-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) #0#) |has| (-2 (|:| -3326 (-1135)) (|:| -1777 (-52))) (-300 (-2 (|:| -3326 (-1135)) (|:| -1777 (-52)))))) +(((#0=(-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) #0#) |has| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (-300 (-2 (|:| -3327 (-1135)) (|:| -1778 (-52)))))) (|has| |#1| (-878)) (|has| |#2| (-354)) -(-1524 (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +(-1525 (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016))) ((((-166 (-370))) . T) (((-217)) . T) (((-370)) . T)) ((((-832)) . T)) (((|#1|) . T)) @@ -2399,11 +2399,11 @@ (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) -(-1524 (|has| |#1| (-298)) (|has| |#1| (-354)) (|has| |#1| (-340))) +(-1525 (|has| |#1| (-298)) (|has| |#1| (-354)) (|has| |#1| (-340))) (|has| |#1| (-38 (-398 (-547)))) (-12 (|has| |#1| (-532)) (|has| |#1| (-802))) ((((-832)) . T)) -((((-1135)) -1524 (-12 (|has| |#1| (-15 * (|#1| (-547) |#1|))) (|has| |#1| (-869 (-1135)))) (-12 (|has| |#1| (-354)) (|has| |#2| (-869 (-1135)))))) +((((-1135)) -1525 (-12 (|has| |#1| (-15 * (|#1| (-547) |#1|))) (|has| |#1| (-869 (-1135)))) (-12 (|has| |#1| (-354)) (|has| |#2| (-869 (-1135)))))) (|has| |#1| (-354)) ((((-1135)) -12 (|has| |#1| (-15 * (|#1| (-398 (-547)) |#1|))) (|has| |#1| (-869 (-1135))))) (|has| |#1| (-354)) @@ -2413,7 +2413,7 @@ (((|#1|) . T)) (((|#2|) |has| |#1| (-354))) (((|#2|) |has| |#1| (-354))) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-169))) (((|#1|) . T)) @@ -2438,30 +2438,30 @@ ((((-370)) -12 (|has| |#1| (-354)) (|has| |#2| (-855 (-370)))) (((-547)) -12 (|has| |#1| (-354)) (|has| |#2| (-855 (-547))))) (|has| |#1| (-354)) (((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) (|has| |#1| (-354)) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) (|has| |#1| (-354)) (|has| |#1| (-539)) (((|#4| |#4|) -12 (|has| |#4| (-300 |#4|)) (|has| |#4| (-1063)))) (((|#3|) . T)) (((|#1|) . T)) -(-1524 (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +(-1525 (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016))) (((|#2|) . T)) (((|#2|) . T)) -(-1524 (|has| |#2| (-169)) (|has| |#2| (-701)) (|has| |#2| (-819)) (|has| |#2| (-1016))) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) -((((-2 (|:| -3326 (-1118)) (|:| -1777 |#1|))) . T)) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +(-1525 (|has| |#2| (-169)) (|has| |#2| (-701)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) +((((-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) (|has| |#1| (-38 (-398 (-547)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-398 (-547)))) -(-1524 (|has| |#1| (-143)) (|has| |#1| (-359))) +(-1525 (|has| |#1| (-143)) (|has| |#1| (-359))) (|has| |#1| (-145)) ((((-1118) |#1|) . T)) -(-1524 (|has| |#1| (-143)) (|has| |#1| (-359))) +(-1525 (|has| |#1| (-143)) (|has| |#1| (-359))) (|has| |#1| (-145)) -(-1524 (|has| |#1| (-143)) (|has| |#1| (-359))) +(-1525 (|has| |#1| (-143)) (|has| |#1| (-359))) (|has| |#1| (-145)) ((((-561 |#1|)) . T)) ((($) . T)) @@ -2469,7 +2469,7 @@ (|has| |#1| (-539)) (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) -(-1524 (|has| |#1| (-143)) (|has| |#1| (-340))) +(-1525 (|has| |#1| (-143)) (|has| |#1| (-340))) (|has| |#1| (-145)) ((((-832)) . T)) ((($) . T)) @@ -2494,7 +2494,7 @@ (|has| |#1| (-765)) (|has| |#1| (-765)) ((((-523)) |has| |#1| (-592 (-523)))) -((((-832)) -1524 (|has| |#1| (-591 (-832))) (|has| |#1| (-821)) (|has| |#1| (-1063)))) +((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-821)) (|has| |#1| (-1063)))) ((((-114)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2515,7 +2515,7 @@ ((((-547)) . T)) ((((-832)) . T)) ((((-547)) . T)) -(-1524 (|has| |#2| (-767)) (|has| |#2| (-819))) +(-1525 (|has| |#2| (-767)) (|has| |#2| (-819))) ((((-166 (-370))) . T) (((-217)) . T) (((-370)) . T)) ((((-832)) . T)) ((((-832)) . T)) @@ -2527,9 +2527,9 @@ (((|#1|) . T) (($) . T) (((-398 (-547))) . T)) (|has| |#1| (-354)) (|has| |#1| (-354)) -((((-832)) -1524 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) -((((-832)) -1524 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) -(-1524 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-463)) (|has| |#1| (-701)) (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016)) (|has| |#1| (-1075)) (|has| |#1| (-1063))) +((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +(-1525 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-463)) (|has| |#1| (-701)) (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016)) (|has| |#1| (-1075)) (|has| |#1| (-1063))) (|has| |#1| (-1111)) ((((-547) |#1|) . T)) (((|#1|) . T)) @@ -2547,8 +2547,8 @@ (((|#1|) . T)) (|has| |#1| (-539)) ((((-398 |#2|)) . T) (((-398 (-547))) . T) (($) . T)) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-539))) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) ((((-370)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2557,7 +2557,7 @@ (|has| |#1| (-539)) (|has| |#1| (-1063)) ((((-754 |#1| (-834 |#2|))) |has| (-754 |#1| (-834 |#2|)) (-300 (-754 |#1| (-834 |#2|))))) -(-1524 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) +(-1525 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -2567,12 +2567,12 @@ (|has| |#1| (-225)) (((|#1| (-519 (-1052 (-1135)))) . T)) (|has| |#2| (-354)) -((((-2 (|:| -3326 (-1118)) (|:| -1777 (-52)))) . T)) +((((-2 (|:| -3327 (-1118)) (|:| -1778 (-52)))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) ((((-832)) . T)) ((((-832)) . T)) -(-1524 (|has| |#3| (-767)) (|has| |#3| (-819))) +(-1525 (|has| |#3| (-767)) (|has| |#3| (-819))) ((((-832)) . T)) ((((-1082)) . T) (((-832)) . T)) ((((-832)) . T)) @@ -2582,8 +2582,8 @@ ((((-547)) . T)) (((|#3|) . T)) ((((-832)) . T)) -(-1524 (|has| |#1| (-298)) (|has| |#1| (-354)) (|has| |#1| (-340))) -(-1524 (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-539)) (|has| |#1| (-1016))) +(-1525 (|has| |#1| (-298)) (|has| |#1| (-354)) (|has| |#1| (-340))) +(-1525 (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-539)) (|has| |#1| (-1016))) (((#0=(-561 |#1|) #0#) . T) (($ $) . T) ((#1=(-398 (-547)) #1#) . T)) ((($ $) . T) ((#0=(-398 (-547)) #0#) . T)) (((|#1|) |has| |#1| (-169))) @@ -2596,7 +2596,7 @@ (((|#1|) . T)) ((((-832)) . T)) ((((-285 |#3|)) . T)) -(((#0=(-398 (-547)) #0#) |has| |#2| (-38 (-398 (-547)))) ((|#2| |#2|) . T) (($ $) -1524 (|has| |#2| (-169)) (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878)))) +(((#0=(-398 (-547)) #0#) |has| |#2| (-38 (-398 (-547)))) ((|#2| |#2|) . T) (($ $) -1525 (|has| |#2| (-169)) (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-398 (-547))) |has| |#2| (-38 (-398 (-547)))) ((|#2|) . T)) @@ -2604,20 +2604,20 @@ (((|#1|) . T) (((-398 (-547))) . T) (($) . T)) (((|#1|) . T) (((-398 (-547))) . T) (($) . T)) (((|#1|) . T) (((-398 (-547))) . T) (($) . T)) -((($ $) -1524 (|has| |#1| (-169)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1| |#1|) . T) ((#0=(-398 (-547)) #0#) |has| |#1| (-38 (-398 (-547))))) -((($ $) -1524 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1| |#1|) . T) ((#0=(-398 (-547)) #0#) |has| |#1| (-38 (-398 (-547))))) +((($ $) -1525 (|has| |#1| (-169)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1| |#1|) . T) ((#0=(-398 (-547)) #0#) |has| |#1| (-38 (-398 (-547))))) +((($ $) -1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1| |#1|) . T) ((#0=(-398 (-547)) #0#) |has| |#1| (-38 (-398 (-547))))) (((|#2|) . T)) -((((-398 (-547))) |has| |#2| (-38 (-398 (-547)))) ((|#2|) . T) (($) -1524 (|has| |#2| (-169)) (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878)))) +((((-398 (-547))) |has| |#2| (-38 (-398 (-547)))) ((|#2|) . T) (($) -1525 (|has| |#2| (-169)) (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878)))) (((|#2|) . T) ((|#6|) . T)) -((($ $) -1524 (|has| |#1| (-169)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1| |#1|) . T) ((#0=(-398 (-547)) #0#) |has| |#1| (-38 (-398 (-547))))) +((($ $) -1525 (|has| |#1| (-169)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1| |#1|) . T) ((#0=(-398 (-547)) #0#) |has| |#1| (-38 (-398 (-547))))) ((((-832)) . T)) -((($) -1524 (|has| |#1| (-169)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) -((($) -1524 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +((($) -1525 (|has| |#1| (-169)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +((($) -1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) (|has| |#2| (-878)) (|has| |#1| (-878)) -((($) -1524 (|has| |#1| (-169)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +((($) -1525 (|has| |#1| (-169)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) (((|#1|) . T)) -((((-2 (|:| -3326 (-1118)) (|:| -1777 |#1|))) . T)) +((((-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) . T)) @@ -2631,10 +2631,10 @@ (((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) (((#0=(-398 (-547)) #0#) . T)) ((((-398 (-547))) . T)) -(-1524 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +(-1525 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016))) (((|#1|) . T)) (((|#1|) . T)) -(-1524 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +(-1525 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-819)) (|has| |#2| (-1016))) ((((-523)) . T)) ((((-832)) . T)) ((((-1135)) |has| |#2| (-869 (-1135))) (((-1045)) . T)) @@ -2649,12 +2649,12 @@ ((($ $) . T) ((#0=(-398 (-547)) #0#) . T)) ((((-1135)) |has| |#1| (-869 (-1135)))) ((((-879 |#1|)) . T) (((-398 (-547))) . T) (($) . T)) -((($) . T) (((-398 (-547))) -1524 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) ((|#1|) . T)) -(((#0=(-398 (-547)) #0#) |has| |#1| (-38 (-398 (-547)))) ((|#1| |#1|) . T) (($ $) -1524 (|has| |#1| (-169)) (|has| |#1| (-539)))) +((($) . T) (((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) ((|#1|) . T)) +(((#0=(-398 (-547)) #0#) |has| |#1| (-38 (-398 (-547)))) ((|#1| |#1|) . T) (($ $) -1525 (|has| |#1| (-169)) (|has| |#1| (-539)))) ((($) . T) (((-398 (-547))) . T)) (((|#1|) . T) (((-398 (-547))) . T) (((-547)) . T) (($) . T)) (((|#2|) |has| |#2| (-1016)) (((-547)) -12 (|has| |#2| (-615 (-547))) (|has| |#2| (-1016)))) -((((-398 (-547))) |has| |#1| (-38 (-398 (-547)))) ((|#1|) . T) (($) -1524 (|has| |#1| (-169)) (|has| |#1| (-539)))) +((((-398 (-547))) |has| |#1| (-38 (-398 (-547)))) ((|#1|) . T) (($) -1525 (|has| |#1| (-169)) (|has| |#1| (-539)))) (|has| |#1| (-539)) (((|#1|) |has| |#1| (-354))) ((((-547)) . T)) @@ -2673,8 +2673,8 @@ ((((-832)) . T)) (|has| |#2| (-794)) (|has| |#2| (-794)) -((((-398 (-547))) -1524 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) ((|#2|) |has| |#1| (-354)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-398 (-547))) -1524 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) . T)) +((((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) ((|#2|) |has| |#1| (-354)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) (((|#1|) . T) (((-547)) |has| |#1| (-1007 (-547))) (((-398 (-547))) |has| |#1| (-1007 (-398 (-547))))) ((((-547)) |has| |#1| (-855 (-547))) (((-370)) |has| |#1| (-855 (-370)))) @@ -2700,12 +2700,12 @@ (((|#2| (-745)) . T)) ((((-1135)) . T)) ((((-839 |#1|)) . T)) -(-1524 (|has| |#3| (-25)) (|has| |#3| (-130)) (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-767)) (|has| |#3| (-819)) (|has| |#3| (-1016))) -(-1524 (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-819)) (|has| |#3| (-1016))) +(-1525 (|has| |#3| (-25)) (|has| |#3| (-130)) (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-767)) (|has| |#3| (-819)) (|has| |#3| (-1016))) +(-1525 (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-819)) (|has| |#3| (-1016))) ((((-832)) . T)) (((|#1|) . T)) -(-1524 (|has| |#2| (-767)) (|has| |#2| (-819))) -(-1524 (-12 (|has| |#1| (-767)) (|has| |#2| (-767))) (-12 (|has| |#1| (-821)) (|has| |#2| (-821)))) +(-1525 (|has| |#2| (-767)) (|has| |#2| (-819))) +(-1525 (-12 (|has| |#1| (-767)) (|has| |#2| (-767))) (-12 (|has| |#1| (-821)) (|has| |#2| (-821)))) ((((-839 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-359)) @@ -2731,7 +2731,7 @@ (((|#1|) . T)) ((((-832)) . T)) (|has| |#2| (-878)) -((((-2 (|:| -3326 (-1135)) (|:| -1777 (-52)))) . T)) +((((-2 (|:| -3327 (-1135)) (|:| -1778 (-52)))) . T)) ((((-523)) |has| |#2| (-592 (-523))) (((-861 (-370))) |has| |#2| (-592 (-861 (-370)))) (((-861 (-547))) |has| |#2| (-592 (-861 (-547))))) ((((-832)) . T)) ((((-832)) . T)) @@ -2764,12 +2764,12 @@ ((((-398 |#2|) |#3|) . T)) (((|#1|) . T)) (|has| |#1| (-1063)) -(((|#2| (-472 (-3763 |#1|) (-745))) . T)) +(((|#2| (-472 (-3764 |#1|) (-745))) . T)) ((((-547) |#1|) . T)) ((((-1118)) . T) (((-832)) . T)) (((|#2| |#2|) . T)) (((|#1| (-519 (-1135))) . T)) -(-1524 (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +(-1525 (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016))) ((((-547)) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -2779,9 +2779,9 @@ ((($) . T) (((-398 (-547))) . T)) ((($) . T)) ((($) . T)) -(-1524 (|has| |#1| (-821)) (|has| |#1| (-1063))) +(-1525 (|has| |#1| (-821)) (|has| |#1| (-1063))) (((|#1|) . T)) -((($) -1524 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +((($) -1525 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) ((((-832)) . T)) ((((-142)) . T)) (((|#1|) . T) (((-398 (-547))) . T)) @@ -2821,27 +2821,27 @@ (|has| |#1| (-225)) (((|#1| (-519 |#3|)) . T)) (|has| |#1| (-359)) -(((|#2| (-232 (-3763 |#1|) (-745))) . T)) +(((|#2| (-232 (-3764 |#1|) (-745))) . T)) (|has| |#1| (-359)) (|has| |#1| (-359)) (((|#1|) . T) (($) . T)) (((|#1| (-519 |#2|)) . 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T)) -(-1524 (|has| |#3| (-169)) (|has| |#3| (-701)) (|has| |#3| (-819)) (|has| |#3| (-1016))) +(-1525 (|has| |#3| (-169)) (|has| |#3| (-701)) (|has| |#3| (-819)) (|has| |#3| (-1016))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-398 (-547)))) ((((-832)) . T)) @@ -2912,15 +2912,15 @@ (((|#1|) |has| |#1| (-169)) (($) |has| |#1| (-539)) (((-398 (-547))) |has| |#1| (-539))) (((|#2|) . T) (((-547)) |has| |#2| (-615 (-547)))) (|has| |#1| (-354)) -(-1524 (|has| |#1| (-15 * (|#1| (-547) |#1|))) (-12 (|has| |#1| (-354)) (|has| |#2| (-225)))) +(-1525 (|has| |#1| (-15 * (|#1| (-547) |#1|))) (-12 (|has| |#1| (-354)) (|has| |#2| (-225)))) (|has| |#1| (-15 * (|#1| (-398 (-547)) |#1|))) (|has| |#1| (-354)) (((|#1|) . T)) -(((#0=(-398 (-547)) #0#) -1524 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($ $) -1524 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) ((|#1| |#1|) . 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T)) (((|#2| |#2|) . T) ((#0=(-398 (-547)) #0#) . T) (($ $) . T)) ((((-547)) . T)) @@ -3017,32 +3017,32 @@ (|has| |#1| (-354)) ((((-1210 |#1| |#2| |#3|)) . T) (((-1182 |#1| |#2| |#3|)) . T)) ((((-1135)) . T) (((-832)) . T)) -((((-398 (-547))) |has| |#2| (-38 (-398 (-547)))) ((|#2|) |has| |#2| (-169)) (($) -1524 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878)))) +((((-398 (-547))) |has| |#2| (-38 (-398 (-547)))) ((|#2|) |has| |#2| (-169)) (($) -1525 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-398 (-547))) |has| |#2| (-38 (-398 (-547)))) ((|#2|) . T)) -((($) -1524 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +((($) -1525 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) ((((-1067)) . T)) ((((-832)) . 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T)) -((((-832)) -1524 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) (((|#1|) |has| |#1| (-169))) (((|#1|) |has| |#1| (-169))) ((((-398 (-547))) . T) (($) . T)) (((|#1| (-547)) . T)) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-340))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-340))) (|has| |#1| (-354)) (|has| |#1| (-354)) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-340))) -(-1524 (|has| |#1| (-169)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-340))) +(-1525 (|has| |#1| (-169)) (|has| |#1| (-539))) (((|#1| (-547)) . T)) (((|#1| (-398 (-547))) . T)) (((|#1| (-745)) . T)) @@ -3057,16 +3057,16 @@ ((((-861 (-370))) . T) (((-861 (-547))) . T) (((-1135)) . T) (((-523)) . T)) (((|#1|) . T)) ((((-832)) . T)) -(-1524 (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016))) -(-1524 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-130)) (|has| |#2| (-130))) (-12 (|has| |#1| (-767)) (|has| |#2| (-767)))) +(-1525 (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +(-1525 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-130)) (|has| |#2| (-130))) (-12 (|has| |#1| (-767)) (|has| |#2| (-767)))) ((((-547)) . T)) ((((-547)) . T)) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-1524 (|has| |#2| (-169)) (|has| |#2| (-701)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +(-1525 (|has| |#2| (-169)) (|has| |#2| (-701)) (|has| |#2| (-819)) (|has| |#2| (-1016))) ((((-1135)) -12 (|has| |#2| (-869 (-1135))) (|has| |#2| (-1016)))) -(-1524 (-12 (|has| |#1| (-463)) (|has| |#2| (-463))) (-12 (|has| |#1| (-701)) (|has| |#2| (-701)))) +(-1525 (-12 (|has| |#1| (-463)) (|has| |#2| (-463))) (-12 (|has| |#1| (-701)) (|has| |#2| (-701)))) (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-354)) @@ -3090,7 +3090,7 @@ ((((-1118) (-1135) (-547) (-217) (-832)) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) -(-1524 (|has| |#1| (-340)) (|has| |#1| (-359))) +(-1525 (|has| |#1| (-340)) (|has| |#1| (-359))) (((|#1| |#2|) . T)) ((($) . T) ((|#1|) . T)) ((((-832)) . T)) @@ -3098,7 +3098,7 @@ ((($) . T) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) (((|#2|) |has| |#2| (-1063)) (((-547)) -12 (|has| |#2| (-1007 (-547))) (|has| |#2| (-1063))) (((-398 (-547))) -12 (|has| |#2| (-1007 (-398 (-547)))) (|has| |#2| (-1063)))) ((((-523)) |has| |#1| (-592 (-523)))) -((((-832)) -1524 (|has| |#1| (-591 (-832))) (|has| |#1| (-821)) (|has| |#1| (-1063)))) +((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-821)) (|has| |#1| (-1063)))) ((($) . T) (((-398 (-547))) . T)) (|has| |#1| (-878)) (|has| |#1| (-878)) @@ -3107,14 +3107,14 @@ ((((-832)) . T)) (((|#2| |#2|) . T)) (((|#1| |#1|) |has| |#1| (-169))) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-539))) -(-1524 (|has| |#1| (-21)) (|has| |#1| (-819))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1525 (|has| |#1| (-21)) (|has| |#1| (-819))) (((|#2|) . T)) -(-1524 (|has| |#1| (-21)) (|has| |#1| (-819))) +(-1525 (|has| |#1| (-21)) (|has| |#1| (-819))) (((|#1|) |has| |#1| (-169))) (((|#1|) . T)) (((|#1|) . T)) -((((-832)) -1524 (-12 (|has| |#1| (-591 (-832))) (|has| |#2| (-591 (-832)))) (-12 (|has| |#1| (-1063)) (|has| |#2| (-1063))))) +((((-832)) -1525 (-12 (|has| |#1| (-591 (-832))) (|has| |#2| (-591 (-832)))) (-12 (|has| |#1| (-1063)) (|has| |#2| (-1063))))) ((((-398 |#2|) |#3|) . T)) ((((-398 (-547))) . T) (($) . T)) (|has| |#1| (-38 (-398 (-547)))) @@ -3126,18 +3126,18 @@ (((|#1|) . T) (((-398 (-547))) . T) (((-547)) . T) (($) . T)) (((#0=(-547) #0#) . T)) ((($) . T) (((-398 (-547))) . T)) -(-1524 (|has| |#4| (-169)) (|has| |#4| (-701)) (|has| |#4| (-819)) (|has| |#4| (-1016))) -(-1524 (|has| |#3| (-169)) (|has| |#3| (-701)) (|has| |#3| (-819)) (|has| |#3| (-1016))) +(-1525 (|has| |#4| (-169)) (|has| |#4| (-701)) (|has| |#4| (-819)) (|has| |#4| (-1016))) +(-1525 (|has| |#3| (-169)) (|has| |#3| (-701)) (|has| |#3| (-819)) (|has| |#3| (-1016))) ((((-832)) . T) (((-1140)) . T)) (|has| |#4| (-767)) -(-1524 (|has| |#4| (-767)) (|has| |#4| (-819))) +(-1525 (|has| |#4| (-767)) (|has| |#4| (-819))) (|has| |#4| (-819)) (|has| |#3| (-767)) -(-1524 (|has| |#3| (-767)) (|has| |#3| (-819))) +(-1525 (|has| |#3| (-767)) (|has| |#3| (-819))) (|has| |#3| (-819)) ((((-547)) . T)) (((|#2|) . T)) -((((-1135)) -1524 (-12 (|has| (-1133 |#1| |#2| |#3|) (-869 (-1135))) (|has| |#1| (-354))) (-12 (|has| |#1| (-15 * (|#1| (-547) |#1|))) (|has| |#1| (-869 (-1135)))))) +((((-1135)) -1525 (-12 (|has| (-1133 |#1| |#2| |#3|) (-869 (-1135))) (|has| |#1| (-354))) (-12 (|has| |#1| (-15 * (|#1| (-547) |#1|))) (|has| |#1| (-869 (-1135)))))) ((((-1135)) -12 (|has| |#1| (-15 * (|#1| (-398 (-547)) |#1|))) (|has| |#1| (-869 (-1135))))) ((((-1135)) -12 (|has| |#1| (-15 * (|#1| (-745) |#1|))) (|has| |#1| (-869 (-1135))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3152,11 +3152,11 @@ ((((-1133 |#1| |#2| |#3|)) |has| |#1| (-354))) ((((-1100 |#1| |#2|)) . T)) ((((-1133 |#1| |#2| |#3|)) |has| |#1| (-354))) -(((|#2|) . T) (((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) -((((-2 (|:| -3326 (-1135)) (|:| -1777 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) +((((-2 (|:| -3327 (-1135)) (|:| -1778 (-52)))) . T)) ((($) . T)) (|has| |#1| (-991)) -(((|#2|) . T) (((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) ((((-832)) . T)) ((((-523)) |has| |#2| (-592 (-523))) (((-861 (-547))) |has| |#2| (-592 (-861 (-547)))) (((-861 (-370))) |has| |#2| (-592 (-861 (-370)))) (((-370)) . #0=(|has| |#2| (-991))) (((-217)) . #0#)) ((((-1135) (-52)) . T)) @@ -3168,15 +3168,15 @@ ((((-1133 |#1| |#2| |#3|)) . T)) ((((-1133 |#1| |#2| |#3|)) . T) (((-1126 |#1| |#2| |#3|)) . T)) ((((-832)) . T)) -((((-832)) -1524 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) ((((-547) |#1|) . T)) ((((-1133 |#1| |#2| |#3|)) |has| |#1| (-354))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-354)) -(((|#3|) . T) ((|#2|) . T) (($) -1524 (|has| |#4| (-169)) (|has| |#4| (-819)) (|has| |#4| (-1016))) ((|#4|) -1524 (|has| |#4| (-169)) (|has| |#4| (-354)) (|has| |#4| (-1016)))) -(((|#2|) . T) (($) -1524 (|has| |#3| (-169)) (|has| |#3| (-819)) (|has| |#3| (-1016))) ((|#3|) -1524 (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-1016)))) +(((|#3|) . T) ((|#2|) . T) (($) -1525 (|has| |#4| (-169)) (|has| |#4| (-819)) (|has| |#4| (-1016))) ((|#4|) -1525 (|has| |#4| (-169)) (|has| |#4| (-354)) (|has| |#4| (-1016)))) +(((|#2|) . T) (($) -1525 (|has| |#3| (-169)) (|has| |#3| (-819)) (|has| |#3| (-1016))) ((|#3|) -1525 (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-1016)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-354)) @@ -3188,7 +3188,7 @@ ((((-832)) . T)) ((((-832)) . T)) (((|#1|) . T)) -((((-832)) -1524 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) ((((-129)) . T) (((-832)) . T)) ((((-547) |#1|) . T)) (((|#1|) . T)) @@ -3196,13 +3196,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-354)) (|has| |#2| (-277 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-878))) -(-1524 (|has| |#1| (-821)) (|has| |#1| (-1063))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-878))) +(-1525 (|has| |#1| (-821)) (|has| |#1| (-1063))) ((((-832)) . T)) ((((-832)) . T)) ((((-832)) . T)) (((|#1| (-519 |#2|)) . T)) -((((-2 (|:| -3326 (-1135)) (|:| -1777 (-52)))) . T)) +((((-2 (|:| -3327 (-1135)) (|:| -1778 (-52)))) . T)) (((|#1| (-547)) . T)) (((|#1| (-398 (-547))) . T)) (((|#1| (-745)) . T)) @@ -3213,20 +3213,20 @@ ((((-832)) . T) (((-1140)) . T)) ((((-832)) . T) (((-1140)) . T)) ((((-832)) . T) (((-1140)) . T)) -(-1524 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) -(-1524 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(-1525 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) +(-1525 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((($) . T)) (((|#2| (-519 (-834 |#1|))) . T)) ((((-832)) . T) (((-1140)) . T)) ((((-547) |#1|) . T)) (((|#2|) . T)) (((|#2| (-745)) . T)) -((((-832)) -1524 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) (((|#1|) . T)) (((|#1| |#2|) . T)) ((((-1118) |#1|) . T)) ((((-398 |#2|)) . T)) -((((-2 (|:| -3326 |#1|) (|:| -1777 |#2|))) . T)) +((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) (|has| |#1| (-539)) (|has| |#1| (-539)) ((($) . T) ((|#2|) . T)) @@ -3234,12 +3234,12 @@ (((|#1| |#2|) . T)) (((|#2| $) |has| |#2| (-277 |#2| |#2|))) (((|#1| (-619 |#1|)) |has| |#1| (-819))) -(-1524 (|has| |#1| (-225)) (|has| |#1| (-340))) -(-1524 (|has| |#1| (-354)) (|has| |#1| (-340))) +(-1525 (|has| |#1| (-225)) (|has| |#1| (-340))) +(-1525 (|has| |#1| (-354)) (|has| |#1| (-340))) (|has| |#1| (-1063)) (((|#1|) . T)) ((((-398 (-547))) . T) (($) . T)) -((((-968 |#1|)) . T) ((|#1|) . T) (((-547)) -1524 (|has| (-968 |#1|) (-1007 (-547))) (|has| |#1| (-1007 (-547)))) (((-398 (-547))) -1524 (|has| (-968 |#1|) (-1007 (-398 (-547)))) (|has| |#1| (-1007 (-398 (-547)))))) +((((-968 |#1|)) . T) ((|#1|) . T) (((-547)) -1525 (|has| (-968 |#1|) (-1007 (-547))) (|has| |#1| (-1007 (-547)))) (((-398 (-547))) -1525 (|has| (-968 |#1|) (-1007 (-398 (-547)))) (|has| |#1| (-1007 (-398 (-547)))))) (((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) (((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) (((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) @@ -3250,10 +3250,10 @@ (((|#1|) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1100 |#1| |#2|) #0#) |has| (-1100 |#1| |#2|) (-300 (-1100 |#1| |#2|)))) -(((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) ((#0=(-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) #0#) |has| (-2 (|:| -3326 |#1|) (|:| -1777 |#2|)) (-300 (-2 (|:| -3326 |#1|) (|:| -1777 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) ((#0=(-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) #0#) |has| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (-300 (-2 (|:| -3327 |#1|) (|:| -1778 |#2|))))) (((#0=(-116 |#1|)) |has| #0# (-300 #0#))) ((($ $) . T)) -(-1524 (|has| |#1| (-821)) (|has| |#1| (-1063))) +(-1525 (|has| |#1| (-821)) (|has| |#1| (-1063))) ((($ $) . T) ((#0=(-834 |#1|) $) . T) ((#0# |#2|) . T)) ((($ $) . T) ((|#2| $) |has| |#1| (-225)) ((|#2| |#1|) |has| |#1| (-225)) ((|#3| |#1|) . T) ((|#3| $) . T)) -(((-468 . -1063) T) ((-255 . -503) 144639) ((-239 . -503) 144582) ((-237 . -1063) 144532) ((-554 . -111) 144517) ((-519 . -23) T) ((-137 . -1063) T) ((-136 . -1063) T) ((-117 . -300) 144474) ((-132 . -1063) T) ((-469 . -503) 144266) ((-668 . -101) T) ((-1101 . -503) 144185) ((-381 . -130) T) ((-1231 . -945) 144154) ((-31 . -92) T) ((-580 . -479) 144138) ((-597 . -130) T) ((-793 . -817) T) ((-512 . -56) 144088) ((-58 . -503) 144021) ((-508 . -503) 143954) ((-409 . -869) 143913) ((-166 . -1016) T) ((-505 . -503) 143846) ((-486 . -503) 143779) ((-485 . -503) 143712) ((-773 . -1007) 143495) ((-673 . -38) 143460) ((-334 . -340) T) ((-1058 . -1057) 143444) ((-1058 . -1063) 143422) ((-166 . -235) 143373) ((-166 . -225) 143324) ((-1058 . -1059) 143282) ((-841 . -277) 143240) ((-217 . -769) T) ((-217 . -766) T) ((-668 . -275) NIL) ((-1110 . -1148) 143219) ((-398 . -961) 143203) ((-675 . -21) T) ((-675 . -25) T) ((-1233 . -622) 143177) ((-307 . -157) 143156) ((-307 . -141) 143135) ((-1110 . 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138482) ((-801 . -1022) 138466) ((-807 . -25) 138418) ((-310 . -539) 138369) ((-547 . -802) T) ((-232 . -1172) T) ((-808 . -111) 138334) ((-801 . -111) 138313) ((-1202 . -591) 138295) ((-1181 . -591) 138277) ((-1181 . -592) 137950) ((-1131 . -878) 137929) ((-1087 . -878) 137908) ((-48 . -38) 137873) ((-1240 . -1075) T) ((-580 . -591) 137785) ((-580 . -592) 137746) ((-1238 . -1075) T) ((-232 . -1007) 137573) ((-1131 . -622) 137498) ((-1087 . -622) 137423) ((-693 . -591) 137405) ((-825 . -622) 137379) ((-480 . -1063) T) ((-1240 . -23) T) ((-1238 . -23) T) ((-1003 . -1016) T) ((-1145 . -277) 137358) ((-166 . -359) 137309) ((-973 . -1172) T) ((-44 . -23) T) ((-469 . -277) 137288) ((-565 . -1063) T) ((-1106 . -1072) 137257) ((-1067 . -1066) 137209) ((-128 . -1172) T) ((-381 . -21) T) ((-381 . -25) T) ((-150 . -1075) T) ((-1246 . -101) T) ((-973 . -853) 137191) ((-973 . -855) 137173) ((-1166 . -692) 137070) ((-599 . -223) 137054) ((-597 . -21) T) ((-280 . -539) T) ((-597 . -25) T) ((-1152 . 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. -19) 135769) ((-58 . -582) 135746) ((-1051 . -1063) T) ((-870 . -101) 135724) ((-825 . -701) T) ((-756 . -1063) T) ((-505 . -582) 135701) ((-485 . -582) 135678) ((-754 . -1063) T) ((-754 . -1030) 135645) ((-451 . -1063) T) ((-444 . -1063) T) ((-565 . -692) 135620) ((-623 . -1063) T) ((-973 . -869) NIL) ((-1210 . -47) 135597) ((-603 . -1075) T) ((-644 . -130) T) ((-1204 . -101) T) ((-1203 . -47) 135567) ((-1182 . -47) 135544) ((-1166 . -169) 135495) ((-1043 . -1176) 135446) ((-266 . -1063) T) ((-84 . -431) T) ((-84 . -386) T) ((-1132 . -298) 135425) ((-1126 . -298) 135404) ((-50 . -1063) T) ((-1043 . -539) 135355) ((-686 . -169) T) ((-574 . -47) 135332) ((-217 . -622) 135297) ((-561 . -1063) T) ((-507 . -1063) T) ((-350 . -1176) T) ((-344 . -1176) T) ((-336 . -1176) T) ((-477 . -794) T) ((-477 . -889) T) ((-310 . -1075) T) ((-107 . -1176) T) ((-330 . -821) T) ((-209 . -889) T) ((-209 . -794) T) ((-689 . -1022) 135267) ((-350 . -539) T) ((-344 . -539) T) ((-336 . -539) T) ((-107 . -539) T) ((-632 . -692) 135237) ((-1126 . -991) NIL) ((-310 . -23) T) ((-66 . -1172) T) ((-969 . -591) 135169) ((-668 . -223) 135151) ((-689 . -111) 135116) ((-619 . -34) T) ((-237 . -479) 135100) ((-1065 . -1061) 135084) ((-168 . -1063) T) ((-921 . -878) 135063) ((-471 . -878) 135042) ((-1246 . -1111) T) ((-1242 . -21) T) ((-1242 . -25) T) ((-1240 . -130) T) ((-1238 . -130) T) ((-1051 . -692) 134891) ((-1027 . -622) 134878) ((-921 . -622) 134803) ((-756 . -692) 134632) ((-523 . -591) 134614) ((-523 . -592) 134595) ((-754 . -692) 134444) ((-1231 . -101) T) ((-1040 . -101) T) ((-372 . -25) T) ((-372 . -21) T) ((-471 . -622) 134369) ((-451 . -692) 134340) ((-444 . -692) 134189) ((-956 . -101) T) ((-1214 . -591) 134155) ((-1203 . -1007) 134090) ((-1182 . -1172) 134069) ((-712 . -101) T) ((-1182 . -855) NIL) ((-1182 . -853) 134021) ((-1145 . -592) NIL) ((-1145 . -591) 134003) ((-519 . -25) T) ((-1102 . -1085) 133948) ((-1013 . -1165) 133877) ((-870 . -300) 133815) ((-334 . -1023) T) ((-139 . -101) T) ((-44 . -130) T) ((-280 . -1075) T) ((-655 . -92) T) ((-650 . -92) T) ((-638 . -591) 133797) ((-620 . -591) 133750) ((-468 . -92) T) ((-346 . -591) 133732) ((-343 . -591) 133714) ((-335 . -591) 133696) ((-255 . -592) 133444) ((-255 . -591) 133426) ((-239 . -591) 133408) ((-239 . -592) 133269) ((-137 . -92) T) ((-136 . -92) T) ((-132 . -92) T) ((-1182 . -1007) 133235) ((-1166 . -503) 133202) ((-1101 . -591) 133184) ((-793 . -828) T) ((-793 . -701) T) ((-580 . -279) 133161) ((-561 . -692) 133126) ((-469 . -592) NIL) ((-469 . -591) 133108) ((-507 . -692) 133053) ((-307 . -101) T) ((-304 . -101) T) ((-280 . -23) T) ((-150 . -130) T) ((-377 . -701) T) ((-841 . -1022) 133005) ((-879 . -591) 132987) ((-879 . -592) 132969) ((-841 . -111) 132907) ((-135 . -101) T) ((-114 . -101) T) ((-687 . -1194) 132891) ((-689 . -1016) T) ((-668 . -340) NIL) ((-508 . -591) 132823) ((-370 . -769) T) ((-215 . -1063) T) ((-370 . -766) T) ((-217 . -768) T) ((-217 . -765) T) ((-58 . -592) 132784) ((-58 . -591) 132696) ((-217 . -701) T) ((-505 . -592) 132657) ((-505 . -591) 132569) ((-486 . -591) 132501) ((-485 . -592) 132462) ((-485 . -591) 132374) ((-1043 . -354) 132325) ((-40 . -402) 132302) ((-76 . -1172) T) ((-840 . -878) NIL) ((-350 . -320) 132286) ((-350 . -354) T) ((-344 . -320) 132270) ((-344 . -354) T) ((-336 . -320) 132254) ((-336 . -354) T) ((-307 . -275) 132233) ((-107 . -354) T) ((-69 . -1172) T) ((-1182 . -329) 132185) ((-840 . -622) 132130) ((-1182 . -368) 132082) ((-933 . -130) 131937) ((-789 . -130) 131807) ((-927 . -625) 131791) ((-1051 . -169) 131702) ((-927 . -364) 131686) ((-1027 . -768) T) ((-1027 . -765) T) ((-756 . -169) 131577) ((-754 . -169) 131488) ((-790 . -47) 131450) ((-1027 . -701) T) ((-318 . -479) 131434) ((-921 . -701) T) ((-444 . -169) 131345) ((-237 . -277) 131322) ((-471 . -701) T) ((-1231 . -300) 131260) ((-1210 . -869) 131173) ((-1203 . -869) 131079) ((-1202 . -1022) 130914) ((-1182 . -869) 130747) ((-1181 . -1022) 130555) ((-1166 . -281) 130534) ((-1106 . -149) 130518) ((-1082 . -101) T) ((-1038 . -101) T) ((-896 . -924) T) ((-74 . -1172) T) ((-712 . -300) 130456) ((-166 . -878) 130409) ((-638 . -373) 130381) ((-30 . -924) T) ((-1 . -591) 130363) ((-1080 . -1063) T) ((-1043 . -23) T) ((-50 . -596) 130347) ((-1043 . -1075) T) ((-972 . -400) 130319) ((-574 . -869) 130232) ((-429 . -101) T) ((-139 . -300) NIL) ((-841 . -1016) T) ((-807 . -821) 130211) ((-80 . -1172) T) ((-686 . -281) T) ((-40 . -1023) T) ((-561 . -169) T) ((-507 . -169) T) ((-500 . -591) 130193) ((-166 . -622) 130103) ((-496 . -591) 130085) ((-342 . -145) 130067) ((-342 . -143) T) ((-350 . -1075) T) ((-344 . -1075) T) ((-336 . -1075) T) ((-973 . -298) T) ((-883 . -298) T) ((-841 . -235) T) ((-107 . -1075) T) ((-841 . -225) 130046) ((-1202 . -111) 129867) ((-1181 . -111) 129656) ((-237 . -1206) 129640) ((-547 . -819) T) ((-350 . -23) T) ((-345 . -340) T) ((-307 . -300) 129627) ((-304 . -300) 129568) ((-344 . -23) T) ((-310 . -130) T) ((-336 . -23) T) 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. -591) 112308) ((-890 . -591) 112290) ((-1076 . -821) 112241) ((-745 . -591) 112223) ((-646 . -591) 112205) ((-1116 . -300) 112143) ((-469 . -34) T) ((-1056 . -1172) T) ((-467 . -442) T) ((-1051 . -1016) T) ((-1101 . -34) T) ((-756 . -1016) T) ((-754 . -1016) T) ((-621 . -227) 112127) ((-608 . -227) 112073) ((-1191 . -298) 112052) ((-1051 . -317) 112013) ((-444 . -1016) T) ((-1137 . -21) T) ((-1051 . -225) 111992) ((-756 . -317) 111969) ((-756 . -225) T) ((-754 . -317) 111941) ((-706 . -1176) 111920) ((-318 . -625) 111904) ((-1137 . -25) T) ((-58 . -34) T) ((-508 . -34) T) ((-505 . -34) T) ((-444 . -317) 111883) ((-318 . -364) 111867) ((-486 . -34) T) ((-485 . -34) T) ((-972 . -1111) NIL) ((-611 . -101) T) ((-585 . -101) T) ((-706 . -539) 111798) ((-346 . -701) T) ((-343 . -701) T) ((-335 . -701) T) ((-255 . -701) T) ((-239 . -701) T) ((-1013 . -300) 111706) ((-870 . -1063) 111684) ((-50 . -1016) T) ((-1230 . -21) T) ((-1230 . -25) T) ((-1133 . -539) 111663) ((-1132 . -1176) 111642) 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T) ((-590 . -821) T) ((-628 . -402) 111157) ((-110 . -821) T) ((-627 . -21) T) ((-627 . -25) T) ((-1241 . -38) 111127) ((-117 . -277) 111078) ((-1218 . -19) 111062) ((-1218 . -582) 111039) ((-1231 . -1063) T) ((-1040 . -1063) T) ((-956 . -1063) T) ((-932 . -130) T) ((-712 . -1063) T) ((-710 . -130) T) ((-690 . -130) T) ((-500 . -767) T) ((-398 . -1111) 111017) ((-443 . -130) T) ((-500 . -768) T) ((-215 . -1016) T) ((-285 . -101) 110799) ((-139 . -1063) T) ((-673 . -971) T) ((-90 . -1172) T) ((-127 . -591) 110731) ((-121 . -591) 110663) ((-1246 . -169) T) ((-1132 . -354) 110642) ((-1126 . -354) 110621) ((-307 . -1063) T) ((-409 . -130) T) ((-304 . -1063) T) ((-398 . -38) 110573) ((-1095 . -101) T) ((-1204 . -692) 110465) ((-628 . -1023) T) ((-310 . -143) 110444) ((-310 . -145) 110423) ((-135 . -1063) T) ((-114 . -1063) T) ((-829 . -101) T) ((-560 . -591) 110405) ((-547 . -592) 110304) ((-547 . -591) 110286) ((-484 . -591) 110268) ((-484 . -592) 110213) ((-475 . -23) T) ((-472 . -821) 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-298) T) ((-310 . -1157) 108497) ((-307 . -169) 108476) ((-304 . -169) T) ((-972 . -223) 108453) ((-883 . -354) T) ((-561 . -1237) 108440) ((-507 . -1237) 108417) ((-350 . -145) 108396) ((-350 . -143) 108347) ((-344 . -145) 108326) ((-344 . -143) 108277) ((-586 . -1148) 108253) ((-336 . -145) 108232) ((-336 . -143) 108183) ((-310 . -35) 108149) ((-465 . -1148) 108128) ((0 . |EnumerationCategory|) T) ((-310 . -94) 108094) ((-370 . -991) T) ((-107 . -145) T) ((-107 . -143) NIL) ((-45 . -227) 108044) ((-628 . -1063) T) ((-586 . -106) 107991) ((-475 . -130) T) ((-465 . -106) 107941) ((-232 . -1075) 107851) ((-841 . -368) 107835) ((-841 . -329) 107819) ((-232 . -23) 107689) ((-1027 . -889) T) ((-1027 . -794) T) ((-561 . -359) T) ((-507 . -359) T) ((-342 . -1111) T) ((-318 . -34) T) ((-44 . -408) 107673) ((-842 . -1172) T) ((-381 . -719) 107657) ((-1231 . -503) 107590) ((-706 . -130) T) ((-1210 . -539) 107569) ((-1203 . -1176) 107548) ((-1203 . -539) 107499) ((-1182 . -1176) 107478) ((-302 . 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-281) T) ((-628 . -692) 106354) ((-142 . -1063) T) ((-48 . -971) T) ((-398 . -223) 106338) ((-286 . -227) 106288) ((-840 . -889) T) ((-840 . -794) NIL) ((-834 . -821) T) ((-1181 . -329) 106258) ((-1181 . -368) 106228) ((-214 . -1083) 106212) ((-1218 . -279) 106189) ((-1166 . -622) 106114) ((-932 . -21) T) ((-932 . -25) T) ((-710 . -21) T) ((-710 . -25) T) ((-690 . -21) T) ((-690 . -25) T) ((-686 . -622) 106079) ((-443 . -21) T) ((-443 . -25) T) ((-330 . -101) T) ((-171 . -101) T) ((-968 . -1023) T) ((-839 . -1016) T) ((-748 . -101) T) ((-1203 . -354) 106058) ((-1202 . -869) 105964) ((-1182 . -354) 105943) ((-1181 . -869) 105794) ((-993 . -591) 105776) ((-398 . -802) 105729) ((-1133 . -482) 105695) ((-166 . -889) 105626) ((-1132 . -482) 105592) ((-1126 . -482) 105558) ((-687 . -1063) T) ((-1088 . -482) 105524) ((-560 . -1022) 105511) ((-547 . -1022) 105498) ((-484 . -1022) 105463) ((-307 . -281) 105442) ((-304 . -281) T) ((-345 . -591) 105424) ((-409 . -25) T) ((-409 . -21) T) ((-98 . 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102117) ((-599 . -1016) T) ((-370 . -395) T) ((-381 . -101) T) ((-255 . -869) 102063) ((-239 . -869) 102040) ((-117 . -1016) T) ((-790 . -1075) T) ((-1051 . -701) T) ((-599 . -225) 102019) ((-597 . -101) T) ((-756 . -701) T) ((-754 . -701) T) ((-404 . -1075) T) ((-117 . -235) T) ((-40 . -359) NIL) ((-117 . -225) NIL) ((-444 . -701) T) ((-790 . -23) T) ((-706 . -25) T) ((-706 . -21) T) ((-677 . -821) T) ((-1040 . -277) 101998) ((-77 . -387) T) ((-77 . -386) T) ((-668 . -1022) 101948) ((-1210 . -130) T) ((-1203 . -130) T) ((-1182 . -130) T) ((-1102 . -402) 101932) ((-611 . -358) 101864) ((-585 . -358) 101796) ((-1116 . -1109) 101780) ((-102 . -1063) 101758) ((-1133 . -25) T) ((-1133 . -21) T) ((-1132 . -21) T) ((-968 . -692) 101706) ((-215 . -622) 101673) ((-668 . -111) 101607) ((-50 . -701) T) ((-1132 . -25) T) ((-342 . -340) T) ((-1126 . -21) T) ((-1043 . -442) 101558) ((-1126 . -25) T) ((-687 . -503) 101505) ((-561 . -701) T) ((-507 . -701) T) ((-1088 . -21) T) ((-1088 . -25) T) 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95020) ((-304 . -1022) 94949) ((-968 . -277) 94907) ((-398 . -692) 94859) ((-128 . -821) T) ((-675 . -819) T) ((-1204 . -1016) T) ((-307 . -111) 94755) ((-304 . -111) 94668) ((-933 . -101) T) ((-789 . -101) 94458) ((-687 . -592) NIL) ((-687 . -591) 94440) ((-632 . -1007) 94336) ((-1204 . -317) 94280) ((-1004 . -279) 94255) ((-560 . -701) T) ((-547 . -768) T) ((-166 . -354) 94206) ((-547 . -765) T) ((-547 . -701) T) ((-484 . -701) T) ((-1106 . -479) 94190) ((-1051 . -855) NIL) ((-840 . -1075) T) ((-117 . -878) NIL) ((-1240 . -1239) 94166) ((-1238 . -1239) 94145) ((-756 . -855) NIL) ((-754 . -855) 94004) ((-1233 . -25) T) ((-1233 . -21) T) ((-1169 . -101) 93982) ((-1069 . -386) T) ((-599 . -622) 93969) ((-444 . -855) NIL) ((-649 . -101) 93947) ((-1051 . -1007) 93774) ((-840 . -23) T) ((-756 . -1007) 93633) ((-754 . -1007) 93490) ((-117 . -622) 93435) ((-444 . -1007) 93311) ((-623 . -1007) 93295) ((-603 . -101) T) ((-214 . -479) 93279) ((-1218 . -34) T) ((-611 . -692) 93263) ((-585 . 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-1225) 91338) ((-628 . -111) 91317) ((-1102 . -479) 91301) ((-789 . -38) 91271) ((-62 . -431) T) ((-62 . -386) T) ((-1119 . -101) T) ((-840 . -130) T) ((-474 . -101) 91249) ((-1246 . -359) T) ((-1043 . -101) T) ((-1026 . -101) T) ((-342 . -692) 91194) ((-706 . -145) 91173) ((-706 . -143) 91152) ((-993 . -622) 91089) ((-512 . -1063) 91067) ((-350 . -101) T) ((-344 . -101) T) ((-336 . -101) T) ((-107 . -101) T) ((-493 . -1063) T) ((-345 . -622) 91012) ((-1131 . -615) 90960) ((-1087 . -615) 90908) ((-376 . -498) 90887) ((-807 . -819) 90866) ((-370 . -1176) T) ((-668 . -701) T) ((-330 . -1023) T) ((-1182 . -961) 90818) ((-171 . -1023) T) ((-102 . -591) 90750) ((-1133 . -143) 90729) ((-1133 . -145) 90708) ((-370 . -539) T) ((-1132 . -145) 90687) ((-1132 . -143) 90666) ((-1126 . -143) 90573) ((-398 . -281) T) ((-1126 . -145) 90480) ((-1088 . -145) 90459) ((-1088 . -143) 90438) ((-310 . -38) 90279) ((-166 . -130) T) ((-304 . -769) NIL) ((-304 . -766) NIL) ((-628 . -1016) T) ((-48 . -622) 90244) ((-963 . -101) T) ((-962 . -21) T) ((-127 . -979) 90228) ((-121 . -979) 90212) ((-962 . -25) T) ((-870 . -119) 90196) ((-1118 . -101) T) ((-790 . -821) 90175) ((-1191 . -130) T) ((-1131 . -25) T) ((-1131 . -21) T) ((-826 . -130) T) ((-1087 . -25) T) ((-1087 . -21) T) ((-825 . -25) T) ((-825 . -21) T) ((-756 . -298) 90154) ((-621 . -101) 90132) ((-608 . -101) T) ((-1119 . -300) 89927) ((-554 . -130) T) ((-597 . -819) 89906) ((-1116 . -479) 89890) ((-1110 . -149) 89840) ((-1106 . -591) 89802) ((-1106 . -592) 89763) ((-993 . -765) T) ((-993 . -768) T) ((-993 . -701) T) ((-474 . -300) 89701) ((-443 . -408) 89671) ((-342 . -169) T) ((-280 . -38) 89658) ((-265 . -101) T) ((-264 . -101) T) ((-263 . -101) T) ((-262 . -101) T) ((-261 . -101) T) ((-260 . -101) T) ((-259 . -101) T) ((-334 . -1007) 89635) ((-204 . -101) T) ((-203 . -101) T) ((-201 . -101) T) ((-200 . -101) T) ((-199 . -101) T) ((-198 . -101) T) ((-195 . -101) T) ((-194 . -101) T) ((-687 . -1022) 89458) ((-193 . -101) T) 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. -35) 88517) ((-1126 . -1157) 88483) ((-1126 . -1160) 88449) ((-1126 . -94) 88415) ((-352 . -1075) T) ((-350 . -1111) 88394) ((-344 . -1111) 88373) ((-336 . -1111) 88352) ((-1126 . -35) 88318) ((-1088 . -35) 88284) ((-1088 . -94) 88250) ((-107 . -1111) T) ((-1088 . -1160) 88216) ((-807 . -1023) 88195) ((-621 . -300) 88133) ((-608 . -300) 87984) ((-1088 . -1157) 87950) ((-687 . -1016) T) ((-1027 . -615) 87932) ((-1043 . -38) 87800) ((-921 . -615) 87748) ((-973 . -145) T) ((-973 . -143) NIL) ((-370 . -1075) T) ((-315 . -25) T) ((-313 . -23) T) ((-912 . -821) 87727) ((-687 . -317) 87704) ((-471 . -615) 87652) ((-40 . -1007) 87540) ((-675 . -692) 87527) ((-687 . -225) T) ((-330 . -1063) T) ((-171 . -1063) T) ((-322 . -821) T) ((-409 . -442) 87477) ((-370 . -23) T) ((-350 . -38) 87442) ((-344 . -38) 87407) ((-336 . -38) 87372) ((-79 . -431) T) ((-79 . -386) T) ((-217 . -25) T) ((-217 . -21) T) ((-808 . -1075) T) ((-107 . -38) 87322) ((-801 . -1075) T) ((-748 . -1063) T) ((-116 . -692) 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. -375) T) ((-83 . -386) T) ((-675 . -169) T) ((-594 . -591) 86079) ((-98 . -701) T) ((-472 . -101) 85869) ((-98 . -463) T) ((-116 . -169) T) ((-1076 . -38) 85839) ((-166 . -615) 85787) ((-1020 . -101) T) ((-840 . -25) T) ((-789 . -230) 85766) ((-840 . -21) T) ((-792 . -101) T) ((-405 . -101) T) ((-376 . -101) T) ((-110 . -300) NIL) ((-219 . -101) 85744) ((-127 . -1172) T) ((-121 . -1172) T) ((-1003 . -130) T) ((-644 . -358) 85728) ((-968 . -1016) T) ((-1191 . -615) 85676) ((-1067 . -591) 85658) ((-972 . -591) 85640) ((-504 . -23) T) ((-499 . -23) T) ((-334 . -298) T) ((-497 . -23) T) ((-313 . -130) T) ((-3 . -1063) T) ((-972 . -592) 85624) ((-968 . -235) 85603) ((-968 . -225) 85582) ((-1246 . -701) T) ((-1210 . -143) 85561) ((-807 . -1063) T) ((-1210 . -145) 85540) ((-1203 . -145) 85519) ((-1203 . -143) 85498) ((-1202 . -1176) 85477) ((-1182 . -143) 85384) ((-1182 . -145) 85291) ((-1181 . -1176) 85270) ((-370 . -130) T) ((-547 . -855) 85252) ((0 . -1063) T) ((-171 . -169) T) ((-166 . 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-359) T) ((-1013 . -592) 84358) ((-1013 . -591) 84301) ((-304 . -878) NIL) ((-673 . -1007) 84246) ((-686 . -889) T) ((-464 . -1176) 84225) ((-1132 . -442) 84204) ((-1126 . -442) 84183) ((-321 . -101) T) ((-841 . -1075) T) ((-307 . -622) 84004) ((-304 . -622) 83933) ((-464 . -539) 83884) ((-330 . -503) 83850) ((-533 . -149) 83800) ((-40 . -298) T) ((-814 . -591) 83782) ((-675 . -281) T) ((-841 . -23) T) ((-370 . -482) T) ((-1043 . -223) 83752) ((-501 . -101) T) ((-398 . -592) 83560) ((-398 . -591) 83542) ((-254 . -591) 83524) ((-116 . -281) T) ((-1204 . -701) T) ((-1202 . -354) 83503) ((-1181 . -354) 83482) ((-1231 . -34) T) ((-117 . -1172) T) ((-107 . -223) 83464) ((-1137 . -101) T) ((-467 . -1063) T) ((-512 . -479) 83448) ((-712 . -34) T) ((-472 . -38) 83418) ((-139 . -34) T) ((-117 . -853) 83395) ((-117 . -855) NIL) ((-599 . -1007) 83278) ((-619 . -821) 83257) ((-1230 . -101) T) ((-286 . -101) T) ((-687 . -359) 83236) ((-117 . -1007) 83213) ((-381 . -692) 83197) ((-597 . -692) 83181) 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T) ((-335 . -320) 80246) ((-335 . -354) T) ((-477 . -101) T) ((-1230 . -38) 80216) ((-512 . -661) 80166) ((-209 . -101) T) ((-993 . -1007) 80046) ((-972 . -111) 79975) ((-1133 . -942) 79944) ((-1132 . -942) 79906) ((-509 . -149) 79890) ((-1043 . -361) 79869) ((-342 . -591) 79851) ((-313 . -21) T) ((-345 . -1007) 79828) ((-313 . -25) T) ((-1126 . -942) 79797) ((-1088 . -942) 79764) ((-75 . -591) 79746) ((-673 . -298) T) ((-166 . -821) 79725) ((-879 . -354) T) ((-370 . -25) T) ((-370 . -21) T) ((-879 . -320) 79712) ((-85 . -591) 79694) ((-673 . -991) T) ((-651 . -821) T) ((-1202 . -130) T) ((-1181 . -130) T) ((-870 . -979) 79678) ((-808 . -21) T) ((-48 . -1007) 79621) ((-808 . -25) T) ((-801 . -25) T) ((-801 . -21) T) ((-1240 . -1023) T) ((-1238 . -1023) T) ((-628 . -701) T) ((-1241 . -1022) 79605) ((-1191 . -821) 79584) ((-789 . -402) 79553) ((-102 . -119) 79537) ((-129 . -1063) T) ((-52 . -1063) T) ((-895 . -591) 79519) ((-840 . -961) 79496) ((-797 . -101) T) ((-1241 . -111) 79475) 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78603) ((-1131 . -145) 78582) ((-1087 . -145) 78561) ((-1087 . -143) 78540) ((-611 . -1022) 78524) ((-585 . -1022) 78508) ((-644 . -1063) T) ((-644 . -1019) 78448) ((-1133 . -1209) 78432) ((-1133 . -1196) 78409) ((-477 . -1111) T) ((-1132 . -1201) 78370) ((-1132 . -1196) 78340) ((-1132 . -1199) 78324) ((-209 . -1111) T) ((-334 . -889) T) ((-792 . -257) 78308) ((-611 . -111) 78287) ((-585 . -111) 78266) ((-1126 . -1180) 78227) ((-814 . -1016) 78206) ((-1126 . -1196) 78183) ((-504 . -25) T) ((-484 . -293) T) ((-500 . -23) T) ((-499 . -25) T) ((-497 . -25) T) ((-496 . -23) T) ((-1126 . -1178) 78167) ((-398 . -1016) T) ((-310 . -1023) T) ((-668 . -298) T) ((-107 . -819) T) ((-398 . -235) T) ((-398 . -225) 78146) ((-687 . -701) T) ((-477 . -38) 78096) ((-209 . -38) 78046) ((-464 . -482) 78012) ((-1118 . -1104) T) ((-1064 . -101) T) ((-675 . -591) 77994) ((-675 . -592) 77909) ((-689 . -21) T) ((-689 . -25) T) ((-205 . -591) 77891) ((-133 . -591) 77873) ((-116 . -591) 77855) ((-154 . -25) T) 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T) ((-870 . -1172) T) ((-48 . -991) T) ((-1181 . -615) 76615) ((-663 . -101) 76593) ((-44 . -692) 76577) ((-533 . -101) T) ((-66 . -374) T) ((-66 . -386) T) ((-636 . -23) T) ((-644 . -736) T) ((-1169 . -1063) 76555) ((-342 . -1022) 76500) ((-649 . -1063) 76478) ((-1027 . -145) T) ((-921 . -145) 76457) ((-921 . -143) 76436) ((-773 . -101) T) ((-150 . -692) 76420) ((-471 . -145) 76399) ((-471 . -143) 76378) ((-342 . -111) 76307) ((-1043 . -1023) T) ((-313 . -821) 76286) ((-1210 . -942) 76255) ((-603 . -1063) T) ((-1203 . -942) 76217) ((-500 . -130) T) ((-496 . -130) T) ((-286 . -221) 76167) ((-350 . -1023) T) ((-344 . -1023) T) ((-336 . -1023) T) ((-285 . -1016) 76109) ((-1182 . -942) 76078) ((-370 . -821) T) ((-107 . -1023) T) ((-968 . -701) T) ((-839 . -889) T) ((-814 . -769) 76057) ((-814 . -766) 76036) ((-409 . -300) 75975) ((-458 . -101) T) ((-574 . -942) 75944) ((-310 . -1063) T) ((-398 . -769) 75923) ((-398 . -766) 75902) ((-489 . -479) 75884) ((-1204 . -1007) 75850) ((-1202 . 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-25) T) ((-464 . -21) T) ((-409 . -38) 74859) ((-307 . -1007) 74522) ((-217 . -1157) T) ((-217 . -1160) T) ((-3 . -591) 74504) ((-304 . -1007) 74434) ((-2 . -1063) T) ((-2 . |RecordCategory|) T) ((-807 . -591) 74416) ((-1076 . -1023) 74346) ((-560 . -889) T) ((-547 . -794) T) ((-547 . -889) T) ((-484 . -889) T) ((-135 . -1007) 74330) ((-217 . -94) T) ((-74 . -431) T) ((-74 . -386) T) ((0 . -591) 74312) ((-166 . -145) 74291) ((-166 . -143) 74242) ((-217 . -35) T) ((-49 . -591) 74224) ((-467 . -1023) T) ((-477 . -223) 74206) ((-474 . -937) 74190) ((-472 . -819) 74169) ((-209 . -223) 74151) ((-80 . -431) T) ((-80 . -386) T) ((-1106 . -34) T) ((-789 . -169) 74130) ((-706 . -101) T) ((-995 . -591) 74097) ((-489 . -277) 74072) ((-307 . -368) 74041) ((-304 . -368) 74002) ((-304 . -329) 73963) ((-1049 . -591) 73945) ((-790 . -918) 73892) ((-636 . -130) T) ((-1191 . -143) 73871) ((-1191 . -145) 73850) ((-1133 . -101) T) ((-1132 . -101) T) ((-1126 . -101) T) ((-1119 . -1063) T) ((-1088 . -101) 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. -38) 69670) ((-330 . -1016) T) ((-1126 . -38) 69466) ((-1043 . -169) T) ((-171 . -1016) T) ((-1088 . -38) 69363) ((-687 . -47) 69340) ((-350 . -169) T) ((-344 . -169) T) ((-508 . -56) 69314) ((-486 . -56) 69264) ((-342 . -1237) 69241) ((-217 . -442) T) ((-310 . -281) 69192) ((-336 . -169) T) ((-171 . -235) T) ((-1181 . -821) 69091) ((-107 . -169) T) ((-841 . -961) 69075) ((-632 . -1075) T) ((-561 . -354) T) ((-561 . -320) 69062) ((-507 . -320) 69039) ((-507 . -354) T) ((-307 . -298) 69018) ((-304 . -298) T) ((-580 . -821) 68997) ((-1076 . -692) 68939) ((-509 . -273) 68923) ((-632 . -23) T) ((-409 . -223) 68907) ((-304 . -991) NIL) ((-327 . -23) T) ((-102 . -979) 68891) ((-45 . -36) 68870) ((-590 . -1063) T) ((-342 . -359) T) ((-513 . -101) T) ((-484 . -27) T) ((-232 . -300) 68808) ((-1051 . -1075) T) ((-1241 . -622) 68782) ((-756 . -1075) T) ((-754 . -1075) T) ((-444 . -1075) T) ((-1027 . -442) T) ((-921 . -442) 68733) ((-110 . -1063) T) ((-1051 . -23) T) ((-791 . -1023) T) ((-756 . 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-1063) T) ((-451 . -130) T) ((-444 . -130) T) ((-45 . -1063) T) ((-376 . -692) 65795) ((-791 . -1063) T) ((-466 . -503) 65728) ((-453 . -503) 65661) ((-443 . -358) 65631) ((-45 . -588) 65610) ((-307 . -293) T) ((-644 . -591) 65572) ((-58 . -821) 65551) ((-1182 . -300) 65436) ((-973 . -391) 65418) ((-789 . -582) 65395) ((-505 . -821) 65374) ((-485 . -821) 65353) ((-40 . -1176) T) ((-968 . -1007) 65249) ((-50 . -130) T) ((-561 . -130) T) ((-507 . -130) T) ((-285 . -622) 65109) ((-334 . -320) 65086) ((-334 . -354) T) ((-313 . -314) 65063) ((-310 . -277) 65048) ((-40 . -539) T) ((-370 . -1157) T) ((-370 . -1160) T) ((-1004 . -1148) 65023) ((-1145 . -227) 64973) ((-1126 . -223) 64925) ((-321 . -1063) T) ((-370 . -94) T) ((-370 . -35) T) ((-1004 . -106) 64871) ((-467 . -1016) T) ((-469 . -227) 64821) ((-1119 . -479) 64755) ((-1242 . -1022) 64739) ((-372 . -1022) 64723) ((-467 . -235) T) ((-790 . -101) T) ((-689 . -145) 64702) ((-689 . -143) 64681) ((-474 . -479) 64665) ((-475 . -326) 64634) 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63285) ((-798 . -101) T) ((-834 . -815) T) ((-285 . -463) 63264) ((-1233 . -101) T) ((-40 . -354) T) ((-841 . -145) 63243) ((-841 . -143) 63222) ((-1118 . -479) 63204) ((-1242 . -1016) T) ((-472 . -503) 63137) ((-1106 . -1172) T) ((-933 . -591) 63119) ((-621 . -479) 63103) ((-608 . -479) 63034) ((-789 . -591) 62765) ((-48 . -27) T) ((-1137 . -692) 62662) ((-627 . -1063) T) ((-427 . -355) 62636) ((-1065 . -101) T) ((-790 . -300) 62623) ((-939 . -1063) T) ((-834 . -1063) T) ((-1238 . -373) 62595) ((-1020 . -503) 62528) ((-1119 . -277) 62504) ((-232 . -223) 62473) ((-1230 . -692) 62443) ((-963 . -92) T) ((-791 . -169) 62422) ((-219 . -503) 62355) ((-597 . -769) 62334) ((-597 . -766) 62313) ((-1169 . -591) 62225) ((-214 . -1172) T) ((-649 . -591) 62157) ((-1116 . -979) 62141) ((-342 . -701) T) ((-912 . -101) 62091) ((-1182 . -391) 62043) ((-1076 . -479) 62027) ((-59 . -300) 61965) ((-322 . -101) T) ((-1166 . -21) T) ((-1166 . -25) T) ((-40 . -1075) T) ((-686 . -21) T) ((-603 . -591) 61947) ((-504 . -314) 61926) ((-686 . -25) T) ((-107 . -277) NIL) ((-890 . -1075) T) ((-40 . -23) T) ((-745 . -1075) T) ((-547 . -1176) T) ((-484 . -1176) T) ((-310 . -591) 61908) ((-973 . -223) 61890) ((-166 . -163) 61874) ((-560 . -539) T) ((-547 . -539) T) ((-484 . -539) T) ((-745 . -23) T) ((-1202 . -145) 61853) ((-1119 . -582) 61829) ((-1202 . -143) 61808) ((-996 . -479) 61792) ((-1181 . -143) 61717) ((-1181 . -145) 61642) ((-1233 . -1239) 61621) ((-466 . -479) 61605) ((-453 . -479) 61589) ((-512 . -34) T) ((-627 . -692) 61559) ((-112 . -936) T) ((-636 . -821) 61538) ((-1137 . -169) 61489) ((-356 . -101) T) ((-232 . -230) 61468) ((-242 . -101) T) ((-241 . -101) T) ((-1191 . -918) 61437) ((-109 . -101) T) ((-237 . -821) 61416) ((-790 . -38) 61265) ((-45 . -503) 61057) ((-1118 . -277) 61032) ((-206 . -1063) T) ((-1110 . -1063) T) ((-1110 . -588) 61011) ((-565 . -25) T) ((-565 . -21) T) ((-1065 . -300) 60949) ((-932 . -402) 60933) ((-673 . -1176) T) ((-608 . -277) 60908) ((-1051 . -615) 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. -21) T) ((-1181 . -991) 102117) ((-599 . -1016) T) ((-370 . -395) T) ((-381 . -101) T) ((-255 . -869) 102063) ((-239 . -869) 102040) ((-117 . -1016) T) ((-790 . -1075) T) ((-1051 . -701) T) ((-599 . -225) 102019) ((-597 . -101) T) ((-756 . -701) T) ((-754 . -701) T) ((-404 . -1075) T) ((-117 . -235) T) ((-40 . -359) NIL) ((-117 . -225) NIL) ((-444 . -701) T) ((-790 . -23) T) ((-706 . -25) T) ((-706 . -21) T) ((-677 . -821) T) ((-1040 . -277) 101998) ((-77 . -387) T) ((-77 . -386) T) ((-668 . -1022) 101948) ((-1210 . -130) T) ((-1203 . -130) T) ((-1182 . -130) T) ((-1102 . -402) 101932) ((-611 . -358) 101864) ((-585 . -358) 101796) ((-1116 . -1109) 101780) ((-102 . -1063) 101758) ((-1133 . -25) T) ((-1133 . -21) T) ((-1132 . -21) T) ((-968 . -692) 101706) ((-215 . -622) 101673) ((-668 . -111) 101607) ((-50 . -701) T) ((-1132 . -25) T) ((-342 . -340) T) ((-1126 . -21) T) ((-1043 . -442) 101558) ((-1126 . -25) T) ((-687 . -503) 101505) ((-561 . -701) T) ((-507 . -701) T) ((-1088 . -21) 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99303) ((-1231 . -591) 99265) ((-1231 . -592) 99226) ((-1040 . -591) 99208) ((-993 . -235) T) ((-345 . -1016) T) ((-789 . -1225) 99178) ((-242 . -23) T) ((-241 . -23) T) ((-956 . -591) 99160) ((-712 . -592) 99121) ((-712 . -591) 99103) ((-773 . -821) 99082) ((-968 . -503) 98994) ((-345 . -225) T) ((-345 . -235) T) ((-1119 . -149) 98941) ((-973 . -25) T) ((-139 . -592) 98900) ((-139 . -591) 98882) ((-879 . -298) T) ((-973 . -21) T) ((-940 . -25) T) ((-883 . -21) T) ((-883 . -25) T) ((-418 . -21) T) ((-418 . -25) T) ((-814 . -402) 98866) ((-48 . -1016) T) ((-1240 . -1232) 98850) ((-1238 . -1232) 98834) ((-1004 . -582) 98809) ((-307 . -592) 98670) ((-307 . -591) 98652) ((-304 . -592) NIL) ((-304 . -591) 98634) ((-48 . -235) T) ((-48 . -225) T) ((-628 . -277) 98595) ((-533 . -227) 98545) ((-135 . -591) 98527) ((-114 . -591) 98509) ((-467 . -38) 98474) ((-1242 . -1239) 98453) ((-1233 . -130) T) ((-1241 . -1023) T) ((-1045 . -101) T) ((-87 . -1172) T) ((-489 . -300) NIL) ((-969 . -106) 98437) ((-858 . -1063) T) ((-854 . -1063) T) ((-1218 . -625) 98421) ((-1218 . -364) 98405) ((-318 . -1172) T) ((-572 . -821) T) ((-1102 . -1063) T) ((-1102 . -1019) 98345) ((-102 . -503) 98278) ((-896 . -591) 98260) ((-334 . -701) T) ((-30 . -591) 98242) ((-835 . -1063) T) ((-814 . -1023) 98221) ((-40 . -622) 98166) ((-217 . -1176) T) ((-398 . -1023) T) ((-1118 . -149) 98148) ((-968 . -281) 98099) ((-594 . -1063) T) ((-217 . -539) T) ((-310 . -1199) 98083) ((-310 . -1196) 98053) ((-1145 . -1148) 98032) ((-1038 . -591) 98014) ((-621 . -149) 97998) ((-608 . -149) 97944) ((-1145 . -106) 97894) ((-469 . -1148) 97873) ((-477 . -145) T) ((-477 . -143) NIL) ((-1082 . -592) 97788) ((-429 . -591) 97770) ((-209 . -145) T) ((-209 . -143) NIL) ((-1082 . -591) 97752) ((-129 . -101) T) ((-52 . -101) T) ((-1182 . -615) 97704) ((-469 . -106) 97654) ((-962 . -23) T) ((-1242 . -38) 97624) ((-1131 . -1075) T) ((-1087 . -1075) T) ((-1027 . -1176) T) ((-302 . -101) T) ((-825 . -1075) T) ((-921 . -1176) 97603) ((-471 . -1176) 97582) ((-706 . -821) 97561) ((-1027 . -539) T) ((-921 . -539) 97492) ((-1131 . -23) T) ((-1087 . -23) T) ((-825 . -23) T) ((-471 . -539) 97423) ((-1102 . -692) 97355) ((-1106 . -503) 97288) ((-1004 . -592) NIL) ((-1004 . -591) 97270) ((-95 . -1047) T) ((-835 . -692) 97240) ((-1166 . -47) 97209) ((-242 . -130) T) ((-241 . -130) T) ((-1067 . -1063) T) ((-972 . -1063) T) ((-61 . -591) 97191) ((-1126 . -821) NIL) ((-993 . -766) T) ((-993 . -769) T) ((-1246 . -1022) 97178) ((-1246 . -111) 97163) ((-839 . -622) 97150) ((-1210 . -25) T) ((-1210 . -21) T) ((-1203 . -21) T) ((-1203 . -25) T) ((-1182 . -21) T) ((-1182 . -25) T) ((-996 . -149) 97134) ((-841 . -794) 97113) ((-841 . -889) T) ((-687 . -277) 97040) ((-575 . -21) T) ((-575 . -25) T) ((-574 . -21) T) ((-40 . -701) T) ((-214 . -503) 96973) ((-574 . -25) T) ((-466 . -149) 96957) ((-453 . -149) 96941) ((-890 . -768) T) ((-890 . -701) T) ((-745 . -767) T) ((-745 . -768) T) ((-495 . -1063) T) ((-491 . -1063) T) 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. -692) 93263) ((-585 . -692) 93247) ((-644 . -38) 93207) ((-310 . -101) T) ((-84 . -591) 93189) ((-50 . -1007) 93173) ((-1082 . -1022) 93160) ((-1051 . -368) 93144) ((-756 . -368) 93128) ((-59 . -56) 93090) ((-673 . -768) T) ((-673 . -765) T) ((-561 . -1007) 93077) ((-507 . -1007) 93054) ((-673 . -701) T) ((-315 . -130) T) ((-307 . -1016) 92944) ((-304 . -1016) T) ((-166 . -1075) T) ((-754 . -368) 92928) ((-45 . -149) 92878) ((-973 . -961) 92860) ((-444 . -368) 92844) ((-398 . -169) T) ((-307 . -235) 92823) ((-304 . -235) T) ((-304 . -225) NIL) ((-285 . -1063) 92605) ((-217 . -130) T) ((-1082 . -111) 92590) ((-166 . -23) T) ((-773 . -145) 92569) ((-773 . -143) 92548) ((-242 . -615) 92454) ((-241 . -615) 92360) ((-310 . -275) 92326) ((-1116 . -503) 92259) ((-1095 . -1063) T) ((-217 . -1025) T) ((-789 . -300) 92197) ((-1051 . -869) 92132) ((-756 . -869) 92075) ((-754 . -869) 92059) ((-1240 . -38) 92029) ((-1238 . -38) 91999) ((-1191 . -1075) T) ((-826 . -1075) T) ((-444 . -869) 91976) 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-1016) T) ((-48 . -622) 90244) ((-963 . -101) T) ((-962 . -21) T) ((-127 . -979) 90228) ((-121 . -979) 90212) ((-962 . -25) T) ((-870 . -119) 90196) ((-1118 . -101) T) ((-790 . -821) 90175) ((-1191 . -130) T) ((-1131 . -25) T) ((-1131 . -21) T) ((-826 . -130) T) ((-1087 . -25) T) ((-1087 . -21) T) ((-825 . -25) T) ((-825 . -21) T) ((-756 . -298) 90154) ((-621 . -101) 90132) ((-608 . -101) T) ((-1119 . -300) 89927) ((-554 . -130) T) ((-597 . -819) 89906) ((-1116 . -479) 89890) ((-1110 . -149) 89840) ((-1106 . -591) 89802) ((-1106 . -592) 89763) ((-993 . -765) T) ((-993 . -768) T) ((-993 . -701) T) ((-474 . -300) 89701) ((-443 . -408) 89671) ((-342 . -169) T) ((-280 . -38) 89658) ((-265 . -101) T) ((-264 . -101) T) ((-263 . -101) T) ((-262 . -101) T) ((-261 . -101) T) ((-260 . -101) T) ((-259 . -101) T) ((-334 . -1007) 89635) ((-204 . -101) T) ((-203 . -101) T) ((-201 . -101) T) ((-200 . -101) T) ((-199 . -101) T) ((-198 . -101) T) ((-195 . -101) T) ((-194 . -101) T) ((-687 . -1022) 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80262) ((-343 . -354) T) ((-335 . -320) 80246) ((-335 . -354) T) ((-477 . -101) T) ((-1230 . -38) 80216) ((-512 . -661) 80166) ((-209 . -101) T) ((-993 . -1007) 80046) ((-972 . -111) 79975) ((-1133 . -942) 79944) ((-1132 . -942) 79906) ((-509 . -149) 79890) ((-1043 . -361) 79869) ((-342 . -591) 79851) ((-313 . -21) T) ((-345 . -1007) 79828) ((-313 . -25) T) ((-1126 . -942) 79797) ((-1088 . -942) 79764) ((-75 . -591) 79746) ((-673 . -298) T) ((-166 . -821) 79725) ((-879 . -354) T) ((-370 . -25) T) ((-370 . -21) T) ((-879 . -320) 79712) ((-85 . -591) 79694) ((-673 . -991) T) ((-651 . -821) T) ((-1202 . -130) T) ((-1181 . -130) T) ((-870 . -979) 79678) ((-808 . -21) T) ((-48 . -1007) 79621) ((-808 . -25) T) ((-801 . -25) T) ((-801 . -21) T) ((-1240 . -1023) T) ((-1238 . -1023) T) ((-628 . -701) T) ((-1241 . -1022) 79605) ((-1191 . -821) 79584) ((-789 . -402) 79553) ((-102 . -119) 79537) ((-129 . -1063) T) ((-52 . -1063) T) ((-895 . -591) 79519) ((-840 . -961) 79496) ((-797 . -101) T) 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78624) ((-1131 . -143) 78603) ((-1131 . -145) 78582) ((-1087 . -145) 78561) ((-1087 . -143) 78540) ((-611 . -1022) 78524) ((-585 . -1022) 78508) ((-644 . -1063) T) ((-644 . -1019) 78448) ((-1133 . -1209) 78432) ((-1133 . -1196) 78409) ((-477 . -1111) T) ((-1132 . -1201) 78370) ((-1132 . -1196) 78340) ((-1132 . -1199) 78324) ((-209 . -1111) T) ((-334 . -889) T) ((-792 . -257) 78308) ((-611 . -111) 78287) ((-585 . -111) 78266) ((-1126 . -1180) 78227) ((-814 . -1016) 78206) ((-1126 . -1196) 78183) ((-504 . -25) T) ((-484 . -293) T) ((-500 . -23) T) ((-499 . -25) T) ((-497 . -25) T) ((-496 . -23) T) ((-1126 . -1178) 78167) ((-398 . -1016) T) ((-310 . -1023) T) ((-668 . -298) T) ((-107 . -819) T) ((-398 . -235) T) ((-398 . -225) 78146) ((-687 . -701) T) ((-477 . -38) 78096) ((-209 . -38) 78046) ((-464 . -482) 78012) ((-1118 . -1104) T) ((-1064 . -101) T) ((-675 . -591) 77994) ((-675 . -592) 77909) ((-689 . -21) T) ((-689 . -25) T) ((-205 . -591) 77891) ((-133 . -591) 77873) ((-116 . -591) 77855) ((-154 . -25) T) ((-1240 . -1063) T) ((-841 . -615) 77803) ((-1238 . -1063) T) ((-932 . -101) T) ((-710 . -101) T) ((-690 . -101) T) ((-443 . -101) T) ((-790 . -442) 77754) ((-44 . -1063) T) ((-1052 . -821) T) ((-638 . -130) T) ((-1028 . -300) 77605) ((-644 . -692) 77589) ((-280 . -1023) T) ((-346 . -130) T) ((-343 . -130) T) ((-335 . -130) T) ((-255 . -130) T) ((-239 . -130) T) ((-409 . -101) T) ((-150 . -1063) T) ((-45 . -221) 77539) ((-927 . -821) 77518) ((-968 . -622) 77456) ((-232 . -1225) 77426) ((-993 . -298) T) ((-285 . -1022) 77347) ((-879 . -130) T) ((-40 . -889) T) ((-477 . -391) 77329) ((-345 . -298) T) ((-209 . -391) 77311) ((-1043 . -402) 77295) ((-285 . -111) 77211) ((-841 . -25) T) ((-841 . -21) T) ((-330 . -591) 77193) ((-1204 . -47) 77137) ((-217 . -145) T) ((-171 . -591) 77119) ((-1076 . -819) 77098) ((-748 . -591) 77080) ((-586 . -227) 77027) ((-465 . -227) 76977) ((-1240 . -692) 76947) ((-48 . -298) T) ((-1238 . -692) 76917) ((-933 . -1063) T) ((-789 . 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. -1007) 75850) ((-1202 . -21) T) ((-1202 . -25) T) ((-1181 . -21) T) ((-1181 . -25) T) ((-789 . -692) 75792) ((-673 . -395) T) ((-584 . -101) T) ((-1231 . -1172) T) ((-1076 . -402) 75761) ((-972 . -359) NIL) ((-645 . -101) T) ((-158 . -101) T) ((-153 . -101) T) ((-102 . -34) T) ((-712 . -1172) T) ((-44 . -736) T) ((-572 . -101) T) ((-76 . -387) T) ((-76 . -386) T) ((-627 . -630) 75745) ((-139 . -1172) T) ((-840 . -145) T) ((-840 . -143) NIL) ((-1171 . -92) T) ((-342 . -1016) T) ((-69 . -374) T) ((-69 . -386) T) ((-1125 . -101) T) ((-644 . -503) 75678) ((-663 . -300) 75616) ((-932 . -38) 75513) ((-710 . -38) 75483) ((-533 . -300) 75287) ((-307 . -1172) T) ((-342 . -225) T) ((-342 . -235) T) ((-304 . -1172) T) ((-280 . -1063) T) ((-1139 . -591) 75269) ((-686 . -1176) T) ((-1116 . -625) 75253) ((-1166 . -539) 75232) ((-686 . -539) T) ((-307 . -853) 75216) ((-307 . -855) 75141) ((-304 . -853) 75102) ((-304 . -855) NIL) ((-773 . -300) 75067) ((-310 . -692) 74908) ((-315 . -314) 74885) 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. -1075) T) ((-1166 . -23) T) ((-1126 . -300) 71833) ((-1088 . -300) 71820) ((-1043 . -692) 71688) ((-835 . -622) 71648) ((-912 . -949) 71632) ((-879 . -21) T) ((-280 . -169) T) ((-879 . -25) T) ((-302 . -92) T) ((-841 . -821) 71583) ((-686 . -1075) T) ((-686 . -23) T) ((-621 . -1063) 71561) ((-608 . -588) 71536) ((-608 . -1063) T) ((-561 . -1176) T) ((-507 . -1176) T) ((-561 . -539) T) ((-507 . -539) T) ((-350 . -692) 71488) ((-344 . -692) 71440) ((-171 . -111) 71351) ((-330 . -1022) 71335) ((-171 . -1022) 71267) ((-107 . -692) 71217) ((-336 . -692) 71169) ((-330 . -111) 71148) ((-265 . -1063) T) ((-264 . -1063) T) ((-263 . -1063) T) ((-262 . -1063) T) ((-675 . -1016) T) ((-261 . -1063) T) ((-260 . -1063) T) ((-259 . -1063) T) ((-204 . -1063) T) ((-203 . -1063) T) ((-201 . -1063) T) ((-166 . -1160) 71126) ((-166 . -1157) 71104) ((-200 . -1063) T) ((-199 . -1063) T) ((-116 . -1016) T) ((-198 . -1063) T) ((-195 . -1063) T) ((-675 . -225) T) ((-194 . -1063) T) ((-193 . -1063) T) ((-192 . 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. -25) T) ((-1132 . -38) 69670) ((-330 . -1016) T) ((-1126 . -38) 69466) ((-1043 . -169) T) ((-171 . -1016) T) ((-1088 . -38) 69363) ((-687 . -47) 69340) ((-350 . -169) T) ((-344 . -169) T) ((-508 . -56) 69314) ((-486 . -56) 69264) ((-342 . -1237) 69241) ((-217 . -442) T) ((-310 . -281) 69192) ((-336 . -169) T) ((-171 . -235) T) ((-1181 . -821) 69091) ((-107 . -169) T) ((-841 . -961) 69075) ((-632 . -1075) T) ((-561 . -354) T) ((-561 . -320) 69062) ((-507 . -320) 69039) ((-507 . -354) T) ((-307 . -298) 69018) ((-304 . -298) T) ((-580 . -821) 68997) ((-1076 . -692) 68939) ((-509 . -273) 68923) ((-632 . -23) T) ((-409 . -223) 68907) ((-304 . -991) NIL) ((-327 . -23) T) ((-102 . -979) 68891) ((-45 . -36) 68870) ((-590 . -1063) T) ((-342 . -359) T) ((-513 . -101) T) ((-484 . -27) T) ((-232 . -300) 68808) ((-1051 . -1075) T) ((-1241 . -622) 68782) ((-756 . -1075) T) ((-754 . -1075) T) ((-444 . -1075) T) ((-1027 . -442) T) ((-921 . -442) 68733) ((-110 . -1063) T) ((-1051 . -23) T) ((-791 . 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63383) ((-285 . -701) 63285) ((-798 . -101) T) ((-834 . -815) T) ((-285 . -463) 63264) ((-1233 . -101) T) ((-40 . -354) T) ((-841 . -145) 63243) ((-841 . -143) 63222) ((-1118 . -479) 63204) ((-1242 . -1016) T) ((-472 . -503) 63137) ((-1106 . -1172) T) ((-933 . -591) 63119) ((-621 . -479) 63103) ((-608 . -479) 63034) ((-789 . -591) 62765) ((-48 . -27) T) ((-1137 . -692) 62662) ((-627 . -1063) T) ((-427 . -355) 62636) ((-1065 . -101) T) ((-790 . -300) 62623) ((-939 . -1063) T) ((-834 . -1063) T) ((-1238 . -373) 62595) ((-1020 . -503) 62528) ((-1119 . -277) 62504) ((-232 . -223) 62473) ((-1230 . -692) 62443) ((-963 . -92) T) ((-791 . -169) 62422) ((-219 . -503) 62355) ((-597 . -769) 62334) ((-597 . -766) 62313) ((-1169 . -591) 62225) ((-214 . -1172) T) ((-649 . -591) 62157) ((-1116 . -979) 62141) ((-342 . -701) T) ((-912 . -101) 62091) ((-1182 . -391) 62043) ((-1076 . -479) 62027) ((-59 . -300) 61965) ((-322 . -101) T) ((-1166 . -21) T) ((-1166 . -25) T) ((-40 . -1075) T) ((-686 . -21) T) 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. -1075) T) ((-166 . -38) 47615) ((-1202 . -942) 47577) ((-1107 . -300) 47515) ((-1181 . -942) 47484) ((-879 . -393) T) ((-1076 . -1016) 47414) ((-1204 . -539) T) ((-1110 . -582) 47393) ((-112 . -821) T) ((-1028 . -479) 47324) ((-560 . -21) T) ((-560 . -25) T) ((-547 . -21) T) ((-547 . -25) T) ((-484 . -25) T) ((-484 . -21) T) ((-1191 . -1111) 47302) ((-1076 . -225) 47254) ((-48 . -130) T) ((-1153 . -101) T) ((-232 . -1063) 47044) ((-840 . -391) 47021) ((-1052 . -101) T) ((-1039 . -101) T) ((-586 . -101) T) ((-465 . -101) T) ((-1191 . -38) 46850) ((-826 . -38) 46820) ((-706 . -169) 46731) ((-627 . -591) 46713) ((-620 . -1047) T) ((-554 . -38) 46700) ((-939 . -591) 46666) ((-927 . -101) 46616) ((-834 . -591) 46598) ((-834 . -592) 46520) ((-572 . -503) NIL) ((-1210 . -1023) T) ((-1203 . -1023) T) ((-1182 . -1023) T) ((-575 . -1023) T) ((-574 . -1023) T) ((-1246 . -1075) T) ((-1133 . -169) 46471) ((-1132 . -169) 46402) ((-1126 . -169) 46333) ((-1088 . -169) 46284) ((-973 . -1063) T) 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-701) T) ((-398 . -821) 1305) ((-166 . -111) 1201) ((-807 . -130) 1153) ((-712 . -149) 1137) ((-1218 . -300) 1075) ((-477 . -298) T) ((-370 . -591) 1042) ((-509 . -979) 1026) ((-370 . -592) 940) ((-209 . -298) T) ((-139 . -149) 922) ((-689 . -277) 901) ((-477 . -991) T) ((-560 . -38) 888) ((-547 . -38) 875) ((-484 . -38) 840) ((-209 . -991) T) ((-840 . -1016) T) ((-808 . -591) 822) ((-801 . -591) 804) ((-799 . -591) 786) ((-790 . -878) 765) ((-1242 . -1075) T) ((-1191 . -1022) 588) ((-826 . -1022) 572) ((-840 . -235) T) ((-840 . -225) NIL) ((-663 . -1172) T) ((-1242 . -23) T) ((-790 . -622) 497) ((-533 . -1172) T) ((-409 . -329) 481) ((-554 . -1022) 468) ((-1191 . -111) 277) ((-675 . -615) 259) ((-826 . -111) 238) ((-372 . -23) T) ((-1145 . -503) 30) ((-636 . -1063) T) ((-655 . -1063) T) ((-650 . -1063) T))
\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 65954de7..f716a8d6 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3430960040) +(30 . 3430962937) (4331 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -468,653 +468,655 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |mapUnivariate| |univariateSolve| |mapUp!| |comment| - |atoms| |primeFactor| |lo| |mesh| |listBranches| |increment| |mapdiv| - |obj| |rootNormalize| |chebyshevU| |comparison| |karatsuba| - |balancedBinaryTree| |totalfract| |incr| |OMbindTCP| |noLinearFactor?| - |notOperand| |dimensionOfIrreducibleRepresentation| |kmax| - |complexEigenvalues| |cache| |linearAssociatedExp| - |basisOfLeftNucloid| |setLabelValue| |hi| |integralLastSubResultant| - |getOperator| |leftUnit| |octon| |tanhIfCan| |f07fdf| - |removeRoughlyRedundantFactorsInContents| |internalZeroSetSplit| - |laplace| |bipolar| |leviCivitaSymbol| |iilog| |swapColumns!| |merge| - |goodnessOfFit| |factorsOfCyclicGroupSize| |enterPointData| - |OMgetString| |char| |mainForm| |integerBound| |shift| - |leftCharacteristicPolynomial| |getExplanations| |sech2cosh| |lyndon?| - |epilogue| |drawToScale| |subHeight| |pr2dmp| |nthRoot| |fortran| - |depth| |hessian| |factorSFBRlcUnit| |tryFunctionalDecomposition| - |bringDown| |nullity| |getVariableOrder| |s17aef| |bracket| - |lineColorDefault| |subResultantChain| |magnitude| |e01sef| |c06gbf| - |coerceImages| |binaryTournament| |besselJ| |space| |normalized?| ~ - |goodPoint| |firstDenom| |tail| |stoseInvertibleSetreg| |solid?| - |algSplitSimple| |critMonD1| |contains?| |thenBranch| |lighting| - |radicalOfLeftTraceForm| |host| |OMgetError| |rightRankPolynomial| - |float| |coord| |f01qdf| |Lazard2| |open| |weights| - |numericalIntegration| |partialNumerators| |polynomialZeros| |tValues| - |clearTable!| |normalise| |nthExpon| |completeSmith| |charpol| |nthr| - |compBound| |irreducibleRepresentation| |exprToXXP| |s21bcf| - |makeResult| |sumOfSquares| |printTypes| |cothIfCan| |c02agf| - |lowerCase!| |extract!| |separate| |shallowExpand| |iExquo| - |lieAdmissible?| |content| |genus| |whatInfinity| |linear| |numer| - |subset?| |whileLoop| |bipolarCylindrical| |coerceL| |fractRadix| - |fractionFreeGauss!| |lazyPseudoRemainder| |symmetricProduct| - |sin2csc| |denom| |LiePolyIfCan| |adaptive| |selectODEIVPRoutines| - |prod| |mvar| |oddintegers| |generate| |btwFact| |polynomial| - |iiasinh| |exponential| |dictionary| |s17aff| |hasoln| - |quasiComponent| |nextPrimitiveNormalPoly| F |pmComplexintegrate| - |e01sff| |isOp| |pi| |rowEchLocal| |over| |pol| |erf| |besselY| - |f01qef| |axesColorDefault| |incrementBy| |const| |stoseInvertible?| - |RittWuCompare| |infinity| |bivariate?| |rationalPower| |union| - |generalTwoFactor| |tubePoints| |hyperelliptic| |selectsecond| - |diophantineSystem| |script| |floor| |expand| |showTypeInOutput| - |wreath| |OMgetObject| |multinomial| |lexGroebner| |splitLinear| - |anticoord| |inf| |OMsupportsSymbol?| |orbit| |filterWhile| |mantissa| - |setright!| |trueEqual| |status| |usingTable?| |makeCrit| |move| - |getStream| |dilog| |gramschmidt| |simplify| |nextsousResultant2| - |stFuncN| |filterUntil| |tracePowMod| |f2df| |exprToUPS| |kernel| - |tRange| |colorFunction| |f02axf| |is?| |overlap| |wholeRadix| |tex| - |sin| |options| |jacobiIdentity?| |select| |draw| |checkRur| |c05adf| - |s21bdf| |level| |addmod| |contractSolve| |pseudoDivide| |result| - |overlabel| |newTypeLists| |cos| |zeroDimPrime?| |invertIfCan| - |sechIfCan| |symmetricDifference| |lowerCase| |setButtonValue| - |semiSubResultantGcdEuclidean2| |toroidal| |deepExpand| |tan| - |initials| |totalDegree| |selectPDERoutines| |getZechTable| - |infinite?| |optimize| |trunc| |ran| |indicialEquationAtInfinity| - |fracPart| |figureUnits| |coerceS| NOT |string| |cot| |dioSolve| - |bernoulliB| |dom| |sinh2csch| |iiacosh| |symmetricPower| |indices| - |symbolTableOf| |f01rcf| |s17agf| OR |relativeApprox| |sec| |xn| |int| - |makeObject| |beauzamyBound| |pmintegrate| |chiSquare| |log2| - |setchildren!| |besselI| AND |ParCondList| |csubst| |csc| - |leastAffineMultiple| |selectfirst| |e02adf| |satisfy?| - |bivariatePolynomials| |rowEchelonLocal| |zag| |simpleBounds?| - |elliptic| |curry| |asin| |unitsColorDefault| |makeRecord| - |OMunhandledSymbol| |stoseInvertibleSet| |OMgetEndApp| |dominantTerm| - |coef| |mainMonomials| |generalSqFr| |tubeRadius| |intcompBasis| - |getRef| |acos| |ceiling| |htrigs| |setleft!| |SFunction| - |printingInfo?| |permutation| |totalGroebner| |qinterval| - |orthonormalBasis| |cycleRagits| |atan| |powerAssociative?| - |permutationGroup| |ef2edf| |exprToGenUPS| |virtualDegree| - |factorList| |title| |modifyPointData| |Is| |overbar| |resultantnaif| - |acot| |copy!| |fixedPointExquo| |cAcsch| |c05nbf| |plot| |curveColor| - |f02bbf| |numerators| |pseudoQuotient| |hcrf| |asec| |basicSet| - |irreducible?| |selectOptimizationRoutines| |numeric| |finite?| - |fortranCompilerName| |difference| |symmetricRemainder| - |decomposeFunc| |rootsOf| |conical| |polyPart| |acsc| |typeLists| - |newLine| |zeroDimPrimary?| |setAttributeButtonStep| |radical| - |cschIfCan| |KrullNumber| |degree| |e| |semiSubResultantGcdEuclidean1| - |derivative| |putColorInfo| |f01rdf| |sinh| |dAndcExp| |minimumDegree| - |tan2trig| |iiatanh| |createZechTable| |highCommonTerms| |reduceLODE| - |clearFortranOutputStack| |s17ahf| |particularSolution| |cosh| - |eulerE| |makeprod| |bombieriNorm| |infieldint| |directSum| |index?| - |argumentListOf| |linearMatrix| |tree| |besselK| * |frobenius| |tanh| - |alternative?| |mapmult| |e02aef| - |removeRoughlyRedundantFactorsInPols| |factorFraction| - |rationalApproximation| |node?| |integralDerivationMatrix| - |makeSeries| |rootOf| |coth| |reducedQPowers| |plus!| - |stoseSquareFreePart| |OMgetEndAtp| |addBadValue| |normalizedDivide| - |postfix| |choosemon| |redpps| |prefixRagits| |sech| |diag| - |selectIntegrationRoutines| |ocf2ocdf| |debug| |makingStats?| - |limitPlus| |mainCoefficients| |twoFactor| |prime| - |antisymmetricTensors| |csch| |pointSizeDefault| |copies| |norm| - |cAsech| D |skewSFunction| |localAbs| |stirling1| |expressIdealMember| - |weight| |addMatchRestricted| |asinh| |infRittWu?| |repSq| - |wordsForStrongGenerators| |li| |asinhIfCan| |listConjugateBases| - |c05pbf| |conditionsForIdempotents| |subspace| |fullPartialFraction| - |composite| |interval| |acosh| |equivOperands| |ode1| |pureLex| - |pointPlot| |intersect| |pointColor| |f02bjf| |appendPoint| |f01ref| - |resultantEuclideannaif| |atanh| |decimal| |rombergo| |tanh2trigh| - |fortranLinkerArgs| |quasiRegular| |positiveRemainder| |unvectorise| - |genericLeftTrace| |s17ajf| |hclf| |mapSolve| |acoth| |primaryDecomp| - |extractPoint| |iiacoth| |rootBound| |unknown| |numberOfVariables| - |resetAttributeButtons| |discriminantEuclidean| |linearPart| - |flexible?| |airyAi| |asech| |externalList| |f04jgf| |monomials| - |e02agf| |createMultiplicationTable| |extendedint| |mapCoef| - |singRicDE| |nary?| |constantOperator| |quote| |minus!| |numericIfCan| - |coleman| |solveLinearPolynomialEquationByFractions| - |removeRoughlyRedundantFactorsInPol| |entries| |returnTypeOf| - |integralRepresents| |showFortranOutputStack| |multiple| |getCurve| - |routines| |deriv| |socf2socdf| |OMgetEndAttr| |uniform| |relerror| - |child?| |primeFrobenius| |transform| |applyQuote| |computePowers| - |sayLength| |rootOfIrreduciblePoly| |entry| |cAcoth| |badValues| - |extractIfCan| |maxint| |infix| |createGenericMatrix| |f02aaf| - |allRootsOf| |expPot| |curryRight| |universe| |true| |print| - |acoshIfCan| |split!| |qelt| |leastMonomial| |setOrder| |insertMatch| - |B1solve| |quadratic| |equiv?| |mightHaveRoots| |stirling2| |totalLex| - |cyclotomicDecomposition| |c06eaf| |principalIdeal| |and| - |nonLinearPart| |subResultantGcd| |ruleset| |viewPosDefault| - |simpsono| |strongGenerators| |matrixGcd| |tan2cot| |part?| |xRange| - |genericRightDiscriminant| |makeViewport3D| |component| |makeVariable| - |lfextlimint| |traverse| |ode2| |singleFactorBound| |calcRanges| - |quasiRegular?| |yRange| |clip| |f02fjf| |innerint| |s17akf| |unit?| - |rewriteIdealWithRemainder| |rightAlternative?| |objects| |iiasech| - |bit?| |e02ahf| |aspFilename| |zRange| |bubbleSort!| SEGMENT - |contract| |supersub| |airyBi| |semiResultantEuclideannaif| |suchThat| - |leftScalarTimes!| |base| |map!| |inverseColeman| |limitedint| - |algebraicDecompose| |getButtonValue| |semiDiscriminantEuclidean| - |unary?| |lexico| |listLoops| |isPlus| |mainSquareFreePart| |qsetelt!| - |df2fi| |createMultiplicationMatrix| |interReduce| |nthCoef| - |polyRicDE| |integralCoordinates| |discreteLog| |typeList| |setnext!| - |complexNumericIfCan| |cAtanh| |prefix| |hasSolution?| |OMgetEndBind| - |key?| |printHeader| |topFortranOutputStack| |f02abf| |qPot| |gderiv| - |dec| |atanhIfCan| |binomial| |insert!| |complexSolve| |distance| - |parabolic| |pow| |cubic| |write!| |impliesOperands| |complement| - |reverseLex| |binaryFunction| |retractable?| |f07aef| |vconcat| - |leadingIndex| |quadratic?| |definingPolynomial| |curryLeft| - |trapezoidalo| |c06ebf| |tanh2coth| |point?| |setlast!| |mainMonomial| - |getOrder| |s14abf| |condition| |BasicMethod| |factorset| |refine| - |defineProperty| |cyclotomicFactorization| |latex| |acsch| |summation| - |LagrangeInterpolation| |outputAsTex| |rewriteIdealWithHeadRemainder| - |viewSizeDefault| |leftAlternative?| |generators| |approxNthRoot| - |divideIfCan!| |constant?| |genericRightTraceForm| |viewport3D| - |finiteBasis| |associates?| |rightScalarTimes!| |presuper| |concat| - |ode| |acosIfCan| |iiacsch| |fixPredicate| |clipBoolean| |f02wef| |Ei| - |pdct| |closed?| |exteriorDifferential| |mainPrimitivePart| |opeval| - |integerIfCan| |dimensionsOf| |algint| |insertionSort!| |deref| - |setprevious!| |leadingSupport| |cos2sec| |decrease| |roughBasicSet| - |transcendentalDecompose| |inspect| |chainSubResultants| |conjugates| - |schema| |diagonalProduct| |previous| |tower| |lookup| |isTimes| - |modularFactor| |binomThmExpt| |createLowComplexityTable| - |OMgetEndBVar| |repeatUntilLoop| |ricDsolve| |iflist2Result| - |monicDecomposeIfCan| |inv| |triangulate| |FormatArabic| |implies?| - |e01bef| |linSolve| |property| |interpretString| |polygon| - |symbolIfCan| |returnType!| |basisOfLeftNucleus| |ground?| |cLog| - |argumentList!| |sup| |compose| |stosePrepareSubResAlgo| - |bezoutMatrix| |complexRoots| |nodes| |parabolicCylindrical| - |realRoots| |ground| |quatern| |reducedContinuedFraction| |read!| - |closeComponent| |operators| |OMputSymbol| |squareMatrix| |printCode| - |makeFloatFunction| |hconcat| |leadingExponent| |unaryFunction| - |writeByteIfCan!| |leadingMonomial| |antiAssociative?| |tablePow| - |constantRight| |singular?| |perfectSquare?| |tanAn| |units| - |distFact| |s14baf| |quasiMonic?| |less?| |exquo| |monic?| - |leadingCoefficient| |rewriteSetWithReduction| |complexNumeric| - |times!| |middle| |atanIfCan| |leftTraceMatrix| |reverse!| |rootSplit| - |baseRDE| |factorials| |psolve| |div| |abs| |wrregime| - |primitiveMonomials| |kernels| |evaluateInverse| |intChoose| - |solveRetract| |principal?| |root| |genericLeftDiscriminant| - |viewDeltaYDefault| |gbasis| |quo| |viewDeltaXDefault| |reductum| - |primlimintfrac| |cycle| |Aleph| |cosh2sech| |contours| |output| - |taylorIfCan| |style| |f02xef| |toScale| |linGenPos| |e04ycf| - |univariate| |phiCoord| |integrate| |approximants| |central?| - |useSingleFactorBound?| |maxPoints| |mirror| |formula| |compile| - |algintegrate| |check| |rem| |ref| |palgintegrate| |diagonal| - |OMwrite| |target| |iisinh| |e01bff| |code| |changeWeightLevel| - |hexDigit?| |shuffle| |pdf2ef| |resultantReduit| |generalPosition| - |cyclic?| |iiperm| |stoseInternalLastSubResultant| |elementary| - |palgint| |drawComplexVectorField| |leftRankPolynomial| - |rightMinimalPolynomial| |monicCompleteDecompose| |cExp| - |solveInField| |halfExtendedResultant2| |factor| BY |mainKernel| - |prinshINFO| |gcdcofactprim| |selectAndPolynomials| |reduction| - |f04mbf| |paraboloidal| |d01gaf| |imagK| |endSubProgram| |sqrt| - |sylvesterSequence| |perfectSqrt| |f02aef| |OMgetApp| - |screenResolution3D| |indicialEquation| |closedCurve?| |nrows| - |basisOfRightNucleus| |leadingTerm| |real| |blankSeparate| - |subPolSet?| |findCycle| |bezoutResultant| |acotIfCan| |s19adf| - |tanNa| |degreeSubResultant| |aLinear| |ncols| |doubleFloatFormat| - |GospersMethod| |compiledFunction| |autoReduced?| - |createPrimitiveNormalPoly| |imag| |tubePlot| |printStatement| - |evaluate| |rightDiscriminant| |transpose| |delete| |argscript| - |ratDenom| |s15adf| |directProduct| |deepestInitial| |primintfldpoly| - |zeroMatrix| |singularAtInfinity?| |cot2trig| |shellSort| |coefChoose| - |trigs2explogs| |identification| |Beta| |critT| |rdregime| |color| - |rectangularMatrix| |useSingleFactorBound| |makeMulti| |meshPar1Var| - |structuralConstants| |lhs| |reseed| |polyRDE| |divisor| |f01brf| - |destruct| |viewZoomDefault| |po| |initializeGroupForWordProblem| - |setRow!| |e01bgf| |mainVariable| |rhs| |monomial?| |lazyPquo| - |quotientByP| |groebgen| |pointColorPalette| |diagonalMatrix| - |complexNormalize| |multiplyCoefficients| |alternating| - |stoseIntegralLastSubResultant| |iicosh| |doubleDisc| |mathieu23| - |removeZeroes| |radicalEigenvectors| |pdf2df| |palginfieldint| - |basisOfCommutingElements| |leftMinimalPolynomial| |escape| - |distribute| |lintgcd| |palgextint| |graphStates| |axes| |shufflein| - |cRationalPower| |resultantReduitEuclidean| |elliptic?| |d01gbf| - |iipow| |approxSqrt| |setMaxPoints3D| |quasiMonicPolynomials| - |reducedForm| |setRealSteps| |node| |fglmIfCan| |quotient| - |divideIfCan| |wronskianMatrix| |imagJ| |monomial| - |internalSubPolSet?| |prindINFO| |generic| |s20acf| |asecIfCan| - |OMgetAtp| |factorSquareFree| |signAround| |setelt| - |basisOfMiddleNucleus| |rdHack1| |logGamma| |initial| - |semicolonSeparate| |currentSubProgram| |multivariate| |sturmSequence| - |partialDenominators| |f02aff| |conjug| |trim| |initTable!| |f04mcf| - |degreeSubResultantEuclidean| |ellipticCylindrical| |writable?| - |expintfldpoly| |initiallyReduced?| |halfExtendedResultant1| - |variables| |binaryTree| |branchPoint?| |coth2trigh| |denomRicDE| - |aQuadratic| |copy| |closedCurve| |nextSubsetGray| |critM| |corrPoly| - |hue| |repeating?| |bezoutDiscriminant| |exponentialOrder| - |useEisensteinCriterion?| |leftDiscriminant| |makeTerm| |substring?| - |superscript| |s15aef| |f01bsf| |iteratedInitials| - |nextIrreduciblePoly| |OMread| |block| |outputSpacing| |e01bhf| - |myDegree| |uniform01| |log10| |swap!| |mappingAst| |digamma| |bsolve| - |scalarMatrix| |match?| |complexElementary| |bitand| - |LyndonCoordinates| |ptFunc| |generic?| |coordinates| - |stoseLastSubResultant| |top| |seed| |suffix?| |autoCoerce| - |useNagFunctions| |rootKerSimp| |viewPhiDefault| - |associatorDependence| |characteristic| |oneDimensionalArray| |bitior| - |functionIsFracPolynomial?| |continue| |BumInSepFFE| |rquo| |lazyPrem| - |monomRDEsys| |curveColorPalette| |totolex| |df2ef| |d02bbf| |taylor| - |movedPoints| |width| |cyclic| |iitanh| |generateIrredPoly| |polyred| - |mathieu24| |prefix?| |moduloP| |bitLength| |radicalEigenvector| - |cPower| |laurent| |internalInfRittWu?| |quoByVar| |hex| |acscIfCan| - |palglimint| |graphState| |controlPanel| |taylorRep| - |basisOfLeftAnnihilator| |sequences| |semiResultantReduitEuclidean| - |imagI| |hypergeometric0F1| |puiseux| |iidsum| |adjoint| |maxPoints3D| - |univariate?| |partialQuotients| |setImagSteps| |noKaratsuba| - |variationOfParameters| |commaSeparate| |doubleResultant| |OMreadFile| - |ord| |csc2sin| |s20adf| |OMgetAttr| |fprindINFO| |invmod| - |prolateSpheroidal| |zeroDim?| = |newSubProgram| |headReduced?| - |equation| |trigs| |useEisensteinCriterion| |rightUnits| |split| - |printInfo!| |f02agf| |semiDegreeSubResultantEuclidean| - |basisOfNucleus| |readable?| |critB| |lieAlgebra?| |boundOfCauchy| - |byte| |e01daf| |branchPointAtInfinity?| |f04qaf| - |leadingCoefficientRicDE| |aCubic| |firstSubsetGray| |lifting| - |f01maf| < |d02bhf| |extendedResultant| |optional| |completeEval| - |stoseInvertible?sqfreg| |represents| |listOfMonoms| |infix?| - |subscript| |say| |s17acf| > |deepestTail| |hermite| - |internalSubQuasiComponent?| |repeating| |problemPoints| - |outputGeneral| |normDeriv2| |normal01| |mask| |fill!| |leftRank| - |polygamma| <= |dmp2rfi| |rotatez| |nextPrimitivePoly| |complexExpand| - |implies| |quoted?| |bounds| |minimumExponent| |rational| - |rationalPoints| |seriesToOutputForm| >= |viewThetaDefault| - |iterationVar| |nullary| |sinhIfCan| |multiplyExponents| |lquo| - |associatedSystem| |pquo| |minPol| |var1Steps| |conjugate| - |primitiveElement| |round| |xor| |getDatabase| |dihedral| |iicoth| - |iidprod| |janko2| |bitCoef| |OMreadStr| |radicalEigenvalues| - |wordInGenerators| |pile| |polygon?| |match| |prinpolINFO| |csch2sinh| - |every?| |palgRDE| |name| |viewpoint| |sylvesterMatrix| |permutations| - |divide| |stronglyReduced?| + |real?| |coefficients| |setClipValue| - |eisensteinIrreducible?| |setMinPoints3D| |univariatePolynomials| - |f02ajf| |body| |distdfact| |critBonD| |karatsubaOnce| |reset| - |factors| - |getCode| |jordanAlgebra?| |e01saf| |s21baf| |OMgetBind| - |powmod| |aQuartic| |basisOfCenter| |inRadical?| |polCase| |f01mcf| - |clearTheSymbolTable| / |d02cjf| |composites| |constructorName| - |stoseInvertibleSetsqfreg| |upperCase!| |startStats!| - |uncouplingMatrices| |lastSubResultantEuclidean| |constantOpIfCan| - |exists?| |zeroDimensional?| |write| |subResultantsChain| - |completeHermite| |subQuasiComponent?| |monomRDE| |zerosOf| - |rationalPoint?| |mergeFactors| |lowerPolynomial| - |constantCoefficientRicDE| |deleteProperty!| |oblateSpheroidal| - |rotatey| |save| |lifting1| |sturmVariationsOf| |weighted| |pade| - |complexIntegrate| |minIndex| |symmetricSquare| |plenaryPower| |lift| - |scripted?| |clipPointsDefault| |finiteBound| |head| |readBytes!| - |recip| |outputFixed| |coshIfCan| |exponential1| |high| |reduce| - |rational?| |s17adf| |iCompose| |se2rfi| |nextNormalPoly| |nextPrime| - |numericalOptimization| |inR?| |mindegTerm| |maximumExponent| |assign| - |Gamma| |queue| |pointColorDefault| |fixedPoint| |OMlistCDs| |sec2cos| - |iisech| |laurentIfCan| |prem| |cosSinInfo| |nonSingularModel| - |var2Steps| |paren| |fractionPart| |complexForm| |mkIntegral| |cap| - |tryFunctionalDecomposition?| |palgLODE| |constant| |ipow| - |rubiksGroup| |bitTruth| |reduced?| |noncommutativeJordanAlgebra?| - |wordInStrongGenerators| |leftUnits| |e01sbf| |center| |any?| - |linear?| |prinb| |dimensions| |critMTonD1| |Lazard| |d02ejf| - |stFunc1| |stoseInvertible?reg| |OMgetBVar| |minPoints3D| |option?| - |f02akf| |separateDegrees| |f01qcf| |nthFactor| |insert| - |removeSuperfluousQuasiComponents| |returns| |singularitiesOf| - |s21bbf| |printStats!| |mulmod| |radicalSolve| |rotatex| |nil| |smith| - |showTheSymbolTable| |in?| |rationalFunction| |LyndonBasis| |isMult| - |t| |clearCache| |upperCase| |associatedEquations| - |semiLastSubResultantEuclidean| |has?| |convergents| |extension| - |readByteIfCan!| |lazyVariations| |subCase?| |absolutelyIrreducible?| - |c02aff| |raisePolynomial| |changeVar| |sortConstraints| |exprex| - |lazyPseudoQuotient| |prevPrime| |factorAndSplit| |factor1| |eq| |low| - |maxIndex| |resetNew| |taylorQuoByVar| |OMlistSymbols| |delta| - 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|sort| |drawComplex| |badNum| |pascalTriangle| |rischDE| |pToDmp| - |thetaCoord| |duplicates?| |HermiteIntegrate| |s19acf| |modularGcd| - |putGraph| |e02daf| |messagePrint| |realEigenvectors| |OMParseError?| - |areEquivalent?| |setScreenResolution3D| |selectOrPolynomials| - |iibinom| |semiIndiceSubResultantEuclidean| |commonDenominator| - |unrankImproperPartitions0| |resetVariableOrder| |delay| |cyclicCopy| - |topPredicate| |lepol| |indicialEquations| |bindings| |denominators| - |df2mf| |createNormalPrimitivePoly| |d01fcf| |source| - |divideExponents| |integralMatrixAtInfinity| |palgRDE0| - |constantToUnaryFunction| |sample| |testModulus| |cSinh| - |identityMatrix| |subTriSet?| |fortranLogical| |precision| |exQuo| - |f07adf| |collectUpper| |random| |heapSort| |explogs2trigs| |s01eaf| - |zeroOf| |definingInequation| |checkForZero| |mr| |square?| |s18aef| - |OMputObject| |lastSubResultantElseSplit| |curve| |meshFun2Var| - |randnum| |genericLeftNorm| |components| |null| |leftExtendedGcd| - |splitNodeOf!| |ParCond| |untab| |setColumn!| |lazyPremWithDefault| - |sin?| |case| |fintegrate| |float?| |cycleLength| |scopes| |nthFlag| - |tubePointsDefault| |bright| |symbolTable| |mix| |mathieu22| - |squareFreeLexTriangular| |rangePascalTriangle| |Zero| - |exprHasAlgebraicWeight| |realSolve| |mapGen| |rootSimp| |pushdterm| - |graphs| |diagonals| |realZeros| |e02dcf| |One| |tanQ| - |mapUnivariateIfCan| |isAbsolutelyIrreducible?| |pleskenSplit| - |toseLastSubResultant| |pushFortranOutputStack| |dark| - |unrankImproperPartitions1| |ksec| |cyclotomic| |binding| |reindex| - |setTopPredicate| |popFortranOutputStack| |varList| |variable?| - |lazyGintegrate| |clearDenominator| |ldf2vmf| |complexEigenvectors| - |OMgetSymbol| |insertRoot!| |unmakeSUP| |iisin| |lfintegrate| - |ODESolve| |outputAsFortran| |cartesian| |cAcsc| - |removeRedundantFactorsInContents| |internalAugment| |nullary?| - |palgLODE0| |curve?| |triangular?| |swapRows!| |deepCopy| |HenselLift| - |sizeMultiplication| |definingEquations| |categories| |endOfFile?| - |bfEntry| |alphanumeric?| |fortranInteger| |OMopenFile| |collect| - |getMeasure| |key| |s13aaf| |leftGcd| |elt| |newReduc| - |numberOfComputedEntries| |s18aff| |OMputEndApp| |nil?| |rightNorm| - |charthRoot| |numberOfComposites| |coefficient| |c06gcf| |rowEchelon| - |generalizedContinuumHypothesisAssumed| |remove!| |filename| |bat1| - |bandedHessian| |cross| |zeroVector| |sizePascalTriangle| - |fixedPoints| |integer?| GE |kroneckerDelta| |eigenvalues| |chvar| - |nthExponent| |not?| |halfExtendedSubResultantGcd2| |belong?| |e02ddf| - |cycleEntry| |positiveSolve| GT |any| |operation| - |inverseIntegralMatrix| |patternVariable| |generalizedInverse| - |pushucoef| |compactFraction| |parse| |mainCharacterization| - |subresultantSequence| |weakBiRank| |callForm?| LE |makeSUP| |moebius| - |toseInvertible?| |port| |clipSurface| |getSyntaxFormsFromFile| - |edf2ef| |exprHasLogarithmicWeights| |vark| LT |arity| |label| - |outputList| |invertibleSet| |characteristicSerie| - |differentialVariables| |rk4| |splitDenominator| |cAsec| - |mapMatrixIfCan| |removeRedundantFactorsInPols| |complex| - |fortranDouble| |position!| |redmat| |solve1| |power| |polar| - |setStatus| |normalizedAssociate| |OMgetType| |s18dcf| |iicos| - |tubeRadiusDefault| |fi2df| |term| |completeHensel| - |leftExactQuotient| |euler| |readIfCan!| |digit?| |subNodeOf?| - |reciprocalPolynomial| |chineseRemainder| |vertConcat| |constDsolve| - |s13acf| |coHeight| |logical?| |possiblyInfinite?| |alphanumeric| - |eigenvector| |plus| |collectUnder| |changeMeasure| |shallowCopy| - |vector| |numberOfComponents| |getMultiplicationMatrix| - |fillPascalTriangle| |c06gqf| |keys| |lowerCase?| |monomialIntegrate| - |OMopenString| |OMputEndAtp| |conditionP| |differentiate| - |zeroSquareMatrix| |e02def| |rst| |symbol?| |currentEnv| |shade| - |buildSyntax| |bat| |leftNorm| |dot| |operator| |SturmHabichtSequence| - |column| |squareFree| |withPredicates| |integralMatrix| - |irreducibleFactor| |find| |jacobian| |algebraicOf| |vedf2vef| - |getIdentifier| |odd?| |generalizedContinuumHypothesisAssumed?| - |vectorise| |pushuconst| |times| |imports| - |halfExtendedSubResultantGcd1| |surface| |cAcot| |removeConstantTerm| - |invmultisect| |search| |fortranReal| |index| |rightRecip| - |toseInvertibleSet| |partialFraction| |firstUncouplingMatrix| - |monicRightFactorIfCan| |quasiAlgebraicSet| |biRank| - |irreducibleFactors| |s18def| |invertible?| |characteristicSet| |rk4a| - |showClipRegion| |cylindrical| |leftRemainder| - |combineFeatureCompatibility| |OMencodingBinary| |option| |iitan| - |nodeOf?| |call| |regime| |extractBottom!| |sincos| |multMonom| - |extendIfCan| |mapBivariate| |readLineIfCan!| |generalizedEigenvector| - |mat| |divisors| |list| |dimension| |monom| |innerEigenvectors| |pair| - |s13adf| |safeCeiling| |box| |character?| |fixedDivisor| |rootRadius| - |monomialIntPoly| |mainVariable?| |car| |horizConcat| |term?| - |create3Space| |e02dff| |c06gsf| |normalize| |testDim| |declare| - |nthRootIfCan| |OMputEndAttr| |cdr| |showTheIFTable| - |changeThreshhold| |identitySquareMatrix| |SturmHabichtCoefficients| - 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|fullDisplay| |e02gaf| |readLine!| |log| |extractTop!| |expIfCan| - |mainVariables| |crest| |neglist| |rules| |outputAsScript| - |SturmHabicht| |doubleComplex?| |outputArgs| |schwerpunkt| - |predicates| |OMputEndBind| |first| |unparse| |squareTop| - |lSpaceBasis| |f2st| |d01ajf| |laguerre| |genericPosition| |pattern| - |truncate| |tab| |rest| |equiv| |selectMultiDimensionalRoutines| |Si| - |cAcos| |rule| |list?| |nextItem| |regularRepresentation| - |scalarTypeOf| |substitute| |minPoints| |clearTheIFTable| - |factorSquareFreePolynomial| |setref| |denominator| |primitive?| - |linearDependenceOverZ| |padecf| |removeDuplicates| |eigenvectors| - |members| |OMsetEncoding| |children| |graphCurves| |partitions| - |monicLeftDivide| |doubleRank| |lazyEvaluate| |prime?| |iprint| - |quotedOperators| |triangularSystems| |alphabetic?| |clipWithRanges| - |leftFactorIfCan| |select!| |zeroSetSplitIntoTriangularSystems| |/\\| - |maxColIndex| |lcm| |normalizeAtInfinity| |logIfCan| |message| - |Hausdorff| |leftTrace| |rk4f| |basisOfRightAnnihilator| - 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|positive?| |blue| |showIntensityFunctions| |infinityNorm| |c06ecf| - |ListOfTerms| |pointLists| |maxrank| |remainder| |hMonic| - |resultantEuclidean| |e02akf| |member?| |setrest!| |ravel| |s17def| - |presub| |viewDefaults| |makeYoungTableau| |makeSketch| |mindeg| - |reshape| |infLex?| |modTree| |open?| |bivariateSLPEBR| |mainContent| - ** |edf2df| |rangeIsFinite| |specialTrigs| |setProperties| - |increasePrecision| |unitCanonical| |padicFraction| |mpsode| |cAsinh| - |leastPower| |internalIntegrate| |limit| |optAttributes| |powers| - |totalDifferential| |makeViewport2D| |asechIfCan| |patternMatch| - |crushedSet| |permutationRepresentation| EQ |showTheFTable| - |OMcloseConn| |shanksDiscLogAlgorithm| |shrinkable| |rightExtendedGcd| - |restorePrecision| |OMgetEndError| |increase| |failed?| - |headRemainder| |fortranTypeOf| |normal?| |isExpt| |coth2tanh| - |internalDecompose| |stripCommentsAndBlanks| |pomopo!| - |pseudoRemainder| |linkToFortran| |super| |ScanArabic| |imagE| - |scaleRoots| |createLowComplexityNormalBasis| |internalIntegrate0| - |argument| |basisOfRightNucloid| |UnVectorise| |setClosed| - |orOperands| |addiag| |flatten| |LyndonWordsList| |e02baf| |c06ekf| - |symbol| |matrix| |rename| |makeGraphImage| |bits| |negative?| - |iomode| |modifyPoint| |geometric| |nextColeman| |enumerate| - |expression| |rspace| |s17dgf| |rightPower| |minrank| |associative?| - |constantLeft| |expenseOfEvaluation| |PDESolve| |maxdeg| |integer| - |userOrdered?| |setEmpty!| |algebraicCoefficients?| |viewWriteDefault| - |power!| |roman| |cCsch| |localReal?| |setfirst!| |mkcomm| - |setProperty| |multiEuclideanTree| |Nul| - |solveLinearPolynomialEquationByRecursion| |primitivePart!| |inrootof| - |infieldIntegrate| |acschIfCan| |f04axf| |isQuotient| - |genericLeftTraceForm| |signature| |categoryFrame| |unitNormal| - |clearTheFTable| |hash| |padicallyExpand| UP2UTS |rightGcd| - |functionIsContinuousAtEndPoints| - |rewriteSetByReducingWithParticularGenerators| |f04adf| |homogeneous?| - |count| |linearlyDependent?| |partition| |roughUnitIdeal?| |cn| - |viewport2D| |idealiser| |removeCosSq| |OMgetEndObject| |mesh?| - |lprop| |not| |systemCommand| |completeEchelonBasis| |OMconnInDevice| - |sub| |reflect| |physicalLength!| |setleaves!| |shiftRoots| - |antiCommutator| |setPrologue!| |morphism| |optpair| |empty| |tube| - |basis| |isPower| |equality| |e02bbf| |makeCos| |patternMatchTimes| - |mapExponents| |double| |shiftLeft| |setLegalFortranSourceExtensions| - |unitNormalize| |FormatRoman| |or?| |continuedFraction| |c06fpf| - |nextLatticePermutation| |height| |decompose| |constantKernel| - |basisOfCentroid| |normal| |Vectorise| |derivationCoordinates| |imagk| - |lazyIntegrate| |hasHi| |numberOfOperations| |representationType| - |setOfMinN| |outerProduct| |rename!| |leader| |graphImage| |zero?| - |purelyTranscendental?| |close!| |addPointLast| |cSech| - |LyndonWordsList1| |RemainderList| |vspace| |s17dhf| |exponents| - |minset| |antiCommutative?| |twist| |pushdown| |rischNormalize| - |ridHack1| |largest| |directory| |setStatus!| |fTable| - |viewWriteAvailable| |gradient| |recoverAfterFail| - |rightExactQuotient| |limitedIntegrate| |leftFactor| - |polarCoordinates| |setProperties!| |complexZeros| |roughEqualIdeals?| - |factorByRecursion| |nextsubResultant2| |removeSinSq| - |rewriteIdealWithQuasiMonicGenerators| |cycleSplit!| - |genericRightNorm| |linearDependence| |ratPoly| |rarrow| - |numberOfFractionalTerms| UTS2UP |degreePartition| |nothing| - |functionIsOscillatory| |OMgetInteger| |f04arf| |declare!| - |createRandomElement| |lfextendedint| |unitVector| |physicalLength| - |getPickedPoints| |e02bcf| |idealiserMatrix| |setTex!| |cond| |llprop| - |getBadValues| |unit| |complete| |reify| |rroot| |nextPartition| - |makeSin| |bernoulli| |balancedFactorisation| |brace| |shiftRight| - |one?| |OMconnOutDevice| |normalElement| |ScanRoman| |replace| - |edf2efi| |c06fqf| |commutator| |linearAssociatedLog| |groebSolve| - |purelyAlgebraic?| |compound?| |andOperands| |nlde| |cCoth| |elements| - |upDateBranches| |constantIfCan| |s17dlf| |unravel| |iisqrt2| - |reopen!| |imagj| |pushup| |alphabetic| |unexpand| |stop| |mainValue| - |failed| |setCondition!| |palgint0| |setPoly| |setsubMatrix!| - |addPoint2| |rightRemainder| |realElementary| |createPrimitiveElement| - |hspace| |value| |getProperties| |roughSubIdeal?| |augment| - |commutative?| |showTheRoutinesTable| |removeCoshSq| - |extendedIntegrate| |lyndonIfCan| |more?| |solveLinear| |flagFactor| - |nextSublist| |divergence| |factorSquareFreeByRecursion| - |factorOfDegree| |OMgetFloat| |interpolate| |imaginary| - |cyclicSubmodule| |splitSquarefree| |var1StepsDefault| - |LazardQuotient2| LODO2FUN |e02bdf| |rightFactorCandidate| - |squareFreeFactors| |genericRightTrace| |resetBadValues| - |divisorCascade| |prepareSubResAlgo| |radPoly| |nthFractionalTerm| - |numberOfImproperPartitions| |setEpilogue!| |concat!| |f04asf| - |karatsubaDivide| |rootPower| |iisqrt3| |flexibleArray| |colorDef| - |dfRange| |changeName| |iiGamma| |or| |lllp| |lflimitedint| |s18acf| - |palgextint0| |length| |separant| |qroot| |cTanh| |moduleSum| |c06frf| - |mapDown!| |qualifier| |scripts| |pole?| |roughBase?| - |minimalPolynomial| |ScanFloatIgnoreSpaces| |reducedDiscriminant| - |chebyshevT| |replaceKthElement| |linearAssociatedOrder| |setValue!| - |OMconnectTCP| |OMputBVar| |and?| |powern| |rightQuotient| - |associator| |triangSolve| |kovacic| |setProperty!| |getOperands| - |bumptab| |rightUnit| |imagi| |removeSinhSq| |validExponential| - |preprocess| |mainDefiningPolynomial| - |inverseIntegralMatrixAtInfinity| |reducedSystem| |sqfrFactor| - |generator| |subMatrix| |addPoint| |factorsOfDegree| |hexDigit| - |varselect| |superHeight| |standardBasisOfCyclicSubmodule| |exponent| - |normalDenom| |rightCharacteristicPolynomial| |deleteRoutine!| - |e02bef| |tableForDiscreteLogarithm| |univariatePolynomialsGcds| - |bfKeys| |setVariableOrder| |hasTopPredicate?| |lastSubResultant| - |internalLastSubResultant| |laplacian| |randomR| |subSet| |lyndon| - |OMgetVariable| |nand| |goto| |monicDivide| |iiexp| |overset?| - |LazardQuotient| RF2UTS |dflist| |nullSpace| |prologue| |solid| - |fortranComplex| |palglimint0| |var2StepsDefault| |rootPoly| - |firstNumer| |cCosh| |iiabs| |measure| |genericRightMinimalPolynomial| - |graeffe| |trivialIdeal?| |elseBranch| |intensity| |idealSimplify| - |c06fuf| |cycleTail| |f04atf| |computeBasis| |rootProduct| - |OMputError| |digit| |froot| |rightLcm| |exprHasWeightCosWXorSinWX| - |incrementKthElement| |lllip| |eigenMatrix| |lfinfieldint| |f04faf| - |bumptab1| |isobaric?| |ScanFloatIgnoreSpacesIfCan| - |expandTrigProducts| |nil| |infinite| |arbitraryExponent| - |approximate| |complex| |shallowMutable| |canonical| |noetherian| - |central| |partiallyOrderedSet| |arbitraryPrecision| - |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| - |additiveValuation| |unitsKnown| |canonicalUnitNormal| - |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| - |commutative|)
\ No newline at end of file + |Record| |Union| |separateDegrees| |maxColIndex| |rightLcm| |comment| + |bernoulliB| |lo| |karatsuba| |halfExtendedSubResultantGcd2| + |iteratedInitials| |physicalLength!| |innerSolve| |obj| + |normalizeAtInfinity| |f01qcf| |exprHasWeightCosWXorSinWX| |sinh2csch| + |balancedBinaryTree| |nextIrreduciblePoly| |belong?| |incr| + |setleaves!| |factorGroebnerBasis| |aspFilename| |cache| |nthFactor| + |logIfCan| |incrementKthElement| |iiacosh| |totalfract| |e02ddf| |hi| + |OMread| |shiftRoots| |listexp| |bubbleSort!| |charpol| + |removeSuperfluousQuasiComponents| |Hausdorff| |lllip| + |symmetricPower| |block| |cycleEntry| |antiCommutator| + |createThreeSpace| |contract| |returns| |leftTrace| |nthr| |char| + |eigenMatrix| |indices| |shift| |mkAnswer| |setPrologue!| |supersub| + |singularitiesOf| |rk4f| |lfinfieldint| |coefChoose| |s01eaf| + |symbolTableOf| |fortran| |depth| |morphism| |iiatan| |airyBi| + |basisOfRightAnnihilator| |s21bbf| |f04faf| |f01rcf| |zeroOf| + |trigs2explogs| |optpair| |bumprow| |semiResultantEuclideannaif| + |safetyMargin| |printStats!| |bumptab1| |s17agf| |identification| + |definingInequation| ~ |romberg| |empty| |tail| |leftScalarTimes!| + |isobaric?| |relativeApprox| |checkForZero| |Beta| |diff| |tube| + |inverseColeman| |factors| |ReduceOrder| |ScanFloatIgnoreSpacesIfCan| + |float| |xn| |critT| |square?| |open| |basis| |e04jaf| |limitedint| + |coord| |getCode| |cAtan| |expandTrigProducts| |int| |s18aef| + |rdregime| |UP2ifCan| |isPower| |f01qdf| |algebraicDecompose| + |rightRank| |jordanAlgebra?| |beauzamyBound| |OMputObject| |color| + |getButtonValue| |frst| |e01saf| |compBound| |pmintegrate| + |rectangularMatrix| |lastSubResultantElseSplit| |totalDifferential| + |selectFiniteRoutines| |external?| |semiDiscriminantEuclidean| + |linear| |s21baf| |numer| |irreducibleRepresentation| |chiSquare| + |useSingleFactorBound| |curve| |makeViewport2D| |perspective| |unary?| + |numberOfMonomials| |OMgetBind| |denom| |log2| |makeMulti| + |meshFun2Var| |rightDivide| |asechIfCan| |generate| |lexico| + |polynomial| |powmod| |solve| |dn| |setchildren!| |meshPar1Var| + |randnum| |patternMatch| F |clipParametric| |listLoops| |aQuartic| + |pi| |denomLODE| |lllp| |genericLeftNorm| |groebner?| |besselI| |erf| + |structuralConstants| |incrementBy| |crushedSet| |basisOfCenter| + |rightTrace| |isPlus| |lflimitedint| |infinity| |cSin| |union| + |processTemplate| |ParCondList| |reseed| |components| |script| + |permutationRepresentation| |expand| |mainSquareFreePart| |inRadical?| + |coordinate| |createNormalPoly| |s18acf| |showTheFTable| |csubst| + |leftExtendedGcd| |polyRDE| |squareFreePrim| |filterWhile| |mantissa| + |getConstant| |df2fi| |polCase| |status| |palgextint0| |OMUnknownCD?| + |divisor| |leastAffineMultiple| |dilog| |OMcloseConn| |splitNodeOf!| + |debug3D| |filterUntil| |shanksDiscLogAlgorithm| + |createMultiplicationMatrix| |kernel| |f01mcf| |radicalSimplify| + |separant| |normalizeIfCan| |f01brf| |selectfirst| |ParCond| |tex| + |sin| |options| |bottom!| |select| |draw| |interReduce| |row| |level| + |clearTheSymbolTable| |lexTriangular| |qroot| |e02adf| |result| + |untab| |cos| |viewZoomDefault| |shrinkable| |gcdPolynomial| |nthCoef| + |reduceBasisAtInfinity| |d02cjf| |cTanh| |stopTableInvSet!| + |setColumn!| |satisfy?| |po| |tan| |rightExtendedGcd| + |collectQuasiMonic| |s19aaf| |polyRicDE| |optimize| |composites| + |moduleSum| |makeUnit| |bivariatePolynomials| NOT + |initializeGroupForWordProblem| |lazyPremWithDefault| |string| |cot| + |tanintegrate| |restorePrecision| |dom| |integralCoordinates| + |toseSquareFreePart| |stoseInvertibleSetsqfreg| |c06frf| |OMputString| + |setRow!| |rowEchelonLocal| OR |sin?| |sec| |OMgetEndError| + |hdmpToDmp| |makeObject| |discreteLog| |sequence| |upperCase!| + |mapDown!| |trapezoidal| |e01bgf| |zag| AND |csc| |fintegrate| + |increase| |d02raf| |typeList| |bandedJacobian| |startStats!| + |outputForm| |qualifier| |simpleBounds?| |makeRecord| |mainVariable| + |float?| |asin| |OMputAttr| |failed?| |uncouplingMatrices| |setnext!| + |rightFactorIfCan| |coef| |pole?| |enqueue!| |elliptic| |acos| + |cycleLength| |monomial?| |headRemainder| |enterInCache| + |complexNumericIfCan| |leftQuotient| |lastSubResultantEuclidean| + |setelt!| |roughBase?| |scopes| |curry| |lazyPquo| |atan| + |innerSolve1| |fortranTypeOf| |constantOpIfCan| |cAtanh| + |minimalPolynomial| |mkPrim| |cyclicEntries| |title| |nthFlag| + |unitsColorDefault| |quotientByP| |acot| |normal?| |connect| + |hasSolution?| |exists?| |even?| |freeOf?| |ScanFloatIgnoreSpaces| + |size?| |groebgen| |OMunhandledSymbol| |asec| |tubePointsDefault| + |kmax| |isExpt| |numeric| |OMgetEndBind| |zeroDimensional?| + |updateStatus!| |reducedDiscriminant| |rischDEsys| |pointColorPalette| + |complexEigenvalues| |stoseInvertibleSet| |mix| |acsc| |npcoef| + |coth2tanh| |e| |radical| |key?| |leftRecip| |subResultantsChain| + |chebyshevT| |midpoints| |diagonalMatrix| |OMgetEndApp| |sinh| + |mathieu22| |companionBlocks| |internalDecompose| |printHeader| + |completeHermite| |medialSet| |showScalarValues| |replaceKthElement| + |squareFreeLexTriangular| |dominantTerm| |cosh| |complexNormalize| + |branchIfCan| |stripCommentsAndBlanks| |topFortranOutputStack| + |integral| |subQuasiComponent?| |linearAssociatedOrder| |tanSum| + |rangePascalTriangle| |tree| |mainMonomials| * |tanh| + |multiplyCoefficients| |pomopo!| |nativeModuleExtension| |f02abf| + |monomRDE| |extendedSubResultantGcd| |quickSort| |setValue!| + |alternating| |generalSqFr| |exprHasAlgebraicWeight| |coth| + |pseudoRemainder| |extensionDegree| |qPot| |spherical| |zerosOf| + |OMconnectTCP| |extractIndex| |tubeRadius| + |stoseIntegralLastSubResultant| |sech| |realSolve| |green| + |linkToFortran| |debug| |gderiv| |rationalPoint?| |algebraicVariables| + |OMputBVar| |writeBytes!| |iicosh| |intcompBasis| |mapGen| |csch| + |super| |semiResultantEuclidean2| D |atanhIfCan| |mergeFactors| + |lazyIrreducibleFactors| |fortranDoubleComplex| |and?| |rootSimp| + |getRef| |doubleDisc| |asinh| |euclideanGroebner| |ScanArabic| |li| + |binomial| |lowerPolynomial| |multisect| |diagonal?| |powern| + |pushdterm| |ceiling| |mathieu23| |acosh| |imagE| |errorInfo| + |insert!| |iicot| |constantCoefficientRicDE| |rightQuotient| + |baseRDEsys| |atanh| |htrigs| |removeZeroes| |graphs| |scaleRoots| + |oddInfiniteProduct| |complexSolve| |deleteProperty!| + |generalizedEigenvectors| |countable?| |associator| |setleft!| + |rightZero| |radicalEigenvectors| |acoth| |diagonals| + |linearAssociatedExp| |createLowComplexityNormalBasis| + |oblateSpheroidal| |distance| |unknown| |invertibleElseSplit?| + |rightTraceMatrix| |triangSolve| |basisOfLeftNucloid| |SFunction| + |pdf2df| |realZeros| |asech| |iiacos| |internalIntegrate0| |parabolic| + |rotatey| |rk4qc| |kovacic| |pastel| |printingInfo?| |palginfieldint| + |e02dcf| |integralAtInfinity?| |argument| |pow| |lifting1| + |gcdPrimitive| |setProperty!| |seriesSolve| |basisOfCommutingElements| + |permutation| |tanQ| |multiple| |basisOfRightNucloid| |updatF| |cubic| + |build| |sturmVariationsOf| |meshPar2Var| |getOperands| + |leftMinimalPolynomial| |totalGroebner| |applyQuote| + |mapUnivariateIfCan| |UnVectorise| |expint| |entry| |write!| + |safeFloor| |weighted| |bumptab| |stronglyReduce| |qinterval| |escape| + |isAbsolutelyIrreducible?| |numberOfNormalPoly| |setClosed| + |sparsityIF| |rightUnit| |print| |impliesOperands| |pade| |qelt| + |true| |d01bbf| |orthonormalBasis| |pleskenSplit| |distribute| + |e04gcf| |orOperands| |complement| |complexIntegrate| |imagi| + |OMencodingSGML| |cycles| |and| |lintgcd| |cycleRagits| + |toseLastSubResultant| |ruleset| |addiag| |direction| |inverseLaplace| + |reverseLex| |minIndex| |xRange| |solveid| |removeSinhSq| + |powerAssociative?| |palgextint| |dark| |ratpart| |LyndonWordsList| + |eulerPhi| |binaryFunction| |symmetricSquare| |yRange| + |validExponential| |modulus| |moebiusMu| |permutationGroup| + |unrankImproperPartitions1| |graphStates| |e02baf| |objects| + |plenaryPower| |s18adf| |retractable?| |sqfree| |zRange| |preprocess| + SEGMENT |ef2edf| |ksec| |commutativeEquality| |suchThat| |axes| + |c06ekf| |base| |map!| |f07aef| |sinhcosh| |scripted?| |nsqfree| + |mainDefiningPolynomial| |exprToGenUPS| |shufflein| |cyclotomic| + |atrapezoidal| |rename| |qsetelt!| |vconcat| |clipPointsDefault| + |showRegion| |inverseIntegralMatrixAtInfinity| |setMaxPoints| + |virtualDegree| |binding| |cRationalPower| |makeGraphImage| + |internal?| |leadingIndex| |prefix| |finiteBound| |s14aaf| F2FG + |reducedSystem| |reindex| |resultantReduitEuclidean| |bits| |pop!| + |quadratic?| |fullDisplay| |dec| |head| |sqfrFactor| + |lazyPseudoDivide| |wreath| |elliptic?| |setTopPredicate| |qfactor| + |negative?| |redPol| |definingPolynomial| |readBytes!| |e02gaf| + |subMatrix| |Lazard2| |OMgetObject| |d01gbf| |variable?| |iomode| + |explicitEntries?| |weights| |curryLeft| |recip| |readLine!| + |moreAlgebraic?| |addPoint| |multinomial| |condition| |iipow| + |lazyGintegrate| |genericLeftMinimalPolynomial| |modifyPoint| + |extractTop!| |outputFixed| |acsch| |factorsOfDegree| + |univariatePolynomial| |lexGroebner| |approxSqrt| |clearDenominator| + |cotIfCan| |geometric| |computePowers| |expIfCan| |coshIfCan| + |hexDigit| |f07fef| |splitLinear| |ldf2vmf| |setMaxPoints3D| + |certainlySubVariety?| |nextColeman| |concat| |sayLength| + |mainVariables| |exponential1| |varselect| |mainExpression| + |anticoord| |complexEigenvectors| |quasiMonicPolynomials| + |scanOneDimSubspaces| |enumerate| |rootOfIrreduciblePoly| |high| + |crest| |superHeight| |findBinding| |inf| |copyInto!| |rspace| + |cAcoth| |neglist| |numericalIntegration| |rational?| + |standardBasisOfCyclicSubmodule| |localIntegralBasis| + |OMsupportsSymbol?| |localUnquote| |elementary| |previous| |tower| + |s17dgf| |parent| |badValues| |partialNumerators| |s17adf| + |outputAsScript| |exponent| |mathieu12| |palgint| |orbit| |inv| + |outlineRender| |gethi| |rightPower| |extractIfCan| |bipolar| + |property| |iCompose| |SturmHabicht| |normalDenom| |radix| |setright!| + |drawComplexVectorField| |ground?| |trailingCoefficient| |d01anf| + |minrank| |maxint| |leviCivitaSymbol| |createNormalElement| + |rightCharacteristicPolynomial| |ground| |trueEqual| + |leftRankPolynomial| |backOldPos| |associative?| |nthExpon| + |minRowIndex| |infix| |fill!| |rk4a| |iilog| |e04ucf| |deleteRoutine!| + |rightMinimalPolynomial| |usingTable?| |primextintfrac| + |leadingMonomial| |constantLeft| |f04maf| |completeSmith| |leftRank| + |createGenericMatrix| |showClipRegion| |units| |subscriptedVariables| + |swapColumns!| |getProperty| |e02bef| |makeCrit| |exquo| + |leadingCoefficient| |monicCompleteDecompose| |complexNumeric| + |expenseOfEvaluation| |OMreceive| |f02aaf| |cylindrical| |polygamma| + |computeInt| |merge| |iiacsc| |tableForDiscreteLogarithm| |div| |move| + |cExp| |primitiveMonomials| |kernels| |allRootsOf| |leftRemainder| + |dmp2rfi| |gcdcofact| |goodnessOfFit| |univariatePolynomialsGcds| + |empty?| |getStream| |quo| |solveInField| |reductum| |d01alf| |create| + |combineFeatureCompatibility| |expPot| |rotatez| |output| + |factorsOfCyclicGroupSize| |bfKeys| |powerSum| |drawComplex| + |gramschmidt| |halfExtendedResultant2| |univariate| |tensorProduct| + |hostPlatform| |mainKernel| |nextPrimitivePoly| |curryRight| |formula| + |OMencodingBinary| |compile| |enterPointData| |setVariableOrder| |sh| + |rem| |simplify| |exp1| |badNum| |setFormula!| |target| |iitan| + |universe| |code| |complexExpand| |OMgetString| |nextsousResultant2| + |pascalTriangle| |prinshINFO| |setvalue!| |quartic| |alphabetic| + |acoshIfCan| |quoted?| |nodeOf?| |legendreP| |mainForm| |iroot| + |stFuncN| |gcdcofactprim| |rischDE| |insertTop!| |factor| BY + |integerBound| |split!| |regime| |bounds| |permanent| |unexpand| + |tracePowMod| |expintegrate| |pToDmp| |selectAndPolynomials| |sqrt| + |squareFreePolynomial| |extractBottom!| |leastMonomial| + |leftCharacteristicPolynomial| |minimumExponent| |mainValue| + |cyclicEqual?| |nrows| |f2df| |reduction| |real| |thetaCoord| + |leftLcm| |evenInfiniteProduct| |minPoly| |setOrder| |rational| + |sincos| |setCondition!| |getExplanations| |ncols| |exprToUPS| + |duplicates?| |f04mbf| |imag| |getMatch| |squareFreePart| + |rationalPoints| |leftRegularRepresentation| |insertMatch| |multMonom| + |palgint0| |delete| |sech2cosh| |paraboloidal| |tRange| + |directProduct| |HermiteIntegrate| |changeNameToObjf| |integral?| + |seriesToOutputForm| |B1solve| |lyndon?| |extendIfCan| |setPoly| + |integralBasis| |colorFunction| |d01gaf| |s19acf| |An| + |transcendenceDegree| |mapBivariate| |setsubMatrix!| |quadratic| |lhs| + |viewThetaDefault| |wholeRagits| |epilogue| |euclideanNormalForm| + |f02axf| |modularGcd| |imagK| |packageCall| |destruct| |drawToScale| + |iterationVar| |equiv?| |rhs| |readLineIfCan!| |monicModulo| + |addPoint2| |is?| |endSubProgram| |putGraph| |numberOfPrimitivePoly| + |scale| |generalizedEigenvector| |mightHaveRoots| |nullary| + |rightRemainder| |headReduce| |subHeight| |overlap| |e02daf| + |sylvesterSequence| |changeBase| |cot2tan| |stirling2| + |realElementary| |mat| |sinhIfCan| |fortranCharacter| |pr2dmp| + |wholeRadix| |perfectSqrt| |messagePrint| |cardinality| + |fortranLiteralLine| |createPrimitiveElement| |totalLex| |divisors| + |multiplyExponents| |lagrange| |nthRoot| |node| |polynomialZeros| + |iiasin| |jacobiIdentity?| |f02aef| |realEigenvectors| |monomial| + |poisson| |cyclotomicDecomposition| |perfectNthRoot| |hessian| + |firstDenom| |dimension| |lquo| |hspace| |setelt| |initial| |tValues| + |checkRur| |mapExpon| |OMgetApp| |OMParseError?| |multivariate| + |discriminant| |associatedSystem| |coerceP| |c06eaf| + |innerEigenvectors| |stoseInvertibleSetreg| |getProperties| + |factorSFBRlcUnit| |PollardSmallFactor| |c05adf| |screenResolution3D| + |areEquivalent?| |variables| |asimpson| |tryFunctionalDecomposition| + |consnewpol| |principalIdeal| |s13adf| |pquo| |roughSubIdeal?| |copy| + |s21bdf| |indicialEquation| |setScreenResolution3D| |positive?| + |birth| |applyRules| |nonLinearPart| |bringDown| |safeCeiling| + |minPol| |augment| |substring?| |addmod| |selectOrPolynomials| + |closedCurve?| |blue| |e04fdf| |var1Steps| |commutative?| + |subResultantGcd| |log10| |character?| |mathieu11| |nullity| + |basisOfRightNucleus| |contractSolve| |iibinom| |explicitlyEmpty?| + |showIntensityFunctions| |match?| |knownInfBasis| |bitand| + |fixedDivisor| |conjugate| |top| |viewPosDefault| + |showTheRoutinesTable| |suffix?| |autoCoerce| |getVariableOrder| + |pseudoDivide| |leadingTerm| |semiIndiceSubResultantEuclidean| + |infinityNorm| |omError| |bitior| |rootRadius| |intermediateResultsIF| + |simpsono| |continue| |primitiveElement| |s17aef| |removeCoshSq| + |jacobi| |overlabel| |blankSeparate| |commonDenominator| |c06ecf| + |taylor| |width| |extendedIntegrate| |monomialIntPoly| + |strongGenerators| |d01asf| |round| |prefix?| |bracket| |d02kef| + |newTypeLists| |subPolSet?| |unrankImproperPartitions0| |laurent| + |ListOfTerms| |matrixGcd| |lyndonIfCan| |getDatabase| |mainVariable?| + |asinIfCan| |lineColorDefault| |pointLists| |zeroDimPrime?| + |findCycle| |resetVariableOrder| |puiseux| |meatAxe| |dihedral| + |tan2cot| |gcdprim| |horizConcat| |more?| |subResultantChain| + |invertIfCan| |bezoutResultant| |delay| |sort!| |maxrank| |iicoth| + |part?| |solveLinear| |term?| |pushNewContour| |magnitude| |acotIfCan| + = |sechIfCan| |cyclicCopy| |remainder| |equation| |pointData| + |iidprod| |genericRightDiscriminant| |flagFactor| |create3Space| + |e01sef| |getGoodPrime| |symmetricDifference| |s19adf| |topPredicate| + |hMonic| |countRealRootsMultiple| |c06gbf| |makeViewport3D| |e02dff| + |janko2| |nextSublist| |drawStyle| |lepol| |lowerCase| < |tanNa| + |resultantEuclidean| |maxRowIndex| |optional| |credPol| |component| + |bitCoef| |c06gsf| |divergence| |infix?| |setButtonValue| |say| + |indicialEquations| > |degreeSubResultant| |e02akf| |nonQsign| + |makeVariable| |leadingIdeal| |normalize| |OMreadStr| |mask| + |factorSquareFreeByRecursion| |bindings| + |semiSubResultantGcdEuclidean2| <= |aLinear| |member?| + |prepareDecompose| |lfextlimint| |implies| |testDim| + |radicalEigenvalues| |factorOfDegree| |algebraicSort| |denominators| + |toroidal| |doubleFloatFormat| >= |setAdaptive| |setrest!| |traverse| + |wordInGenerators| |nthRootIfCan| |OMgetFloat| |makeop| |deepExpand| + |df2mf| |GospersMethod| |s17def| |removeRedundantFactors| |xor| |ode2| + |OMputEndAttr| |pile| |adaptive3D?| |interpolate| |euclideanSize| + |setLabelValue| |initials| |createNormalPrimitivePoly| + |compiledFunction| |presub| |match| |imaginary| |singleFactorBound| + |showTheIFTable| |polygon?| |name| |algebraic?| |linears| |d01fcf| + |totalDegree| |autoReduced?| + |viewDefaults| + |integralLastSubResultant| |recolor| |calcRanges| |prinpolINFO| + |changeThreshhold| |cyclicSubmodule| |body| |getlo| + |createPrimitiveNormalPoly| |selectPDERoutines| |reset| + |divideExponents| - |makeYoungTableau| |getOperator| |quasiRegular?| + |identitySquareMatrix| |csch2sinh| |splitSquarefree| |getGraph| + |makeSketch| |tubePlot| |integralMatrixAtInfinity| |getZechTable| + |leftUnit| / |ffactor| |lowerCase!| |constructorName| |clip| |every?| + |SturmHabichtCoefficients| |e04naf| |var1StepsDefault| + |radicalOfLeftTraceForm| |printStatement| |infinite?| |write| + |palgRDE0| |coerceListOfPairs| |mindeg| |octon| |f02fjf| |palgRDE| + |string?| |ignore?| |LazardQuotient2| |leftOne| + |constantToUnaryFunction| |save| |trunc| |host| |evaluate| |infLex?| + |tanhIfCan| |innerint| |explicitlyFinite?| |viewpoint| |lift| |dmpToP| + LODO2FUN |ran| |rightDiscriminant| |sample| |modTree| |OMputEndObject| + |sylvesterMatrix| |s17akf| |iifact| |setPredicates| |e02bdf| |reduce| + |indicialEquationAtInfinity| |testModulus| |transpose| |open?| + |clikeUniv| |unit?| |permutations| |setMinPoints| + |rightFactorCandidate| |expandLog| |fracPart| |cSinh| |argscript| + |nor| |bivariateSLPEBR| |rewriteIdealWithRemainder| |divide| |tab1| + |iiasec| |squareFreeFactors| |figureUnits| |ratDenom| |identityMatrix| + |mainContent| |primPartElseUnitCanonical!| |solid?| + |rightAlternative?| |solveLinearPolynomialEquation| |stronglyReduced?| + |constant| |genericRightTrace| |s19abf| |s15adf| |subTriSet?| |edf2df| + |cSec| |iiasech| |algSplitSimple| |center| |numberOfChildren| |real?| + |modularGcdPrimitive| |resetBadValues| |fortranLogical| + |deepestInitial| |rangeIsFinite| |d01amf| |bit?| |Ci| |coefficients| + |divisorCascade| |determinant| |specialTrigs| |primintfldpoly| |exQuo| + |insert| |evenlambert| |besselJ| |e02ahf| |setClipValue| |df2st| + |explimitedint| |prepareSubResAlgo| |setProperties| |nil| |zeroMatrix| + |f07adf| |logpart| |f07fdf| |space| |getMultiplicationTable| + |eisensteinIrreducible?| |t| |clearCache| |radPoly| |realEigenvalues| + |cycleElt| |singularAtInfinity?| |collectUpper| |increasePrecision| + |removeRoughlyRedundantFactorsInContents| |pointColor| + |setMinPoints3D| |linearlyDependentOverZ?| |numberOfFactors| + |nthFractionalTerm| |heapSort| |cot2trig| |unitCanonical| |inverse| + |f02bjf| |nilFactor| |eq| |univariatePolynomials| + |sumOfKthPowerDivisors| |numberOfImproperPartitions| |shellSort| + |explogs2trigs| |elColumn2!| |retract| |padicFraction| |approximate| + |delta| Y |appendPoint| |iter| |f02ajf| |extend| + |extractSplittingLeaf| |setEpilogue!| |abelianGroup| |mpsode| |f01ref| + |distdfact| |OMclose| |minGbasis| |concat!| |rewriteSetWithReduction| + |cAsinh| |back| |resultantEuclideannaif| |close| |upperCase?| + |critBonD| |f04asf| |indiceSubResultantEuclidean| |eval| |times!| + |systemSizeIF| |leastPower| |decimal| |karatsubaOnce| |scan| + |att2Result| |karatsubaDivide| |middle| |internalIntegrate| |null?| + |rombergo| |display| |rootPower| |rCoord| |atanIfCan| |limit| + |tanIfCan| |tanh2trigh| |eigenvector| |maxPoints3D| |kind| |iisqrt3| + |showAllElements| |leftTraceMatrix| |optAttributes| |minimize| + |retractIfCan| |fortranLinkerArgs| |collectUnder| |univariate?| + |forLoop| |exp| |flexibleArray| |op| |reverse!| |reorder| |lambda| + |powers| |partialQuotients| |quasiRegular| |dim| |changeMeasure| + |e01baf| |colorDef| |rootSplit| |positiveRemainder| |setImagSteps| + |shallowCopy| |dfRange| |ramifiedAtInfinity?| |baseRDE| |identity| + |groebner| |input| |unvectorise| |numberOfComponents| |noKaratsuba| + |changeName| |selectPolynomials| |extract!| |factorials| |showSummary| + |wholePart| |solveLinearlyOverQ| |genericLeftTrace| |library| + |getMultiplicationMatrix| |variationOfParameters| |setPosition| + |iiGamma| |psolve| |addMatch| |terms| |s17ajf| |fillPascalTriangle| + |commaSeparate| |showAttributes| |abs| |cup| |OMputApp| |hclf| + |doubleResultant| |c06gqf| |doublyTransitive?| |nextsubResultant2| + |properties| |wrregime| |linearPolynomials| |rur| |lowerCase?| + |mapSolve| |OMreadFile| |ptree| |anfactor| |removeSinSq| |translate| + |evaluateInverse| |factorial| |redPo| |ord| |primaryDecomp| |set| + |monomialIntegrate| |lp| |ideal| + |rewriteIdealWithQuasiMonicGenerators| |intChoose| |iFTable| + |supRittWu?| |map| |point| |extractPoint| |OMopenString| |csc2sin| + |perfectNthPower?| |cycleSplit!| |solveRetract| |delete!| |e04dgf| + |iiacoth| |s20adf| |OMputEndAtp| |genericRightNorm| |heap| + |principal?| |setFieldInfo| |parseString| |rootBound| |OMgetAttr| + |conditionP| |linearDependence| |transcendent?| |root| |sum| |orbits| + |resultant| |predicate| |update| |series| |zeroSquareMatrix| + |numberOfVariables| |fprindINFO| |second| |ratPoly| |red| + |genericLeftDiscriminant| |fortranLiteral| |rootDirectory| + |resetAttributeButtons| |invmod| |e02def| |third| |dequeue| |rarrow| + |viewDeltaYDefault| |critpOrder| |Frobenius| |convert| + |discriminantEuclidean| |prolateSpheroidal| |rst| |groebnerFactorize| + |numberOfFractionalTerms| |gbasis| |aromberg| |resize| |linearPart| + |zeroDim?| |symbol?| |d01aqf| UTS2UP |interpret| |viewDeltaXDefault| + |SturmHabichtMultiple| |child| |min| |flexible?| |shade| + |newSubProgram| |degreePartition| |hdmpToP| |primlimintfrac| + |quadraticNorm| |primes| |arguments| |internalZeroSetSplit| |airyAi| + |buildSyntax| |headReduced?| |functionIsOscillatory| |cscIfCan| + |cycle| |primintegrate| |stFunc2| |laplace| |position| |externalList| + |show| |OMgetError| |bat| |trigs| |charClass| |OMgetInteger| |Aleph| + |lazy?| |d02gbf| |leftNorm| |f04jgf| |useEisensteinCriterion| + |rightRankPolynomial| |f04arf| |setAdaptive3D| + |unprotectedRemoveRedundantFactors| |cosh2sech| |midpoint| |void| + |parameters| |monomials| |trace| |rightUnits| |dot| |updatD| + |createRandomElement| |contours| |ranges| |sts2stst| |e02agf| + |operator| |split| |makeEq| |lfextendedint| |taylorIfCan| |range| + |iicsc| |createMultiplicationTable| |SturmHabichtSequence| + |printInfo!| |e04mbf| |unitVector| |style| |complementaryBasis| + |f02awf| |extendedint| |f02agf| |column| |physicalLength| + |characteristicPolynomial| |f02xef| |sdf2lst| |someBasis| |mapCoef| + |semiDegreeSubResultantEuclidean| |squareFree| |supDimElseRittWu?| + |getPickedPoints| |toScale| |trace2PowMod| |primitivePart| + |sumOfSquares| |singRicDE| |basisOfNucleus| |withPredicates| |e02bcf| + |OMserve| |linGenPos| |e02ajf| |OMsupportsCD?| |printTypes| |nary?| + |integralMatrix| |readable?| |brillhartTrials| |idealiserMatrix| + |e04ycf| |normalForm| |removeSuperfluousCases| |constantOperator| + |irreducibleFactor| |critB| |iiacot| |setTex!| |phiCoord| + |startPolynomial| |minColIndex| |quote| |find| |lieAlgebra?| + |subtractIfCan| |llprop| |expr| |integrate| |OMputEndError| |light| + |minus!| |jacobian| |boundOfCauchy| |getBadValues| + |indiceSubResultant| |approximants| |submod| |s17dcf| |byte| + |numericIfCan| |parts| |algebraicOf| |unit| |minordet| |central?| + |extendedEuclidean| |radicalRoots| |coleman| |vedf2vef| |e01daf| + |leadingBasisTerm| |complete| |useSingleFactorBound?| |harmonic| + |cCsc| |solveLinearPolynomialEquationByFractions| |getIdentifier| + |branchPointAtInfinity?| |reify| |showAll?| |variable| |maxPoints| + |element?| |numFunEvals| |subst| |removeRoughlyRedundantFactorsInPol| + |f04qaf| |odd?| |rroot| |expandPower| |loadNativeModule| |iterators| + |mirror| |removeDuplicates!| |LowTriBddDenomInv| |entries| + |generalizedContinuumHypothesisAssumed?| |leadingCoefficientRicDE| + |ramified?| |nextPartition| |algintegrate| |rightOne| + |listYoungTableaus| |returnTypeOf| |aCubic| |vectorise| |makeSin| + |sumOfDivisors| |check| |inHallBasis?| |OMencodingUnknown| |error| + |next| |integralRepresents| |firstSubsetGray| |pushuconst| |simpson| + |plusInfinity| |bernoulli| |ref| |cyclePartition| |slex| |assert| + |balancedFactorisation| |showFortranOutputStack| |imports| |lifting| + |algDsolve| |minusInfinity| |palgintegrate| |init| |arrayStack| + |subNode?| |reverse| |getCurve| |f01maf| + |halfExtendedSubResultantGcd1| |measure2Result| |shiftRight| + |diagonal| |binarySearchTree| |subResultantGcdEuclidean| |routines| + |d02bhf| |surface| |createPrimitivePoly| |one?| |OMwrite| + |quadraticForm| |exactQuotient| |datalist| |deriv| |cAcot| + |extendedResultant| |primlimitedint| |OMconnOutDevice| |iisinh| + |edf2fi| |notelem| |socf2socdf| |completeEval| |removeConstantTerm| + |stopMusserTrials| |normalElement| |e01bff| |randomLC| |sign| + |OMgetEndAttr| |stoseInvertible?sqfreg| |invmultisect| |rightMult| + |ScanRoman| |changeWeightLevel| |plotPolar| |generalLambert| |type| + |uniform| |represents| |fortranReal| |edf2efi| |probablyZeroDim?| + |hexDigit?| |normalDeriv| |yCoordinates| |relerror| |listOfMonoms| + |rightRecip| |c06fqf| |extractClosed| |shuffle| |decreasePrecision| + |ratDsolve| |rank| |child?| |toseInvertibleSet| |subscript| |separate| + |commutator| |leaf?| |segment| |pdf2ef| |OMmakeConn| |leftDivide| + |shallowExpand| |primeFrobenius| |OMbindTCP| |s17acf| + |partialFraction| |linearAssociatedLog| |cCos| |resultantReduit| + |elRow2!| |dmpToHdmp| |noLinearFactor?| |iExquo| |transform| + |firstUncouplingMatrix| |deepestTail| |groebSolve| |matrixConcat3D| + |generalPosition| |alternatingGroup| |atom?| |normalized?| + |lieAdmissible?| |hermite| |monicRightFactorIfCan| |zCoord| + |purelyAlgebraic?| |cyclic?| |cAcosh| |cosIfCan| |goodPoint| + |cothIfCan| |frobenius| |quasiAlgebraicSet| + |internalSubQuasiComponent?| |number?| |compound?| |iiperm| + |stiffnessAndStabilityOfODEIF| |mergeDifference| |cons| |c02agf| + |alternative?| |biRank| |repeating| |d03faf| |andOperands| |atoms| + |stoseInternalLastSubResultant| |double?| |OMputAtp| |lists| |mapmult| + |problemPoints| |irreducibleFactors| |OMputVariable| |nlde| + |primeFactor| |entry?| |complexLimit| |e02aef| |outputGeneral| + |s18def| |sort| |cCoth| |showArrayValues| |schema| |mesh| |f02adf| + |symFunc| |removeRoughlyRedundantFactorsInPols| |normDeriv2| + |invertible?| |LiePoly| |elements| |diagonalProduct| |listBranches| + |bag| |parametersOf| |factorFraction| |normal01| |characteristicSet| + |dequeue!| |upDateBranches| |content| |lookup| |increment| + |selectSumOfSquaresRoutines| |reduceByQuasiMonic| + |rationalApproximation| |constantIfCan| |OMUnknownSymbol?| |genus| + |isTimes| |mapdiv| |sn| |source| |eyeDistance| |node?| |outputSpacing| + |positiveSolve| |s17dlf| |symmetric?| |whatInfinity| |modularFactor| + |normFactors| |acothIfCan| |integralDerivationMatrix| + |inverseIntegralMatrix| |critMonD1| |precision| |e01bhf| |random| + |unravel| |startTableInvSet!| |subset?| |rootNormalize| |binomThmExpt| + |saturate| |mr| |multiple?| |contains?| |makeSeries| |myDegree| + |patternVariable| |iisqrt2| |screenResolution| |whileLoop| + |createLowComplexityTable| |null| |chebyshevU| |rootOf| + |generalizedInverse| |uniform01| |reopen!| |listOfLists| + |bipolarCylindrical| |OMgetEndBVar| |case| |mulmod| |intPatternMatch| + |reducedQPowers| |swap!| |pushucoef| FG2F |symbolTable| |imagj| + |bright| |coerceL| |repeatUntilLoop| |Zero| |numberOfCycles| + |radicalSolve| |plus!| |mappingAst| |compactFraction| |exptMod| + |pushup| |fractRadix| |ricDsolve| |One| |rotatex| |hasPredicate?| + |stoseSquareFreePart| |mainCharacterization| |digamma| + |pushFortranOutputStack| |fractionFreeGauss!| |iflist2Result| |iisec| + |smith| |equality| |OMgetEndAtp| |bsolve| |subresultantSequence| + |varList| |popFortranOutputStack| |generalInfiniteProduct| + |lazyPseudoRemainder| |monicDecomposeIfCan| |leftPower| + |showTheSymbolTable| |weakBiRank| |addBadValue| |e02bbf| + |scalarMatrix| |fmecg| |outputAsFortran| |symmetricProduct| + |triangulate| |in?| |duplicates| |callForm?| |normalizedDivide| + |coerceImages| |complexElementary| |makeCos| |secIfCan| |sin2csc| + |categories| |FormatArabic| |subresultantVector| |rationalFunction| + |brillhartIrreducible?| |binaryTournament| |postfix| + |LyndonCoordinates| |makeSUP| |patternMatchTimes| |key| |LiePolyIfCan| + |implies?| |elt| |LyndonBasis| |e02zaf| |choosemon| |ptFunc| |moebius| + |mapExponents| |numberOfDivisors| |adaptive| |e01bef| |isMult| + |removeIrreducibleRedundantFactors| |filename| |redpps| |generic?| + |toseInvertible?| |semiResultantEuclidean1| |shiftLeft| + |selectODEIVPRoutines| |linSolve| |upperCase| |revert| GE + |setLegalFortranSourceExtensions| |prefixRagits| |port| |coordinates| + |not?| |extractProperty| |prod| |interpretString| + |associatedEquations| |order| GT |any| |operation| |unitNormalize| + |diag| |stoseLastSubResultant| |clipSurface| |push!| |parse| |mvar| + |polygon| |fibonacci| |semiLastSubResultantEuclidean| LE + |selectIntegrationRoutines| |getSyntaxFormsFromFile| |seed| + |createIrreduciblePoly| |FormatRoman| |oddintegers| |symbolIfCan| + |has?| |purelyAlgebraicLeadingMonomial?| LT |ocf2ocdf| |edf2ef| + |outputList| |useNagFunctions| |label| |d01apf| |or?| |btwFact| + |returnType!| |convergents| |multiEuclidean| |complex| |makingStats?| + |rootKerSimp| |exprHasLogarithmicWeights| |push| |continuedFraction| + |iiasinh| |basisOfLeftNucleus| |extension| |exactQuotient!| + |limitPlus| |vark| |viewPhiDefault| |c06fpf| |OMsend| |exponential| + |cLog| |readByteIfCan!| |countRealRoots| |arity| |mainCoefficients| + |digit?| |associatorDependence| |integralBasisAtInfinity| + |nextLatticePermutation| |dictionary| |argumentList!| + |stiffnessAndStabilityFactor| |lazyVariations| |plus| |characteristic| + |twoFactor| |invertibleSet| |possiblyNewVariety?| |decompose| |vector| + |s17aff| |sup| |keys| |OMencodingXML| |subCase?| |oneDimensionalArray| + |prime| |simplifyPower| |characteristicSerie| |constantKernel| + |differentiate| |hasoln| |compose| |absolutelyIrreducible?| + |fortranCarriageReturn| |basisOfCentroid| |antisymmetricTensors| + |differentialVariables| |functionIsFracPolynomial?| |currentEnv| + |root?| |quasiComponent| |stosePrepareSubResAlgo| |c02aff| + |inconsistent?| |pointSizeDefault| |rk4| |BumInSepFFE| |outputMeasure| + |Vectorise| |nextPrimitiveNormalPoly| |bezoutMatrix| |raisePolynomial| + |removeSquaresIfCan| |copies| |times| |splitDenominator| |rquo| + |matrixDimensions| |derivationCoordinates| |pmComplexintegrate| + |complexRoots| |elRow1!| |changeVar| |search| |cAsec| |norm| |index| + |lazyPrem| |imagk| |stopTable!| |e01sff| |nodes| |sortConstraints| + |symmetricGroup| |cAsech| |mapMatrixIfCan| |monomRDEsys| + |lazyIntegrate| |simplifyLog| |isOp| |parabolicCylindrical| |ldf2lst| + |exprex| |skewSFunction| |curveColorPalette| |option| |call| + |removeRedundantFactorsInPols| |leftMult| |hasHi| |rowEchLocal| + |realRoots| |relationsIdeal| |lazyPseudoQuotient| |numberOfOperations| + |localAbs| |fortranDouble| |totolex| |list| |monom| |OMputFloat| + |pair| |over| |box| |quatern| |prevPrime| |writeLine!| |position!| + |stirling1| |df2ef| |car| |representationType| |sorted?| |pol| + |reducedContinuedFraction| |factorAndSplit| |d02gaf| |declare| + |d02bbf| |expressIdealMember| |redmat| |cdr| GF2FG |setOfMinN| + |besselY| |read!| |factor1| |OMputEndBVar| |arg1| |weight| |common| + |solve1| |setDifference| |movedPoints| |cTan| |rename!| |f01qef| + |checkPrecision| |closeComponent| |low| |cfirst| |arg2| |function| + |cyclic| |addMatchRestricted| |setIntersection| |power| |graphImage| + |expextendedint| |max| |axesColorDefault| |operators| |maxIndex| + |selectNonFiniteRoutines| |polar| |infRittWu?| |iitanh| |setUnion| + |antisymmetric?| |zero?| |const| |OMputSymbol| |rightTrim| |resetNew| + |hitherPlane| |leaves| |conditions| |repSq| |generateIrredPoly| + |apply| |setStatus| |musserTrials| |purelyTranscendental?| + |stoseInvertible?| |squareMatrix| |cAsin| |taylorQuoByVar| |leftTrim| + |wordsForStrongGenerators| |normalizedAssociate| |polyred| |close!| + |expt| |RittWuCompare| |printCode| |complex?| |OMlistSymbols| + |OMgetType| |asinhIfCan| |mathieu24| |size| |addPointLast| |tableau| + |bivariate?| |makeFloatFunction| |legendre| |mdeg| + |listConjugateBases| |s18dcf| |moduloP| |cSech| |separateFactors| + |rationalPower| |setErrorBound| |hconcat| |integers| |log| |iicos| + |c05pbf| |bitLength| |LyndonWordsList1| |fractRagits| |rules| + |generalTwoFactor| |leadingExponent| |elem?| |lex| + |conditionsForIdempotents| |radicalEigenvector| |first| + |tubeRadiusDefault| |rotate!| |RemainderList| |tubePoints| + |unaryFunction| |insertBottom!| |chiSquare1| |fi2df| |cPower| + |subspace| |pattern| |rest| |vspace| |listRepresentation| + |hyperelliptic| |writeByteIfCan!| |rule| |factorPolynomial| |product| + |fullPartialFraction| |substitute| |term| |internalInfRittWu?| + |s17dhf| |yCoord| |selectsecond| |antiAssociative?| |outputFloating| + |numerator| |notOperand| |removeDuplicates| |composite| + |completeHensel| |quoByVar| |exponents| |d03eef| |diophantineSystem| + |tablePow| |d01akf| |rationalIfCan| + |dimensionOfIrreducibleRepresentation| |interval| |hex| + |leftExactQuotient| |rightRegularRepresentation| |minset| |floor| + |nextNormalPrimitivePoly| |constantRight| |normInvertible?| |/\\| + |lcm| |message| |equivOperands| |euler| |acscIfCan| |antiCommutative?| + |setScreenResolution| |showTypeInOutput| |singular?| |pack!| + |UpTriBddDenomInv| |\\/| |ode1| |palglimint| |readIfCan!| |domainOf| + |twist| |perfectSquare?| |id| |traceMatrix| |sinIfCan| |append| + |pureLex| |subNodeOf?| |graphState| |pushdown| |lazyResidueClass| + |tanAn| |iicsch| |lfunc| |gcd| |pointPlot| |reciprocalPolynomial| + |controlPanel| |rischNormalize| |laguerreL| |distFact| |table| + |binary| |isList| |false| |intersect| |chineseRemainder| |taylorRep| + |OMReadError?| |ridHack1| |s14baf| |new| |rowEch| |drawCurves| + |basisOfLeftAnnihilator| |vertConcat| |largest| |lambert| + |quasiMonic?| |slash| |pair?| |factorList| |constDsolve| |sequences| + |stopTableGcd!| |setStatus!| |droot| |less?| |monicRightDivide| + |printInfo| |test| |modifyPointData| |fTable| |s13acf| + |semiResultantReduitEuclidean| |univcase| |zero| |jordanAdmissible?| + |monic?| |exprToXXP| |infiniteProduct| |comp| |#| |Is| |imagI| + |coHeight| |viewWriteAvailable| |qqq| |inc| |recur| |symmetricTensors| + |overbar| |hypergeometric0F1| |logical?| |gradient| |torsionIfCan| + |And| |trapezoidalo| |numberOfHues| |optional?| |s21bcf| + |resultantnaif| |iidsum| |possiblyInfinite?| |dihedralGroup| + |recoverAfterFail| |Or| |c06ebf| |splitConstant| |multiset| + |makeResult| |copy!| |alphanumeric| |adjoint| |rightExactQuotient| + |initiallyReduce| |Not| |tanh2coth| |parametric?| |remove| |stack| + |laurentRep| |fixedPointExquo| |accuracyIF| |limitedIntegrate| + |point?| |youngGroup| |merge!| |cAcsch| |reducedForm| |OMgetSymbol| + |leftFactor| |cyclicParents| |setlast!| |numberOfIrreduciblePoly| + |loopPoints| |last| |c05nbf| |insertRoot!| |setRealSteps| + |polarCoordinates| |swap| ~= |mainMonomial| |assoc| |left| + |sumSquares| |zeroSetSplit| |plot| |fglmIfCan| |unmakeSUP| + |computeCycleEntry| |setProperties!| |coerce| |getOrder| |right| + |curveColor| |iisin| |quotient| |complexZeros| |currentScope| + |construct| |s14abf| |doubleComplex?| |se2rfi| |f02bbf| |lfintegrate| + |divideIfCan| |roughEqualIdeals?| |points| |BasicMethod| + |nextNormalPoly| |outputArgs| |numerators| |ODESolve| + |wronskianMatrix| |factorByRecursion| |rotate| |factorset| + |schwerpunkt| |nextPrime| |ravel| |pseudoQuotient| |cartesian| |imagJ| + |refine| |numericalOptimization| |predicates| |reshape| |hcrf| |cAcsc| + |internalSubPolSet?| |OMputInteger| |PDESolve| ** |defineProperty| + |OMputEndBind| |inR?| |basicSet| |prindINFO| + |removeRedundantFactorsInContents| |digits| |maxdeg| + |cyclotomicFactorization| |unparse| |mindegTerm| |irreducible?| + |generic| |internalAugment| |adaptive?| |userOrdered?| |latex| + |squareTop| |maximumExponent| |selectOptimizationRoutines| EQ + |nullary?| |s20acf| |sizeLess?| |setEmpty!| |summation| |lSpaceBasis| + |assign| |hasTopPredicate?| |finite?| |palgLODE0| |asecIfCan| |ddFact| + |algebraicCoefficients?| |LagrangeInterpolation| |f2st| |Gamma| + |lastSubResultant| |fortranCompilerName| |OMgetAtp| |curve?| |cCot| + |viewWriteDefault| |outputAsTex| |d01ajf| |queue| + |internalLastSubResultant| |difference| |triangular?| + |factorSquareFree| |power!| |coercePreimagesImages| |flatten| + |laguerre| |rewriteIdealWithHeadRemainder| |pointColorDefault| + |symbol| |laplacian| |matrix| |symmetricRemainder| |signAround| + |swapRows!| |roman| |startTable!| |genericPosition| |viewSizeDefault| + |fixedPoint| |expression| |randomR| |decomposeFunc| + |basisOfMiddleNucleus| |deepCopy| |cCsch| |simplifyExp| + |leftAlternative?| |OMlistCDs| |truncate| |integer| |subSet| |rootsOf| + |HenselLift| |rdHack1| |localReal?| |maxrow| |generators| |tab| + |sec2cos| |lyndon| |conical| |logGamma| |sizeMultiplication| + |henselFact| |setfirst!| |iisech| |approxNthRoot| |isQuotient| |equiv| + |signature| |OMgetVariable| |polyPart| |semicolonSeparate| + |definingEquations| |hash| |mkcomm| |weierstrass| |divideIfCan!| + |selectMultiDimensionalRoutines| |laurentIfCan| |nand| |objectOf| + |count| |typeLists| |currentSubProgram| |endOfFile?| |setProperty| + |cn| |mapUnivariate| |constant?| |Si| |prem| |goto| |not| |newLine| + |systemCommand| |bfEntry| |sturmSequence| |multiEuclideanTree| + |primPartElseUnitCanonical| |genericRightTraceForm| |cAcos| + |cosSinInfo| |univariateSolve| |monicDivide| |zeroDimPrimary?| + |alphanumeric?| |partialDenominators| |Nul| |sncndn| |mapUp!| + |viewport3D| |nonSingularModel| |list?| |iiexp| |double| + |setAttributeButtonStep| |fortranInteger| |f02aff| + |solveLinearPolynomialEquationByRecursion| |front| |clearTable!| + |var2Steps| |finiteBasis| |height| |nextItem| |overset?| |cschIfCan| + |normal| |OMopenFile| |conjug| |primitivePart!| |oddlambert| + |normalise| |regularRepresentation| |associates?| |paren| + |outerProduct| |LazardQuotient| |leader| |KrullNumber| |collect| + |trim| |inrootof| |makeFR| |rightScalarTimes!| |scalarTypeOf| + |fractionPart| RF2UTS |degree| |getMeasure| |initTable!| + |computeCycleLength| |infieldIntegrate| |presuper| |minPoints| + |complexForm| |dflist| |directory| |semiSubResultantGcdEuclidean1| + |f04mcf| |s13aaf| |module| |acschIfCan| |ode| |mkIntegral| + |clearTheIFTable| |nullSpace| |derivative| |leftGcd| + |degreeSubResultantEuclidean| |f04axf| |torsion?| |acosIfCan| |cap| + |factorSquareFreePolynomial| |prologue| |putColorInfo| + |ellipticCylindrical| |newReduc| |genericLeftTraceForm| |cyclicGroup| + |iiacsch| |nothing| |tryFunctionalDecomposition?| |setref| |solid| + |declare!| |f01rdf| |writable?| |numberOfComputedEntries| + |categoryFrame| |hermiteH| |fixPredicate| |palgLODE| |denominator| + |cond| |fortranComplex| |dAndcExp| |expintfldpoly| |s18aff| + |expenseOfEvaluationIF| |unitNormal| |clipBoolean| |ipow| |primitive?| + |palglimint0| |brace| |minimumDegree| |OMputEndApp| + |initiallyReduced?| |clearTheFTable| |primextendedint| |replace| + |f02wef| |rubiksGroup| |linearDependenceOverZ| |var2StepsDefault| + |tan2trig| |halfExtendedResultant1| |nil?| |d03edf| |padicallyExpand| + |Ei| |bitTruth| |padecf| |rootPoly| |iiatanh| |binaryTree| |rightNorm| + |headAst| UP2UTS |pdct| |eigenvectors| |reduced?| |stop| |firstNumer| + |failed| |createZechTable| |branchPoint?| |charthRoot| |compdegd| + |rightGcd| |closed?| |noncommutativeJordanAlgebra?| |members| |cCosh| + |value| |highCommonTerms| |numberOfComposites| |coth2trigh| + |functionIsContinuousAtEndPoints| |region| |exteriorDifferential| + |OMsetEncoding| |wordInStrongGenerators| |iiabs| |reduceLODE| + |denomRicDE| |coefficient| + |rewriteSetByReducingWithParticularGenerators| |zoom| + |mainPrimitivePart| |leftUnits| |children| |measure| + |clearFortranOutputStack| |c06gcf| |aQuadratic| |f04adf| |removeZero| + |opeval| |e01sbf| |graphCurves| |genericRightMinimalPolynomial| + |s17ahf| |rowEchelon| |closedCurve| |homogeneous?| |groebnerIdeal| + |integerIfCan| |any?| |partitions| |graeffe| |particularSolution| + |generalizedContinuumHypothesisAssumed| |nextSubsetGray| + |linearlyDependent?| |xCoord| |dimensionsOf| |monicLeftDivide| + |linear?| |or| |trivialIdeal?| |critM| |eulerE| |length| |remove!| + |partition| |startTableGcd!| |algint| |doubleRank| |prinb| + |elseBranch| |corrPoly| |makeprod| |scripts| |bat1| |numFunEvals3D| + |roughUnitIdeal?| |insertionSort!| |lazyEvaluate| |dimensions| + |intensity| |bombieriNorm| |bandedHessian| |hue| + |currentCategoryFrame| |viewport2D| |deref| |critMTonD1| |prime?| + |idealSimplify| |infieldint| |repeating?| |cross| |yellow| |idealiser| + |setprevious!| |iprint| |Lazard| |c06fuf| |bezoutDiscriminant| + |directSum| |zeroVector| |generator| |top!| |removeCosSq| + |leadingSupport| |d02ejf| |quotedOperators| |cycleTail| |index?| + |exponentialOrder| |sizePascalTriangle| |eq?| |OMgetEndObject| + |cos2sec| |triangularSystems| |stFunc1| |thenBranch| |f04atf| + |argumentListOf| |useEisensteinCriterion?| |fixedPoints| |errorKind| + |mesh?| |decrease| |alphabetic?| |stoseInvertible?reg| |computeBasis| + |lighting| |linearMatrix| |leftDiscriminant| |integer?| |pToHdmp| + |lprop| |roughBasicSet| |clipWithRanges| |OMgetBVar| |rootProduct| + |besselK| |kroneckerDelta| |makeTerm| |leftZero| + |completeEchelonBasis| |transcendentalDecompose| |minPoints3D| + |leftFactorIfCan| |OMputError| |eigenvalues| |superscript| + |OMconnInDevice| |OMputBind| |inspect| |option?| |select!| |digit| + |coerceS| |chvar| |s15aef| |sub| |inGroundField?| |chainSubResultants| + |f02akf| |zeroSetSplitIntoTriangularSystems| |froot| |dioSolve| + |comparison| |nthExponent| |f01bsf| |reflect| |sPol| |conjugates| + |nil| |infinite| |arbitraryExponent| |approximate| |complex| + |shallowMutable| |canonical| |noetherian| |central| + |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| + |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| + |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| + |finiteAggregate| |shallowlyMutable| |commutative|)
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T) ((-38 |#2|) |has| |#2| (-169)) ((-101) -1524 (|has| |#2| (-1063)) (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-767)) (|has| |#2| (-701)) (|has| |#2| (-359)) (|has| |#2| (-354)) (|has| |#2| (-169)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -1524 (|has| |#2| (-1016)) (|has| |#2| (-354)) (|has| |#2| (-169))) ((-111 $ $) |has| |#2| (-169)) ((-130) -1524 (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-767)) (|has| |#2| (-354)) (|has| |#2| (-169)) (|has| |#2| (-130))) ((-591 (-832)) -1524 (|has| |#2| (-1063)) (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-767)) (|has| |#2| (-701)) (|has| |#2| (-359)) (|has| |#2| (-354)) (|has| |#2| (-169)) (|has| |#2| (-591 (-832))) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-591 (-1218 |#2|)) . T) ((-169) |has| |#2| (-169)) ((-223 |#2|) |has| |#2| (-1016)) ((-225) -12 (|has| |#2| (-225)) (|has| |#2| (-1016))) ((-277 #0=(-547) |#2|) . T) ((-279 #0# |#2|) . T) ((-300 |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) ((-359) |has| |#2| (-359)) ((-368 |#2|) |has| |#2| (-1016)) ((-402 |#2|) |has| |#2| (-1063)) ((-479 |#2|) . T) ((-582 #0# |#2|) . T) ((-503 |#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) ((-622 |#2|) -1524 (|has| |#2| (-1016)) (|has| |#2| (-354)) (|has| |#2| (-169))) ((-622 $) -1524 (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-169))) ((-615 (-547)) -12 (|has| |#2| (-615 (-547))) (|has| |#2| (-1016))) ((-615 |#2|) |has| |#2| (-1016)) ((-692 |#2|) -1524 (|has| |#2| (-354)) (|has| |#2| (-169))) ((-701) -1524 (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-701)) (|has| |#2| (-169))) ((-765) |has| |#2| (-819)) ((-766) -1524 (|has| |#2| (-819)) (|has| |#2| (-767))) ((-767) |has| |#2| (-767)) ((-768) -1524 (|has| |#2| (-819)) (|has| |#2| (-767))) ((-769) -1524 (|has| |#2| (-819)) (|has| |#2| (-767))) ((-819) |has| |#2| (-819)) ((-821) -1524 (|has| |#2| (-819)) (|has| |#2| (-767))) ((-869 (-1135)) -12 (|has| |#2| (-869 (-1135))) (|has| |#2| (-1016))) ((-1007 (-398 (-547))) -12 (|has| |#2| (-1007 (-398 (-547)))) (|has| |#2| (-1063))) ((-1007 (-547)) -12 (|has| |#2| (-1007 (-547))) (|has| |#2| (-1063))) ((-1007 |#2|) |has| |#2| (-1063)) ((-1022 |#2|) -1524 (|has| |#2| (-1016)) (|has| |#2| (-354)) (|has| |#2| (-169))) ((-1022 $) |has| |#2| (-169)) ((-1016) -1524 (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-169))) ((-1023) -1524 (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-169))) ((-1075) -1524 (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-701)) (|has| |#2| (-169))) ((-1063) -1524 (|has| |#2| (-1063)) (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-767)) (|has| |#2| (-701)) (|has| |#2| (-359)) (|has| |#2| (-354)) (|has| |#2| (-169)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-1172) . T) ((-1225 |#2|) |has| |#2| (-354))) -((-3562 (((-232 |#1| |#3|) (-1 |#3| |#2| |#3|) (-232 |#1| |#2|) |#3|) 21)) (-2542 ((|#3| (-1 |#3| |#2| |#3|) (-232 |#1| |#2|) |#3|) 23)) (-2781 (((-232 |#1| |#3|) (-1 |#3| |#2|) (-232 |#1| |#2|)) 18))) -(((-231 |#1| |#2| |#3|) (-10 -7 (-15 -3562 ((-232 |#1| |#3|) (-1 |#3| |#2| |#3|) (-232 |#1| |#2|) |#3|)) (-15 -2542 (|#3| (-1 |#3| |#2| |#3|) (-232 |#1| |#2|) |#3|)) (-15 -2781 ((-232 |#1| |#3|) (-1 |#3| |#2|) (-232 |#1| |#2|)))) (-745) (-1172) (-1172)) (T -231)) -((-2781 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-232 *5 *6)) (-14 *5 (-745)) (-4 *6 (-1172)) (-4 *7 (-1172)) (-5 *2 (-232 *5 *7)) (-5 *1 (-231 *5 *6 *7)))) (-2542 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-232 *5 *6)) (-14 *5 (-745)) (-4 *6 (-1172)) (-4 *2 (-1172)) (-5 *1 (-231 *5 *6 *2)))) (-3562 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-232 *6 *7)) (-14 *6 (-745)) (-4 *7 (-1172)) (-4 *5 (-1172)) (-5 *2 (-232 *6 *5)) (-5 *1 (-231 *6 *7 *5))))) -(-10 -7 (-15 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(|has| |#2| (-701))) (($ |#2| $) 43 (|has| |#2| (-701))) (($ (-745) $) NIL (|has| |#2| (-130))) (($ (-890) $) NIL (|has| |#2| (-25)))) (-3763 (((-745) $) NIL (|has| $ (-6 -4328))))) +((-2156 (*1 *1 *2) (-12 (-5 *2 (-1218 *4)) (-4 *4 (-1172)) (-4 *1 (-230 *3 *4)))) (-2911 (*1 *1 *2) (-12 (-5 *2 (-890)) (-4 *1 (-230 *3 *4)) (-4 *4 (-1016)) (-4 *4 (-1172)))) (-2893 (*1 *2 *1 *1) (-12 (-4 *1 (-230 *3 *2)) (-4 *2 (-1172)) (-4 *2 (-1016)))) (* (*1 *1 *1 *2) (-12 (-4 *1 (-230 *3 *2)) (-4 *2 (-1172)) (-4 *2 (-701)))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-230 *3 *2)) (-4 *2 (-1172)) (-4 *2 (-701))))) +(-13 (-582 (-547) |t#2|) (-591 (-1218 |t#2|)) (-10 -8 (-6 -4328) (-15 -2156 ($ (-1218 |t#2|))) (IF (|has| |t#2| (-1063)) (-6 (-402 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-1016)) (PROGN (-6 (-111 |t#2| |t#2|)) (-6 (-223 |t#2|)) (-6 (-368 |t#2|)) (-15 -2911 ($ (-890))) (-15 -2893 (|t#2| $ $))) |%noBranch|) (IF (|has| |t#2| (-25)) (-6 (-25)) |%noBranch|) (IF (|has| |t#2| (-130)) (-6 (-130)) |%noBranch|) (IF 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T) ((-38 |#2|) |has| |#2| (-169)) ((-101) -1525 (|has| |#2| (-1063)) (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-767)) (|has| |#2| (-701)) (|has| |#2| (-359)) (|has| |#2| (-354)) (|has| |#2| (-169)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -1525 (|has| |#2| (-1016)) (|has| |#2| (-354)) (|has| |#2| (-169))) ((-111 $ $) |has| |#2| (-169)) ((-130) -1525 (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-767)) (|has| |#2| (-354)) (|has| |#2| (-169)) (|has| |#2| (-130))) ((-591 (-832)) -1525 (|has| |#2| (-1063)) (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-767)) (|has| |#2| (-701)) (|has| |#2| (-359)) (|has| |#2| (-354)) (|has| |#2| (-169)) (|has| |#2| (-591 (-832))) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-591 (-1218 |#2|)) . T) ((-169) |has| |#2| (-169)) ((-223 |#2|) |has| |#2| (-1016)) ((-225) -12 (|has| |#2| (-225)) (|has| |#2| (-1016))) ((-277 #0=(-547) |#2|) . T) ((-279 #0# |#2|) . T) ((-300 |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) ((-359) |has| |#2| (-359)) ((-368 |#2|) |has| |#2| (-1016)) ((-402 |#2|) |has| |#2| (-1063)) ((-479 |#2|) . T) ((-582 #0# |#2|) . T) ((-503 |#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) ((-622 |#2|) -1525 (|has| |#2| (-1016)) (|has| |#2| (-354)) (|has| |#2| (-169))) ((-622 $) -1525 (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-169))) ((-615 (-547)) -12 (|has| |#2| (-615 (-547))) (|has| |#2| (-1016))) ((-615 |#2|) |has| |#2| (-1016)) ((-692 |#2|) -1525 (|has| |#2| (-354)) (|has| |#2| (-169))) ((-701) -1525 (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-701)) (|has| |#2| (-169))) ((-765) |has| |#2| (-819)) ((-766) -1525 (|has| |#2| (-819)) (|has| |#2| (-767))) ((-767) |has| |#2| (-767)) ((-768) -1525 (|has| |#2| (-819)) (|has| |#2| (-767))) ((-769) -1525 (|has| |#2| (-819)) (|has| |#2| (-767))) ((-819) |has| |#2| (-819)) ((-821) -1525 (|has| |#2| (-819)) (|has| |#2| (-767))) ((-869 (-1135)) -12 (|has| |#2| (-869 (-1135))) (|has| |#2| (-1016))) ((-1007 (-398 (-547))) -12 (|has| |#2| (-1007 (-398 (-547)))) (|has| |#2| (-1063))) ((-1007 (-547)) -12 (|has| |#2| (-1007 (-547))) (|has| |#2| (-1063))) ((-1007 |#2|) |has| |#2| (-1063)) ((-1022 |#2|) -1525 (|has| |#2| (-1016)) (|has| |#2| (-354)) (|has| |#2| (-169))) ((-1022 $) |has| |#2| (-169)) ((-1016) -1525 (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-169))) ((-1023) -1525 (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-169))) ((-1075) -1525 (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-701)) (|has| |#2| (-169))) ((-1063) -1525 (|has| |#2| (-1063)) (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-767)) (|has| |#2| (-701)) (|has| |#2| (-359)) (|has| |#2| (-354)) (|has| |#2| (-169)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-1172) . T) ((-1225 |#2|) |has| |#2| (-354))) +((-2677 (((-232 |#1| |#3|) (-1 |#3| |#2| |#3|) (-232 |#1| |#2|) |#3|) 21)) (-2544 ((|#3| (-1 |#3| |#2| |#3|) (-232 |#1| |#2|) |#3|) 23)) (-2782 (((-232 |#1| |#3|) (-1 |#3| |#2|) (-232 |#1| |#2|)) 18))) +(((-231 |#1| |#2| |#3|) (-10 -7 (-15 -2677 ((-232 |#1| |#3|) (-1 |#3| |#2| |#3|) (-232 |#1| |#2|) |#3|)) (-15 -2544 (|#3| (-1 |#3| |#2| |#3|) (-232 |#1| |#2|) |#3|)) (-15 -2782 ((-232 |#1| |#3|) (-1 |#3| |#2|) (-232 |#1| |#2|)))) (-745) (-1172) (-1172)) (T -231)) +((-2782 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-232 *5 *6)) (-14 *5 (-745)) (-4 *6 (-1172)) (-4 *7 (-1172)) (-5 *2 (-232 *5 *7)) (-5 *1 (-231 *5 *6 *7)))) (-2544 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-232 *5 *6)) (-14 *5 (-745)) (-4 *6 (-1172)) (-4 *2 (-1172)) (-5 *1 (-231 *5 *6 *2)))) (-2677 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-232 *6 *7)) (-14 *6 (-745)) (-4 *7 (-1172)) (-4 *5 (-1172)) (-5 *2 (-232 *6 *5)) (-5 *1 (-231 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-398 (-547))) |has| |#1| (-38 (-398 (-547)))) ((-38 |#1|) |has| |#1| (-169)) ((-38 $) -1524 (|has| |#1| (-878)) (|has| |#1| (-539)) (|has| |#1| (-442))) ((-101) . T) ((-111 #0# #0#) |has| |#1| (-38 (-398 (-547)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -1524 (|has| |#1| (-878)) (|has| |#1| (-539)) (|has| |#1| (-442)) (|has| |#1| (-169))) ((-130) . T) ((-143) |has| |#1| (-143)) ((-145) |has| |#1| (-145)) ((-591 (-832)) . T) ((-169) -1524 (|has| |#1| (-878)) (|has| |#1| (-539)) (|has| |#1| (-442)) (|has| |#1| (-169))) ((-592 (-523)) -12 (|has| |#1| (-592 (-523))) (|has| |#3| (-592 (-523)))) ((-592 (-861 (-370))) -12 (|has| |#1| (-592 (-861 (-370)))) (|has| |#3| (-592 (-861 (-370))))) ((-592 (-861 (-547))) -12 (|has| |#1| (-592 (-861 (-547)))) (|has| |#3| (-592 (-861 (-547))))) ((-223 |#1|) . T) ((-225) |has| |#1| (-225)) ((-281) -1524 (|has| |#1| (-878)) (|has| |#1| (-539)) (|has| |#1| (-442))) ((-300 $) . T) ((-317 |#1| |#4|) . T) ((-368 |#1|) . T) ((-402 |#1|) . T) ((-442) -1524 (|has| |#1| (-878)) (|has| |#1| (-442))) ((-503 |#2| |#1|) |has| |#1| (-225)) ((-503 |#2| $) |has| |#1| (-225)) ((-503 |#3| |#1|) . T) ((-503 |#3| $) . T) ((-503 $ $) . T) ((-539) -1524 (|has| |#1| (-878)) (|has| |#1| (-539)) (|has| |#1| (-442))) ((-622 #0#) |has| |#1| (-38 (-398 (-547)))) ((-622 |#1|) . T) ((-622 $) . T) ((-615 (-547)) |has| |#1| (-615 (-547))) ((-615 |#1|) . T) ((-692 #0#) |has| |#1| (-38 (-398 (-547)))) ((-692 |#1|) |has| |#1| (-169)) ((-692 $) -1524 (|has| |#1| (-878)) (|has| |#1| (-539)) (|has| |#1| (-442))) ((-701) . T) ((-821) |has| |#1| (-821)) ((-869 (-1135)) |has| |#1| (-869 (-1135))) ((-869 |#3|) . T) ((-855 (-370)) -12 (|has| |#1| (-855 (-370))) (|has| |#3| (-855 (-370)))) ((-855 (-547)) -12 (|has| |#1| (-855 (-547))) (|has| |#3| (-855 (-547)))) ((-918 |#1| |#4| |#3|) . T) ((-878) |has| |#1| (-878)) ((-1007 (-398 (-547))) |has| |#1| (-1007 (-398 (-547)))) ((-1007 (-547)) |has| |#1| (-1007 (-547))) ((-1007 |#1|) . T) ((-1007 |#2|) . T) ((-1007 |#3|) . T) ((-1022 #0#) |has| |#1| (-38 (-398 (-547)))) ((-1022 |#1|) . T) ((-1022 $) -1524 (|has| |#1| (-878)) (|has| |#1| (-539)) (|has| |#1| (-442)) (|has| |#1| (-169))) ((-1016) . T) ((-1023) . T) ((-1075) . T) ((-1063) . 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-398 (-547))) |has| |#1| (-38 (-398 (-547)))) ((-38 |#1|) |has| |#1| (-169)) ((-38 $) -1525 (|has| |#1| (-878)) (|has| |#1| (-539)) (|has| |#1| (-442))) ((-101) . T) ((-111 #0# #0#) |has| |#1| (-38 (-398 (-547)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -1525 (|has| |#1| (-878)) (|has| |#1| (-539)) (|has| |#1| (-442)) (|has| |#1| (-169))) ((-130) . T) ((-143) |has| |#1| (-143)) ((-145) |has| |#1| (-145)) ((-591 (-832)) . T) ((-169) -1525 (|has| |#1| (-878)) (|has| |#1| (-539)) (|has| |#1| (-442)) (|has| |#1| (-169))) ((-592 (-523)) -12 (|has| |#1| (-592 (-523))) (|has| |#3| (-592 (-523)))) ((-592 (-861 (-370))) -12 (|has| |#1| (-592 (-861 (-370)))) (|has| |#3| (-592 (-861 (-370))))) ((-592 (-861 (-547))) -12 (|has| |#1| (-592 (-861 (-547)))) (|has| |#3| (-592 (-861 (-547))))) ((-223 |#1|) . T) ((-225) |has| |#1| (-225)) ((-281) -1525 (|has| |#1| (-878)) (|has| |#1| (-539)) (|has| |#1| (-442))) ((-300 $) . T) ((-317 |#1| |#4|) . T) ((-368 |#1|) . T) ((-402 |#1|) . T) ((-442) -1525 (|has| |#1| (-878)) (|has| |#1| (-442))) ((-503 |#2| |#1|) |has| |#1| (-225)) ((-503 |#2| $) |has| |#1| (-225)) ((-503 |#3| |#1|) . T) ((-503 |#3| $) . T) ((-503 $ $) . T) ((-539) -1525 (|has| |#1| (-878)) (|has| |#1| (-539)) (|has| |#1| (-442))) ((-622 #0#) |has| |#1| (-38 (-398 (-547)))) ((-622 |#1|) . T) ((-622 $) . T) ((-615 (-547)) |has| |#1| (-615 (-547))) ((-615 |#1|) . T) ((-692 #0#) |has| |#1| (-38 (-398 (-547)))) ((-692 |#1|) |has| |#1| (-169)) ((-692 $) -1525 (|has| |#1| (-878)) (|has| |#1| (-539)) (|has| |#1| (-442))) ((-701) . T) ((-821) |has| |#1| (-821)) ((-869 (-1135)) |has| |#1| (-869 (-1135))) ((-869 |#3|) . T) ((-855 (-370)) -12 (|has| |#1| (-855 (-370))) (|has| |#3| (-855 (-370)))) ((-855 (-547)) -12 (|has| |#1| (-855 (-547))) (|has| |#3| (-855 (-547)))) ((-918 |#1| |#4| |#3|) . 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T) ((-111 #0# #0#) |has| |#1| (-539)) ((-111 |#1| |#1|) |has| |#1| (-169)) ((-111 $ $) |has| |#1| (-539)) ((-130) -1524 (|has| |#1| (-1016)) (|has| |#1| (-539)) (|has| |#1| (-169)) (|has| |#1| (-145)) (|has| |#1| (-143)) (|has| |#1| (-21))) ((-143) |has| |#1| (-143)) ((-145) |has| |#1| (-145)) ((-591 (-832)) . T) ((-169) |has| |#1| (-539)) ((-592 (-523)) |has| |#1| (-592 (-523))) ((-592 (-861 (-370))) |has| |#1| (-592 (-861 (-370)))) ((-592 (-861 (-547))) |has| |#1| (-592 (-861 (-547)))) ((-235) |has| |#1| (-539)) ((-281) |has| |#1| (-539)) ((-298) |has| |#1| (-539)) ((-300 $) . T) ((-293) . T) ((-354) |has| |#1| (-539)) ((-368 |#1|) |has| |#1| (-1016)) ((-391 |#1|) . T) ((-402 |#1|) . T) ((-442) |has| |#1| (-539)) ((-463) |has| |#1| (-463)) ((-503 (-590 $) $) . T) ((-503 $ $) . T) ((-539) |has| |#1| (-539)) ((-622 #0#) |has| |#1| (-539)) ((-622 |#1|) |has| |#1| (-169)) ((-622 $) -1524 (|has| |#1| (-1016)) (|has| |#1| (-539)) (|has| |#1| (-169)) (|has| |#1| (-145)) (|has| |#1| (-143))) ((-615 (-547)) -12 (|has| |#1| (-615 (-547))) (|has| |#1| (-1016))) ((-615 |#1|) |has| |#1| (-1016)) ((-692 #0#) |has| |#1| (-539)) ((-692 |#1|) |has| |#1| (-169)) ((-692 $) |has| |#1| (-539)) ((-701) -1524 (|has| |#1| (-1075)) (|has| |#1| (-1016)) (|has| |#1| (-539)) (|has| |#1| (-463)) (|has| |#1| (-169)) (|has| |#1| (-145)) (|has| |#1| (-143))) ((-821) . T) ((-869 (-1135)) |has| |#1| (-1016)) ((-855 (-370)) |has| |#1| (-855 (-370))) ((-855 (-547)) |has| |#1| (-855 (-547))) ((-853 |#1|) . T) ((-889) |has| |#1| (-539)) ((-1007 (-398 (-547))) -1524 (|has| |#1| (-1007 (-398 (-547)))) (-12 (|has| |#1| (-539)) (|has| |#1| (-1007 (-547))))) ((-1007 (-398 (-921 |#1|))) |has| |#1| (-539)) ((-1007 (-547)) |has| |#1| (-1007 (-547))) ((-1007 (-590 $)) . 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T) ((-23) . T) ((-47 |#1| #0=(-547)) . T) ((-25) . T) ((-38 #1=(-398 (-547))) -1524 (|has| |#1| (-354)) (|has| |#1| (-38 (-398 (-547))))) ((-38 |#1|) |has| |#1| (-169)) ((-38 |#2|) |has| |#1| (-354)) ((-38 $) -1524 (|has| |#1| (-539)) (|has| |#1| (-354))) ((-35) |has| |#1| (-38 (-398 (-547)))) ((-94) |has| |#1| (-38 (-398 (-547)))) ((-101) . T) ((-111 #1# #1#) -1524 (|has| |#1| (-354)) (|has| |#1| (-38 (-398 (-547))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-354)) ((-111 $ $) -1524 (|has| |#1| (-539)) (|has| |#1| (-354)) (|has| |#1| (-169))) ((-130) . T) ((-143) -1524 (-12 (|has| |#1| (-354)) (|has| |#2| (-143))) (|has| |#1| (-143))) ((-145) -1524 (-12 (|has| |#1| (-354)) (|has| |#2| (-145))) (|has| |#1| (-145))) ((-591 (-832)) . 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T) ((-622 |#2|) |has| |#1| (-354)) ((-622 $) . T) ((-615 (-547)) -12 (|has| |#1| (-354)) (|has| |#2| (-615 (-547)))) ((-615 |#2|) |has| |#1| (-354)) ((-692 #1#) -1524 (|has| |#1| (-354)) (|has| |#1| (-38 (-398 (-547))))) ((-692 |#1|) |has| |#1| (-169)) ((-692 |#2|) |has| |#1| (-354)) ((-692 $) -1524 (|has| |#1| (-539)) (|has| |#1| (-354))) ((-701) . T) ((-765) -12 (|has| |#1| (-354)) (|has| |#2| (-794))) ((-766) -12 (|has| |#1| (-354)) (|has| |#2| (-794))) ((-768) -12 (|has| |#1| (-354)) (|has| |#2| (-794))) ((-769) -12 (|has| |#1| (-354)) (|has| |#2| (-794))) ((-794) -12 (|has| |#1| (-354)) (|has| |#2| (-794))) ((-819) -12 (|has| |#1| (-354)) (|has| |#2| (-794))) ((-821) -1524 (-12 (|has| |#1| (-354)) (|has| |#2| (-821))) (-12 (|has| |#1| (-354)) (|has| |#2| (-794)))) ((-869 (-1135)) -1524 (-12 (|has| |#1| (-354)) (|has| |#2| (-869 (-1135)))) (-12 (|has| |#1| (-15 * (|#1| (-547) |#1|))) (|has| |#1| (-869 (-1135))))) ((-855 (-370)) -12 (|has| |#1| (-354)) (|has| |#2| (-855 (-370)))) ((-855 (-547)) -12 (|has| |#1| (-354)) (|has| |#2| (-855 (-547)))) ((-853 |#2|) |has| |#1| (-354)) ((-878) -12 (|has| |#1| (-354)) (|has| |#2| (-878))) ((-942 |#1| #0# (-1045)) . T) ((-889) |has| |#1| (-354)) ((-961 |#2|) |has| |#1| (-354)) ((-971) |has| |#1| (-38 (-398 (-547)))) ((-991) -12 (|has| |#1| (-354)) (|has| |#2| (-991))) ((-1007 (-398 (-547))) -12 (|has| |#1| (-354)) (|has| |#2| (-1007 (-547)))) ((-1007 (-547)) -12 (|has| |#1| (-354)) (|has| |#2| (-1007 (-547)))) ((-1007 (-1135)) -12 (|has| |#1| (-354)) (|has| |#2| (-1007 (-1135)))) ((-1007 |#2|) . T) ((-1022 #1#) -1524 (|has| |#1| (-354)) (|has| |#1| (-38 (-398 (-547))))) ((-1022 |#1|) . T) ((-1022 |#2|) |has| |#1| (-354)) ((-1022 $) -1524 (|has| |#1| (-539)) (|has| |#1| (-354)) (|has| |#1| (-169))) ((-1016) . T) ((-1023) . T) ((-1075) . T) ((-1063) . T) ((-1111) -12 (|has| |#1| (-354)) (|has| |#2| (-1111))) ((-1157) |has| |#1| (-38 (-398 (-547)))) ((-1160) |has| |#1| (-38 (-398 (-547)))) ((-1172) |has| |#1| (-354)) ((-1176) |has| |#1| (-354)) ((-1178 |#1|) . T) ((-1196 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-547)) . T) ((-25) . T) ((-38 #1=(-398 (-547))) -1525 (|has| |#1| (-354)) (|has| |#1| (-38 (-398 (-547))))) ((-38 |#1|) |has| |#1| (-169)) ((-38 |#2|) |has| |#1| (-354)) ((-38 $) -1525 (|has| |#1| (-539)) (|has| |#1| (-354))) ((-35) |has| |#1| (-38 (-398 (-547)))) ((-94) |has| |#1| (-38 (-398 (-547)))) ((-101) . T) ((-111 #1# #1#) -1525 (|has| |#1| (-354)) (|has| |#1| (-38 (-398 (-547))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-354)) ((-111 $ $) -1525 (|has| |#1| (-539)) (|has| |#1| (-354)) (|has| |#1| (-169))) ((-130) . T) ((-143) -1525 (-12 (|has| |#1| (-354)) (|has| |#2| (-143))) (|has| |#1| (-143))) ((-145) -1525 (-12 (|has| |#1| (-354)) (|has| |#2| (-145))) (|has| |#1| (-145))) ((-591 (-832)) . 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T) ((-622 |#2|) |has| |#1| (-354)) ((-622 $) . T) ((-615 (-547)) -12 (|has| |#1| (-354)) (|has| |#2| (-615 (-547)))) ((-615 |#2|) |has| |#1| (-354)) ((-692 #1#) -1525 (|has| |#1| (-354)) (|has| |#1| (-38 (-398 (-547))))) ((-692 |#1|) |has| |#1| (-169)) ((-692 |#2|) |has| |#1| (-354)) ((-692 $) -1525 (|has| |#1| (-539)) (|has| |#1| (-354))) ((-701) . 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T) ((-23) . T) ((-47 |#1| #0=(-745)) . T) ((-25) . T) ((-38 #1=(-398 (-547))) |has| |#1| (-38 (-398 (-547)))) ((-38 |#1|) |has| |#1| (-169)) ((-38 $) -1525 (|has| |#1| (-878)) (|has| |#1| (-539)) (|has| |#1| (-442)) (|has| |#1| (-354))) ((-101) . T) ((-111 #1# #1#) |has| |#1| (-38 (-398 (-547)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -1525 (|has| |#1| (-878)) (|has| |#1| (-539)) (|has| |#1| (-442)) (|has| |#1| (-354)) (|has| |#1| (-169))) ((-130) . T) ((-143) |has| |#1| (-143)) ((-145) |has| |#1| (-145)) ((-591 (-832)) . T) ((-169) -1525 (|has| |#1| (-878)) (|has| |#1| (-539)) (|has| |#1| (-442)) (|has| |#1| (-354)) (|has| |#1| (-169))) ((-592 (-523)) -12 (|has| (-1045) (-592 (-523))) (|has| |#1| (-592 (-523)))) ((-592 (-861 (-370))) -12 (|has| (-1045) (-592 (-861 (-370)))) (|has| |#1| (-592 (-861 (-370))))) ((-592 (-861 (-547))) -12 (|has| (-1045) (-592 (-861 (-547)))) (|has| |#1| (-592 (-861 (-547))))) ((-223 |#1|) . T) ((-225) . T) ((-277 (-398 $) (-398 $)) |has| |#1| (-539)) ((-277 |#1| |#1|) . T) ((-277 $ $) . T) ((-281) -1525 (|has| |#1| (-878)) (|has| |#1| (-539)) (|has| |#1| (-442)) (|has| |#1| (-354))) ((-298) |has| |#1| (-354)) ((-300 $) . T) ((-317 |#1| #0#) . T) ((-368 |#1|) . T) ((-402 |#1|) . T) ((-442) -1525 (|has| |#1| (-878)) (|has| |#1| (-442)) (|has| |#1| (-354))) ((-503 #2=(-1045) |#1|) . T) ((-503 #2# $) . T) ((-503 $ $) . T) ((-539) -1525 (|has| |#1| (-878)) (|has| |#1| (-539)) (|has| |#1| (-442)) (|has| |#1| (-354))) ((-622 #1#) |has| |#1| (-38 (-398 (-547)))) ((-622 |#1|) . T) ((-622 $) . T) ((-615 (-547)) |has| |#1| (-615 (-547))) ((-615 |#1|) . T) ((-692 #1#) |has| |#1| (-38 (-398 (-547)))) ((-692 |#1|) |has| |#1| (-169)) ((-692 $) -1525 (|has| |#1| (-878)) (|has| |#1| (-539)) (|has| |#1| (-442)) (|has| |#1| (-354))) ((-701) . T) ((-821) |has| |#1| (-821)) ((-869 #2#) . T) ((-869 (-1135)) |has| |#1| (-869 (-1135))) ((-855 (-370)) -12 (|has| (-1045) (-855 (-370))) (|has| |#1| (-855 (-370)))) ((-855 (-547)) -12 (|has| (-1045) (-855 (-547))) (|has| |#1| (-855 (-547)))) ((-918 |#1| #0# #2#) . T) ((-878) |has| |#1| (-878)) ((-889) |has| |#1| (-354)) ((-1007 (-398 (-547))) |has| |#1| (-1007 (-398 (-547)))) ((-1007 (-547)) |has| |#1| (-1007 (-547))) ((-1007 #2#) . T) ((-1007 |#1|) . T) ((-1022 #1#) |has| |#1| (-38 (-398 (-547)))) ((-1022 |#1|) . T) ((-1022 $) -1525 (|has| |#1| (-878)) (|has| |#1| (-539)) (|has| |#1| (-442)) (|has| |#1| (-354)) (|has| |#1| (-169))) ((-1016) . T) ((-1023) . T) ((-1075) . T) ((-1063) . T) ((-1111) |has| |#1| (-1111)) ((-1176) |has| |#1| (-878))) +((-2259 (((-619 (-1045)) $) 28)) (-2055 (($ $) 25)) (-2230 (($ |#2| |#3|) NIL) (($ $ (-1045) |#3|) 22) (($ $ (-619 (-1045)) (-619 |#3|)) 21)) (-2014 (($ $) 14)) (-2028 ((|#2| $) 12)) (-4054 ((|#3| $) 10))) +(((-1195 |#1| |#2| |#3|) (-10 -8 (-15 -2259 ((-619 (-1045)) |#1|)) (-15 -2230 (|#1| |#1| (-619 (-1045)) (-619 |#3|))) (-15 -2230 (|#1| |#1| (-1045) |#3|)) (-15 -2055 (|#1| |#1|)) (-15 -2230 (|#1| |#2| |#3|)) (-15 -4054 (|#3| |#1|)) (-15 -2014 (|#1| |#1|)) (-15 -2028 (|#2| |#1|))) (-1196 |#2| |#3|) (-1016) (-766)) (T -1195)) +NIL +(-10 -8 (-15 -2259 ((-619 (-1045)) |#1|)) (-15 -2230 (|#1| |#1| (-619 (-1045)) (-619 |#3|))) (-15 -2230 (|#1| |#1| (-1045) |#3|)) (-15 -2055 (|#1| |#1|)) (-15 -2230 (|#1| |#2| |#3|)) (-15 -4054 (|#3| |#1|)) (-15 -2014 (|#1| |#1|)) (-15 -2028 (|#2| |#1|))) +((-3824 (((-112) $ $) 7)) (-3574 (((-112) $) 16)) (-2259 (((-619 (-1045)) $) 72)) (-2996 (((-1135) $) 101)) (-4107 (((-2 (|:| -2978 $) (|:| 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(-1111)) @@ -5120,4 +5120,4 @@ NIL NIL NIL NIL -((-3 3160516 3160521 3160526 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-2 3160501 3160506 3160511 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1 3160486 3160491 3160496 NIL NIL NIL NIL (NIL) -8 NIL NIL) (0 3160471 3160476 3160481 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1246 3159647 3160346 3160423 "ZMOD" 3160428 NIL ZMOD (NIL NIL) -8 NIL NIL) (-1245 3158757 3158921 3159130 "ZLINDEP" 3159479 NIL ZLINDEP (NIL T) -7 NIL NIL) (-1244 3148133 3149885 3151844 "ZDSOLVE" 3156899 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL) (-1243 3147379 3147520 3147709 "YSTREAM" 3147979 NIL YSTREAM (NIL T) -7 NIL NIL) (-1242 3145190 3146680 3146884 "XRPOLY" 3147222 NIL XRPOLY (NIL T T) -8 NIL NIL) (-1241 3141682 3142965 3143549 "XPR" 3144653 NIL XPR (NIL T T) -8 NIL NIL) (-1240 3139438 3141013 3141217 "XPOLY" 3141513 NIL XPOLY (NIL T) -8 NIL NIL) (-1239 3137287 3138621 3138676 "XPOLYC" 3138964 NIL XPOLYC (NIL T T) -9 NIL 3139077) (-1238 3133705 3135804 3136192 "XPBWPOLY" 3136945 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1237 3129690 3131938 3131980 "XF" 3132601 NIL XF (NIL T) -9 NIL 3133001) (-1236 3129311 3129399 3129568 "XF-" 3129573 NIL XF- (NIL T T) -8 NIL NIL) (-1235 3124703 3125958 3126013 "XFALG" 3128185 NIL XFALG (NIL T T) -9 NIL 3128974) (-1234 3123836 3123940 3124145 "XEXPPKG" 3124595 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1233 3121980 3123686 3123782 "XDPOLY" 3123787 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1232 3120896 3121462 3121505 "XALG" 3121568 NIL XALG (NIL T) -9 NIL 3121688) (-1231 3114365 3118873 3119367 "WUTSET" 3120488 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1230 3112216 3112977 3113330 "WP" 3114146 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1229 3111862 3112038 3112108 "WHILEAST" 3112168 T WHILEAST (NIL) -8 NIL NIL) (-1228 3111378 3111579 3111673 "WHEREAST" 3111790 T WHEREAST (NIL) -8 NIL NIL) (-1227 3110264 3110462 3110757 "WFFINTBS" 3111175 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1226 3108168 3108595 3109057 "WEIER" 3109836 NIL WEIER (NIL T) -7 NIL NIL) (-1225 3107315 3107739 3107781 "VSPACE" 3107917 NIL VSPACE (NIL T) -9 NIL 3107991) (-1224 3107153 3107180 3107271 "VSPACE-" 3107276 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1223 3106899 3106942 3107013 "VOID" 3107104 T VOID (NIL) -8 NIL NIL) (-1222 3105035 3105394 3105800 "VIEW" 3106515 T VIEW (NIL) -7 NIL NIL) (-1221 3101460 3102098 3102835 "VIEWDEF" 3104320 T VIEWDEF (NIL) -7 NIL NIL) (-1220 3090798 3093008 3095181 "VIEW3D" 3099309 T VIEW3D (NIL) -8 NIL NIL) (-1219 3083080 3084709 3086288 "VIEW2D" 3089241 T VIEW2D (NIL) -8 NIL NIL) (-1218 3078484 3082850 3082942 "VECTOR" 3083023 NIL VECTOR (NIL T) -8 NIL NIL) (-1217 3077061 3077320 3077638 "VECTOR2" 3078214 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1216 3070588 3074845 3074888 "VECTCAT" 3075881 NIL VECTCAT (NIL T) -9 NIL 3076467) (-1215 3069602 3069856 3070246 "VECTCAT-" 3070251 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1214 3069083 3069253 3069373 "VARIABLE" 3069517 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1213 3069016 3069021 3069051 "UTYPE" 3069056 T UTYPE (NIL) -9 NIL NIL) (-1212 3067846 3068000 3068262 "UTSODETL" 3068842 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1211 3065286 3065746 3066270 "UTSODE" 3067387 NIL UTSODE (NIL T T) -7 NIL NIL) (-1210 3057162 3062912 3063401 "UTS" 3064855 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1209 3048535 3053854 3053897 "UTSCAT" 3055009 NIL UTSCAT (NIL T) -9 NIL 3055766) (-1208 3045889 3046605 3047594 "UTSCAT-" 3047599 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1207 3045516 3045559 3045692 "UTS2" 3045840 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1206 3039791 3042356 3042399 "URAGG" 3044469 NIL URAGG (NIL T) -9 NIL 3045191) (-1205 3036730 3037593 3038716 "URAGG-" 3038721 NIL URAGG- (NIL T T) -8 NIL NIL) (-1204 3032454 3035344 3035816 "UPXSSING" 3036394 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1203 3024424 3031569 3031851 "UPXS" 3032230 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1202 3017537 3024328 3024400 "UPXSCONS" 3024405 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1201 3007895 3014640 3014702 "UPXSCCA" 3015358 NIL UPXSCCA (NIL T T) -9 NIL 3015600) (-1200 3007533 3007618 3007792 "UPXSCCA-" 3007797 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1199 2997817 3004335 3004378 "UPXSCAT" 3005026 NIL UPXSCAT (NIL T) -9 NIL 3005634) (-1198 2997247 2997326 2997505 "UPXS2" 2997732 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1197 2995901 2996154 2996505 "UPSQFREE" 2996990 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1196 2989819 2992828 2992883 "UPSCAT" 2994044 NIL UPSCAT (NIL T T) -9 NIL 2994818) (-1195 2989023 2989230 2989557 "UPSCAT-" 2989562 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1194 2975114 2983110 2983153 "UPOLYC" 2985254 NIL UPOLYC (NIL T) -9 NIL 2986475) (-1193 2966443 2968868 2972015 "UPOLYC-" 2972020 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1192 2966070 2966113 2966246 "UPOLYC2" 2966394 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1191 2957527 2965636 2965774 "UP" 2965980 NIL UP (NIL NIL T) -8 NIL NIL) (-1190 2956866 2956973 2957137 "UPMP" 2957416 NIL UPMP (NIL T T) -7 NIL NIL) (-1189 2956419 2956500 2956639 "UPDIVP" 2956779 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1188 2954987 2955236 2955552 "UPDECOMP" 2956168 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1187 2954222 2954334 2954519 "UPCDEN" 2954871 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1186 2953741 2953810 2953959 "UP2" 2954147 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1185 2952258 2952945 2953222 "UNISEG" 2953499 NIL UNISEG (NIL T) -8 NIL NIL) (-1184 2951473 2951600 2951805 "UNISEG2" 2952101 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1183 2950533 2950713 2950939 "UNIFACT" 2951289 NIL UNIFACT (NIL T) -7 NIL NIL) (-1182 2934502 2949710 2949961 "ULS" 2950340 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1181 2922544 2934406 2934478 "ULSCONS" 2934483 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1180 2905348 2917283 2917345 "ULSCCAT" 2918065 NIL ULSCCAT (NIL T T) -9 NIL 2918362) (-1179 2904398 2904643 2905031 "ULSCCAT-" 2905036 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1178 2894459 2900891 2900934 "ULSCAT" 2901797 NIL ULSCAT (NIL T) -9 NIL 2902527) (-1177 2893889 2893968 2894147 "ULS2" 2894374 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1176 2892327 2893250 2893280 "UFD" 2893492 T UFD (NIL) -9 NIL 2893606) (-1175 2892121 2892167 2892262 "UFD-" 2892267 NIL UFD- (NIL T) -8 NIL NIL) (-1174 2891203 2891386 2891602 "UDVO" 2891927 T UDVO (NIL) -7 NIL NIL) (-1173 2889019 2889428 2889899 "UDPO" 2890767 NIL UDPO (NIL T) -7 NIL NIL) (-1172 2888952 2888957 2888987 "TYPE" 2888992 T TYPE (NIL) -9 NIL NIL) (-1171 2888606 2888774 2888844 "TYPEAST" 2888904 T TYPEAST (NIL) -8 NIL NIL) (-1170 2887577 2887779 2888019 "TWOFACT" 2888400 NIL TWOFACT (NIL T) -7 NIL NIL) (-1169 2886515 2886852 2887115 "TUPLE" 2887349 NIL TUPLE (NIL T) -8 NIL NIL) (-1168 2884206 2884725 2885264 "TUBETOOL" 2885998 T TUBETOOL (NIL) -7 NIL NIL) (-1167 2883055 2883260 2883501 "TUBE" 2883999 NIL TUBE (NIL T) -8 NIL NIL) (-1166 2877819 2882027 2882310 "TS" 2882807 NIL TS (NIL T) -8 NIL NIL) (-1165 2866486 2870578 2870675 "TSETCAT" 2875944 NIL TSETCAT (NIL T T T T) -9 NIL 2877475) (-1164 2861220 2862818 2864709 "TSETCAT-" 2864714 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1163 2855483 2856329 2857271 "TRMANIP" 2860356 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1162 2854924 2854987 2855150 "TRIMAT" 2855415 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1161 2852720 2852957 2853321 "TRIGMNIP" 2854673 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1160 2852240 2852353 2852383 "TRIGCAT" 2852596 T TRIGCAT (NIL) -9 NIL NIL) (-1159 2851909 2851988 2852129 "TRIGCAT-" 2852134 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1158 2848808 2850769 2851049 "TREE" 2851664 NIL TREE (NIL T) -8 NIL NIL) (-1157 2848082 2848610 2848640 "TRANFUN" 2848675 T TRANFUN (NIL) -9 NIL 2848741) (-1156 2847361 2847552 2847832 "TRANFUN-" 2847837 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1155 2847165 2847197 2847258 "TOPSP" 2847322 T TOPSP (NIL) -7 NIL NIL) (-1154 2846513 2846628 2846782 "TOOLSIGN" 2847046 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1153 2845174 2845690 2845929 "TEXTFILE" 2846296 T TEXTFILE (NIL) -8 NIL NIL) (-1152 2843039 2843553 2843991 "TEX" 2844758 T TEX (NIL) -8 NIL NIL) (-1151 2842820 2842851 2842923 "TEX1" 2843002 NIL TEX1 (NIL T) -7 NIL NIL) (-1150 2842468 2842531 2842621 "TEMUTL" 2842752 T TEMUTL (NIL) -7 NIL NIL) (-1149 2840622 2840902 2841227 "TBCMPPK" 2842191 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1148 2832510 2838782 2838838 "TBAGG" 2839238 NIL TBAGG (NIL T T) -9 NIL 2839449) (-1147 2827580 2829068 2830822 "TBAGG-" 2830827 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1146 2826964 2827071 2827216 "TANEXP" 2827469 NIL TANEXP (NIL T) -7 NIL NIL) (-1145 2820465 2826821 2826914 "TABLE" 2826919 NIL TABLE (NIL T T) -8 NIL NIL) (-1144 2819877 2819976 2820114 "TABLEAU" 2820362 NIL TABLEAU (NIL T) -8 NIL NIL) (-1143 2814485 2815705 2816953 "TABLBUMP" 2818663 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1142 2813913 2814013 2814141 "SYSTEM" 2814379 T SYSTEM (NIL) -7 NIL NIL) (-1141 2810376 2811071 2811854 "SYSSOLP" 2813164 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1140 2806667 2807375 2808109 "SYNTAX" 2809664 T SYNTAX (NIL) -8 NIL NIL) (-1139 2803825 2804427 2805059 "SYMTAB" 2806057 T SYMTAB (NIL) -8 NIL NIL) (-1138 2799074 2799976 2800959 "SYMS" 2802864 T SYMS (NIL) -8 NIL NIL) (-1137 2796346 2798532 2798762 "SYMPOLY" 2798879 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1136 2795863 2795938 2796061 "SYMFUNC" 2796258 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1135 2791840 2793100 2793922 "SYMBOL" 2795063 T SYMBOL (NIL) -8 NIL NIL) (-1134 2785379 2787068 2788788 "SWITCH" 2790142 T SWITCH (NIL) -8 NIL NIL) (-1133 2778649 2784200 2784503 "SUTS" 2785134 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1132 2770618 2777764 2778046 "SUPXS" 2778425 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1131 2762147 2770236 2770362 "SUP" 2770527 NIL SUP (NIL T) -8 NIL NIL) (-1130 2761306 2761433 2761650 "SUPFRACF" 2762015 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1129 2760927 2760986 2761099 "SUP2" 2761241 NIL SUP2 (NIL T T) -7 NIL NIL) (-1128 2759340 2759614 2759977 "SUMRF" 2760626 NIL SUMRF (NIL T) -7 NIL NIL) (-1127 2758654 2758720 2758919 "SUMFS" 2759261 NIL SUMFS (NIL T T) -7 NIL NIL) (-1126 2742663 2757831 2758082 "SULS" 2758461 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1125 2741985 2742188 2742328 "SUCH" 2742571 NIL SUCH (NIL T T) -8 NIL NIL) (-1124 2735879 2736891 2737850 "SUBSPACE" 2741073 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1123 2735309 2735399 2735563 "SUBRESP" 2735767 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1122 2728678 2729974 2731285 "STTF" 2734045 NIL STTF (NIL T) -7 NIL NIL) (-1121 2722851 2723971 2725118 "STTFNC" 2727578 NIL STTFNC (NIL T) -7 NIL NIL) (-1120 2714166 2716033 2717827 "STTAYLOR" 2721092 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1119 2707410 2714030 2714113 "STRTBL" 2714118 NIL STRTBL (NIL T) -8 NIL NIL) (-1118 2702801 2707365 2707396 "STRING" 2707401 T STRING (NIL) -8 NIL NIL) (-1117 2697689 2702174 2702204 "STRICAT" 2702263 T STRICAT (NIL) -9 NIL 2702325) (-1116 2690402 2695212 2695832 "STREAM" 2697104 NIL STREAM (NIL T) -8 NIL NIL) (-1115 2689912 2689989 2690133 "STREAM3" 2690319 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1114 2688894 2689077 2689312 "STREAM2" 2689725 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1113 2688582 2688634 2688727 "STREAM1" 2688836 NIL STREAM1 (NIL T) -7 NIL NIL) (-1112 2687598 2687779 2688010 "STINPROD" 2688398 NIL STINPROD (NIL T) -7 NIL NIL) (-1111 2687176 2687360 2687390 "STEP" 2687470 T STEP (NIL) -9 NIL 2687548) (-1110 2680719 2687075 2687152 "STBL" 2687157 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1109 2675894 2679941 2679984 "STAGG" 2680137 NIL STAGG (NIL T) -9 NIL 2680226) (-1108 2673596 2674198 2675070 "STAGG-" 2675075 NIL STAGG- (NIL T T) -8 NIL NIL) (-1107 2671791 2673366 2673458 "STACK" 2673539 NIL STACK (NIL T) -8 NIL NIL) (-1106 2664516 2669932 2670388 "SREGSET" 2671421 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1105 2656942 2658310 2659823 "SRDCMPK" 2663122 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1104 2649909 2654382 2654412 "SRAGG" 2655715 T SRAGG (NIL) -9 NIL 2656323) (-1103 2648926 2649181 2649560 "SRAGG-" 2649565 NIL SRAGG- (NIL T) -8 NIL NIL) (-1102 2643412 2647841 2648269 "SQMATRIX" 2648545 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1101 2637164 2640132 2640858 "SPLTREE" 2642758 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1100 2633154 2633820 2634466 "SPLNODE" 2636590 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1099 2632201 2632434 2632464 "SPFCAT" 2632908 T SPFCAT (NIL) -9 NIL NIL) (-1098 2630938 2631148 2631412 "SPECOUT" 2631959 T SPECOUT (NIL) -7 NIL NIL) (-1097 2630699 2630739 2630808 "SPADPRSR" 2630891 T SPADPRSR (NIL) -7 NIL NIL) (-1096 2622670 2624417 2624460 "SPACEC" 2628833 NIL SPACEC (NIL T) -9 NIL 2630649) (-1095 2620841 2622602 2622651 "SPACE3" 2622656 NIL SPACE3 (NIL T) -8 NIL NIL) (-1094 2619593 2619764 2620055 "SORTPAK" 2620646 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1093 2617643 2617946 2618365 "SOLVETRA" 2619257 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1092 2616654 2616876 2617150 "SOLVESER" 2617416 NIL SOLVESER (NIL T) -7 NIL NIL) (-1091 2611874 2612755 2613757 "SOLVERAD" 2615706 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1090 2607689 2608298 2609027 "SOLVEFOR" 2611241 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1089 2601986 2607038 2607135 "SNTSCAT" 2607140 NIL SNTSCAT (NIL T T T T) -9 NIL 2607210) (-1088 2596129 2600309 2600700 "SMTS" 2601676 NIL SMTS (NIL T T T) -8 NIL NIL) (-1087 2590579 2596017 2596094 "SMP" 2596099 NIL SMP (NIL T T) -8 NIL NIL) (-1086 2588738 2589039 2589437 "SMITH" 2590276 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1085 2581721 2585876 2585979 "SMATCAT" 2587330 NIL SMATCAT (NIL NIL T T T) -9 NIL 2587880) (-1084 2578661 2579484 2580662 "SMATCAT-" 2580667 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1083 2576374 2577897 2577940 "SKAGG" 2578201 NIL SKAGG (NIL T) -9 NIL 2578336) (-1082 2572490 2575478 2575756 "SINT" 2576118 T SINT (NIL) -8 NIL NIL) (-1081 2572262 2572300 2572366 "SIMPAN" 2572446 T SIMPAN (NIL) -7 NIL NIL) (-1080 2571569 2571797 2571937 "SIG" 2572144 T SIG (NIL) -8 NIL NIL) (-1079 2570407 2570628 2570903 "SIGNRF" 2571328 NIL SIGNRF (NIL T) -7 NIL NIL) (-1078 2569212 2569363 2569654 "SIGNEF" 2570236 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1077 2566902 2567356 2567862 "SHP" 2568753 NIL SHP (NIL T NIL) -7 NIL NIL) (-1076 2560808 2566803 2566879 "SHDP" 2566884 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1075 2560407 2560573 2560603 "SGROUP" 2560696 T SGROUP (NIL) -9 NIL 2560758) (-1074 2560265 2560291 2560364 "SGROUP-" 2560369 NIL SGROUP- (NIL T) -8 NIL NIL) (-1073 2557101 2557798 2558521 "SGCF" 2559564 T SGCF (NIL) -7 NIL NIL) (-1072 2551496 2556548 2556645 "SFRTCAT" 2556650 NIL SFRTCAT (NIL T T T T) -9 NIL 2556689) (-1071 2544920 2545935 2547071 "SFRGCD" 2550479 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1070 2538048 2539119 2540305 "SFQCMPK" 2543853 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1069 2537670 2537759 2537869 "SFORT" 2537989 NIL SFORT (NIL T T) -8 NIL NIL) (-1068 2536815 2537510 2537631 "SEXOF" 2537636 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1067 2535949 2536696 2536764 "SEX" 2536769 T SEX (NIL) -8 NIL NIL) (-1066 2530725 2531414 2531509 "SEXCAT" 2535280 NIL SEXCAT (NIL T T T T T) -9 NIL 2535899) (-1065 2527905 2530659 2530707 "SET" 2530712 NIL SET (NIL T) -8 NIL NIL) (-1064 2526156 2526618 2526923 "SETMN" 2527646 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1063 2525762 2525888 2525918 "SETCAT" 2526035 T SETCAT (NIL) -9 NIL 2526120) (-1062 2525542 2525594 2525693 "SETCAT-" 2525698 NIL SETCAT- (NIL T) -8 NIL NIL) (-1061 2521929 2524003 2524046 "SETAGG" 2524916 NIL SETAGG (NIL T) -9 NIL 2525256) (-1060 2521387 2521503 2521740 "SETAGG-" 2521745 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1059 2520591 2520884 2520945 "SEGXCAT" 2521231 NIL SEGXCAT (NIL T T) -9 NIL 2521351) (-1058 2519647 2520257 2520439 "SEG" 2520444 NIL SEG (NIL T) -8 NIL NIL) (-1057 2518554 2518767 2518810 "SEGCAT" 2519392 NIL SEGCAT (NIL T) -9 NIL 2519630) (-1056 2517603 2517933 2518133 "SEGBIND" 2518389 NIL SEGBIND (NIL T) -8 NIL NIL) (-1055 2517224 2517283 2517396 "SEGBIND2" 2517538 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1054 2516842 2517025 2517102 "SEGAST" 2517169 T SEGAST (NIL) -8 NIL NIL) (-1053 2516061 2516187 2516391 "SEG2" 2516686 NIL SEG2 (NIL T T) -7 NIL NIL) (-1052 2515498 2515996 2516043 "SDVAR" 2516048 NIL SDVAR (NIL T) -8 NIL NIL) (-1051 2507788 2515268 2515398 "SDPOL" 2515403 NIL SDPOL (NIL T) -8 NIL NIL) (-1050 2506381 2506647 2506966 "SCPKG" 2507503 NIL SCPKG (NIL T) -7 NIL NIL) (-1049 2505517 2505697 2505897 "SCOPE" 2506203 T SCOPE (NIL) -8 NIL NIL) (-1048 2504738 2504871 2505050 "SCACHE" 2505372 NIL SCACHE (NIL T) -7 NIL NIL) (-1047 2504464 2504607 2504637 "SASTCAT" 2504642 T SASTCAT (NIL) -9 NIL 2504655) (-1046 2504253 2504298 2504396 "SASTCAT-" 2504401 NIL SASTCAT- (NIL T) -8 NIL NIL) (-1045 2503692 2504013 2504098 "SAOS" 2504190 T SAOS (NIL) -8 NIL NIL) (-1044 2503257 2503292 2503465 "SAERFFC" 2503651 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1043 2497231 2503154 2503234 "SAE" 2503239 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1042 2496824 2496859 2497018 "SAEFACT" 2497190 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1041 2495145 2495459 2495860 "RURPK" 2496490 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1040 2493781 2494060 2494372 "RULESET" 2494979 NIL RULESET (NIL T T T) -8 NIL NIL) (-1039 2490968 2491471 2491936 "RULE" 2493462 NIL RULE (NIL T T T) -8 NIL NIL) (-1038 2490607 2490762 2490845 "RULECOLD" 2490920 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1037 2485456 2486250 2487170 "RSETGCD" 2489806 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1036 2474713 2479765 2479862 "RSETCAT" 2483981 NIL RSETCAT (NIL T T T T) -9 NIL 2485078) (-1035 2472640 2473179 2474003 "RSETCAT-" 2474008 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1034 2465027 2466402 2467922 "RSDCMPK" 2471239 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1033 2463032 2463473 2463547 "RRCC" 2464633 NIL RRCC (NIL T T) -9 NIL 2464977) (-1032 2462383 2462557 2462836 "RRCC-" 2462841 NIL RRCC- (NIL T T T) -8 NIL NIL) (-1031 2461870 2462079 2462180 "RPTAST" 2462304 T RPTAST (NIL) -8 NIL NIL) (-1030 2436098 2445683 2445750 "RPOLCAT" 2456414 NIL RPOLCAT (NIL T T T) -9 NIL 2459573) (-1029 2427598 2429936 2433058 "RPOLCAT-" 2433063 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-1028 2418645 2425809 2426291 "ROUTINE" 2427138 T ROUTINE (NIL) -8 NIL NIL) (-1027 2415391 2418196 2418345 "ROMAN" 2418518 T ROMAN (NIL) -8 NIL NIL) (-1026 2413666 2414251 2414511 "ROIRC" 2415196 NIL ROIRC (NIL T T) -8 NIL NIL) (-1025 2410117 2412356 2412386 "RNS" 2412690 T RNS (NIL) -9 NIL 2412962) (-1024 2408626 2409009 2409543 "RNS-" 2409618 NIL RNS- (NIL T) -8 NIL NIL) (-1023 2408075 2408457 2408487 "RNG" 2408492 T RNG (NIL) -9 NIL 2408513) (-1022 2407467 2407829 2407872 "RMODULE" 2407934 NIL RMODULE (NIL T) -9 NIL 2407976) (-1021 2406303 2406397 2406733 "RMCAT2" 2407368 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-1020 2403008 2405477 2405802 "RMATRIX" 2406037 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-1019 2395950 2398184 2398299 "RMATCAT" 2401658 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2402640) (-1018 2395325 2395472 2395779 "RMATCAT-" 2395784 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-1017 2394892 2394967 2395095 "RINTERP" 2395244 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-1016 2393980 2394500 2394530 "RING" 2394642 T RING (NIL) -9 NIL 2394737) (-1015 2393772 2393816 2393913 "RING-" 2393918 NIL RING- (NIL T) -8 NIL NIL) (-1014 2392613 2392850 2393108 "RIDIST" 2393536 T RIDIST (NIL) -7 NIL NIL) (-1013 2383929 2392081 2392287 "RGCHAIN" 2392461 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-1012 2380923 2381537 2382207 "RF" 2383293 NIL RF (NIL T) -7 NIL NIL) (-1011 2380569 2380632 2380735 "RFFACTOR" 2380854 NIL RFFACTOR (NIL T) -7 NIL NIL) (-1010 2380294 2380329 2380426 "RFFACT" 2380528 NIL RFFACT (NIL T) -7 NIL NIL) (-1009 2378411 2378775 2379157 "RFDIST" 2379934 T RFDIST (NIL) -7 NIL NIL) (-1008 2377864 2377956 2378119 "RETSOL" 2378313 NIL RETSOL (NIL T T) -7 NIL NIL) (-1007 2377452 2377532 2377575 "RETRACT" 2377768 NIL RETRACT (NIL T) -9 NIL NIL) (-1006 2377301 2377326 2377413 "RETRACT-" 2377418 NIL RETRACT- (NIL T T) -8 NIL NIL) (-1005 2376947 2377123 2377193 "RETAST" 2377253 T RETAST (NIL) -8 NIL NIL) (-1004 2369801 2376600 2376727 "RESULT" 2376842 T RESULT (NIL) -8 NIL NIL) (-1003 2368427 2369070 2369269 "RESRING" 2369704 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-1002 2368063 2368112 2368210 "RESLATC" 2368364 NIL RESLATC (NIL T) -7 NIL NIL) (-1001 2367769 2367803 2367910 "REPSQ" 2368022 NIL REPSQ (NIL T) -7 NIL NIL) (-1000 2365191 2365771 2366373 "REP" 2367189 T REP (NIL) -7 NIL NIL) (-999 2364892 2364926 2365035 "REPDB" 2365150 NIL REPDB (NIL T) -7 NIL NIL) (-998 2358820 2360199 2361420 "REP2" 2363704 NIL REP2 (NIL T) -7 NIL NIL) (-997 2355212 2355893 2356699 "REP1" 2358047 NIL REP1 (NIL T) -7 NIL NIL) (-996 2347950 2353365 2353819 "REGSET" 2354842 NIL REGSET (NIL T T T T) -8 NIL NIL) (-995 2346771 2347106 2347354 "REF" 2347735 NIL REF (NIL T) -8 NIL NIL) (-994 2346152 2346255 2346420 "REDORDER" 2346655 NIL REDORDER (NIL T T) -7 NIL NIL) (-993 2342172 2345380 2345603 "RECLOS" 2345981 NIL RECLOS (NIL T) -8 NIL NIL) (-992 2341229 2341410 2341623 "REALSOLV" 2341979 T REALSOLV (NIL) -7 NIL NIL) (-991 2341077 2341118 2341146 "REAL" 2341151 T REAL (NIL) -9 NIL 2341186) (-990 2337568 2338370 2339252 "REAL0Q" 2340242 NIL REAL0Q (NIL T) -7 NIL NIL) (-989 2333179 2334167 2335226 "REAL0" 2336549 NIL REAL0 (NIL T) -7 NIL NIL) (-988 2332699 2332900 2332992 "RDUCEAST" 2333107 T RDUCEAST (NIL) -8 NIL NIL) (-987 2332107 2332179 2332384 "RDIV" 2332621 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-986 2331180 2331354 2331565 "RDIST" 2331929 NIL RDIST (NIL T) -7 NIL NIL) (-985 2329781 2330068 2330438 "RDETRS" 2330888 NIL RDETRS (NIL T T) -7 NIL NIL) (-984 2327598 2328052 2328588 "RDETR" 2329323 NIL RDETR (NIL T T) -7 NIL NIL) (-983 2326212 2326490 2326892 "RDEEFS" 2327314 NIL RDEEFS (NIL T T) -7 NIL NIL) (-982 2324710 2325016 2325446 "RDEEF" 2325900 NIL RDEEF (NIL T T) -7 NIL NIL) (-981 2319047 2321918 2321946 "RCFIELD" 2323223 T RCFIELD (NIL) -9 NIL 2323953) (-980 2317116 2317620 2318313 "RCFIELD-" 2318386 NIL RCFIELD- (NIL T) -8 NIL NIL) (-979 2313447 2315232 2315273 "RCAGG" 2316344 NIL RCAGG (NIL T) -9 NIL 2316809) (-978 2313078 2313172 2313332 "RCAGG-" 2313337 NIL RCAGG- (NIL T T) -8 NIL NIL) (-977 2312418 2312530 2312693 "RATRET" 2312962 NIL RATRET (NIL T) -7 NIL NIL) (-976 2311975 2312042 2312161 "RATFACT" 2312346 NIL RATFACT (NIL T) -7 NIL NIL) (-975 2311290 2311410 2311560 "RANDSRC" 2311845 T RANDSRC (NIL) -7 NIL NIL) (-974 2311027 2311071 2311142 "RADUTIL" 2311239 T RADUTIL (NIL) -7 NIL NIL) (-973 2304092 2309770 2310087 "RADIX" 2310742 NIL RADIX (NIL NIL) -8 NIL NIL) (-972 2295748 2303936 2304064 "RADFF" 2304069 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-971 2295400 2295475 2295503 "RADCAT" 2295660 T RADCAT (NIL) -9 NIL NIL) (-970 2295185 2295233 2295330 "RADCAT-" 2295335 NIL RADCAT- (NIL T) -8 NIL NIL) (-969 2293336 2294960 2295049 "QUEUE" 2295129 NIL QUEUE (NIL T) -8 NIL NIL) (-968 2289912 2293273 2293318 "QUAT" 2293323 NIL QUAT (NIL T) -8 NIL NIL) (-967 2289550 2289593 2289720 "QUATCT2" 2289863 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-966 2283410 2286711 2286751 "QUATCAT" 2287531 NIL QUATCAT (NIL T) -9 NIL 2288297) (-965 2279554 2280591 2281978 "QUATCAT-" 2282072 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-964 2277074 2278638 2278679 "QUAGG" 2279054 NIL QUAGG (NIL T) -9 NIL 2279229) (-963 2276723 2276899 2276967 "QQUTAST" 2277026 T QQUTAST (NIL) -8 NIL NIL) (-962 2275648 2276121 2276293 "QFORM" 2276595 NIL QFORM (NIL NIL T) -8 NIL NIL) (-961 2266981 2272184 2272224 "QFCAT" 2272882 NIL QFCAT (NIL T) -9 NIL 2273881) (-960 2262553 2263754 2265345 "QFCAT-" 2265439 NIL QFCAT- (NIL T T) -8 NIL NIL) (-959 2262191 2262234 2262361 "QFCAT2" 2262504 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-958 2261651 2261761 2261891 "QEQUAT" 2262081 T QEQUAT (NIL) -8 NIL NIL) (-957 2254799 2255870 2257054 "QCMPACK" 2260584 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-956 2252375 2252796 2253224 "QALGSET" 2254454 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-955 2251620 2251794 2252026 "QALGSET2" 2252195 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-954 2250311 2250534 2250851 "PWFFINTB" 2251393 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-953 2248493 2248661 2249015 "PUSHVAR" 2250125 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-952 2244411 2245465 2245506 "PTRANFN" 2247390 NIL PTRANFN (NIL T) -9 NIL NIL) (-951 2242813 2243104 2243426 "PTPACK" 2244122 NIL PTPACK (NIL T) -7 NIL NIL) (-950 2242445 2242502 2242611 "PTFUNC2" 2242750 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-949 2236911 2241256 2241297 "PTCAT" 2241670 NIL PTCAT (NIL T) -9 NIL 2241832) (-948 2236569 2236604 2236728 "PSQFR" 2236870 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-947 2235164 2235462 2235796 "PSEUDLIN" 2236267 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-946 2221933 2224298 2226622 "PSETPK" 2232924 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-945 2214977 2217691 2217787 "PSETCAT" 2220808 NIL PSETCAT (NIL T T T T) -9 NIL 2221622) (-944 2212813 2213447 2214268 "PSETCAT-" 2214273 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-943 2212162 2212327 2212355 "PSCURVE" 2212623 T PSCURVE (NIL) -9 NIL 2212790) (-942 2208643 2210125 2210190 "PSCAT" 2211034 NIL PSCAT (NIL T T T) -9 NIL 2211274) (-941 2207706 2207922 2208322 "PSCAT-" 2208327 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-940 2206358 2206991 2207205 "PRTITION" 2207512 T PRTITION (NIL) -8 NIL NIL) (-939 2205878 2206079 2206171 "PRTDAST" 2206286 T PRTDAST (NIL) -8 NIL NIL) (-938 2194976 2197182 2199370 "PRS" 2203740 NIL PRS (NIL T T) -7 NIL NIL) (-937 2192834 2194326 2194366 "PRQAGG" 2194549 NIL PRQAGG (NIL T) -9 NIL 2194651) (-936 2192220 2192449 2192477 "PROPLOG" 2192662 T PROPLOG (NIL) -9 NIL 2192784) (-935 2189390 2190034 2190498 "PROPFRML" 2191788 NIL PROPFRML (NIL T) -8 NIL NIL) (-934 2188850 2188960 2189090 "PROPERTY" 2189280 T PROPERTY (NIL) -8 NIL NIL) (-933 2182935 2187016 2187836 "PRODUCT" 2188076 NIL PRODUCT (NIL T T) -8 NIL NIL) (-932 2180248 2182393 2182627 "PR" 2182746 NIL PR (NIL T T) -8 NIL NIL) (-931 2180044 2180076 2180135 "PRINT" 2180209 T PRINT (NIL) -7 NIL NIL) (-930 2179384 2179501 2179653 "PRIMES" 2179924 NIL PRIMES (NIL T) -7 NIL NIL) (-929 2177449 2177850 2178316 "PRIMELT" 2178963 NIL PRIMELT (NIL T) -7 NIL NIL) (-928 2177178 2177227 2177255 "PRIMCAT" 2177379 T PRIMCAT (NIL) -9 NIL NIL) (-927 2173339 2177116 2177161 "PRIMARR" 2177166 NIL PRIMARR (NIL T) -8 NIL NIL) (-926 2172346 2172524 2172752 "PRIMARR2" 2173157 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-925 2171989 2172045 2172156 "PREASSOC" 2172284 NIL PREASSOC (NIL T T) -7 NIL NIL) (-924 2171464 2171597 2171625 "PPCURVE" 2171830 T PPCURVE (NIL) -9 NIL 2171966) (-923 2171086 2171259 2171342 "PORTNUM" 2171401 T PORTNUM (NIL) -8 NIL NIL) (-922 2168445 2168844 2169436 "POLYROOT" 2170667 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-921 2162390 2168049 2168209 "POLY" 2168318 NIL POLY (NIL T) -8 NIL NIL) (-920 2161773 2161831 2162065 "POLYLIFT" 2162326 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-919 2158048 2158497 2159126 "POLYCATQ" 2161318 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-918 2145087 2150443 2150508 "POLYCAT" 2154022 NIL POLYCAT (NIL T T T) -9 NIL 2155950) (-917 2138537 2140398 2142782 "POLYCAT-" 2142787 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-916 2138124 2138192 2138312 "POLY2UP" 2138463 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-915 2137756 2137813 2137922 "POLY2" 2138061 NIL POLY2 (NIL T T) -7 NIL NIL) (-914 2136441 2136680 2136956 "POLUTIL" 2137530 NIL POLUTIL (NIL T T) -7 NIL NIL) (-913 2134796 2135073 2135404 "POLTOPOL" 2136163 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-912 2130314 2134732 2134778 "POINT" 2134783 NIL POINT (NIL T) -8 NIL NIL) (-911 2128501 2128858 2129233 "PNTHEORY" 2129959 T PNTHEORY (NIL) -7 NIL NIL) (-910 2126920 2127217 2127629 "PMTOOLS" 2128199 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-909 2126513 2126591 2126708 "PMSYM" 2126836 NIL PMSYM (NIL T) -7 NIL NIL) (-908 2126023 2126092 2126266 "PMQFCAT" 2126438 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-907 2125378 2125488 2125644 "PMPRED" 2125900 NIL PMPRED (NIL T) -7 NIL NIL) (-906 2124774 2124860 2125021 "PMPREDFS" 2125279 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-905 2123417 2123625 2124010 "PMPLCAT" 2124536 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-904 2122949 2123028 2123180 "PMLSAGG" 2123332 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-903 2122424 2122500 2122681 "PMKERNEL" 2122867 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-902 2122041 2122116 2122229 "PMINS" 2122343 NIL PMINS (NIL T) -7 NIL NIL) (-901 2121469 2121538 2121754 "PMFS" 2121966 NIL PMFS (NIL T T T) -7 NIL NIL) (-900 2120697 2120815 2121020 "PMDOWN" 2121346 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-899 2119860 2120019 2120201 "PMASS" 2120535 T PMASS (NIL) -7 NIL NIL) (-898 2119134 2119245 2119408 "PMASSFS" 2119746 NIL PMASSFS (NIL T T) -7 NIL NIL) (-897 2118789 2118857 2118951 "PLOTTOOL" 2119060 T PLOTTOOL (NIL) -7 NIL NIL) (-896 2113411 2114600 2115748 "PLOT" 2117661 T PLOT (NIL) -8 NIL NIL) (-895 2109225 2110259 2111180 "PLOT3D" 2112510 T PLOT3D (NIL) -8 NIL NIL) (-894 2108137 2108314 2108549 "PLOT1" 2109029 NIL PLOT1 (NIL T) -7 NIL NIL) (-893 2083531 2088203 2093054 "PLEQN" 2103403 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-892 2082849 2082971 2083151 "PINTERP" 2083396 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-891 2082542 2082589 2082692 "PINTERPA" 2082796 NIL PINTERPA (NIL T T) -7 NIL NIL) (-890 2081827 2082348 2082435 "PI" 2082475 T PI (NIL) -8 NIL NIL) (-889 2080259 2081200 2081228 "PID" 2081410 T PID (NIL) -9 NIL 2081544) (-888 2079984 2080021 2080109 "PICOERCE" 2080216 NIL PICOERCE (NIL T) -7 NIL NIL) (-887 2079304 2079443 2079619 "PGROEB" 2079840 NIL PGROEB (NIL T) -7 NIL NIL) (-886 2074891 2075705 2076610 "PGE" 2078419 T PGE (NIL) -7 NIL NIL) (-885 2073015 2073261 2073627 "PGCD" 2074608 NIL PGCD (NIL T T T T) -7 NIL NIL) (-884 2072353 2072456 2072617 "PFRPAC" 2072899 NIL PFRPAC (NIL T) -7 NIL NIL) (-883 2069033 2070901 2071254 "PFR" 2072032 NIL PFR (NIL T) -8 NIL NIL) (-882 2067422 2067666 2067991 "PFOTOOLS" 2068780 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-881 2065955 2066194 2066545 "PFOQ" 2067179 NIL PFOQ (NIL T T T) -7 NIL NIL) (-880 2064428 2064640 2065003 "PFO" 2065739 NIL PFO (NIL T T T T T) -7 NIL NIL) (-879 2061016 2064317 2064386 "PF" 2064391 NIL PF (NIL NIL) -8 NIL NIL) (-878 2058485 2059722 2059750 "PFECAT" 2060335 T PFECAT (NIL) -9 NIL 2060719) (-877 2057930 2058084 2058298 "PFECAT-" 2058303 NIL PFECAT- (NIL T) -8 NIL NIL) (-876 2056534 2056785 2057086 "PFBRU" 2057679 NIL PFBRU (NIL T T) -7 NIL NIL) (-875 2054401 2054752 2055184 "PFBR" 2056185 NIL PFBR (NIL T T T T) -7 NIL NIL) (-874 2050317 2051777 2052453 "PERM" 2053758 NIL PERM (NIL T) -8 NIL NIL) (-873 2045583 2046524 2047394 "PERMGRP" 2049480 NIL PERMGRP (NIL T) -8 NIL NIL) (-872 2043715 2044646 2044687 "PERMCAT" 2045133 NIL PERMCAT (NIL T) -9 NIL 2045438) (-871 2043368 2043409 2043533 "PERMAN" 2043668 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-870 2040808 2042937 2043068 "PENDTREE" 2043270 NIL PENDTREE (NIL T) -8 NIL NIL) (-869 2038921 2039655 2039696 "PDRING" 2040353 NIL PDRING (NIL T) -9 NIL 2040639) (-868 2038024 2038242 2038604 "PDRING-" 2038609 NIL PDRING- (NIL T T) -8 NIL NIL) (-867 2035165 2035916 2036607 "PDEPROB" 2037353 T PDEPROB (NIL) -8 NIL NIL) (-866 2032712 2033214 2033769 "PDEPACK" 2034630 T PDEPACK (NIL) -7 NIL NIL) (-865 2031624 2031814 2032065 "PDECOMP" 2032511 NIL PDECOMP (NIL T T) -7 NIL NIL) (-864 2029229 2030046 2030074 "PDECAT" 2030861 T PDECAT (NIL) -9 NIL 2031574) (-863 2028980 2029013 2029103 "PCOMP" 2029190 NIL PCOMP (NIL T T) -7 NIL NIL) (-862 2027185 2027781 2028078 "PBWLB" 2028709 NIL PBWLB (NIL T) -8 NIL NIL) (-861 2019689 2021258 2022596 "PATTERN" 2025868 NIL PATTERN (NIL T) -8 NIL NIL) (-860 2019321 2019378 2019487 "PATTERN2" 2019626 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-859 2017078 2017466 2017923 "PATTERN1" 2018910 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-858 2014473 2015027 2015508 "PATRES" 2016643 NIL PATRES (NIL T T) -8 NIL NIL) (-857 2014037 2014104 2014236 "PATRES2" 2014400 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-856 2011920 2012325 2012732 "PATMATCH" 2013704 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-855 2011456 2011639 2011680 "PATMAB" 2011787 NIL PATMAB (NIL T) -9 NIL 2011870) (-854 2010001 2010310 2010568 "PATLRES" 2011261 NIL PATLRES (NIL T T T) -8 NIL NIL) (-853 2009547 2009670 2009711 "PATAB" 2009716 NIL PATAB (NIL T) -9 NIL 2009888) (-852 2007028 2007560 2008133 "PARTPERM" 2008994 T PARTPERM (NIL) -7 NIL NIL) (-851 2006649 2006712 2006814 "PARSURF" 2006959 NIL PARSURF (NIL T) -8 NIL NIL) (-850 2006281 2006338 2006447 "PARSU2" 2006586 NIL PARSU2 (NIL T T) -7 NIL NIL) (-849 2006045 2006085 2006152 "PARSER" 2006234 T PARSER (NIL) -7 NIL NIL) (-848 2005666 2005729 2005831 "PARSCURV" 2005976 NIL PARSCURV (NIL T) -8 NIL NIL) (-847 2005298 2005355 2005464 "PARSC2" 2005603 NIL PARSC2 (NIL T T) -7 NIL NIL) (-846 2004937 2004995 2005092 "PARPCURV" 2005234 NIL PARPCURV (NIL T) -8 NIL NIL) (-845 2004569 2004626 2004735 "PARPC2" 2004874 NIL PARPC2 (NIL T T) -7 NIL NIL) (-844 2004089 2004175 2004294 "PAN2EXPR" 2004470 T PAN2EXPR (NIL) -7 NIL NIL) (-843 2002895 2003210 2003438 "PALETTE" 2003881 T PALETTE (NIL) -8 NIL NIL) (-842 2001363 2001900 2002260 "PAIR" 2002581 NIL PAIR (NIL T T) -8 NIL NIL) (-841 1995271 2000622 2000816 "PADICRC" 2001218 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-840 1988537 1994617 1994801 "PADICRAT" 1995119 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-839 1986887 1988474 1988519 "PADIC" 1988524 NIL PADIC (NIL NIL) -8 NIL NIL) (-838 1984132 1985662 1985702 "PADICCT" 1986283 NIL PADICCT (NIL NIL) -9 NIL 1986565) (-837 1983089 1983289 1983557 "PADEPAC" 1983919 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-836 1982301 1982434 1982640 "PADE" 1982951 NIL PADE (NIL T T T) -7 NIL NIL) (-835 1980351 1981137 1981454 "OWP" 1982068 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-834 1979460 1979956 1980128 "OVAR" 1980219 NIL OVAR (NIL NIL) -8 NIL NIL) (-833 1978724 1978845 1979006 "OUT" 1979319 T OUT (NIL) -7 NIL NIL) (-832 1967778 1969949 1972119 "OUTFORM" 1976574 T OUTFORM (NIL) -8 NIL NIL) (-831 1967415 1967498 1967526 "OUTBCON" 1967677 T OUTBCON (NIL) -9 NIL 1967762) (-830 1967255 1967290 1967366 "OUTBCON-" 1967371 NIL OUTBCON- (NIL T) -8 NIL NIL) (-829 1966663 1966984 1967073 "OSI" 1967186 T OSI (NIL) -8 NIL NIL) (-828 1966219 1966531 1966559 "OSGROUP" 1966564 T OSGROUP (NIL) -9 NIL 1966586) (-827 1964964 1965191 1965476 "ORTHPOL" 1965966 NIL ORTHPOL (NIL T) -7 NIL NIL) (-826 1962374 1964623 1964762 "OREUP" 1964907 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-825 1959812 1962065 1962192 "ORESUP" 1962316 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-824 1957340 1957840 1958401 "OREPCTO" 1959301 NIL OREPCTO (NIL T T) -7 NIL NIL) (-823 1951251 1953418 1953459 "OREPCAT" 1955807 NIL OREPCAT (NIL T) -9 NIL 1956911) (-822 1948398 1949180 1950238 "OREPCAT-" 1950243 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-821 1947575 1947847 1947875 "ORDSET" 1948184 T ORDSET (NIL) -9 NIL 1948348) (-820 1947094 1947216 1947409 "ORDSET-" 1947414 NIL ORDSET- (NIL T) -8 NIL NIL) (-819 1945748 1946505 1946533 "ORDRING" 1946735 T ORDRING (NIL) -9 NIL 1946860) (-818 1945393 1945487 1945631 "ORDRING-" 1945636 NIL ORDRING- (NIL T) -8 NIL NIL) (-817 1944799 1945236 1945264 "ORDMON" 1945269 T ORDMON (NIL) -9 NIL 1945290) (-816 1943961 1944108 1944303 "ORDFUNS" 1944648 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-815 1943472 1943831 1943859 "ORDFIN" 1943864 T ORDFIN (NIL) -9 NIL 1943885) (-814 1940064 1942058 1942467 "ORDCOMP" 1943096 NIL ORDCOMP (NIL T) -8 NIL NIL) (-813 1939330 1939457 1939643 "ORDCOMP2" 1939924 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-812 1935837 1936720 1937557 "OPTPROB" 1938513 T OPTPROB (NIL) -8 NIL NIL) (-811 1932639 1933278 1933982 "OPTPACK" 1935153 T OPTPACK (NIL) -7 NIL NIL) (-810 1930352 1931092 1931120 "OPTCAT" 1931939 T OPTCAT (NIL) -9 NIL 1932589) (-809 1930120 1930159 1930225 "OPQUERY" 1930306 T OPQUERY (NIL) -7 NIL NIL) (-808 1927286 1928431 1928935 "OP" 1929649 NIL OP (NIL T) -8 NIL NIL) (-807 1924131 1926083 1926452 "ONECOMP" 1926950 NIL ONECOMP (NIL T) -8 NIL NIL) (-806 1923436 1923551 1923725 "ONECOMP2" 1924003 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-805 1922855 1922961 1923091 "OMSERVER" 1923326 T OMSERVER (NIL) -7 NIL NIL) (-804 1919743 1922295 1922335 "OMSAGG" 1922396 NIL OMSAGG (NIL T) -9 NIL 1922460) (-803 1918366 1918629 1918911 "OMPKG" 1919481 T OMPKG (NIL) -7 NIL NIL) (-802 1917796 1917899 1917927 "OM" 1918226 T OM (NIL) -9 NIL NIL) (-801 1916378 1917345 1917514 "OMLO" 1917677 NIL OMLO (NIL T T) -8 NIL NIL) (-800 1915303 1915450 1915677 "OMEXPR" 1916204 NIL OMEXPR (NIL T) -7 NIL NIL) (-799 1914621 1914849 1914985 "OMERR" 1915187 T OMERR (NIL) -8 NIL NIL) (-798 1913799 1914042 1914202 "OMERRK" 1914481 T OMERRK (NIL) -8 NIL NIL) (-797 1913277 1913476 1913584 "OMENC" 1913711 T OMENC (NIL) -8 NIL NIL) (-796 1907172 1908357 1909528 "OMDEV" 1912126 T OMDEV (NIL) -8 NIL NIL) (-795 1906241 1906412 1906606 "OMCONN" 1906998 T OMCONN (NIL) -8 NIL NIL) (-794 1904897 1905839 1905867 "OINTDOM" 1905872 T OINTDOM (NIL) -9 NIL 1905893) (-793 1900703 1901887 1902603 "OFMONOID" 1904213 NIL OFMONOID (NIL T) -8 NIL NIL) (-792 1900141 1900640 1900685 "ODVAR" 1900690 NIL ODVAR (NIL T) -8 NIL NIL) (-791 1897351 1899638 1899823 "ODR" 1900016 NIL ODR (NIL T T NIL) -8 NIL NIL) (-790 1889695 1897127 1897253 "ODPOL" 1897258 NIL ODPOL (NIL T) -8 NIL NIL) (-789 1883571 1889567 1889672 "ODP" 1889677 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-788 1882337 1882552 1882827 "ODETOOLS" 1883345 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-787 1879306 1879962 1880678 "ODESYS" 1881670 NIL ODESYS (NIL T T) -7 NIL NIL) (-786 1874188 1875096 1876121 "ODERTRIC" 1878381 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-785 1873614 1873696 1873890 "ODERED" 1874100 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-784 1870502 1871050 1871727 "ODERAT" 1873037 NIL ODERAT (NIL T T) -7 NIL NIL) (-783 1867462 1867926 1868523 "ODEPRRIC" 1870031 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-782 1865331 1865900 1866409 "ODEPROB" 1866973 T ODEPROB (NIL) -8 NIL NIL) (-781 1861853 1862336 1862983 "ODEPRIM" 1864810 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-780 1861102 1861204 1861464 "ODEPAL" 1861745 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-779 1857264 1858055 1858919 "ODEPACK" 1860258 T ODEPACK (NIL) -7 NIL NIL) (-778 1856297 1856404 1856633 "ODEINT" 1857153 NIL ODEINT (NIL T T) -7 NIL NIL) (-777 1850398 1851823 1853270 "ODEIFTBL" 1854870 T ODEIFTBL (NIL) -8 NIL NIL) (-776 1845733 1846519 1847478 "ODEEF" 1849557 NIL ODEEF (NIL T T) -7 NIL NIL) (-775 1845068 1845157 1845387 "ODECONST" 1845638 NIL ODECONST (NIL T T T) -7 NIL NIL) (-774 1843219 1843854 1843882 "ODECAT" 1844487 T ODECAT (NIL) -9 NIL 1845018) (-773 1840126 1842931 1843050 "OCT" 1843132 NIL OCT (NIL T) -8 NIL NIL) (-772 1839764 1839807 1839934 "OCTCT2" 1840077 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-771 1834625 1837025 1837065 "OC" 1838162 NIL OC (NIL T) -9 NIL 1839020) (-770 1831852 1832600 1833590 "OC-" 1833684 NIL OC- (NIL T T) -8 NIL NIL) (-769 1831230 1831672 1831700 "OCAMON" 1831705 T OCAMON (NIL) -9 NIL 1831726) (-768 1830787 1831102 1831130 "OASGP" 1831135 T OASGP (NIL) -9 NIL 1831155) (-767 1830074 1830537 1830565 "OAMONS" 1830605 T OAMONS (NIL) -9 NIL 1830648) (-766 1829514 1829921 1829949 "OAMON" 1829954 T OAMON (NIL) -9 NIL 1829974) (-765 1828818 1829310 1829338 "OAGROUP" 1829343 T OAGROUP (NIL) -9 NIL 1829363) (-764 1828508 1828558 1828646 "NUMTUBE" 1828762 NIL NUMTUBE (NIL T) -7 NIL NIL) (-763 1822081 1823599 1825135 "NUMQUAD" 1826992 T NUMQUAD (NIL) -7 NIL NIL) (-762 1817837 1818825 1819850 "NUMODE" 1821076 T NUMODE (NIL) -7 NIL NIL) (-761 1815218 1816072 1816100 "NUMINT" 1817023 T NUMINT (NIL) -9 NIL 1817787) (-760 1814166 1814363 1814581 "NUMFMT" 1815020 T NUMFMT (NIL) -7 NIL NIL) (-759 1800525 1803470 1806002 "NUMERIC" 1811673 NIL NUMERIC (NIL T) -7 NIL NIL) (-758 1794922 1799974 1800069 "NTSCAT" 1800074 NIL NTSCAT (NIL T T T T) -9 NIL 1800113) (-757 1794116 1794281 1794474 "NTPOLFN" 1794761 NIL NTPOLFN (NIL T) -7 NIL NIL) (-756 1781956 1790941 1791753 "NSUP" 1793337 NIL NSUP (NIL T) -8 NIL NIL) (-755 1781588 1781645 1781754 "NSUP2" 1781893 NIL NSUP2 (NIL T T) -7 NIL NIL) (-754 1771585 1781362 1781495 "NSMP" 1781500 NIL NSMP (NIL T T) -8 NIL NIL) (-753 1770017 1770318 1770675 "NREP" 1771273 NIL NREP (NIL T) -7 NIL NIL) (-752 1768608 1768860 1769218 "NPCOEF" 1769760 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-751 1767674 1767789 1768005 "NORMRETR" 1768489 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-750 1765715 1766005 1766414 "NORMPK" 1767382 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-749 1765400 1765428 1765552 "NORMMA" 1765681 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-748 1765227 1765357 1765386 "NONE" 1765391 T NONE (NIL) -8 NIL NIL) (-747 1765016 1765045 1765114 "NONE1" 1765191 NIL NONE1 (NIL T) -7 NIL NIL) (-746 1764499 1764561 1764747 "NODE1" 1764948 NIL NODE1 (NIL T T) -7 NIL NIL) (-745 1762839 1763662 1763917 "NNI" 1764264 T NNI (NIL) -8 NIL NIL) (-744 1761259 1761572 1761936 "NLINSOL" 1762507 NIL NLINSOL (NIL T) -7 NIL NIL) (-743 1757426 1758394 1759316 "NIPROB" 1760357 T NIPROB (NIL) -8 NIL NIL) (-742 1756183 1756417 1756719 "NFINTBAS" 1757188 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-741 1754891 1755122 1755403 "NCODIV" 1755951 NIL NCODIV (NIL T T) -7 NIL NIL) (-740 1754653 1754690 1754765 "NCNTFRAC" 1754848 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-739 1752833 1753197 1753617 "NCEP" 1754278 NIL NCEP (NIL T) -7 NIL NIL) (-738 1751744 1752483 1752511 "NASRING" 1752621 T NASRING (NIL) -9 NIL 1752695) (-737 1751539 1751583 1751677 "NASRING-" 1751682 NIL NASRING- (NIL T) -8 NIL NIL) (-736 1750692 1751191 1751219 "NARNG" 1751336 T NARNG (NIL) -9 NIL 1751427) (-735 1750384 1750451 1750585 "NARNG-" 1750590 NIL NARNG- (NIL T) -8 NIL NIL) (-734 1749263 1749470 1749705 "NAGSP" 1750169 T NAGSP (NIL) -7 NIL NIL) (-733 1740535 1742219 1743892 "NAGS" 1747610 T NAGS (NIL) -7 NIL NIL) (-732 1739083 1739391 1739722 "NAGF07" 1740224 T NAGF07 (NIL) -7 NIL NIL) (-731 1733621 1734912 1736219 "NAGF04" 1737796 T NAGF04 (NIL) -7 NIL NIL) (-730 1726589 1728203 1729836 "NAGF02" 1732008 T NAGF02 (NIL) -7 NIL NIL) (-729 1721813 1722913 1724030 "NAGF01" 1725492 T NAGF01 (NIL) -7 NIL NIL) (-728 1715441 1717007 1718592 "NAGE04" 1720248 T NAGE04 (NIL) -7 NIL NIL) (-727 1706610 1708731 1710861 "NAGE02" 1713331 T NAGE02 (NIL) -7 NIL NIL) (-726 1702563 1703510 1704474 "NAGE01" 1705666 T NAGE01 (NIL) -7 NIL NIL) (-725 1700358 1700892 1701450 "NAGD03" 1702025 T NAGD03 (NIL) -7 NIL NIL) (-724 1692108 1694036 1695990 "NAGD02" 1698424 T NAGD02 (NIL) -7 NIL NIL) (-723 1685919 1687344 1688784 "NAGD01" 1690688 T NAGD01 (NIL) -7 NIL NIL) (-722 1682128 1682950 1683787 "NAGC06" 1685102 T NAGC06 (NIL) -7 NIL NIL) (-721 1680593 1680925 1681281 "NAGC05" 1681792 T NAGC05 (NIL) -7 NIL NIL) (-720 1679969 1680088 1680232 "NAGC02" 1680469 T NAGC02 (NIL) -7 NIL NIL) (-719 1679029 1679586 1679626 "NAALG" 1679705 NIL NAALG (NIL T) -9 NIL 1679766) (-718 1678864 1678893 1678983 "NAALG-" 1678988 NIL NAALG- (NIL T T) -8 NIL NIL) (-717 1672814 1673922 1675109 "MULTSQFR" 1677760 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-716 1672133 1672208 1672392 "MULTFACT" 1672726 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-715 1665356 1669221 1669274 "MTSCAT" 1670344 NIL MTSCAT (NIL T T) -9 NIL 1670858) (-714 1665068 1665122 1665214 "MTHING" 1665296 NIL MTHING (NIL T) -7 NIL NIL) (-713 1664860 1664893 1664953 "MSYSCMD" 1665028 T MSYSCMD (NIL) -7 NIL NIL) (-712 1660972 1663615 1663935 "MSET" 1664573 NIL MSET (NIL T) -8 NIL NIL) (-711 1658067 1660533 1660574 "MSETAGG" 1660579 NIL MSETAGG (NIL T) -9 NIL 1660613) (-710 1653950 1655446 1656191 "MRING" 1657367 NIL MRING (NIL T T) -8 NIL NIL) (-709 1653516 1653583 1653714 "MRF2" 1653877 NIL MRF2 (NIL T T T) -7 NIL NIL) (-708 1653134 1653169 1653313 "MRATFAC" 1653475 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-707 1650746 1651041 1651472 "MPRFF" 1652839 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-706 1644806 1650600 1650697 "MPOLY" 1650702 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-705 1644296 1644331 1644539 "MPCPF" 1644765 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-704 1643810 1643853 1644037 "MPC3" 1644247 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-703 1643005 1643086 1643307 "MPC2" 1643725 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-702 1641306 1641643 1642033 "MONOTOOL" 1642665 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-701 1640557 1640848 1640876 "MONOID" 1641095 T MONOID (NIL) -9 NIL 1641242) (-700 1640103 1640222 1640403 "MONOID-" 1640408 NIL MONOID- (NIL T) -8 NIL NIL) (-699 1631153 1637059 1637118 "MONOGEN" 1637792 NIL MONOGEN (NIL T T) -9 NIL 1638248) (-698 1628371 1629106 1630106 "MONOGEN-" 1630225 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-697 1627230 1627650 1627678 "MONADWU" 1628070 T MONADWU (NIL) -9 NIL 1628308) (-696 1626602 1626761 1627009 "MONADWU-" 1627014 NIL MONADWU- (NIL T) -8 NIL NIL) (-695 1625987 1626205 1626233 "MONAD" 1626440 T MONAD (NIL) -9 NIL 1626552) (-694 1625672 1625750 1625882 "MONAD-" 1625887 NIL MONAD- (NIL T) -8 NIL NIL) (-693 1623988 1624585 1624864 "MOEBIUS" 1625425 NIL MOEBIUS (NIL T) -8 NIL NIL) (-692 1623380 1623758 1623798 "MODULE" 1623803 NIL MODULE (NIL T) -9 NIL 1623829) (-691 1622948 1623044 1623234 "MODULE-" 1623239 NIL MODULE- (NIL T T) -8 NIL NIL) (-690 1620663 1621312 1621639 "MODRING" 1622772 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-689 1617649 1618768 1619289 "MODOP" 1620192 NIL MODOP (NIL T T) -8 NIL NIL) (-688 1615836 1616288 1616629 "MODMONOM" 1617448 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-687 1605544 1614028 1614451 "MODMON" 1615464 NIL MODMON (NIL T T) -8 NIL NIL) (-686 1602735 1604388 1604664 "MODFIELD" 1605419 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-685 1601739 1602016 1602206 "MMLFORM" 1602565 T MMLFORM (NIL) -8 NIL NIL) (-684 1601265 1601308 1601487 "MMAP" 1601690 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-683 1599534 1600267 1600308 "MLO" 1600731 NIL MLO (NIL T) -9 NIL 1600973) (-682 1596901 1597416 1598018 "MLIFT" 1599015 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-681 1596292 1596376 1596530 "MKUCFUNC" 1596812 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-680 1595891 1595961 1596084 "MKRECORD" 1596215 NIL MKRECORD (NIL T T) -7 NIL NIL) (-679 1594939 1595100 1595328 "MKFUNC" 1595702 NIL MKFUNC (NIL T) -7 NIL NIL) (-678 1594327 1594431 1594587 "MKFLCFN" 1594822 NIL MKFLCFN (NIL T) -7 NIL NIL) (-677 1593753 1594120 1594209 "MKCHSET" 1594271 NIL MKCHSET (NIL T) -8 NIL NIL) (-676 1593030 1593132 1593317 "MKBCFUNC" 1593646 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-675 1589760 1592584 1592720 "MINT" 1592914 T MINT (NIL) -8 NIL NIL) (-674 1588572 1588815 1589092 "MHROWRED" 1589515 NIL MHROWRED (NIL T) -7 NIL NIL) (-673 1583904 1587013 1587439 "MFLOAT" 1588166 T MFLOAT (NIL) -8 NIL NIL) (-672 1583261 1583337 1583508 "MFINFACT" 1583816 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-671 1579576 1580424 1581308 "MESH" 1582397 T MESH (NIL) -7 NIL NIL) (-670 1577966 1578278 1578631 "MDDFACT" 1579263 NIL MDDFACT (NIL T) -7 NIL NIL) (-669 1574808 1577125 1577166 "MDAGG" 1577421 NIL MDAGG (NIL T) -9 NIL 1577564) (-668 1564588 1574101 1574308 "MCMPLX" 1574621 T MCMPLX (NIL) -8 NIL NIL) (-667 1563729 1563875 1564075 "MCDEN" 1564437 NIL MCDEN (NIL T T) -7 NIL NIL) (-666 1561619 1561889 1562269 "MCALCFN" 1563459 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-665 1560530 1560703 1560944 "MAYBE" 1561417 NIL MAYBE (NIL T) -8 NIL NIL) (-664 1558142 1558665 1559227 "MATSTOR" 1560001 NIL MATSTOR (NIL T) -7 NIL NIL) (-663 1554148 1557514 1557762 "MATRIX" 1557927 NIL MATRIX (NIL T) -8 NIL NIL) (-662 1549917 1550621 1551357 "MATLIN" 1553505 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-661 1540071 1543209 1543286 "MATCAT" 1548166 NIL MATCAT (NIL T T T) -9 NIL 1549583) (-660 1536435 1537448 1538804 "MATCAT-" 1538809 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-659 1535029 1535182 1535515 "MATCAT2" 1536270 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-658 1533141 1533465 1533849 "MAPPKG3" 1534704 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-657 1532122 1532295 1532517 "MAPPKG2" 1532965 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-656 1530621 1530905 1531232 "MAPPKG1" 1531828 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-655 1529744 1530027 1530204 "MAPPAST" 1530464 T MAPPAST (NIL) -8 NIL NIL) (-654 1529355 1529413 1529536 "MAPHACK3" 1529680 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-653 1528947 1529008 1529122 "MAPHACK2" 1529287 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-652 1528385 1528488 1528630 "MAPHACK1" 1528838 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-651 1526491 1527085 1527389 "MAGMA" 1528113 NIL MAGMA (NIL T) -8 NIL NIL) (-650 1525986 1526194 1526292 "MACROAST" 1526413 T MACROAST (NIL) -8 NIL NIL) (-649 1522453 1524225 1524686 "M3D" 1525558 NIL M3D (NIL T) -8 NIL NIL) (-648 1516608 1520823 1520864 "LZSTAGG" 1521646 NIL LZSTAGG (NIL T) -9 NIL 1521941) (-647 1512581 1513739 1515196 "LZSTAGG-" 1515201 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-646 1509695 1510472 1510959 "LWORD" 1512126 NIL LWORD (NIL T) -8 NIL NIL) (-645 1509315 1509499 1509574 "LSTAST" 1509640 T LSTAST (NIL) -8 NIL NIL) (-644 1502516 1509086 1509220 "LSQM" 1509225 NIL LSQM (NIL NIL T) -8 NIL NIL) (-643 1501740 1501879 1502107 "LSPP" 1502371 NIL LSPP (NIL T T T T) -7 NIL NIL) (-642 1499552 1499853 1500309 "LSMP" 1501429 NIL LSMP (NIL T T T T) -7 NIL NIL) (-641 1496331 1497005 1497735 "LSMP1" 1498854 NIL LSMP1 (NIL T) -7 NIL NIL) (-640 1490257 1495499 1495540 "LSAGG" 1495602 NIL LSAGG (NIL T) -9 NIL 1495680) (-639 1486952 1487876 1489089 "LSAGG-" 1489094 NIL LSAGG- (NIL T T) -8 NIL NIL) (-638 1484578 1486096 1486345 "LPOLY" 1486747 NIL LPOLY (NIL T T) -8 NIL NIL) (-637 1484160 1484245 1484368 "LPEFRAC" 1484487 NIL LPEFRAC (NIL T) -7 NIL NIL) (-636 1482507 1483254 1483507 "LO" 1483992 NIL LO (NIL T T T) -8 NIL NIL) (-635 1482159 1482271 1482299 "LOGIC" 1482410 T LOGIC (NIL) -9 NIL 1482491) (-634 1482021 1482044 1482115 "LOGIC-" 1482120 NIL LOGIC- (NIL T) -8 NIL NIL) (-633 1481214 1481354 1481547 "LODOOPS" 1481877 NIL LODOOPS (NIL T T) -7 NIL NIL) (-632 1478672 1481130 1481196 "LODO" 1481201 NIL LODO (NIL T NIL) -8 NIL NIL) (-631 1477210 1477445 1477798 "LODOF" 1478419 NIL LODOF (NIL T T) -7 NIL NIL) (-630 1473653 1476050 1476091 "LODOCAT" 1476529 NIL LODOCAT (NIL T) -9 NIL 1476740) (-629 1473386 1473444 1473571 "LODOCAT-" 1473576 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-628 1470741 1473227 1473345 "LODO2" 1473350 NIL LODO2 (NIL T T) -8 NIL NIL) (-627 1468211 1470678 1470723 "LODO1" 1470728 NIL LODO1 (NIL T) -8 NIL NIL) (-626 1467071 1467236 1467548 "LODEEF" 1468034 NIL LODEEF (NIL T T T) -7 NIL NIL) (-625 1462357 1465201 1465242 "LNAGG" 1466189 NIL LNAGG (NIL T) -9 NIL 1466633) (-624 1461504 1461718 1462060 "LNAGG-" 1462065 NIL LNAGG- (NIL T T) -8 NIL NIL) (-623 1457667 1458429 1459068 "LMOPS" 1460919 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-622 1457062 1457424 1457465 "LMODULE" 1457526 NIL LMODULE (NIL T) -9 NIL 1457568) (-621 1454308 1456707 1456830 "LMDICT" 1456972 NIL LMDICT (NIL T) -8 NIL NIL) (-620 1454052 1454216 1454276 "LITERAL" 1454281 NIL LITERAL (NIL T) -8 NIL NIL) (-619 1447279 1452998 1453296 "LIST" 1453787 NIL LIST (NIL T) -8 NIL NIL) (-618 1446804 1446878 1447017 "LIST3" 1447199 NIL LIST3 (NIL T T T) -7 NIL NIL) (-617 1445811 1445989 1446217 "LIST2" 1446622 NIL LIST2 (NIL T T) -7 NIL NIL) (-616 1443945 1444257 1444656 "LIST2MAP" 1445458 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-615 1442695 1443331 1443372 "LINEXP" 1443627 NIL LINEXP (NIL T) -9 NIL 1443776) (-614 1441342 1441602 1441899 "LINDEP" 1442447 NIL LINDEP (NIL T T) -7 NIL NIL) (-613 1438109 1438828 1439605 "LIMITRF" 1440597 NIL LIMITRF (NIL T) -7 NIL NIL) (-612 1436385 1436680 1437096 "LIMITPS" 1437804 NIL LIMITPS (NIL T T) -7 NIL NIL) (-611 1430840 1435896 1436124 "LIE" 1436206 NIL LIE (NIL T T) -8 NIL NIL) (-610 1429889 1430332 1430372 "LIECAT" 1430512 NIL LIECAT (NIL T) -9 NIL 1430663) (-609 1429730 1429757 1429845 "LIECAT-" 1429850 NIL LIECAT- (NIL T T) -8 NIL NIL) (-608 1422342 1429179 1429344 "LIB" 1429585 T LIB (NIL) -8 NIL NIL) (-607 1417979 1418860 1419795 "LGROBP" 1421459 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-606 1415845 1416119 1416481 "LF" 1417700 NIL LF (NIL T T) -7 NIL NIL) (-605 1414685 1415377 1415405 "LFCAT" 1415612 T LFCAT (NIL) -9 NIL 1415751) (-604 1411589 1412217 1412905 "LEXTRIPK" 1414049 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-603 1408360 1409159 1409662 "LEXP" 1411169 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-602 1407880 1408081 1408173 "LETAST" 1408288 T LETAST (NIL) -8 NIL NIL) (-601 1406278 1406591 1406992 "LEADCDET" 1407562 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-600 1405468 1405542 1405771 "LAZM3PK" 1406199 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-599 1400424 1403545 1404083 "LAUPOL" 1404980 NIL LAUPOL (NIL T T) -8 NIL NIL) (-598 1399989 1400033 1400201 "LAPLACE" 1400374 NIL LAPLACE (NIL T T) -7 NIL NIL) (-597 1397963 1399090 1399341 "LA" 1399822 NIL LA (NIL T T T) -8 NIL NIL) (-596 1397064 1397614 1397655 "LALG" 1397717 NIL LALG (NIL T) -9 NIL 1397776) (-595 1396778 1396837 1396973 "LALG-" 1396978 NIL LALG- (NIL T T) -8 NIL NIL) (-594 1395578 1395995 1396224 "KTVLOGIC" 1396569 T KTVLOGIC (NIL) -8 NIL NIL) (-593 1394482 1394669 1394968 "KOVACIC" 1395378 NIL KOVACIC (NIL T T) -7 NIL NIL) (-592 1394317 1394341 1394382 "KONVERT" 1394444 NIL KONVERT (NIL T) -9 NIL NIL) (-591 1394152 1394176 1394217 "KOERCE" 1394279 NIL KOERCE (NIL T) -9 NIL NIL) (-590 1391886 1392646 1393039 "KERNEL" 1393791 NIL KERNEL (NIL T) -8 NIL NIL) (-589 1391388 1391469 1391599 "KERNEL2" 1391800 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-588 1385239 1389927 1389981 "KDAGG" 1390358 NIL KDAGG (NIL T T) -9 NIL 1390564) (-587 1384768 1384892 1385097 "KDAGG-" 1385102 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-586 1377943 1384429 1384584 "KAFILE" 1384646 NIL KAFILE (NIL T) -8 NIL NIL) (-585 1372398 1377454 1377682 "JORDAN" 1377764 NIL JORDAN (NIL T T) -8 NIL NIL) (-584 1371822 1372047 1372168 "JOINAST" 1372297 T JOINAST (NIL) -8 NIL NIL) (-583 1371551 1371610 1371697 "JAVACODE" 1371755 T JAVACODE (NIL) -8 NIL NIL) (-582 1367850 1369756 1369810 "IXAGG" 1370739 NIL IXAGG (NIL T T) -9 NIL 1371198) (-581 1366769 1367075 1367494 "IXAGG-" 1367499 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-580 1362349 1366691 1366750 "IVECTOR" 1366755 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-579 1361115 1361352 1361618 "ITUPLE" 1362116 NIL ITUPLE (NIL T) -8 NIL NIL) (-578 1359551 1359728 1360034 "ITRIGMNP" 1360937 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-577 1358296 1358500 1358783 "ITFUN3" 1359327 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-576 1357928 1357985 1358094 "ITFUN2" 1358233 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-575 1355765 1356790 1357089 "ITAYLOR" 1357662 NIL ITAYLOR (NIL T) -8 NIL NIL) (-574 1344759 1349911 1351071 "ISUPS" 1354638 NIL ISUPS (NIL T) -8 NIL NIL) (-573 1343863 1344003 1344239 "ISUMP" 1344606 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-572 1339127 1343664 1343743 "ISTRING" 1343816 NIL ISTRING (NIL NIL) -8 NIL NIL) (-571 1338647 1338848 1338940 "ISAST" 1339055 T ISAST (NIL) -8 NIL NIL) (-570 1337857 1337938 1338154 "IRURPK" 1338561 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-569 1336793 1336994 1337234 "IRSN" 1337637 T IRSN (NIL) -7 NIL NIL) (-568 1334822 1335177 1335613 "IRRF2F" 1336431 NIL IRRF2F (NIL T) -7 NIL NIL) (-567 1334569 1334607 1334683 "IRREDFFX" 1334778 NIL IRREDFFX (NIL T) -7 NIL NIL) (-566 1333184 1333443 1333742 "IROOT" 1334302 NIL IROOT (NIL T) -7 NIL NIL) (-565 1329816 1330868 1331560 "IR" 1332524 NIL IR (NIL T) -8 NIL NIL) (-564 1327429 1327924 1328490 "IR2" 1329294 NIL IR2 (NIL T T) -7 NIL NIL) (-563 1326501 1326614 1326835 "IR2F" 1327312 NIL IR2F (NIL T T) -7 NIL NIL) (-562 1326292 1326326 1326386 "IPRNTPK" 1326461 T IPRNTPK (NIL) -7 NIL NIL) (-561 1322911 1326181 1326250 "IPF" 1326255 NIL IPF (NIL NIL) -8 NIL NIL) (-560 1321274 1322836 1322893 "IPADIC" 1322898 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-559 1321038 1321178 1321206 "IOBCON" 1321211 T IOBCON (NIL) -9 NIL 1321232) (-558 1320535 1320593 1320783 "INVLAPLA" 1320974 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-557 1310184 1312537 1314923 "INTTR" 1318199 NIL INTTR (NIL T T) -7 NIL NIL) (-556 1306528 1307270 1308134 "INTTOOLS" 1309369 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-555 1306114 1306205 1306322 "INTSLPE" 1306431 T INTSLPE (NIL) -7 NIL NIL) (-554 1304109 1306037 1306096 "INTRVL" 1306101 NIL INTRVL (NIL T) -8 NIL NIL) (-553 1301711 1302223 1302798 "INTRF" 1303594 NIL INTRF (NIL T) -7 NIL NIL) (-552 1301122 1301219 1301361 "INTRET" 1301609 NIL INTRET (NIL T) -7 NIL NIL) (-551 1299119 1299508 1299978 "INTRAT" 1300730 NIL INTRAT (NIL T T) -7 NIL NIL) (-550 1296347 1296930 1297556 "INTPM" 1298604 NIL INTPM (NIL T T) -7 NIL NIL) (-549 1293050 1293649 1294394 "INTPAF" 1295733 NIL INTPAF (NIL T T T) -7 NIL NIL) (-548 1288229 1289191 1290242 "INTPACK" 1292019 T INTPACK (NIL) -7 NIL NIL) (-547 1285141 1287958 1288085 "INT" 1288122 T INT (NIL) -8 NIL NIL) (-546 1284393 1284545 1284753 "INTHERTR" 1284983 NIL INTHERTR (NIL T T) -7 NIL NIL) (-545 1283832 1283912 1284100 "INTHERAL" 1284307 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-544 1281678 1282121 1282578 "INTHEORY" 1283395 T INTHEORY (NIL) -7 NIL NIL) (-543 1272986 1274607 1276386 "INTG0" 1280030 NIL INTG0 (NIL T T T) -7 NIL NIL) (-542 1253559 1258349 1263159 "INTFTBL" 1268196 T INTFTBL (NIL) -8 NIL NIL) (-541 1252808 1252946 1253119 "INTFACT" 1253418 NIL INTFACT (NIL T) -7 NIL NIL) (-540 1250193 1250639 1251203 "INTEF" 1252362 NIL INTEF (NIL T T) -7 NIL NIL) (-539 1248695 1249400 1249428 "INTDOM" 1249729 T INTDOM (NIL) -9 NIL 1249936) (-538 1248064 1248238 1248480 "INTDOM-" 1248485 NIL INTDOM- (NIL T) -8 NIL NIL) (-537 1244597 1246483 1246537 "INTCAT" 1247336 NIL INTCAT (NIL T) -9 NIL 1247656) (-536 1244070 1244172 1244300 "INTBIT" 1244489 T INTBIT (NIL) -7 NIL NIL) (-535 1242741 1242895 1243209 "INTALG" 1243915 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-534 1242198 1242288 1242458 "INTAF" 1242645 NIL INTAF (NIL T T) -7 NIL NIL) (-533 1235652 1242008 1242148 "INTABL" 1242153 NIL INTABL (NIL T T T) -8 NIL NIL) (-532 1230707 1233378 1233406 "INS" 1234340 T INS (NIL) -9 NIL 1235004) (-531 1227947 1228718 1229692 "INS-" 1229765 NIL INS- (NIL T) -8 NIL NIL) (-530 1226722 1226949 1227247 "INPSIGN" 1227700 NIL INPSIGN (NIL T T) -7 NIL NIL) (-529 1225840 1225957 1226154 "INPRODPF" 1226602 NIL INPRODPF (NIL T T) -7 NIL NIL) (-528 1224734 1224851 1225088 "INPRODFF" 1225720 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-527 1223734 1223886 1224146 "INNMFACT" 1224570 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-526 1222931 1223028 1223216 "INMODGCD" 1223633 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-525 1221440 1221684 1222008 "INFSP" 1222676 NIL INFSP (NIL T T T) -7 NIL NIL) (-524 1220624 1220741 1220924 "INFPROD0" 1221320 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-523 1217506 1218689 1219204 "INFORM" 1220117 T INFORM (NIL) -8 NIL NIL) (-522 1217116 1217176 1217274 "INFORM1" 1217441 NIL INFORM1 (NIL T) -7 NIL NIL) (-521 1216639 1216728 1216842 "INFINITY" 1217022 T INFINITY (NIL) -7 NIL NIL) (-520 1215256 1215505 1215826 "INEP" 1216387 NIL INEP (NIL T T T) -7 NIL NIL) (-519 1214532 1215153 1215218 "INDE" 1215223 NIL INDE (NIL T) -8 NIL NIL) (-518 1214096 1214164 1214281 "INCRMAPS" 1214459 NIL INCRMAPS (NIL T) -7 NIL NIL) (-517 1209407 1210332 1211276 "INBFF" 1213184 NIL INBFF (NIL T) -7 NIL NIL) (-516 1209076 1209152 1209180 "INBCON" 1209313 T INBCON (NIL) -9 NIL 1209391) (-515 1208916 1208951 1209027 "INBCON-" 1209032 NIL INBCON- (NIL T) -8 NIL NIL) (-514 1208435 1208637 1208729 "INAST" 1208844 T INAST (NIL) -8 NIL NIL) (-513 1207906 1208114 1208220 "IMPTAST" 1208349 T IMPTAST (NIL) -8 NIL NIL) (-512 1204400 1207750 1207854 "IMATRIX" 1207859 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-511 1203112 1203235 1203550 "IMATQF" 1204256 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-510 1201332 1201559 1201896 "IMATLIN" 1202868 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-509 1195958 1201256 1201314 "ILIST" 1201319 NIL ILIST (NIL T NIL) -8 NIL NIL) (-508 1193911 1195818 1195931 "IIARRAY2" 1195936 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-507 1189344 1193822 1193886 "IFF" 1193891 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-506 1188735 1188961 1189077 "IFAST" 1189248 T IFAST (NIL) -8 NIL NIL) (-505 1183778 1188027 1188215 "IFARRAY" 1188592 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-504 1182985 1183682 1183755 "IFAMON" 1183760 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-503 1182569 1182634 1182688 "IEVALAB" 1182895 NIL IEVALAB (NIL T T) -9 NIL NIL) (-502 1182244 1182312 1182472 "IEVALAB-" 1182477 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-501 1181902 1182158 1182221 "IDPO" 1182226 NIL IDPO (NIL T T) -8 NIL NIL) (-500 1181179 1181791 1181866 "IDPOAMS" 1181871 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-499 1180513 1181068 1181143 "IDPOAM" 1181148 NIL IDPOAM (NIL T T) -8 NIL NIL) (-498 1179598 1179848 1179901 "IDPC" 1180314 NIL IDPC (NIL T T) -9 NIL 1180463) (-497 1179094 1179490 1179563 "IDPAM" 1179568 NIL IDPAM (NIL T T) -8 NIL NIL) (-496 1178497 1178986 1179059 "IDPAG" 1179064 NIL IDPAG (NIL T T) -8 NIL NIL) (-495 1178245 1178412 1178462 "IDENT" 1178467 T IDENT (NIL) -8 NIL NIL) (-494 1174500 1175348 1176243 "IDECOMP" 1177402 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-493 1167373 1168423 1169470 "IDEAL" 1173536 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-492 1166537 1166649 1166848 "ICDEN" 1167257 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-491 1165636 1166017 1166164 "ICARD" 1166410 T ICARD (NIL) -8 NIL NIL) (-490 1163696 1164009 1164414 "IBPTOOLS" 1165313 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-489 1159330 1163316 1163429 "IBITS" 1163615 NIL IBITS (NIL NIL) -8 NIL NIL) (-488 1156053 1156629 1157324 "IBATOOL" 1158747 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-487 1153833 1154294 1154827 "IBACHIN" 1155588 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-486 1151710 1153679 1153782 "IARRAY2" 1153787 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-485 1147863 1151636 1151693 "IARRAY1" 1151698 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-484 1141858 1146277 1146757 "IAN" 1147403 T IAN (NIL) -8 NIL NIL) (-483 1141369 1141426 1141599 "IALGFACT" 1141795 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-482 1140897 1141010 1141038 "HYPCAT" 1141245 T HYPCAT (NIL) -9 NIL NIL) (-481 1140435 1140552 1140738 "HYPCAT-" 1140743 NIL HYPCAT- (NIL T) -8 NIL NIL) (-480 1140057 1140230 1140313 "HOSTNAME" 1140372 T HOSTNAME (NIL) -8 NIL NIL) (-479 1136736 1138067 1138108 "HOAGG" 1139089 NIL HOAGG (NIL T) -9 NIL 1139768) (-478 1135330 1135729 1136255 "HOAGG-" 1136260 NIL HOAGG- (NIL T T) -8 NIL NIL) (-477 1129218 1134771 1134937 "HEXADEC" 1135184 T HEXADEC (NIL) -8 NIL NIL) (-476 1127966 1128188 1128451 "HEUGCD" 1128995 NIL HEUGCD (NIL T) -7 NIL NIL) (-475 1127069 1127803 1127933 "HELLFDIV" 1127938 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-474 1125297 1126846 1126934 "HEAP" 1127013 NIL HEAP (NIL T) -8 NIL NIL) (-473 1124605 1124849 1124983 "HEADAST" 1125183 T HEADAST (NIL) -8 NIL NIL) (-472 1118525 1124520 1124582 "HDP" 1124587 NIL HDP (NIL NIL T) -8 NIL NIL) (-471 1112276 1118160 1118312 "HDMP" 1118426 NIL HDMP (NIL NIL T) -8 NIL NIL) (-470 1111601 1111740 1111904 "HB" 1112132 T HB (NIL) -7 NIL NIL) (-469 1105098 1111447 1111551 "HASHTBL" 1111556 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-468 1104618 1104819 1104911 "HASAST" 1105026 T HASAST (NIL) -8 NIL NIL) (-467 1102432 1104242 1104423 "HACKPI" 1104457 T HACKPI (NIL) -8 NIL NIL) (-466 1098127 1102285 1102398 "GTSET" 1102403 NIL GTSET (NIL T T T T) -8 NIL NIL) (-465 1091653 1098005 1098103 "GSTBL" 1098108 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-464 1083966 1090684 1090949 "GSERIES" 1091444 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-463 1083133 1083524 1083552 "GROUP" 1083755 T GROUP (NIL) -9 NIL 1083889) (-462 1082499 1082658 1082909 "GROUP-" 1082914 NIL GROUP- (NIL T) -8 NIL NIL) (-461 1080868 1081187 1081574 "GROEBSOL" 1082176 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-460 1079808 1080070 1080121 "GRMOD" 1080650 NIL GRMOD (NIL T T) -9 NIL 1080818) (-459 1079576 1079612 1079740 "GRMOD-" 1079745 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-458 1074901 1075930 1076930 "GRIMAGE" 1078596 T GRIMAGE (NIL) -8 NIL NIL) (-457 1073368 1073628 1073952 "GRDEF" 1074597 T GRDEF (NIL) -7 NIL NIL) (-456 1072812 1072928 1073069 "GRAY" 1073247 T GRAY (NIL) -7 NIL NIL) (-455 1072043 1072423 1072474 "GRALG" 1072627 NIL GRALG (NIL T T) -9 NIL 1072720) (-454 1071704 1071777 1071940 "GRALG-" 1071945 NIL GRALG- (NIL T T T) -8 NIL NIL) (-453 1068508 1071289 1071467 "GPOLSET" 1071611 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-452 1067862 1067919 1068177 "GOSPER" 1068445 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-451 1063621 1064300 1064826 "GMODPOL" 1067561 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-450 1062626 1062810 1063048 "GHENSEL" 1063433 NIL GHENSEL (NIL T T) -7 NIL NIL) (-449 1056677 1057520 1058547 "GENUPS" 1061710 NIL GENUPS (NIL T T) -7 NIL NIL) (-448 1056374 1056425 1056514 "GENUFACT" 1056620 NIL GENUFACT (NIL T) -7 NIL NIL) (-447 1055786 1055863 1056028 "GENPGCD" 1056292 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-446 1055260 1055295 1055508 "GENMFACT" 1055745 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-445 1053828 1054083 1054390 "GENEEZ" 1055003 NIL GENEEZ (NIL T T) -7 NIL NIL) (-444 1047741 1053439 1053601 "GDMP" 1053751 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-443 1037118 1041512 1042618 "GCNAALG" 1046724 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-442 1035580 1036408 1036436 "GCDDOM" 1036691 T GCDDOM (NIL) -9 NIL 1036848) (-441 1035050 1035177 1035392 "GCDDOM-" 1035397 NIL GCDDOM- (NIL T) -8 NIL NIL) (-440 1033722 1033907 1034211 "GB" 1034829 NIL GB (NIL T T T T) -7 NIL NIL) (-439 1022342 1024668 1027060 "GBINTERN" 1031413 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-438 1020179 1020471 1020892 "GBF" 1022017 NIL GBF (NIL T T T T) -7 NIL NIL) (-437 1018960 1019125 1019392 "GBEUCLID" 1019995 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-436 1018309 1018434 1018583 "GAUSSFAC" 1018831 T GAUSSFAC (NIL) -7 NIL NIL) (-435 1016676 1016978 1017292 "GALUTIL" 1018028 NIL GALUTIL (NIL T) -7 NIL NIL) (-434 1014984 1015258 1015582 "GALPOLYU" 1016403 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-433 1012349 1012639 1013046 "GALFACTU" 1014681 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-432 1004155 1005654 1007262 "GALFACT" 1010781 NIL GALFACT (NIL T) -7 NIL NIL) (-431 1001543 1002201 1002229 "FVFUN" 1003385 T FVFUN (NIL) -9 NIL 1004105) (-430 1000809 1000991 1001019 "FVC" 1001310 T FVC (NIL) -9 NIL 1001493) (-429 1000451 1000606 1000687 "FUNCTION" 1000761 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-428 998121 998672 999161 "FT" 999982 T FT (NIL) -8 NIL NIL) (-427 996939 997422 997625 "FTEM" 997938 T FTEM (NIL) -8 NIL NIL) (-426 995195 995484 995888 "FSUPFACT" 996630 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-425 993592 993881 994213 "FST" 994883 T FST (NIL) -8 NIL NIL) (-424 992763 992869 993064 "FSRED" 993474 NIL FSRED (NIL T T) -7 NIL NIL) (-423 991442 991697 992051 "FSPRMELT" 992478 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-422 988527 988965 989464 "FSPECF" 991005 NIL FSPECF (NIL T T) -7 NIL NIL) (-421 970969 979411 979451 "FS" 983299 NIL FS (NIL T) -9 NIL 985588) (-420 959619 962609 966665 "FS-" 966962 NIL FS- (NIL T T) -8 NIL NIL) (-419 959133 959187 959364 "FSINT" 959560 NIL FSINT (NIL T T) -7 NIL NIL) (-418 957460 958126 958429 "FSERIES" 958912 NIL FSERIES (NIL T T) -8 NIL NIL) (-417 956474 956590 956821 "FSCINT" 957340 NIL FSCINT (NIL T T) -7 NIL NIL) (-416 952708 955418 955459 "FSAGG" 955829 NIL FSAGG (NIL T) -9 NIL 956088) (-415 950470 951071 951867 "FSAGG-" 951962 NIL FSAGG- (NIL T T) -8 NIL NIL) (-414 949512 949655 949882 "FSAGG2" 950323 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-413 947167 947446 948000 "FS2UPS" 949230 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-412 946749 946792 946947 "FS2" 947118 NIL FS2 (NIL T T T T) -7 NIL NIL) (-411 945606 945777 946086 "FS2EXPXP" 946574 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-410 945032 945147 945299 "FRUTIL" 945486 NIL FRUTIL (NIL T) -7 NIL NIL) (-409 936493 940531 941887 "FR" 943708 NIL FR (NIL T) -8 NIL NIL) (-408 931568 934211 934251 "FRNAALG" 935647 NIL FRNAALG (NIL T) -9 NIL 936254) (-407 927246 928317 929592 "FRNAALG-" 930342 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-406 926884 926927 927054 "FRNAAF2" 927197 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-405 925291 925738 926033 "FRMOD" 926696 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-404 923070 923674 923991 "FRIDEAL" 925082 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-403 922265 922352 922641 "FRIDEAL2" 922977 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-402 921507 921921 921962 "FRETRCT" 921967 NIL FRETRCT (NIL T) -9 NIL 922143) (-401 920619 920850 921201 "FRETRCT-" 921206 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-400 917869 919045 919104 "FRAMALG" 919986 NIL FRAMALG (NIL T T) -9 NIL 920278) (-399 916003 916458 917088 "FRAMALG-" 917311 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-398 909963 915478 915754 "FRAC" 915759 NIL FRAC (NIL T) -8 NIL NIL) (-397 909599 909656 909763 "FRAC2" 909900 NIL FRAC2 (NIL T T) -7 NIL NIL) (-396 909235 909292 909399 "FR2" 909536 NIL FR2 (NIL T T) -7 NIL NIL) (-395 903965 906813 906841 "FPS" 907960 T FPS (NIL) -9 NIL 908517) (-394 903414 903523 903687 "FPS-" 903833 NIL FPS- (NIL T) -8 NIL NIL) (-393 900920 902555 902583 "FPC" 902808 T FPC (NIL) -9 NIL 902950) (-392 900713 900753 900850 "FPC-" 900855 NIL FPC- (NIL T) -8 NIL NIL) (-391 899591 900201 900242 "FPATMAB" 900247 NIL FPATMAB (NIL T) -9 NIL 900399) (-390 897291 897767 898193 "FPARFRAC" 899228 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-389 892684 893183 893865 "FORTRAN" 896723 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-388 890400 890900 891439 "FORT" 892165 T FORT (NIL) -7 NIL NIL) (-387 888076 888638 888666 "FORTFN" 889726 T FORTFN (NIL) -9 NIL 890350) (-386 887840 887890 887918 "FORTCAT" 887977 T FORTCAT (NIL) -9 NIL 888039) (-385 885900 886383 886782 "FORMULA" 887461 T FORMULA (NIL) -8 NIL NIL) (-384 885688 885718 885787 "FORMULA1" 885864 NIL FORMULA1 (NIL T) -7 NIL NIL) (-383 885211 885263 885436 "FORDER" 885630 NIL FORDER (NIL T T T T) -7 NIL NIL) (-382 884307 884471 884664 "FOP" 885038 T FOP (NIL) -7 NIL NIL) (-381 882915 883587 883761 "FNLA" 884189 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-380 881583 881972 882000 "FNCAT" 882572 T FNCAT (NIL) -9 NIL 882865) (-379 881149 881542 881570 "FNAME" 881575 T FNAME (NIL) -8 NIL NIL) (-378 879847 880776 880804 "FMTC" 880809 T FMTC (NIL) -9 NIL 880845) (-377 876209 877370 877999 "FMONOID" 879251 NIL FMONOID (NIL T) -8 NIL NIL) (-376 875428 875951 876100 "FM" 876105 NIL FM (NIL T T) -8 NIL NIL) (-375 872852 873498 873526 "FMFUN" 874670 T FMFUN (NIL) -9 NIL 875378) (-374 872121 872302 872330 "FMC" 872620 T FMC (NIL) -9 NIL 872802) (-373 869333 870167 870221 "FMCAT" 871416 NIL FMCAT (NIL T T) -9 NIL 871911) (-372 868226 869099 869199 "FM1" 869278 NIL FM1 (NIL T T) -8 NIL NIL) (-371 866000 866416 866910 "FLOATRP" 867777 NIL FLOATRP (NIL T) -7 NIL NIL) (-370 859551 863656 864286 "FLOAT" 865390 T FLOAT (NIL) -8 NIL NIL) (-369 856989 857489 858067 "FLOATCP" 859018 NIL FLOATCP (NIL T) -7 NIL NIL) (-368 855818 856622 856663 "FLINEXP" 856668 NIL FLINEXP (NIL T) -9 NIL 856761) (-367 854972 855207 855535 "FLINEXP-" 855540 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-366 854048 854192 854416 "FLASORT" 854824 NIL FLASORT (NIL T T) -7 NIL NIL) (-365 851265 852107 852159 "FLALG" 853386 NIL FLALG (NIL T T) -9 NIL 853853) (-364 845049 848751 848792 "FLAGG" 850054 NIL FLAGG (NIL T) -9 NIL 850706) (-363 843775 844114 844604 "FLAGG-" 844609 NIL FLAGG- (NIL T T) -8 NIL NIL) (-362 842817 842960 843187 "FLAGG2" 843628 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-361 839830 840804 840863 "FINRALG" 841991 NIL FINRALG (NIL T T) -9 NIL 842499) (-360 838990 839219 839558 "FINRALG-" 839563 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-359 838396 838609 838637 "FINITE" 838833 T FINITE (NIL) -9 NIL 838940) (-358 830854 833015 833055 "FINAALG" 836722 NIL FINAALG (NIL T) -9 NIL 838175) (-357 826195 827236 828380 "FINAALG-" 829759 NIL FINAALG- (NIL T T) -8 NIL NIL) (-356 825590 825950 826053 "FILE" 826125 NIL FILE (NIL T) -8 NIL NIL) (-355 824274 824586 824640 "FILECAT" 825324 NIL FILECAT (NIL T T) -9 NIL 825540) (-354 822194 823688 823716 "FIELD" 823756 T FIELD (NIL) -9 NIL 823836) (-353 820814 821199 821710 "FIELD-" 821715 NIL FIELD- (NIL T) -8 NIL NIL) (-352 818692 819449 819796 "FGROUP" 820500 NIL FGROUP (NIL T) -8 NIL NIL) (-351 817782 817946 818166 "FGLMICPK" 818524 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-350 813649 817707 817764 "FFX" 817769 NIL FFX (NIL T NIL) -8 NIL NIL) (-349 813250 813311 813446 "FFSLPE" 813582 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-348 809243 810022 810818 "FFPOLY" 812486 NIL FFPOLY (NIL T) -7 NIL NIL) (-347 808747 808783 808992 "FFPOLY2" 809201 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-346 804633 808666 808729 "FFP" 808734 NIL FFP (NIL T NIL) -8 NIL NIL) (-345 800066 804544 804608 "FF" 804613 NIL FF (NIL NIL NIL) -8 NIL NIL) (-344 795227 799409 799599 "FFNBX" 799920 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-343 790201 794362 794620 "FFNBP" 795081 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-342 784869 789485 789696 "FFNB" 790034 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-341 783701 783899 784214 "FFINTBAS" 784666 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-340 779985 782160 782188 "FFIELDC" 782808 T FFIELDC (NIL) -9 NIL 783184) (-339 778648 779018 779515 "FFIELDC-" 779520 NIL FFIELDC- (NIL T) -8 NIL NIL) (-338 778218 778263 778387 "FFHOM" 778590 NIL FFHOM (NIL T T T) -7 NIL NIL) (-337 775916 776400 776917 "FFF" 777733 NIL FFF (NIL T) -7 NIL NIL) (-336 771569 775658 775759 "FFCGX" 775859 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-335 767236 771301 771408 "FFCGP" 771512 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-334 762454 766963 767071 "FFCG" 767172 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-333 744512 753548 753634 "FFCAT" 758799 NIL FFCAT (NIL T T T) -9 NIL 760250) (-332 739710 740757 742071 "FFCAT-" 743301 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-331 739121 739164 739399 "FFCAT2" 739661 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-330 728333 732093 733313 "FEXPR" 737973 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-329 727333 727768 727809 "FEVALAB" 727893 NIL FEVALAB (NIL T) -9 NIL 728154) (-328 726492 726702 727040 "FEVALAB-" 727045 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-327 725085 725875 726078 "FDIV" 726391 NIL FDIV (NIL T T T T) -8 NIL NIL) (-326 722151 722866 722981 "FDIVCAT" 724549 NIL FDIVCAT (NIL T T T T) -9 NIL 724986) (-325 721913 721940 722110 "FDIVCAT-" 722115 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-324 721133 721220 721497 "FDIV2" 721820 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-323 719819 720078 720367 "FCPAK1" 720864 T FCPAK1 (NIL) -7 NIL NIL) (-322 718947 719319 719460 "FCOMP" 719710 NIL FCOMP (NIL T) -8 NIL NIL) (-321 702582 705996 709557 "FC" 715406 T FC (NIL) -8 NIL NIL) (-320 695235 699216 699256 "FAXF" 701058 NIL FAXF (NIL T) -9 NIL 701750) (-319 692514 693169 693994 "FAXF-" 694459 NIL FAXF- (NIL T T) -8 NIL NIL) (-318 687614 691890 692066 "FARRAY" 692371 NIL FARRAY (NIL T) -8 NIL NIL) (-317 683021 685053 685106 "FAMR" 686129 NIL FAMR (NIL T T) -9 NIL 686589) (-316 681911 682213 682648 "FAMR-" 682653 NIL FAMR- (NIL T T T) -8 NIL NIL) (-315 681107 681833 681886 "FAMONOID" 681891 NIL FAMONOID (NIL T) -8 NIL NIL) (-314 678937 679621 679674 "FAMONC" 680615 NIL FAMONC (NIL T T) -9 NIL 681001) (-313 677629 678691 678828 "FAGROUP" 678833 NIL FAGROUP (NIL T) -8 NIL NIL) (-312 675424 675743 676146 "FACUTIL" 677310 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-311 674523 674708 674930 "FACTFUNC" 675234 NIL FACTFUNC (NIL T) -7 NIL NIL) (-310 666928 673774 673986 "EXPUPXS" 674379 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-309 664411 664951 665537 "EXPRTUBE" 666362 T EXPRTUBE (NIL) -7 NIL NIL) (-308 660605 661197 661934 "EXPRODE" 663750 NIL EXPRODE (NIL T T) -7 NIL NIL) (-307 645979 659260 659688 "EXPR" 660209 NIL EXPR (NIL T) -8 NIL NIL) (-306 640386 640973 641786 "EXPR2UPS" 645277 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-305 640022 640079 640186 "EXPR2" 640323 NIL EXPR2 (NIL T T) -7 NIL NIL) (-304 631429 639154 639451 "EXPEXPAN" 639859 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-303 631256 631386 631415 "EXIT" 631420 T EXIT (NIL) -8 NIL NIL) (-302 630780 630980 631071 "EXITAST" 631185 T EXITAST (NIL) -8 NIL NIL) (-301 630407 630469 630582 "EVALCYC" 630712 NIL EVALCYC (NIL T) -7 NIL NIL) (-300 629948 630066 630107 "EVALAB" 630277 NIL EVALAB (NIL T) -9 NIL 630381) (-299 629429 629551 629772 "EVALAB-" 629777 NIL EVALAB- (NIL T T) -8 NIL NIL) (-298 626932 628200 628228 "EUCDOM" 628783 T EUCDOM (NIL) -9 NIL 629133) (-297 625337 625779 626369 "EUCDOM-" 626374 NIL EUCDOM- (NIL T) -8 NIL NIL) (-296 612877 615635 618385 "ESTOOLS" 622607 T ESTOOLS (NIL) -7 NIL NIL) (-295 612509 612566 612675 "ESTOOLS2" 612814 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-294 612260 612302 612382 "ESTOOLS1" 612461 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-293 606185 607913 607941 "ES" 610709 T ES (NIL) -9 NIL 612118) (-292 601132 602419 604236 "ES-" 604400 NIL ES- (NIL T) -8 NIL NIL) (-291 597507 598267 599047 "ESCONT" 600372 T ESCONT (NIL) -7 NIL NIL) (-290 597252 597284 597366 "ESCONT1" 597469 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-289 596927 596977 597077 "ES2" 597196 NIL ES2 (NIL T T) -7 NIL NIL) (-288 596557 596615 596724 "ES1" 596863 NIL ES1 (NIL T T) -7 NIL NIL) (-287 595773 595902 596078 "ERROR" 596401 T ERROR (NIL) -7 NIL NIL) (-286 589276 595632 595723 "EQTBL" 595728 NIL EQTBL (NIL T T) -8 NIL NIL) (-285 581833 584590 586039 "EQ" 587860 NIL -3896 (NIL T) -8 NIL NIL) (-284 581465 581522 581631 "EQ2" 581770 NIL EQ2 (NIL T T) -7 NIL NIL) (-283 576757 577803 578896 "EP" 580404 NIL EP (NIL T) -7 NIL NIL) (-282 575339 575640 575957 "ENV" 576460 T ENV (NIL) -8 NIL NIL) (-281 574538 575058 575086 "ENTIRER" 575091 T ENTIRER (NIL) -9 NIL 575137) (-280 571040 572493 572863 "EMR" 574337 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-279 570184 570369 570423 "ELTAGG" 570803 NIL ELTAGG (NIL T T) -9 NIL 571014) (-278 569903 569965 570106 "ELTAGG-" 570111 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-277 569692 569721 569775 "ELTAB" 569859 NIL ELTAB (NIL T T) -9 NIL NIL) (-276 568818 568964 569163 "ELFUTS" 569543 NIL ELFUTS (NIL T T) -7 NIL NIL) (-275 568560 568616 568644 "ELEMFUN" 568749 T ELEMFUN (NIL) -9 NIL NIL) (-274 568430 568451 568519 "ELEMFUN-" 568524 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-273 563321 566530 566571 "ELAGG" 567511 NIL ELAGG (NIL T) -9 NIL 567974) (-272 561606 562040 562703 "ELAGG-" 562708 NIL ELAGG- (NIL T T) -8 NIL NIL) (-271 560263 560543 560838 "ELABEXPR" 561331 T ELABEXPR (NIL) -8 NIL NIL) (-270 553129 554930 555757 "EFUPXS" 559539 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-269 546579 548380 549190 "EFULS" 552405 NIL EFULS (NIL T T T) -8 NIL NIL) (-268 544001 544359 544838 "EFSTRUC" 546211 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-267 533073 534638 536198 "EF" 542516 NIL EF (NIL T T) -7 NIL NIL) (-266 532174 532558 532707 "EAB" 532944 T EAB (NIL) -8 NIL NIL) (-265 531383 532133 532161 "E04UCFA" 532166 T E04UCFA (NIL) -8 NIL NIL) (-264 530592 531342 531370 "E04NAFA" 531375 T E04NAFA (NIL) -8 NIL NIL) (-263 529801 530551 530579 "E04MBFA" 530584 T E04MBFA (NIL) -8 NIL NIL) (-262 529010 529760 529788 "E04JAFA" 529793 T E04JAFA (NIL) -8 NIL NIL) (-261 528221 528969 528997 "E04GCFA" 529002 T E04GCFA (NIL) -8 NIL NIL) (-260 527432 528180 528208 "E04FDFA" 528213 T E04FDFA (NIL) -8 NIL NIL) (-259 526641 527391 527419 "E04DGFA" 527424 T E04DGFA (NIL) -8 NIL NIL) (-258 520819 522166 523530 "E04AGNT" 525297 T E04AGNT (NIL) -7 NIL NIL) (-257 519543 520023 520063 "DVARCAT" 520538 NIL DVARCAT (NIL T) -9 NIL 520737) (-256 518747 518959 519273 "DVARCAT-" 519278 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-255 511647 518546 518675 "DSMP" 518680 NIL DSMP (NIL T T T) -8 NIL NIL) (-254 506457 507592 508660 "DROPT" 510599 T DROPT (NIL) -8 NIL NIL) (-253 506122 506181 506279 "DROPT1" 506392 NIL DROPT1 (NIL T) -7 NIL NIL) (-252 501237 502363 503500 "DROPT0" 505005 T DROPT0 (NIL) -7 NIL NIL) (-251 499582 499907 500293 "DRAWPT" 500871 T DRAWPT (NIL) -7 NIL NIL) (-250 494169 495092 496171 "DRAW" 498556 NIL DRAW (NIL T) -7 NIL NIL) (-249 493802 493855 493973 "DRAWHACK" 494110 NIL DRAWHACK (NIL T) -7 NIL NIL) (-248 492533 492802 493093 "DRAWCX" 493531 T DRAWCX (NIL) -7 NIL NIL) (-247 492049 492117 492268 "DRAWCURV" 492459 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-246 482520 484479 486594 "DRAWCFUN" 489954 T DRAWCFUN (NIL) -7 NIL NIL) (-245 479333 481215 481256 "DQAGG" 481885 NIL DQAGG (NIL T) -9 NIL 482158) (-244 467852 474549 474632 "DPOLCAT" 476484 NIL DPOLCAT (NIL T T T T) -9 NIL 477029) (-243 462691 464037 465995 "DPOLCAT-" 466000 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-242 455846 462552 462650 "DPMO" 462655 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-241 448904 455626 455793 "DPMM" 455798 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-240 448324 448527 448641 "DOMAIN" 448810 T DOMAIN (NIL) -8 NIL NIL) (-239 442075 447959 448111 "DMP" 448225 NIL DMP (NIL NIL T) -8 NIL NIL) (-238 441675 441731 441875 "DLP" 442013 NIL DLP (NIL T) -7 NIL NIL) (-237 435319 440776 441003 "DLIST" 441480 NIL DLIST (NIL T) -8 NIL NIL) (-236 432165 434174 434215 "DLAGG" 434765 NIL DLAGG (NIL T) -9 NIL 434994) (-235 431015 431645 431673 "DIVRING" 431765 T DIVRING (NIL) -9 NIL 431848) (-234 430252 430442 430742 "DIVRING-" 430747 NIL DIVRING- (NIL T) -8 NIL NIL) (-233 428354 428711 429117 "DISPLAY" 429866 T DISPLAY (NIL) -7 NIL NIL) (-232 422296 428268 428331 "DIRPROD" 428336 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-231 421144 421347 421612 "DIRPROD2" 422089 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-230 410682 416634 416687 "DIRPCAT" 417097 NIL DIRPCAT (NIL NIL T) -9 NIL 417937) (-229 408008 408650 409531 "DIRPCAT-" 409868 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-228 407295 407455 407641 "DIOSP" 407842 T DIOSP (NIL) -7 NIL NIL) (-227 403997 406207 406248 "DIOPS" 406682 NIL DIOPS (NIL T) -9 NIL 406911) (-226 403546 403660 403851 "DIOPS-" 403856 NIL DIOPS- (NIL T T) -8 NIL NIL) (-225 402458 403052 403080 "DIFRING" 403267 T DIFRING (NIL) -9 NIL 403377) (-224 402104 402181 402333 "DIFRING-" 402338 NIL DIFRING- (NIL T) -8 NIL NIL) (-223 399929 401167 401208 "DIFEXT" 401571 NIL DIFEXT (NIL T) -9 NIL 401865) (-222 398214 398642 399308 "DIFEXT-" 399313 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-221 395536 397746 397787 "DIAGG" 397792 NIL DIAGG (NIL T) -9 NIL 397812) (-220 394920 395077 395329 "DIAGG-" 395334 NIL DIAGG- (NIL T T) -8 NIL NIL) (-219 390385 393879 394156 "DHMATRIX" 394689 NIL DHMATRIX (NIL T) -8 NIL NIL) (-218 385997 386906 387916 "DFSFUN" 389395 T DFSFUN (NIL) -7 NIL NIL) (-217 380965 384812 385154 "DFLOAT" 385675 T DFLOAT (NIL) -8 NIL NIL) (-216 379193 379474 379870 "DFINTTLS" 380673 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-215 376258 377214 377614 "DERHAM" 378859 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-214 374107 376033 376122 "DEQUEUE" 376202 NIL DEQUEUE (NIL T) -8 NIL NIL) (-213 373322 373455 373651 "DEGRED" 373969 NIL DEGRED (NIL T T) -7 NIL NIL) (-212 369717 370462 371315 "DEFINTRF" 372550 NIL DEFINTRF (NIL T) -7 NIL NIL) (-211 367244 367713 368312 "DEFINTEF" 369236 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-210 366610 366843 366965 "DEFAST" 367142 T DEFAST (NIL) -8 NIL NIL) (-209 360498 366051 366217 "DECIMAL" 366464 T DECIMAL (NIL) -8 NIL NIL) (-208 358010 358468 358974 "DDFACT" 360042 NIL DDFACT (NIL T T) -7 NIL NIL) (-207 357606 357649 357800 "DBLRESP" 357961 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-206 355316 355650 356019 "DBASE" 357364 NIL DBASE (NIL T) -8 NIL NIL) (-205 354585 354796 354942 "DATABUF" 355215 NIL DATABUF (NIL NIL T) -8 NIL NIL) (-204 353718 354544 354572 "D03FAFA" 354577 T D03FAFA (NIL) -8 NIL NIL) (-203 352852 353677 353705 "D03EEFA" 353710 T D03EEFA (NIL) -8 NIL NIL) (-202 350802 351268 351757 "D03AGNT" 352383 T D03AGNT (NIL) -7 NIL NIL) (-201 350118 350761 350789 "D02EJFA" 350794 T D02EJFA (NIL) -8 NIL NIL) (-200 349434 350077 350105 "D02CJFA" 350110 T D02CJFA (NIL) -8 NIL NIL) (-199 348750 349393 349421 "D02BHFA" 349426 T D02BHFA (NIL) -8 NIL NIL) (-198 348066 348709 348737 "D02BBFA" 348742 T D02BBFA (NIL) -8 NIL NIL) (-197 341264 342852 344458 "D02AGNT" 346480 T D02AGNT (NIL) -7 NIL NIL) (-196 339033 339555 340101 "D01WGTS" 340738 T D01WGTS (NIL) -7 NIL NIL) (-195 338128 338992 339020 "D01TRNS" 339025 T D01TRNS (NIL) -8 NIL NIL) (-194 337223 338087 338115 "D01GBFA" 338120 T D01GBFA (NIL) -8 NIL NIL) (-193 336318 337182 337210 "D01FCFA" 337215 T D01FCFA (NIL) -8 NIL NIL) (-192 335413 336277 336305 "D01ASFA" 336310 T D01ASFA (NIL) -8 NIL NIL) (-191 334508 335372 335400 "D01AQFA" 335405 T D01AQFA (NIL) -8 NIL NIL) (-190 333603 334467 334495 "D01APFA" 334500 T D01APFA (NIL) -8 NIL NIL) (-189 332698 333562 333590 "D01ANFA" 333595 T D01ANFA (NIL) -8 NIL NIL) (-188 331793 332657 332685 "D01AMFA" 332690 T D01AMFA (NIL) -8 NIL NIL) (-187 330888 331752 331780 "D01ALFA" 331785 T D01ALFA (NIL) -8 NIL NIL) (-186 329983 330847 330875 "D01AKFA" 330880 T D01AKFA (NIL) -8 NIL NIL) (-185 329078 329942 329970 "D01AJFA" 329975 T D01AJFA (NIL) -8 NIL NIL) (-184 322375 323926 325487 "D01AGNT" 327537 T D01AGNT (NIL) -7 NIL NIL) (-183 321712 321840 321992 "CYCLOTOM" 322243 T CYCLOTOM (NIL) -7 NIL NIL) (-182 318447 319160 319887 "CYCLES" 321005 T CYCLES (NIL) -7 NIL NIL) (-181 317759 317893 318064 "CVMP" 318308 NIL CVMP (NIL T) -7 NIL NIL) (-180 315530 315788 316164 "CTRIGMNP" 317487 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-179 315041 315230 315329 "CTORCALL" 315451 T CTORCALL (NIL) -8 NIL NIL) (-178 314415 314514 314667 "CSTTOOLS" 314938 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-177 310214 310871 311629 "CRFP" 313727 NIL CRFP (NIL T T) -7 NIL NIL) (-176 309261 309446 309674 "CRAPACK" 310018 NIL CRAPACK (NIL T) -7 NIL NIL) (-175 308645 308746 308950 "CPMATCH" 309137 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-174 308370 308398 308504 "CPIMA" 308611 NIL CPIMA (NIL T T T) -7 NIL NIL) (-173 304734 305406 306124 "COORDSYS" 307705 NIL COORDSYS (NIL T) -7 NIL NIL) (-172 304118 304247 304397 "CONTOUR" 304604 T CONTOUR (NIL) -8 NIL NIL) (-171 300044 302121 302613 "CONTFRAC" 303658 NIL CONTFRAC (NIL T) -8 NIL NIL) (-170 299924 299945 299973 "CONDUIT" 300010 T CONDUIT (NIL) -9 NIL NIL) (-169 299117 299637 299665 "COMRING" 299670 T COMRING (NIL) -9 NIL 299722) (-168 298198 298475 298659 "COMPPROP" 298953 T COMPPROP (NIL) -8 NIL NIL) (-167 297859 297894 298022 "COMPLPAT" 298157 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-166 287918 297668 297777 "COMPLEX" 297782 NIL COMPLEX (NIL T) -8 NIL NIL) (-165 287554 287611 287718 "COMPLEX2" 287855 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-164 287272 287307 287405 "COMPFACT" 287513 NIL COMPFACT (NIL T T) -7 NIL NIL) (-163 271670 281886 281926 "COMPCAT" 282930 NIL COMPCAT (NIL T) -9 NIL 284325) (-162 261185 264109 267736 "COMPCAT-" 268092 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-161 260914 260942 261045 "COMMUPC" 261151 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-160 260709 260742 260801 "COMMONOP" 260875 T COMMONOP (NIL) -7 NIL NIL) (-159 260292 260460 260547 "COMM" 260642 T COMM (NIL) -8 NIL NIL) (-158 259913 260096 260171 "COMMAAST" 260237 T COMMAAST (NIL) -8 NIL NIL) (-157 259162 259356 259384 "COMBOPC" 259722 T COMBOPC (NIL) -9 NIL 259897) (-156 258058 258268 258510 "COMBINAT" 258952 NIL COMBINAT (NIL T) -7 NIL NIL) (-155 254256 254829 255469 "COMBF" 257480 NIL COMBF (NIL T T) -7 NIL NIL) (-154 253042 253372 253607 "COLOR" 254041 T COLOR (NIL) -8 NIL NIL) (-153 252562 252763 252855 "COLONAST" 252970 T COLONAST (NIL) -8 NIL NIL) (-152 252202 252249 252374 "CMPLXRT" 252509 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-151 247704 248732 249812 "CLIP" 251142 T CLIP (NIL) -7 NIL NIL) (-150 246086 246810 247049 "CLIF" 247531 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-149 242308 244232 244273 "CLAGG" 245202 NIL CLAGG (NIL T) -9 NIL 245738) (-148 240730 241187 241770 "CLAGG-" 241775 NIL CLAGG- (NIL T T) -8 NIL NIL) (-147 240274 240359 240499 "CINTSLPE" 240639 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-146 237775 238246 238794 "CHVAR" 239802 NIL CHVAR (NIL T T T) -7 NIL NIL) (-145 237038 237558 237586 "CHARZ" 237591 T CHARZ (NIL) -9 NIL 237606) (-144 236792 236832 236910 "CHARPOL" 236992 NIL CHARPOL (NIL T) -7 NIL NIL) (-143 235939 236492 236520 "CHARNZ" 236567 T CHARNZ (NIL) -9 NIL 236623) (-142 233964 234629 234964 "CHAR" 235624 T CHAR (NIL) -8 NIL NIL) (-141 233690 233751 233779 "CFCAT" 233890 T CFCAT (NIL) -9 NIL NIL) (-140 232935 233046 233228 "CDEN" 233574 NIL CDEN (NIL T T T) -7 NIL NIL) (-139 228927 232088 232368 "CCLASS" 232675 T CCLASS (NIL) -8 NIL NIL) (-138 228846 228872 228907 "CATEGORY" 228912 T -10 (NIL) -8 NIL NIL) (-137 228337 228546 228645 "CATAST" 228767 T CATAST (NIL) -8 NIL NIL) (-136 227857 228058 228150 "CASEAST" 228265 T CASEAST (NIL) -8 NIL NIL) (-135 222909 223886 224639 "CARTEN" 227160 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-134 222017 222165 222386 "CARTEN2" 222756 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-133 220359 221167 221424 "CARD" 221780 T CARD (NIL) -8 NIL NIL) (-132 219979 220163 220238 "CAPSLAST" 220304 T CAPSLAST (NIL) -8 NIL NIL) (-131 219351 219679 219707 "CACHSET" 219839 T CACHSET (NIL) -9 NIL 219916) (-130 218847 219143 219171 "CABMON" 219221 T CABMON (NIL) -9 NIL 219277) (-129 218016 218394 218537 "BYTE" 218724 T BYTE (NIL) -8 NIL NIL) (-128 213964 217963 217997 "BYTEARY" 218002 T BYTEARY (NIL) -8 NIL NIL) (-127 211521 213656 213763 "BTREE" 213890 NIL BTREE (NIL T) -8 NIL NIL) (-126 209019 211169 211291 "BTOURN" 211431 NIL BTOURN (NIL T) -8 NIL NIL) (-125 206437 208490 208531 "BTCAT" 208599 NIL BTCAT (NIL T) -9 NIL 208676) (-124 206104 206184 206333 "BTCAT-" 206338 NIL BTCAT- (NIL T T) -8 NIL NIL) (-123 201396 205247 205275 "BTAGG" 205497 T BTAGG (NIL) -9 NIL 205658) (-122 200886 201011 201217 "BTAGG-" 201222 NIL BTAGG- (NIL T) -8 NIL NIL) (-121 197930 200164 200379 "BSTREE" 200703 NIL BSTREE (NIL T) -8 NIL NIL) (-120 197068 197194 197378 "BRILL" 197786 NIL BRILL (NIL T) -7 NIL NIL) (-119 193769 195796 195837 "BRAGG" 196486 NIL BRAGG (NIL T) -9 NIL 196743) (-118 192298 192704 193259 "BRAGG-" 193264 NIL BRAGG- (NIL T T) -8 NIL NIL) (-117 185564 191644 191828 "BPADICRT" 192146 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-116 183914 185501 185546 "BPADIC" 185551 NIL BPADIC (NIL NIL) -8 NIL NIL) (-115 183612 183642 183756 "BOUNDZRO" 183878 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-114 179127 180218 181085 "BOP" 182765 T BOP (NIL) -8 NIL NIL) (-113 176748 177192 177712 "BOP1" 178640 NIL BOP1 (NIL T) -7 NIL NIL) (-112 175472 176158 176358 "BOOLEAN" 176568 T BOOLEAN (NIL) -8 NIL NIL) (-111 174834 175212 175266 "BMODULE" 175271 NIL BMODULE (NIL T T) -9 NIL 175336) (-110 170664 174632 174705 "BITS" 174781 T BITS (NIL) -8 NIL NIL) (-109 169761 170196 170348 "BINFILE" 170532 T BINFILE (NIL) -8 NIL NIL) (-108 169173 169295 169437 "BINDING" 169639 T BINDING (NIL) -8 NIL NIL) (-107 163065 168617 168782 "BINARY" 169028 T BINARY (NIL) -8 NIL NIL) (-106 160892 162320 162361 "BGAGG" 162621 NIL BGAGG (NIL T) -9 NIL 162758) (-105 160723 160755 160846 "BGAGG-" 160851 NIL BGAGG- (NIL T T) -8 NIL NIL) (-104 159821 160107 160312 "BFUNCT" 160538 T BFUNCT (NIL) -8 NIL NIL) (-103 158511 158689 158977 "BEZOUT" 159645 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-102 155028 157363 157693 "BBTREE" 158214 NIL BBTREE (NIL T) -8 NIL NIL) (-101 154762 154815 154843 "BASTYPE" 154962 T BASTYPE (NIL) -9 NIL NIL) (-100 154614 154643 154716 "BASTYPE-" 154721 NIL BASTYPE- (NIL T) -8 NIL NIL) (-99 154052 154128 154278 "BALFACT" 154525 NIL BALFACT (NIL T T) -7 NIL NIL) (-98 152935 153467 153653 "AUTOMOR" 153897 NIL AUTOMOR (NIL T) -8 NIL NIL) (-97 152661 152666 152692 "ATTREG" 152697 T ATTREG (NIL) -9 NIL NIL) (-96 150940 151358 151710 "ATTRBUT" 152327 T ATTRBUT (NIL) -8 NIL NIL) (-95 150592 150768 150834 "ATTRAST" 150892 T ATTRAST (NIL) -8 NIL NIL) (-94 150128 150241 150267 "ATRIG" 150468 T ATRIG (NIL) -9 NIL NIL) (-93 149937 149978 150065 "ATRIG-" 150070 NIL ATRIG- (NIL T) -8 NIL NIL) (-92 149662 149805 149831 "ASTCAT" 149836 T ASTCAT (NIL) -9 NIL 149866) (-91 149459 149502 149594 "ASTCAT-" 149599 NIL ASTCAT- (NIL T) -8 NIL NIL) (-90 147656 149235 149323 "ASTACK" 149402 NIL ASTACK (NIL T) -8 NIL NIL) (-89 146161 146458 146823 "ASSOCEQ" 147338 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-88 145193 145820 145944 "ASP9" 146068 NIL ASP9 (NIL NIL) -8 NIL NIL) (-87 144957 145141 145180 "ASP8" 145185 NIL ASP8 (NIL NIL) -8 NIL NIL) (-86 143826 144562 144704 "ASP80" 144846 NIL ASP80 (NIL NIL) -8 NIL NIL) (-85 142725 143461 143593 "ASP7" 143725 NIL ASP7 (NIL NIL) -8 NIL NIL) (-84 141679 142402 142520 "ASP78" 142638 NIL ASP78 (NIL NIL) -8 NIL NIL) (-83 140648 141359 141476 "ASP77" 141593 NIL ASP77 (NIL NIL) -8 NIL NIL) (-82 139560 140286 140417 "ASP74" 140548 NIL ASP74 (NIL NIL) -8 NIL NIL) (-81 138460 139195 139327 "ASP73" 139459 NIL ASP73 (NIL NIL) -8 NIL NIL) (-80 137415 138137 138255 "ASP6" 138373 NIL ASP6 (NIL NIL) -8 NIL NIL) (-79 136363 137092 137210 "ASP55" 137328 NIL ASP55 (NIL NIL) -8 NIL NIL) (-78 135313 136037 136156 "ASP50" 136275 NIL ASP50 (NIL NIL) -8 NIL NIL) (-77 134401 135014 135124 "ASP4" 135234 NIL ASP4 (NIL NIL) -8 NIL NIL) (-76 133489 134102 134212 "ASP49" 134322 NIL ASP49 (NIL NIL) -8 NIL NIL) (-75 132274 133028 133196 "ASP42" 133378 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-74 131051 131807 131977 "ASP41" 132161 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130001 130728 130846 "ASP35" 130964 NIL ASP35 (NIL NIL) -8 NIL NIL) (-72 129766 129949 129988 "ASP34" 129993 NIL ASP34 (NIL NIL) -8 NIL NIL) (-71 129503 129570 129646 "ASP33" 129721 NIL ASP33 (NIL NIL) -8 NIL NIL) (-70 128398 129138 129270 "ASP31" 129402 NIL ASP31 (NIL NIL) -8 NIL NIL) (-69 128163 128346 128385 "ASP30" 128390 NIL ASP30 (NIL NIL) -8 NIL NIL) (-68 127898 127967 128043 "ASP29" 128118 NIL ASP29 (NIL NIL) -8 NIL NIL) (-67 127663 127846 127885 "ASP28" 127890 NIL ASP28 (NIL NIL) -8 NIL NIL) (-66 127428 127611 127650 "ASP27" 127655 NIL ASP27 (NIL NIL) -8 NIL NIL) (-65 126512 127126 127237 "ASP24" 127348 NIL ASP24 (NIL NIL) -8 NIL NIL) (-64 125428 126153 126283 "ASP20" 126413 NIL ASP20 (NIL NIL) -8 NIL NIL) (-63 124516 125129 125239 "ASP1" 125349 NIL ASP1 (NIL NIL) -8 NIL NIL) (-62 123460 124190 124309 "ASP19" 124428 NIL ASP19 (NIL NIL) -8 NIL NIL) (-61 123197 123264 123340 "ASP12" 123415 NIL ASP12 (NIL NIL) -8 NIL NIL) (-60 122049 122796 122940 "ASP10" 123084 NIL ASP10 (NIL NIL) -8 NIL NIL) (-59 119948 121893 121984 "ARRAY2" 121989 NIL ARRAY2 (NIL T) -8 NIL NIL) (-58 115764 119596 119710 "ARRAY1" 119865 NIL ARRAY1 (NIL T) -8 NIL NIL) (-57 114796 114969 115190 "ARRAY12" 115587 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-56 109155 111026 111101 "ARR2CAT" 113731 NIL ARR2CAT (NIL T T T) -9 NIL 114489) (-55 106589 107333 108287 "ARR2CAT-" 108292 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-54 105337 105489 105795 "APPRULE" 106425 NIL APPRULE (NIL T T T) -7 NIL NIL) (-53 104988 105036 105155 "APPLYORE" 105283 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-52 103962 104253 104448 "ANY" 104811 T ANY (NIL) -8 NIL NIL) (-51 103240 103363 103520 "ANY1" 103836 NIL ANY1 (NIL T) -7 NIL NIL) (-50 100805 101677 102004 "ANTISYM" 102964 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-49 100320 100509 100606 "ANON" 100726 T ANON (NIL) -8 NIL NIL) (-48 94454 98861 99314 "AN" 99885 T AN (NIL) -8 NIL NIL) (-47 90835 92189 92240 "AMR" 92988 NIL AMR (NIL T T) -9 NIL 93588) (-46 89947 90168 90531 "AMR-" 90536 NIL AMR- (NIL T T T) -8 NIL NIL) (-45 74497 89864 89925 "ALIST" 89930 NIL ALIST (NIL T T) -8 NIL NIL) (-44 71334 74091 74260 "ALGSC" 74415 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-43 67890 68444 69051 "ALGPKG" 70774 NIL ALGPKG (NIL T T) -7 NIL NIL) (-42 67167 67268 67452 "ALGMFACT" 67776 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-41 62906 63591 64246 "ALGMANIP" 66690 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-40 54312 62532 62682 "ALGFF" 62839 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-39 53508 53639 53818 "ALGFACT" 54170 NIL ALGFACT (NIL T) -7 NIL NIL) (-38 52538 53104 53142 "ALGEBRA" 53202 NIL ALGEBRA (NIL T) -9 NIL 53261) (-37 52256 52315 52447 "ALGEBRA-" 52452 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-36 34516 50259 50311 "ALAGG" 50447 NIL ALAGG (NIL T T) -9 NIL 50608) (-35 34052 34165 34191 "AHYP" 34392 T AHYP (NIL) -9 NIL NIL) (-34 32983 33231 33257 "AGG" 33756 T AGG (NIL) -9 NIL 34035) (-33 32417 32579 32793 "AGG-" 32798 NIL AGG- (NIL T) -8 NIL NIL) (-32 30094 30516 30934 "AF" 32059 NIL AF (NIL T T) -7 NIL NIL) (-31 29618 29819 29909 "ADDAST" 30022 T ADDAST (NIL) -8 NIL NIL) (-30 28887 29145 29301 "ACPLOT" 29480 T ACPLOT (NIL) -8 NIL NIL) (-29 18358 26279 26330 "ACFS" 27041 NIL ACFS (NIL T) -9 NIL 27280) (-28 16372 16862 17637 "ACFS-" 17642 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12697 14591 14617 "ACF" 15496 T ACF (NIL) -9 NIL 15908) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL) (-25 10999 11168 11194 "ABELSG" 11286 T ABELSG (NIL) -9 NIL 11351) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10235 10496 10522 "ABELMON" 10692 T ABELMON (NIL) -9 NIL 10804) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9233 9579 9605 "ABELGRP" 9730 T ABELGRP (NIL) -9 NIL 9812) (-20 8696 8825 9041 "ABELGRP-" 9046 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 3160478 3160483 3160488 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-2 3160463 3160468 3160473 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1 3160448 3160453 3160458 NIL NIL NIL NIL (NIL) -8 NIL NIL) (0 3160433 3160438 3160443 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1246 3159609 3160308 3160385 "ZMOD" 3160390 NIL ZMOD (NIL NIL) -8 NIL NIL) (-1245 3158719 3158883 3159092 "ZLINDEP" 3159441 NIL ZLINDEP (NIL T) -7 NIL NIL) (-1244 3148095 3149847 3151806 "ZDSOLVE" 3156861 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL) (-1243 3147341 3147482 3147671 "YSTREAM" 3147941 NIL YSTREAM (NIL T) -7 NIL NIL) (-1242 3145152 3146642 3146846 "XRPOLY" 3147184 NIL XRPOLY (NIL T T) -8 NIL NIL) (-1241 3141644 3142927 3143511 "XPR" 3144615 NIL XPR (NIL T T) -8 NIL NIL) (-1240 3139400 3140975 3141179 "XPOLY" 3141475 NIL XPOLY (NIL T) -8 NIL NIL) (-1239 3137249 3138583 3138638 "XPOLYC" 3138926 NIL XPOLYC (NIL T T) -9 NIL 3139039) (-1238 3133667 3135766 3136154 "XPBWPOLY" 3136907 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1237 3129652 3131900 3131942 "XF" 3132563 NIL XF (NIL T) -9 NIL 3132963) (-1236 3129273 3129361 3129530 "XF-" 3129535 NIL XF- (NIL T T) -8 NIL NIL) (-1235 3124665 3125920 3125975 "XFALG" 3128147 NIL XFALG (NIL T T) -9 NIL 3128936) (-1234 3123798 3123902 3124107 "XEXPPKG" 3124557 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1233 3121942 3123648 3123744 "XDPOLY" 3123749 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1232 3120858 3121424 3121467 "XALG" 3121530 NIL XALG (NIL T) -9 NIL 3121650) (-1231 3114327 3118835 3119329 "WUTSET" 3120450 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1230 3112178 3112939 3113292 "WP" 3114108 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1229 3111824 3112000 3112070 "WHILEAST" 3112130 T WHILEAST (NIL) -8 NIL NIL) (-1228 3111340 3111541 3111635 "WHEREAST" 3111752 T WHEREAST (NIL) -8 NIL NIL) (-1227 3110226 3110424 3110719 "WFFINTBS" 3111137 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1226 3108130 3108557 3109019 "WEIER" 3109798 NIL WEIER (NIL T) -7 NIL NIL) (-1225 3107277 3107701 3107743 "VSPACE" 3107879 NIL VSPACE (NIL T) -9 NIL 3107953) (-1224 3107115 3107142 3107233 "VSPACE-" 3107238 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1223 3106861 3106904 3106975 "VOID" 3107066 T VOID (NIL) -8 NIL NIL) (-1222 3104997 3105356 3105762 "VIEW" 3106477 T VIEW (NIL) -7 NIL NIL) (-1221 3101422 3102060 3102797 "VIEWDEF" 3104282 T VIEWDEF (NIL) -7 NIL NIL) (-1220 3090760 3092970 3095143 "VIEW3D" 3099271 T VIEW3D (NIL) -8 NIL NIL) (-1219 3083042 3084671 3086250 "VIEW2D" 3089203 T VIEW2D (NIL) -8 NIL NIL) (-1218 3078446 3082812 3082904 "VECTOR" 3082985 NIL VECTOR (NIL T) -8 NIL NIL) (-1217 3077023 3077282 3077600 "VECTOR2" 3078176 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1216 3070550 3074807 3074850 "VECTCAT" 3075843 NIL VECTCAT (NIL T) -9 NIL 3076429) (-1215 3069564 3069818 3070208 "VECTCAT-" 3070213 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1214 3069045 3069215 3069335 "VARIABLE" 3069479 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1213 3068978 3068983 3069013 "UTYPE" 3069018 T UTYPE (NIL) -9 NIL NIL) (-1212 3067808 3067962 3068224 "UTSODETL" 3068804 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1211 3065248 3065708 3066232 "UTSODE" 3067349 NIL UTSODE (NIL T T) -7 NIL NIL) (-1210 3057124 3062874 3063363 "UTS" 3064817 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1209 3048497 3053816 3053859 "UTSCAT" 3054971 NIL UTSCAT (NIL T) -9 NIL 3055728) (-1208 3045851 3046567 3047556 "UTSCAT-" 3047561 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1207 3045478 3045521 3045654 "UTS2" 3045802 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1206 3039753 3042318 3042361 "URAGG" 3044431 NIL URAGG (NIL T) -9 NIL 3045153) (-1205 3036692 3037555 3038678 "URAGG-" 3038683 NIL URAGG- (NIL T T) -8 NIL NIL) (-1204 3032416 3035306 3035778 "UPXSSING" 3036356 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1203 3024386 3031531 3031813 "UPXS" 3032192 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1202 3017499 3024290 3024362 "UPXSCONS" 3024367 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1201 3007857 3014602 3014664 "UPXSCCA" 3015320 NIL UPXSCCA (NIL T T) -9 NIL 3015562) (-1200 3007495 3007580 3007754 "UPXSCCA-" 3007759 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1199 2997779 3004297 3004340 "UPXSCAT" 3004988 NIL UPXSCAT (NIL T) -9 NIL 3005596) (-1198 2997209 2997288 2997467 "UPXS2" 2997694 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1197 2995863 2996116 2996467 "UPSQFREE" 2996952 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1196 2989781 2992790 2992845 "UPSCAT" 2994006 NIL UPSCAT (NIL T T) -9 NIL 2994780) (-1195 2988985 2989192 2989519 "UPSCAT-" 2989524 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1194 2975076 2983072 2983115 "UPOLYC" 2985216 NIL UPOLYC (NIL T) -9 NIL 2986437) (-1193 2966405 2968830 2971977 "UPOLYC-" 2971982 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1192 2966032 2966075 2966208 "UPOLYC2" 2966356 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1191 2957489 2965598 2965736 "UP" 2965942 NIL UP (NIL NIL T) -8 NIL NIL) (-1190 2956828 2956935 2957099 "UPMP" 2957378 NIL UPMP (NIL T T) -7 NIL NIL) (-1189 2956381 2956462 2956601 "UPDIVP" 2956741 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1188 2954949 2955198 2955514 "UPDECOMP" 2956130 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1187 2954184 2954296 2954481 "UPCDEN" 2954833 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1186 2953703 2953772 2953921 "UP2" 2954109 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1185 2952220 2952907 2953184 "UNISEG" 2953461 NIL UNISEG (NIL T) -8 NIL NIL) (-1184 2951435 2951562 2951767 "UNISEG2" 2952063 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1183 2950495 2950675 2950901 "UNIFACT" 2951251 NIL UNIFACT (NIL T) -7 NIL NIL) (-1182 2934464 2949672 2949923 "ULS" 2950302 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1181 2922506 2934368 2934440 "ULSCONS" 2934445 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1180 2905310 2917245 2917307 "ULSCCAT" 2918027 NIL ULSCCAT (NIL T T) -9 NIL 2918324) (-1179 2904360 2904605 2904993 "ULSCCAT-" 2904998 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1178 2894421 2900853 2900896 "ULSCAT" 2901759 NIL ULSCAT (NIL T) -9 NIL 2902489) (-1177 2893851 2893930 2894109 "ULS2" 2894336 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1176 2892289 2893212 2893242 "UFD" 2893454 T UFD (NIL) -9 NIL 2893568) (-1175 2892083 2892129 2892224 "UFD-" 2892229 NIL UFD- (NIL T) -8 NIL NIL) (-1174 2891165 2891348 2891564 "UDVO" 2891889 T UDVO (NIL) -7 NIL NIL) (-1173 2888981 2889390 2889861 "UDPO" 2890729 NIL UDPO (NIL T) -7 NIL NIL) (-1172 2888914 2888919 2888949 "TYPE" 2888954 T TYPE (NIL) -9 NIL NIL) (-1171 2888568 2888736 2888806 "TYPEAST" 2888866 T TYPEAST (NIL) -8 NIL NIL) (-1170 2887539 2887741 2887981 "TWOFACT" 2888362 NIL TWOFACT (NIL T) -7 NIL NIL) (-1169 2886477 2886814 2887077 "TUPLE" 2887311 NIL TUPLE (NIL T) -8 NIL NIL) (-1168 2884168 2884687 2885226 "TUBETOOL" 2885960 T TUBETOOL (NIL) -7 NIL NIL) (-1167 2883017 2883222 2883463 "TUBE" 2883961 NIL TUBE (NIL T) -8 NIL NIL) (-1166 2877781 2881989 2882272 "TS" 2882769 NIL TS (NIL T) -8 NIL NIL) (-1165 2866448 2870540 2870637 "TSETCAT" 2875906 NIL TSETCAT (NIL T T T T) -9 NIL 2877437) (-1164 2861182 2862780 2864671 "TSETCAT-" 2864676 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1163 2855445 2856291 2857233 "TRMANIP" 2860318 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1162 2854886 2854949 2855112 "TRIMAT" 2855377 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1161 2852682 2852919 2853283 "TRIGMNIP" 2854635 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1160 2852202 2852315 2852345 "TRIGCAT" 2852558 T TRIGCAT (NIL) -9 NIL NIL) (-1159 2851871 2851950 2852091 "TRIGCAT-" 2852096 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1158 2848770 2850731 2851011 "TREE" 2851626 NIL TREE (NIL T) -8 NIL NIL) (-1157 2848044 2848572 2848602 "TRANFUN" 2848637 T TRANFUN (NIL) -9 NIL 2848703) (-1156 2847323 2847514 2847794 "TRANFUN-" 2847799 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1155 2847127 2847159 2847220 "TOPSP" 2847284 T TOPSP (NIL) -7 NIL NIL) (-1154 2846475 2846590 2846744 "TOOLSIGN" 2847008 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1153 2845136 2845652 2845891 "TEXTFILE" 2846258 T TEXTFILE (NIL) -8 NIL NIL) (-1152 2843001 2843515 2843953 "TEX" 2844720 T TEX (NIL) -8 NIL NIL) (-1151 2842782 2842813 2842885 "TEX1" 2842964 NIL TEX1 (NIL T) -7 NIL NIL) (-1150 2842430 2842493 2842583 "TEMUTL" 2842714 T TEMUTL (NIL) -7 NIL NIL) (-1149 2840584 2840864 2841189 "TBCMPPK" 2842153 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1148 2832472 2838744 2838800 "TBAGG" 2839200 NIL TBAGG (NIL T T) -9 NIL 2839411) (-1147 2827542 2829030 2830784 "TBAGG-" 2830789 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1146 2826926 2827033 2827178 "TANEXP" 2827431 NIL TANEXP (NIL T) -7 NIL NIL) (-1145 2820427 2826783 2826876 "TABLE" 2826881 NIL TABLE (NIL T T) -8 NIL NIL) (-1144 2819839 2819938 2820076 "TABLEAU" 2820324 NIL TABLEAU (NIL T) -8 NIL NIL) (-1143 2814447 2815667 2816915 "TABLBUMP" 2818625 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1142 2813875 2813975 2814103 "SYSTEM" 2814341 T SYSTEM (NIL) -7 NIL NIL) (-1141 2810338 2811033 2811816 "SYSSOLP" 2813126 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1140 2806629 2807337 2808071 "SYNTAX" 2809626 T SYNTAX (NIL) -8 NIL NIL) (-1139 2803787 2804389 2805021 "SYMTAB" 2806019 T SYMTAB (NIL) -8 NIL NIL) (-1138 2799036 2799938 2800921 "SYMS" 2802826 T SYMS (NIL) -8 NIL NIL) (-1137 2796308 2798494 2798724 "SYMPOLY" 2798841 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1136 2795825 2795900 2796023 "SYMFUNC" 2796220 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1135 2791802 2793062 2793884 "SYMBOL" 2795025 T SYMBOL (NIL) -8 NIL NIL) (-1134 2785341 2787030 2788750 "SWITCH" 2790104 T SWITCH (NIL) -8 NIL NIL) (-1133 2778611 2784162 2784465 "SUTS" 2785096 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1132 2770580 2777726 2778008 "SUPXS" 2778387 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1131 2762109 2770198 2770324 "SUP" 2770489 NIL SUP (NIL T) -8 NIL NIL) (-1130 2761268 2761395 2761612 "SUPFRACF" 2761977 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1129 2760889 2760948 2761061 "SUP2" 2761203 NIL SUP2 (NIL T T) -7 NIL NIL) (-1128 2759302 2759576 2759939 "SUMRF" 2760588 NIL SUMRF (NIL T) -7 NIL NIL) (-1127 2758616 2758682 2758881 "SUMFS" 2759223 NIL SUMFS (NIL T T) -7 NIL NIL) (-1126 2742625 2757793 2758044 "SULS" 2758423 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1125 2741947 2742150 2742290 "SUCH" 2742533 NIL SUCH (NIL T T) -8 NIL NIL) (-1124 2735841 2736853 2737812 "SUBSPACE" 2741035 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1123 2735271 2735361 2735525 "SUBRESP" 2735729 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1122 2728640 2729936 2731247 "STTF" 2734007 NIL STTF (NIL T) -7 NIL NIL) (-1121 2722813 2723933 2725080 "STTFNC" 2727540 NIL STTFNC (NIL T) -7 NIL NIL) (-1120 2714128 2715995 2717789 "STTAYLOR" 2721054 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1119 2707372 2713992 2714075 "STRTBL" 2714080 NIL STRTBL (NIL T) -8 NIL NIL) (-1118 2702763 2707327 2707358 "STRING" 2707363 T STRING (NIL) -8 NIL NIL) (-1117 2697651 2702136 2702166 "STRICAT" 2702225 T STRICAT (NIL) -9 NIL 2702287) (-1116 2690364 2695174 2695794 "STREAM" 2697066 NIL STREAM (NIL T) -8 NIL NIL) (-1115 2689874 2689951 2690095 "STREAM3" 2690281 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1114 2688856 2689039 2689274 "STREAM2" 2689687 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1113 2688544 2688596 2688689 "STREAM1" 2688798 NIL STREAM1 (NIL T) -7 NIL NIL) (-1112 2687560 2687741 2687972 "STINPROD" 2688360 NIL STINPROD (NIL T) -7 NIL NIL) (-1111 2687138 2687322 2687352 "STEP" 2687432 T STEP (NIL) -9 NIL 2687510) (-1110 2680681 2687037 2687114 "STBL" 2687119 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1109 2675856 2679903 2679946 "STAGG" 2680099 NIL STAGG (NIL T) -9 NIL 2680188) (-1108 2673558 2674160 2675032 "STAGG-" 2675037 NIL STAGG- (NIL T T) -8 NIL NIL) (-1107 2671753 2673328 2673420 "STACK" 2673501 NIL STACK (NIL T) -8 NIL NIL) (-1106 2664478 2669894 2670350 "SREGSET" 2671383 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1105 2656904 2658272 2659785 "SRDCMPK" 2663084 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1104 2649871 2654344 2654374 "SRAGG" 2655677 T SRAGG (NIL) -9 NIL 2656285) (-1103 2648888 2649143 2649522 "SRAGG-" 2649527 NIL SRAGG- (NIL T) -8 NIL NIL) (-1102 2643374 2647803 2648231 "SQMATRIX" 2648507 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1101 2637126 2640094 2640820 "SPLTREE" 2642720 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1100 2633116 2633782 2634428 "SPLNODE" 2636552 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1099 2632163 2632396 2632426 "SPFCAT" 2632870 T SPFCAT (NIL) -9 NIL NIL) (-1098 2630900 2631110 2631374 "SPECOUT" 2631921 T SPECOUT (NIL) -7 NIL NIL) (-1097 2630661 2630701 2630770 "SPADPRSR" 2630853 T SPADPRSR (NIL) -7 NIL NIL) (-1096 2622632 2624379 2624422 "SPACEC" 2628795 NIL SPACEC (NIL T) -9 NIL 2630611) (-1095 2620803 2622564 2622613 "SPACE3" 2622618 NIL SPACE3 (NIL T) -8 NIL NIL) (-1094 2619555 2619726 2620017 "SORTPAK" 2620608 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1093 2617605 2617908 2618327 "SOLVETRA" 2619219 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1092 2616616 2616838 2617112 "SOLVESER" 2617378 NIL SOLVESER (NIL T) -7 NIL NIL) (-1091 2611836 2612717 2613719 "SOLVERAD" 2615668 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1090 2607651 2608260 2608989 "SOLVEFOR" 2611203 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1089 2601948 2607000 2607097 "SNTSCAT" 2607102 NIL SNTSCAT (NIL T T T T) -9 NIL 2607172) (-1088 2596091 2600271 2600662 "SMTS" 2601638 NIL SMTS (NIL T T T) -8 NIL NIL) (-1087 2590541 2595979 2596056 "SMP" 2596061 NIL SMP (NIL T T) -8 NIL NIL) (-1086 2588700 2589001 2589399 "SMITH" 2590238 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1085 2581683 2585838 2585941 "SMATCAT" 2587292 NIL SMATCAT (NIL NIL T T T) -9 NIL 2587842) (-1084 2578623 2579446 2580624 "SMATCAT-" 2580629 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1083 2576336 2577859 2577902 "SKAGG" 2578163 NIL SKAGG (NIL T) -9 NIL 2578298) (-1082 2572452 2575440 2575718 "SINT" 2576080 T SINT (NIL) -8 NIL NIL) (-1081 2572224 2572262 2572328 "SIMPAN" 2572408 T SIMPAN (NIL) -7 NIL NIL) (-1080 2571531 2571759 2571899 "SIG" 2572106 T SIG (NIL) -8 NIL NIL) (-1079 2570369 2570590 2570865 "SIGNRF" 2571290 NIL SIGNRF (NIL T) -7 NIL NIL) (-1078 2569174 2569325 2569616 "SIGNEF" 2570198 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1077 2566864 2567318 2567824 "SHP" 2568715 NIL SHP (NIL T NIL) -7 NIL NIL) (-1076 2560770 2566765 2566841 "SHDP" 2566846 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1075 2560369 2560535 2560565 "SGROUP" 2560658 T SGROUP (NIL) -9 NIL 2560720) (-1074 2560227 2560253 2560326 "SGROUP-" 2560331 NIL SGROUP- (NIL T) -8 NIL NIL) (-1073 2557063 2557760 2558483 "SGCF" 2559526 T SGCF (NIL) -7 NIL NIL) (-1072 2551458 2556510 2556607 "SFRTCAT" 2556612 NIL SFRTCAT (NIL T T T T) -9 NIL 2556651) (-1071 2544882 2545897 2547033 "SFRGCD" 2550441 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1070 2538010 2539081 2540267 "SFQCMPK" 2543815 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1069 2537632 2537721 2537831 "SFORT" 2537951 NIL SFORT (NIL T T) -8 NIL NIL) (-1068 2536777 2537472 2537593 "SEXOF" 2537598 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1067 2535911 2536658 2536726 "SEX" 2536731 T SEX (NIL) -8 NIL NIL) (-1066 2530687 2531376 2531471 "SEXCAT" 2535242 NIL SEXCAT (NIL T T T T T) -9 NIL 2535861) (-1065 2527867 2530621 2530669 "SET" 2530674 NIL SET (NIL T) -8 NIL NIL) (-1064 2526118 2526580 2526885 "SETMN" 2527608 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1063 2525724 2525850 2525880 "SETCAT" 2525997 T SETCAT (NIL) -9 NIL 2526082) (-1062 2525504 2525556 2525655 "SETCAT-" 2525660 NIL SETCAT- (NIL T) -8 NIL NIL) (-1061 2521891 2523965 2524008 "SETAGG" 2524878 NIL SETAGG (NIL T) -9 NIL 2525218) (-1060 2521349 2521465 2521702 "SETAGG-" 2521707 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1059 2520553 2520846 2520907 "SEGXCAT" 2521193 NIL SEGXCAT (NIL T T) -9 NIL 2521313) (-1058 2519609 2520219 2520401 "SEG" 2520406 NIL SEG (NIL T) -8 NIL NIL) (-1057 2518516 2518729 2518772 "SEGCAT" 2519354 NIL SEGCAT (NIL T) -9 NIL 2519592) (-1056 2517565 2517895 2518095 "SEGBIND" 2518351 NIL SEGBIND (NIL T) -8 NIL NIL) (-1055 2517186 2517245 2517358 "SEGBIND2" 2517500 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1054 2516804 2516987 2517064 "SEGAST" 2517131 T SEGAST (NIL) -8 NIL NIL) (-1053 2516023 2516149 2516353 "SEG2" 2516648 NIL SEG2 (NIL T T) -7 NIL NIL) (-1052 2515460 2515958 2516005 "SDVAR" 2516010 NIL SDVAR (NIL T) -8 NIL NIL) (-1051 2507750 2515230 2515360 "SDPOL" 2515365 NIL SDPOL (NIL T) -8 NIL NIL) (-1050 2506343 2506609 2506928 "SCPKG" 2507465 NIL SCPKG (NIL T) -7 NIL NIL) (-1049 2505479 2505659 2505859 "SCOPE" 2506165 T SCOPE (NIL) -8 NIL NIL) (-1048 2504700 2504833 2505012 "SCACHE" 2505334 NIL SCACHE (NIL T) -7 NIL NIL) (-1047 2504426 2504569 2504599 "SASTCAT" 2504604 T SASTCAT (NIL) -9 NIL 2504617) (-1046 2504215 2504260 2504358 "SASTCAT-" 2504363 NIL SASTCAT- (NIL T) -8 NIL NIL) (-1045 2503654 2503975 2504060 "SAOS" 2504152 T SAOS (NIL) -8 NIL NIL) (-1044 2503219 2503254 2503427 "SAERFFC" 2503613 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1043 2497193 2503116 2503196 "SAE" 2503201 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1042 2496786 2496821 2496980 "SAEFACT" 2497152 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1041 2495107 2495421 2495822 "RURPK" 2496452 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1040 2493743 2494022 2494334 "RULESET" 2494941 NIL RULESET (NIL T T T) -8 NIL NIL) (-1039 2490930 2491433 2491898 "RULE" 2493424 NIL RULE (NIL T T T) -8 NIL NIL) (-1038 2490569 2490724 2490807 "RULECOLD" 2490882 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1037 2485418 2486212 2487132 "RSETGCD" 2489768 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1036 2474675 2479727 2479824 "RSETCAT" 2483943 NIL RSETCAT (NIL T T T T) -9 NIL 2485040) (-1035 2472602 2473141 2473965 "RSETCAT-" 2473970 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1034 2464989 2466364 2467884 "RSDCMPK" 2471201 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1033 2462994 2463435 2463509 "RRCC" 2464595 NIL RRCC (NIL T T) -9 NIL 2464939) (-1032 2462345 2462519 2462798 "RRCC-" 2462803 NIL RRCC- (NIL T T T) -8 NIL NIL) (-1031 2461832 2462041 2462142 "RPTAST" 2462266 T RPTAST (NIL) -8 NIL NIL) (-1030 2436060 2445645 2445712 "RPOLCAT" 2456376 NIL RPOLCAT (NIL T T T) -9 NIL 2459535) (-1029 2427560 2429898 2433020 "RPOLCAT-" 2433025 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-1028 2418607 2425771 2426253 "ROUTINE" 2427100 T ROUTINE (NIL) -8 NIL NIL) (-1027 2415365 2418158 2418307 "ROMAN" 2418480 T ROMAN (NIL) -8 NIL NIL) (-1026 2413640 2414225 2414485 "ROIRC" 2415170 NIL ROIRC (NIL T T) -8 NIL NIL) (-1025 2410091 2412330 2412360 "RNS" 2412664 T RNS (NIL) -9 NIL 2412936) (-1024 2408600 2408983 2409517 "RNS-" 2409592 NIL RNS- (NIL T) -8 NIL NIL) (-1023 2408049 2408431 2408461 "RNG" 2408466 T RNG (NIL) -9 NIL 2408487) (-1022 2407441 2407803 2407846 "RMODULE" 2407908 NIL RMODULE (NIL T) -9 NIL 2407950) (-1021 2406277 2406371 2406707 "RMCAT2" 2407342 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-1020 2402982 2405451 2405776 "RMATRIX" 2406011 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-1019 2395924 2398158 2398273 "RMATCAT" 2401632 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2402614) (-1018 2395299 2395446 2395753 "RMATCAT-" 2395758 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-1017 2394866 2394941 2395069 "RINTERP" 2395218 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-1016 2393954 2394474 2394504 "RING" 2394616 T RING (NIL) -9 NIL 2394711) (-1015 2393746 2393790 2393887 "RING-" 2393892 NIL RING- (NIL T) -8 NIL NIL) (-1014 2392587 2392824 2393082 "RIDIST" 2393510 T RIDIST (NIL) -7 NIL NIL) (-1013 2383903 2392055 2392261 "RGCHAIN" 2392435 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-1012 2380897 2381511 2382181 "RF" 2383267 NIL RF (NIL T) -7 NIL NIL) (-1011 2380543 2380606 2380709 "RFFACTOR" 2380828 NIL RFFACTOR (NIL T) -7 NIL NIL) (-1010 2380268 2380303 2380400 "RFFACT" 2380502 NIL RFFACT (NIL T) -7 NIL NIL) (-1009 2378385 2378749 2379131 "RFDIST" 2379908 T RFDIST (NIL) -7 NIL NIL) (-1008 2377838 2377930 2378093 "RETSOL" 2378287 NIL RETSOL (NIL T T) -7 NIL NIL) (-1007 2377426 2377506 2377549 "RETRACT" 2377742 NIL RETRACT (NIL T) -9 NIL NIL) (-1006 2377275 2377300 2377387 "RETRACT-" 2377392 NIL RETRACT- (NIL T T) -8 NIL NIL) (-1005 2376921 2377097 2377167 "RETAST" 2377227 T RETAST (NIL) -8 NIL NIL) (-1004 2369775 2376574 2376701 "RESULT" 2376816 T RESULT (NIL) -8 NIL NIL) (-1003 2368401 2369044 2369243 "RESRING" 2369678 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-1002 2368037 2368086 2368184 "RESLATC" 2368338 NIL RESLATC (NIL T) -7 NIL NIL) (-1001 2367743 2367777 2367884 "REPSQ" 2367996 NIL REPSQ (NIL T) -7 NIL NIL) (-1000 2365165 2365745 2366347 "REP" 2367163 T REP (NIL) -7 NIL NIL) (-999 2364866 2364900 2365009 "REPDB" 2365124 NIL REPDB (NIL T) -7 NIL NIL) (-998 2358794 2360173 2361394 "REP2" 2363678 NIL REP2 (NIL T) -7 NIL NIL) (-997 2355186 2355867 2356673 "REP1" 2358021 NIL REP1 (NIL T) -7 NIL NIL) (-996 2347924 2353339 2353793 "REGSET" 2354816 NIL REGSET (NIL T T T T) -8 NIL NIL) (-995 2346745 2347080 2347328 "REF" 2347709 NIL REF (NIL T) -8 NIL NIL) (-994 2346126 2346229 2346394 "REDORDER" 2346629 NIL REDORDER (NIL T T) -7 NIL NIL) (-993 2342146 2345354 2345577 "RECLOS" 2345955 NIL RECLOS (NIL T) -8 NIL NIL) (-992 2341203 2341384 2341597 "REALSOLV" 2341953 T REALSOLV (NIL) -7 NIL NIL) (-991 2341051 2341092 2341120 "REAL" 2341125 T REAL (NIL) -9 NIL 2341160) (-990 2337542 2338344 2339226 "REAL0Q" 2340216 NIL REAL0Q (NIL T) -7 NIL NIL) (-989 2333153 2334141 2335200 "REAL0" 2336523 NIL REAL0 (NIL T) -7 NIL NIL) (-988 2332673 2332874 2332966 "RDUCEAST" 2333081 T RDUCEAST (NIL) -8 NIL NIL) (-987 2332081 2332153 2332358 "RDIV" 2332595 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-986 2331154 2331328 2331539 "RDIST" 2331903 NIL RDIST (NIL T) -7 NIL NIL) (-985 2329755 2330042 2330412 "RDETRS" 2330862 NIL RDETRS (NIL T T) -7 NIL NIL) (-984 2327572 2328026 2328562 "RDETR" 2329297 NIL RDETR (NIL T T) -7 NIL NIL) (-983 2326186 2326464 2326866 "RDEEFS" 2327288 NIL RDEEFS (NIL T T) -7 NIL NIL) (-982 2324684 2324990 2325420 "RDEEF" 2325874 NIL RDEEF (NIL T T) -7 NIL NIL) (-981 2319021 2321892 2321920 "RCFIELD" 2323197 T RCFIELD (NIL) -9 NIL 2323927) (-980 2317090 2317594 2318287 "RCFIELD-" 2318360 NIL RCFIELD- (NIL T) -8 NIL NIL) (-979 2313421 2315206 2315247 "RCAGG" 2316318 NIL RCAGG (NIL T) -9 NIL 2316783) (-978 2313052 2313146 2313306 "RCAGG-" 2313311 NIL RCAGG- (NIL T T) -8 NIL NIL) (-977 2312392 2312504 2312667 "RATRET" 2312936 NIL RATRET (NIL T) -7 NIL NIL) (-976 2311949 2312016 2312135 "RATFACT" 2312320 NIL RATFACT (NIL T) -7 NIL NIL) (-975 2311264 2311384 2311534 "RANDSRC" 2311819 T RANDSRC (NIL) -7 NIL NIL) (-974 2311001 2311045 2311116 "RADUTIL" 2311213 T RADUTIL (NIL) -7 NIL NIL) (-973 2304066 2309744 2310061 "RADIX" 2310716 NIL RADIX (NIL NIL) -8 NIL NIL) (-972 2295722 2303910 2304038 "RADFF" 2304043 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-971 2295374 2295449 2295477 "RADCAT" 2295634 T RADCAT (NIL) -9 NIL NIL) (-970 2295159 2295207 2295304 "RADCAT-" 2295309 NIL RADCAT- (NIL T) -8 NIL NIL) (-969 2293310 2294934 2295023 "QUEUE" 2295103 NIL QUEUE (NIL T) -8 NIL NIL) (-968 2289886 2293247 2293292 "QUAT" 2293297 NIL QUAT (NIL T) -8 NIL NIL) (-967 2289524 2289567 2289694 "QUATCT2" 2289837 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-966 2283384 2286685 2286725 "QUATCAT" 2287505 NIL QUATCAT (NIL T) -9 NIL 2288271) (-965 2279528 2280565 2281952 "QUATCAT-" 2282046 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-964 2277048 2278612 2278653 "QUAGG" 2279028 NIL QUAGG (NIL T) -9 NIL 2279203) (-963 2276697 2276873 2276941 "QQUTAST" 2277000 T QQUTAST (NIL) -8 NIL NIL) (-962 2275622 2276095 2276267 "QFORM" 2276569 NIL QFORM (NIL NIL T) -8 NIL NIL) (-961 2266955 2272158 2272198 "QFCAT" 2272856 NIL QFCAT (NIL T) -9 NIL 2273855) (-960 2262527 2263728 2265319 "QFCAT-" 2265413 NIL QFCAT- (NIL T T) -8 NIL NIL) (-959 2262165 2262208 2262335 "QFCAT2" 2262478 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-958 2261625 2261735 2261865 "QEQUAT" 2262055 T QEQUAT (NIL) -8 NIL NIL) (-957 2254773 2255844 2257028 "QCMPACK" 2260558 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-956 2252349 2252770 2253198 "QALGSET" 2254428 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-955 2251594 2251768 2252000 "QALGSET2" 2252169 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-954 2250285 2250508 2250825 "PWFFINTB" 2251367 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-953 2248467 2248635 2248989 "PUSHVAR" 2250099 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-952 2244385 2245439 2245480 "PTRANFN" 2247364 NIL PTRANFN (NIL T) -9 NIL NIL) (-951 2242787 2243078 2243400 "PTPACK" 2244096 NIL PTPACK (NIL T) -7 NIL NIL) (-950 2242419 2242476 2242585 "PTFUNC2" 2242724 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-949 2236885 2241230 2241271 "PTCAT" 2241644 NIL PTCAT (NIL T) -9 NIL 2241806) (-948 2236543 2236578 2236702 "PSQFR" 2236844 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-947 2235138 2235436 2235770 "PSEUDLIN" 2236241 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-946 2221907 2224272 2226596 "PSETPK" 2232898 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-945 2214951 2217665 2217761 "PSETCAT" 2220782 NIL PSETCAT (NIL T T T T) -9 NIL 2221596) (-944 2212787 2213421 2214242 "PSETCAT-" 2214247 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-943 2212136 2212301 2212329 "PSCURVE" 2212597 T PSCURVE (NIL) -9 NIL 2212764) (-942 2208617 2210099 2210164 "PSCAT" 2211008 NIL PSCAT (NIL T T T) -9 NIL 2211248) (-941 2207680 2207896 2208296 "PSCAT-" 2208301 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-940 2206332 2206965 2207179 "PRTITION" 2207486 T PRTITION (NIL) -8 NIL NIL) (-939 2205852 2206053 2206145 "PRTDAST" 2206260 T PRTDAST (NIL) -8 NIL NIL) (-938 2194950 2197156 2199344 "PRS" 2203714 NIL PRS (NIL T T) -7 NIL NIL) (-937 2192808 2194300 2194340 "PRQAGG" 2194523 NIL PRQAGG (NIL T) -9 NIL 2194625) (-936 2192194 2192423 2192451 "PROPLOG" 2192636 T PROPLOG (NIL) -9 NIL 2192758) (-935 2189364 2190008 2190472 "PROPFRML" 2191762 NIL PROPFRML (NIL T) -8 NIL NIL) (-934 2188824 2188934 2189064 "PROPERTY" 2189254 T PROPERTY (NIL) -8 NIL NIL) (-933 2182909 2186990 2187810 "PRODUCT" 2188050 NIL PRODUCT (NIL T T) -8 NIL NIL) (-932 2180222 2182367 2182601 "PR" 2182720 NIL PR (NIL T T) -8 NIL NIL) (-931 2180018 2180050 2180109 "PRINT" 2180183 T PRINT (NIL) -7 NIL NIL) (-930 2179358 2179475 2179627 "PRIMES" 2179898 NIL PRIMES (NIL T) -7 NIL NIL) (-929 2177423 2177824 2178290 "PRIMELT" 2178937 NIL PRIMELT (NIL T) -7 NIL NIL) (-928 2177152 2177201 2177229 "PRIMCAT" 2177353 T PRIMCAT (NIL) -9 NIL NIL) (-927 2173313 2177090 2177135 "PRIMARR" 2177140 NIL PRIMARR (NIL T) -8 NIL NIL) (-926 2172320 2172498 2172726 "PRIMARR2" 2173131 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-925 2171963 2172019 2172130 "PREASSOC" 2172258 NIL PREASSOC (NIL T T) -7 NIL NIL) (-924 2171438 2171571 2171599 "PPCURVE" 2171804 T PPCURVE (NIL) -9 NIL 2171940) (-923 2171060 2171233 2171316 "PORTNUM" 2171375 T PORTNUM (NIL) -8 NIL NIL) (-922 2168419 2168818 2169410 "POLYROOT" 2170641 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-921 2162364 2168023 2168183 "POLY" 2168292 NIL POLY (NIL T) -8 NIL NIL) (-920 2161747 2161805 2162039 "POLYLIFT" 2162300 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-919 2158022 2158471 2159100 "POLYCATQ" 2161292 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-918 2145061 2150417 2150482 "POLYCAT" 2153996 NIL POLYCAT (NIL T T T) -9 NIL 2155924) (-917 2138511 2140372 2142756 "POLYCAT-" 2142761 NIL POLYCAT- (NIL T T T T) 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T) -7 NIL NIL) (-891 2082516 2082563 2082666 "PINTERPA" 2082770 NIL PINTERPA (NIL T T) -7 NIL NIL) (-890 2081801 2082322 2082409 "PI" 2082449 T PI (NIL) -8 NIL NIL) (-889 2080233 2081174 2081202 "PID" 2081384 T PID (NIL) -9 NIL 2081518) (-888 2079958 2079995 2080083 "PICOERCE" 2080190 NIL PICOERCE (NIL T) -7 NIL NIL) (-887 2079278 2079417 2079593 "PGROEB" 2079814 NIL PGROEB (NIL T) -7 NIL NIL) (-886 2074865 2075679 2076584 "PGE" 2078393 T PGE (NIL) -7 NIL NIL) (-885 2072989 2073235 2073601 "PGCD" 2074582 NIL PGCD (NIL T T T T) -7 NIL NIL) (-884 2072327 2072430 2072591 "PFRPAC" 2072873 NIL PFRPAC (NIL T) -7 NIL NIL) (-883 2069007 2070875 2071228 "PFR" 2072006 NIL PFR (NIL T) -8 NIL NIL) (-882 2067396 2067640 2067965 "PFOTOOLS" 2068754 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-881 2065929 2066168 2066519 "PFOQ" 2067153 NIL PFOQ (NIL T T T) -7 NIL NIL) (-880 2064402 2064614 2064977 "PFO" 2065713 NIL PFO (NIL T T T T T) -7 NIL NIL) (-879 2060990 2064291 2064360 "PF" 2064365 NIL PF (NIL NIL) -8 NIL NIL) (-878 2058459 2059696 2059724 "PFECAT" 2060309 T PFECAT (NIL) -9 NIL 2060693) (-877 2057904 2058058 2058272 "PFECAT-" 2058277 NIL PFECAT- (NIL T) -8 NIL NIL) (-876 2056508 2056759 2057060 "PFBRU" 2057653 NIL PFBRU (NIL T T) -7 NIL NIL) (-875 2054375 2054726 2055158 "PFBR" 2056159 NIL PFBR (NIL T T T T) -7 NIL NIL) (-874 2050291 2051751 2052427 "PERM" 2053732 NIL PERM (NIL T) -8 NIL NIL) (-873 2045557 2046498 2047368 "PERMGRP" 2049454 NIL PERMGRP (NIL T) -8 NIL NIL) (-872 2043689 2044620 2044661 "PERMCAT" 2045107 NIL PERMCAT (NIL T) -9 NIL 2045412) (-871 2043342 2043383 2043507 "PERMAN" 2043642 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-870 2040782 2042911 2043042 "PENDTREE" 2043244 NIL PENDTREE (NIL T) -8 NIL NIL) (-869 2038895 2039629 2039670 "PDRING" 2040327 NIL PDRING (NIL T) -9 NIL 2040613) (-868 2037998 2038216 2038578 "PDRING-" 2038583 NIL PDRING- (NIL T T) -8 NIL NIL) (-867 2035139 2035890 2036581 "PDEPROB" 2037327 T PDEPROB (NIL) -8 NIL NIL) (-866 2032686 2033188 2033743 "PDEPACK" 2034604 T PDEPACK (NIL) -7 NIL NIL) (-865 2031598 2031788 2032039 "PDECOMP" 2032485 NIL PDECOMP (NIL T T) -7 NIL NIL) (-864 2029203 2030020 2030048 "PDECAT" 2030835 T PDECAT (NIL) -9 NIL 2031548) (-863 2028954 2028987 2029077 "PCOMP" 2029164 NIL PCOMP (NIL T T) -7 NIL NIL) (-862 2027159 2027755 2028052 "PBWLB" 2028683 NIL PBWLB (NIL T) -8 NIL NIL) (-861 2019663 2021232 2022570 "PATTERN" 2025842 NIL PATTERN (NIL T) -8 NIL NIL) (-860 2019295 2019352 2019461 "PATTERN2" 2019600 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-859 2017052 2017440 2017897 "PATTERN1" 2018884 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-858 2014447 2015001 2015482 "PATRES" 2016617 NIL PATRES (NIL T T) -8 NIL NIL) (-857 2014011 2014078 2014210 "PATRES2" 2014374 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-856 2011894 2012299 2012706 "PATMATCH" 2013678 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-855 2011430 2011613 2011654 "PATMAB" 2011761 NIL PATMAB (NIL T) -9 NIL 2011844) (-854 2009975 2010284 2010542 "PATLRES" 2011235 NIL PATLRES (NIL T T T) -8 NIL NIL) (-853 2009521 2009644 2009685 "PATAB" 2009690 NIL PATAB (NIL T) -9 NIL 2009862) (-852 2007002 2007534 2008107 "PARTPERM" 2008968 T PARTPERM (NIL) -7 NIL NIL) (-851 2006623 2006686 2006788 "PARSURF" 2006933 NIL PARSURF (NIL T) -8 NIL NIL) (-850 2006255 2006312 2006421 "PARSU2" 2006560 NIL PARSU2 (NIL T T) -7 NIL NIL) (-849 2006019 2006059 2006126 "PARSER" 2006208 T PARSER (NIL) -7 NIL NIL) (-848 2005640 2005703 2005805 "PARSCURV" 2005950 NIL PARSCURV (NIL T) -8 NIL NIL) (-847 2005272 2005329 2005438 "PARSC2" 2005577 NIL PARSC2 (NIL T T) -7 NIL NIL) (-846 2004911 2004969 2005066 "PARPCURV" 2005208 NIL PARPCURV (NIL T) -8 NIL NIL) (-845 2004543 2004600 2004709 "PARPC2" 2004848 NIL PARPC2 (NIL T T) -7 NIL NIL) (-844 2004063 2004149 2004268 "PAN2EXPR" 2004444 T PAN2EXPR (NIL) -7 NIL NIL) (-843 2002869 2003184 2003412 "PALETTE" 2003855 T PALETTE (NIL) -8 NIL NIL) (-842 2001337 2001874 2002234 "PAIR" 2002555 NIL PAIR (NIL T T) -8 NIL NIL) (-841 1995245 2000596 2000790 "PADICRC" 2001192 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-840 1988511 1994591 1994775 "PADICRAT" 1995093 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-839 1986861 1988448 1988493 "PADIC" 1988498 NIL PADIC (NIL NIL) -8 NIL NIL) (-838 1984106 1985636 1985676 "PADICCT" 1986257 NIL PADICCT (NIL NIL) -9 NIL 1986539) (-837 1983063 1983263 1983531 "PADEPAC" 1983893 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-836 1982275 1982408 1982614 "PADE" 1982925 NIL PADE (NIL T T T) -7 NIL NIL) (-835 1980325 1981111 1981428 "OWP" 1982042 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-834 1979434 1979930 1980102 "OVAR" 1980193 NIL OVAR (NIL NIL) -8 NIL NIL) (-833 1978698 1978819 1978980 "OUT" 1979293 T OUT (NIL) -7 NIL NIL) (-832 1967752 1969923 1972093 "OUTFORM" 1976548 T OUTFORM (NIL) -8 NIL NIL) (-831 1967389 1967472 1967500 "OUTBCON" 1967651 T OUTBCON (NIL) -9 NIL 1967736) (-830 1967229 1967264 1967340 "OUTBCON-" 1967345 NIL OUTBCON- (NIL T) -8 NIL NIL) (-829 1966637 1966958 1967047 "OSI" 1967160 T OSI (NIL) -8 NIL NIL) (-828 1966193 1966505 1966533 "OSGROUP" 1966538 T OSGROUP (NIL) -9 NIL 1966560) (-827 1964938 1965165 1965450 "ORTHPOL" 1965940 NIL ORTHPOL (NIL T) -7 NIL NIL) (-826 1962348 1964597 1964736 "OREUP" 1964881 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-825 1959786 1962039 1962166 "ORESUP" 1962290 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-824 1957314 1957814 1958375 "OREPCTO" 1959275 NIL OREPCTO (NIL T T) -7 NIL NIL) (-823 1951225 1953392 1953433 "OREPCAT" 1955781 NIL OREPCAT (NIL T) -9 NIL 1956885) (-822 1948372 1949154 1950212 "OREPCAT-" 1950217 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-821 1947549 1947821 1947849 "ORDSET" 1948158 T ORDSET (NIL) -9 NIL 1948322) (-820 1947068 1947190 1947383 "ORDSET-" 1947388 NIL ORDSET- (NIL T) -8 NIL NIL) (-819 1945722 1946479 1946507 "ORDRING" 1946709 T ORDRING (NIL) -9 NIL 1946834) (-818 1945367 1945461 1945605 "ORDRING-" 1945610 NIL ORDRING- (NIL T) -8 NIL NIL) (-817 1944773 1945210 1945238 "ORDMON" 1945243 T ORDMON (NIL) -9 NIL 1945264) (-816 1943935 1944082 1944277 "ORDFUNS" 1944622 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-815 1943446 1943805 1943833 "ORDFIN" 1943838 T ORDFIN (NIL) -9 NIL 1943859) (-814 1940038 1942032 1942441 "ORDCOMP" 1943070 NIL ORDCOMP (NIL T) -8 NIL NIL) (-813 1939304 1939431 1939617 "ORDCOMP2" 1939898 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-812 1935811 1936694 1937531 "OPTPROB" 1938487 T OPTPROB (NIL) -8 NIL NIL) (-811 1932613 1933252 1933956 "OPTPACK" 1935127 T OPTPACK (NIL) -7 NIL NIL) (-810 1930326 1931066 1931094 "OPTCAT" 1931913 T OPTCAT (NIL) -9 NIL 1932563) (-809 1930094 1930133 1930199 "OPQUERY" 1930280 T OPQUERY (NIL) -7 NIL NIL) (-808 1927260 1928405 1928909 "OP" 1929623 NIL OP (NIL T) -8 NIL NIL) (-807 1924105 1926057 1926426 "ONECOMP" 1926924 NIL ONECOMP (NIL T) -8 NIL NIL) (-806 1923410 1923525 1923699 "ONECOMP2" 1923977 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-805 1922829 1922935 1923065 "OMSERVER" 1923300 T OMSERVER (NIL) -7 NIL NIL) (-804 1919717 1922269 1922309 "OMSAGG" 1922370 NIL OMSAGG (NIL T) -9 NIL 1922434) (-803 1918340 1918603 1918885 "OMPKG" 1919455 T OMPKG (NIL) -7 NIL NIL) (-802 1917770 1917873 1917901 "OM" 1918200 T OM (NIL) -9 NIL NIL) (-801 1916352 1917319 1917488 "OMLO" 1917651 NIL OMLO (NIL T T) -8 NIL NIL) (-800 1915277 1915424 1915651 "OMEXPR" 1916178 NIL OMEXPR (NIL T) -7 NIL NIL) (-799 1914595 1914823 1914959 "OMERR" 1915161 T OMERR (NIL) -8 NIL NIL) (-798 1913773 1914016 1914176 "OMERRK" 1914455 T OMERRK (NIL) -8 NIL NIL) (-797 1913251 1913450 1913558 "OMENC" 1913685 T OMENC (NIL) -8 NIL NIL) (-796 1907146 1908331 1909502 "OMDEV" 1912100 T OMDEV (NIL) -8 NIL NIL) (-795 1906215 1906386 1906580 "OMCONN" 1906972 T OMCONN (NIL) -8 NIL NIL) (-794 1904871 1905813 1905841 "OINTDOM" 1905846 T OINTDOM (NIL) -9 NIL 1905867) (-793 1900677 1901861 1902577 "OFMONOID" 1904187 NIL OFMONOID (NIL T) -8 NIL NIL) (-792 1900115 1900614 1900659 "ODVAR" 1900664 NIL ODVAR (NIL T) -8 NIL NIL) (-791 1897325 1899612 1899797 "ODR" 1899990 NIL ODR (NIL T T NIL) -8 NIL NIL) (-790 1889669 1897101 1897227 "ODPOL" 1897232 NIL ODPOL (NIL T) -8 NIL NIL) (-789 1883545 1889541 1889646 "ODP" 1889651 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-788 1882311 1882526 1882801 "ODETOOLS" 1883319 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-787 1879280 1879936 1880652 "ODESYS" 1881644 NIL ODESYS (NIL T T) -7 NIL NIL) (-786 1874162 1875070 1876095 "ODERTRIC" 1878355 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-785 1873588 1873670 1873864 "ODERED" 1874074 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-784 1870476 1871024 1871701 "ODERAT" 1873011 NIL ODERAT (NIL T T) -7 NIL NIL) (-783 1867436 1867900 1868497 "ODEPRRIC" 1870005 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-782 1865305 1865874 1866383 "ODEPROB" 1866947 T ODEPROB (NIL) -8 NIL NIL) (-781 1861827 1862310 1862957 "ODEPRIM" 1864784 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-780 1861076 1861178 1861438 "ODEPAL" 1861719 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-779 1857238 1858029 1858893 "ODEPACK" 1860232 T ODEPACK (NIL) -7 NIL NIL) (-778 1856271 1856378 1856607 "ODEINT" 1857127 NIL ODEINT (NIL T T) -7 NIL NIL) (-777 1850372 1851797 1853244 "ODEIFTBL" 1854844 T ODEIFTBL (NIL) -8 NIL NIL) (-776 1845707 1846493 1847452 "ODEEF" 1849531 NIL ODEEF (NIL T T) -7 NIL NIL) (-775 1845042 1845131 1845361 "ODECONST" 1845612 NIL ODECONST (NIL T T T) -7 NIL NIL) (-774 1843193 1843828 1843856 "ODECAT" 1844461 T ODECAT (NIL) -9 NIL 1844992) (-773 1840100 1842905 1843024 "OCT" 1843106 NIL OCT (NIL T) -8 NIL NIL) (-772 1839738 1839781 1839908 "OCTCT2" 1840051 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-771 1834599 1836999 1837039 "OC" 1838136 NIL OC (NIL T) -9 NIL 1838994) (-770 1831826 1832574 1833564 "OC-" 1833658 NIL OC- (NIL T T) -8 NIL NIL) (-769 1831204 1831646 1831674 "OCAMON" 1831679 T OCAMON (NIL) -9 NIL 1831700) (-768 1830761 1831076 1831104 "OASGP" 1831109 T OASGP (NIL) -9 NIL 1831129) (-767 1830048 1830511 1830539 "OAMONS" 1830579 T OAMONS (NIL) -9 NIL 1830622) (-766 1829488 1829895 1829923 "OAMON" 1829928 T OAMON (NIL) -9 NIL 1829948) (-765 1828792 1829284 1829312 "OAGROUP" 1829317 T OAGROUP (NIL) -9 NIL 1829337) (-764 1828482 1828532 1828620 "NUMTUBE" 1828736 NIL NUMTUBE (NIL T) -7 NIL NIL) (-763 1822055 1823573 1825109 "NUMQUAD" 1826966 T NUMQUAD (NIL) -7 NIL NIL) (-762 1817811 1818799 1819824 "NUMODE" 1821050 T NUMODE (NIL) -7 NIL NIL) (-761 1815192 1816046 1816074 "NUMINT" 1816997 T NUMINT (NIL) -9 NIL 1817761) (-760 1814140 1814337 1814555 "NUMFMT" 1814994 T NUMFMT (NIL) -7 NIL NIL) (-759 1800499 1803444 1805976 "NUMERIC" 1811647 NIL NUMERIC (NIL T) -7 NIL NIL) (-758 1794896 1799948 1800043 "NTSCAT" 1800048 NIL NTSCAT (NIL T T T T) -9 NIL 1800087) (-757 1794090 1794255 1794448 "NTPOLFN" 1794735 NIL NTPOLFN (NIL T) -7 NIL NIL) (-756 1781930 1790915 1791727 "NSUP" 1793311 NIL NSUP (NIL T) -8 NIL NIL) (-755 1781562 1781619 1781728 "NSUP2" 1781867 NIL NSUP2 (NIL T T) -7 NIL NIL) (-754 1771559 1781336 1781469 "NSMP" 1781474 NIL NSMP (NIL T T) -8 NIL NIL) (-753 1769991 1770292 1770649 "NREP" 1771247 NIL NREP (NIL T) -7 NIL NIL) (-752 1768582 1768834 1769192 "NPCOEF" 1769734 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-751 1767648 1767763 1767979 "NORMRETR" 1768463 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-750 1765689 1765979 1766388 "NORMPK" 1767356 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-749 1765374 1765402 1765526 "NORMMA" 1765655 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-748 1765201 1765331 1765360 "NONE" 1765365 T NONE (NIL) -8 NIL NIL) (-747 1764990 1765019 1765088 "NONE1" 1765165 NIL NONE1 (NIL T) -7 NIL NIL) (-746 1764473 1764535 1764721 "NODE1" 1764922 NIL NODE1 (NIL T T) -7 NIL NIL) (-745 1762813 1763636 1763891 "NNI" 1764238 T NNI (NIL) -8 NIL NIL) (-744 1761233 1761546 1761910 "NLINSOL" 1762481 NIL NLINSOL (NIL T) -7 NIL NIL) (-743 1757400 1758368 1759290 "NIPROB" 1760331 T NIPROB (NIL) -8 NIL NIL) (-742 1756157 1756391 1756693 "NFINTBAS" 1757162 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-741 1754865 1755096 1755377 "NCODIV" 1755925 NIL NCODIV (NIL T T) -7 NIL NIL) (-740 1754627 1754664 1754739 "NCNTFRAC" 1754822 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-739 1752807 1753171 1753591 "NCEP" 1754252 NIL NCEP (NIL T) -7 NIL NIL) (-738 1751718 1752457 1752485 "NASRING" 1752595 T NASRING (NIL) -9 NIL 1752669) (-737 1751513 1751557 1751651 "NASRING-" 1751656 NIL NASRING- (NIL T) -8 NIL NIL) (-736 1750666 1751165 1751193 "NARNG" 1751310 T NARNG (NIL) -9 NIL 1751401) (-735 1750358 1750425 1750559 "NARNG-" 1750564 NIL NARNG- (NIL T) -8 NIL NIL) (-734 1749237 1749444 1749679 "NAGSP" 1750143 T NAGSP (NIL) -7 NIL NIL) (-733 1740509 1742193 1743866 "NAGS" 1747584 T NAGS (NIL) -7 NIL NIL) (-732 1739057 1739365 1739696 "NAGF07" 1740198 T NAGF07 (NIL) -7 NIL NIL) (-731 1733595 1734886 1736193 "NAGF04" 1737770 T NAGF04 (NIL) -7 NIL NIL) (-730 1726563 1728177 1729810 "NAGF02" 1731982 T NAGF02 (NIL) -7 NIL NIL) (-729 1721787 1722887 1724004 "NAGF01" 1725466 T NAGF01 (NIL) -7 NIL NIL) (-728 1715415 1716981 1718566 "NAGE04" 1720222 T NAGE04 (NIL) -7 NIL NIL) (-727 1706584 1708705 1710835 "NAGE02" 1713305 T NAGE02 (NIL) -7 NIL NIL) (-726 1702537 1703484 1704448 "NAGE01" 1705640 T NAGE01 (NIL) -7 NIL NIL) (-725 1700332 1700866 1701424 "NAGD03" 1701999 T NAGD03 (NIL) -7 NIL NIL) (-724 1692082 1694010 1695964 "NAGD02" 1698398 T NAGD02 (NIL) -7 NIL NIL) (-723 1685893 1687318 1688758 "NAGD01" 1690662 T NAGD01 (NIL) -7 NIL NIL) (-722 1682102 1682924 1683761 "NAGC06" 1685076 T NAGC06 (NIL) -7 NIL NIL) (-721 1680567 1680899 1681255 "NAGC05" 1681766 T NAGC05 (NIL) -7 NIL NIL) (-720 1679943 1680062 1680206 "NAGC02" 1680443 T NAGC02 (NIL) -7 NIL NIL) (-719 1679003 1679560 1679600 "NAALG" 1679679 NIL NAALG (NIL T) -9 NIL 1679740) (-718 1678838 1678867 1678957 "NAALG-" 1678962 NIL NAALG- (NIL T T) -8 NIL NIL) (-717 1672788 1673896 1675083 "MULTSQFR" 1677734 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-716 1672107 1672182 1672366 "MULTFACT" 1672700 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-715 1665330 1669195 1669248 "MTSCAT" 1670318 NIL MTSCAT (NIL T T) -9 NIL 1670832) (-714 1665042 1665096 1665188 "MTHING" 1665270 NIL MTHING (NIL T) -7 NIL NIL) (-713 1664834 1664867 1664927 "MSYSCMD" 1665002 T MSYSCMD (NIL) -7 NIL NIL) (-712 1660946 1663589 1663909 "MSET" 1664547 NIL MSET (NIL T) -8 NIL NIL) (-711 1658041 1660507 1660548 "MSETAGG" 1660553 NIL MSETAGG (NIL T) -9 NIL 1660587) (-710 1653924 1655420 1656165 "MRING" 1657341 NIL MRING (NIL T T) -8 NIL NIL) (-709 1653490 1653557 1653688 "MRF2" 1653851 NIL MRF2 (NIL T T T) -7 NIL NIL) (-708 1653108 1653143 1653287 "MRATFAC" 1653449 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-707 1650720 1651015 1651446 "MPRFF" 1652813 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-706 1644780 1650574 1650671 "MPOLY" 1650676 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-705 1644270 1644305 1644513 "MPCPF" 1644739 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-704 1643784 1643827 1644011 "MPC3" 1644221 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-703 1642979 1643060 1643281 "MPC2" 1643699 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-702 1641280 1641617 1642007 "MONOTOOL" 1642639 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-701 1640531 1640822 1640850 "MONOID" 1641069 T MONOID (NIL) -9 NIL 1641216) (-700 1640077 1640196 1640377 "MONOID-" 1640382 NIL MONOID- (NIL T) -8 NIL NIL) (-699 1631127 1637033 1637092 "MONOGEN" 1637766 NIL MONOGEN (NIL T T) -9 NIL 1638222) (-698 1628345 1629080 1630080 "MONOGEN-" 1630199 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-697 1627204 1627624 1627652 "MONADWU" 1628044 T MONADWU (NIL) -9 NIL 1628282) (-696 1626576 1626735 1626983 "MONADWU-" 1626988 NIL MONADWU- (NIL T) -8 NIL NIL) (-695 1625961 1626179 1626207 "MONAD" 1626414 T MONAD (NIL) -9 NIL 1626526) (-694 1625646 1625724 1625856 "MONAD-" 1625861 NIL MONAD- (NIL T) -8 NIL NIL) (-693 1623962 1624559 1624838 "MOEBIUS" 1625399 NIL MOEBIUS (NIL T) -8 NIL NIL) (-692 1623354 1623732 1623772 "MODULE" 1623777 NIL MODULE (NIL T) -9 NIL 1623803) (-691 1622922 1623018 1623208 "MODULE-" 1623213 NIL MODULE- (NIL T T) -8 NIL NIL) (-690 1620637 1621286 1621613 "MODRING" 1622746 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-689 1617623 1618742 1619263 "MODOP" 1620166 NIL MODOP (NIL T T) -8 NIL NIL) (-688 1615810 1616262 1616603 "MODMONOM" 1617422 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-687 1605518 1614002 1614425 "MODMON" 1615438 NIL MODMON (NIL T T) -8 NIL NIL) (-686 1602709 1604362 1604638 "MODFIELD" 1605393 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-685 1601713 1601990 1602180 "MMLFORM" 1602539 T MMLFORM (NIL) -8 NIL NIL) (-684 1601239 1601282 1601461 "MMAP" 1601664 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-683 1599508 1600241 1600282 "MLO" 1600705 NIL MLO (NIL T) -9 NIL 1600947) (-682 1596875 1597390 1597992 "MLIFT" 1598989 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-681 1596266 1596350 1596504 "MKUCFUNC" 1596786 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-680 1595865 1595935 1596058 "MKRECORD" 1596189 NIL MKRECORD (NIL T T) -7 NIL NIL) (-679 1594913 1595074 1595302 "MKFUNC" 1595676 NIL MKFUNC (NIL T) -7 NIL NIL) (-678 1594301 1594405 1594561 "MKFLCFN" 1594796 NIL MKFLCFN (NIL T) -7 NIL NIL) (-677 1593727 1594094 1594183 "MKCHSET" 1594245 NIL MKCHSET (NIL T) -8 NIL NIL) (-676 1593004 1593106 1593291 "MKBCFUNC" 1593620 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-675 1589746 1592558 1592694 "MINT" 1592888 T MINT (NIL) -8 NIL NIL) (-674 1588558 1588801 1589078 "MHROWRED" 1589501 NIL MHROWRED (NIL T) -7 NIL NIL) (-673 1583890 1586999 1587425 "MFLOAT" 1588152 T MFLOAT (NIL) -8 NIL NIL) (-672 1583247 1583323 1583494 "MFINFACT" 1583802 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-671 1579562 1580410 1581294 "MESH" 1582383 T MESH (NIL) -7 NIL NIL) (-670 1577952 1578264 1578617 "MDDFACT" 1579249 NIL MDDFACT (NIL T) -7 NIL NIL) (-669 1574794 1577111 1577152 "MDAGG" 1577407 NIL MDAGG (NIL T) -9 NIL 1577550) (-668 1564574 1574087 1574294 "MCMPLX" 1574607 T MCMPLX (NIL) -8 NIL NIL) (-667 1563715 1563861 1564061 "MCDEN" 1564423 NIL MCDEN (NIL T T) -7 NIL NIL) (-666 1561605 1561875 1562255 "MCALCFN" 1563445 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-665 1560516 1560689 1560930 "MAYBE" 1561403 NIL MAYBE (NIL T) -8 NIL NIL) (-664 1558128 1558651 1559213 "MATSTOR" 1559987 NIL MATSTOR (NIL T) -7 NIL NIL) (-663 1554134 1557500 1557748 "MATRIX" 1557913 NIL MATRIX (NIL T) -8 NIL NIL) (-662 1549903 1550607 1551343 "MATLIN" 1553491 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-661 1540057 1543195 1543272 "MATCAT" 1548152 NIL MATCAT (NIL T T T) -9 NIL 1549569) (-660 1536421 1537434 1538790 "MATCAT-" 1538795 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-659 1535015 1535168 1535501 "MATCAT2" 1536256 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-658 1533127 1533451 1533835 "MAPPKG3" 1534690 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-657 1532108 1532281 1532503 "MAPPKG2" 1532951 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-656 1530607 1530891 1531218 "MAPPKG1" 1531814 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-655 1529730 1530013 1530190 "MAPPAST" 1530450 T MAPPAST (NIL) -8 NIL NIL) (-654 1529341 1529399 1529522 "MAPHACK3" 1529666 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-653 1528933 1528994 1529108 "MAPHACK2" 1529273 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-652 1528371 1528474 1528616 "MAPHACK1" 1528824 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-651 1526477 1527071 1527375 "MAGMA" 1528099 NIL MAGMA (NIL T) -8 NIL NIL) (-650 1525972 1526180 1526278 "MACROAST" 1526399 T MACROAST (NIL) -8 NIL NIL) (-649 1522439 1524211 1524672 "M3D" 1525544 NIL M3D (NIL T) -8 NIL NIL) (-648 1516594 1520809 1520850 "LZSTAGG" 1521632 NIL LZSTAGG (NIL T) -9 NIL 1521927) (-647 1512567 1513725 1515182 "LZSTAGG-" 1515187 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-646 1509681 1510458 1510945 "LWORD" 1512112 NIL LWORD (NIL T) -8 NIL NIL) (-645 1509301 1509485 1509560 "LSTAST" 1509626 T LSTAST (NIL) -8 NIL NIL) (-644 1502502 1509072 1509206 "LSQM" 1509211 NIL LSQM (NIL NIL T) -8 NIL NIL) (-643 1501726 1501865 1502093 "LSPP" 1502357 NIL LSPP (NIL T T T T) -7 NIL NIL) (-642 1499538 1499839 1500295 "LSMP" 1501415 NIL LSMP (NIL T T T T) -7 NIL NIL) (-641 1496317 1496991 1497721 "LSMP1" 1498840 NIL LSMP1 (NIL T) -7 NIL NIL) (-640 1490243 1495485 1495526 "LSAGG" 1495588 NIL LSAGG (NIL T) -9 NIL 1495666) (-639 1486938 1487862 1489075 "LSAGG-" 1489080 NIL LSAGG- (NIL T T) -8 NIL NIL) (-638 1484564 1486082 1486331 "LPOLY" 1486733 NIL LPOLY (NIL T T) -8 NIL NIL) (-637 1484146 1484231 1484354 "LPEFRAC" 1484473 NIL LPEFRAC (NIL T) -7 NIL NIL) (-636 1482493 1483240 1483493 "LO" 1483978 NIL LO (NIL T T T) -8 NIL NIL) (-635 1482145 1482257 1482285 "LOGIC" 1482396 T LOGIC (NIL) -9 NIL 1482477) (-634 1482007 1482030 1482101 "LOGIC-" 1482106 NIL LOGIC- (NIL T) -8 NIL NIL) (-633 1481200 1481340 1481533 "LODOOPS" 1481863 NIL LODOOPS (NIL T T) -7 NIL NIL) (-632 1478658 1481116 1481182 "LODO" 1481187 NIL LODO (NIL T NIL) -8 NIL NIL) (-631 1477196 1477431 1477784 "LODOF" 1478405 NIL LODOF (NIL T T) -7 NIL NIL) (-630 1473639 1476036 1476077 "LODOCAT" 1476515 NIL LODOCAT (NIL T) -9 NIL 1476726) (-629 1473372 1473430 1473557 "LODOCAT-" 1473562 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-628 1470727 1473213 1473331 "LODO2" 1473336 NIL LODO2 (NIL T T) -8 NIL NIL) (-627 1468197 1470664 1470709 "LODO1" 1470714 NIL LODO1 (NIL T) -8 NIL NIL) (-626 1467057 1467222 1467534 "LODEEF" 1468020 NIL LODEEF (NIL T T T) -7 NIL NIL) (-625 1462343 1465187 1465228 "LNAGG" 1466175 NIL LNAGG (NIL T) -9 NIL 1466619) (-624 1461490 1461704 1462046 "LNAGG-" 1462051 NIL LNAGG- (NIL T T) -8 NIL NIL) (-623 1457653 1458415 1459054 "LMOPS" 1460905 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-622 1457048 1457410 1457451 "LMODULE" 1457512 NIL LMODULE (NIL T) -9 NIL 1457554) (-621 1454294 1456693 1456816 "LMDICT" 1456958 NIL LMDICT (NIL T) -8 NIL NIL) (-620 1454038 1454202 1454262 "LITERAL" 1454267 NIL LITERAL (NIL T) -8 NIL NIL) (-619 1447265 1452984 1453282 "LIST" 1453773 NIL LIST (NIL T) -8 NIL NIL) (-618 1446790 1446864 1447003 "LIST3" 1447185 NIL LIST3 (NIL T T T) -7 NIL NIL) (-617 1445797 1445975 1446203 "LIST2" 1446608 NIL LIST2 (NIL T T) -7 NIL NIL) (-616 1443931 1444243 1444642 "LIST2MAP" 1445444 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-615 1442681 1443317 1443358 "LINEXP" 1443613 NIL LINEXP (NIL T) -9 NIL 1443762) (-614 1441328 1441588 1441885 "LINDEP" 1442433 NIL LINDEP (NIL T T) -7 NIL NIL) (-613 1438095 1438814 1439591 "LIMITRF" 1440583 NIL LIMITRF (NIL T) -7 NIL NIL) (-612 1436371 1436666 1437082 "LIMITPS" 1437790 NIL LIMITPS (NIL T T) -7 NIL NIL) (-611 1430826 1435882 1436110 "LIE" 1436192 NIL LIE (NIL T T) -8 NIL NIL) (-610 1429875 1430318 1430358 "LIECAT" 1430498 NIL LIECAT (NIL T) -9 NIL 1430649) (-609 1429716 1429743 1429831 "LIECAT-" 1429836 NIL LIECAT- (NIL T T) -8 NIL NIL) (-608 1422328 1429165 1429330 "LIB" 1429571 T LIB (NIL) -8 NIL NIL) (-607 1417965 1418846 1419781 "LGROBP" 1421445 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-606 1415831 1416105 1416467 "LF" 1417686 NIL LF (NIL T T) -7 NIL NIL) (-605 1414671 1415363 1415391 "LFCAT" 1415598 T LFCAT (NIL) -9 NIL 1415737) (-604 1411575 1412203 1412891 "LEXTRIPK" 1414035 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-603 1408346 1409145 1409648 "LEXP" 1411155 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-602 1407866 1408067 1408159 "LETAST" 1408274 T LETAST (NIL) -8 NIL NIL) (-601 1406264 1406577 1406978 "LEADCDET" 1407548 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-600 1405454 1405528 1405757 "LAZM3PK" 1406185 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-599 1400410 1403531 1404069 "LAUPOL" 1404966 NIL LAUPOL (NIL T T) -8 NIL NIL) (-598 1399975 1400019 1400187 "LAPLACE" 1400360 NIL LAPLACE (NIL T T) -7 NIL NIL) (-597 1397949 1399076 1399327 "LA" 1399808 NIL LA (NIL T T T) -8 NIL NIL) (-596 1397050 1397600 1397641 "LALG" 1397703 NIL LALG (NIL T) -9 NIL 1397762) (-595 1396764 1396823 1396959 "LALG-" 1396964 NIL LALG- (NIL T T) -8 NIL NIL) (-594 1395564 1395981 1396210 "KTVLOGIC" 1396555 T KTVLOGIC (NIL) -8 NIL NIL) (-593 1394468 1394655 1394954 "KOVACIC" 1395364 NIL KOVACIC (NIL T T) -7 NIL NIL) (-592 1394303 1394327 1394368 "KONVERT" 1394430 NIL KONVERT (NIL T) -9 NIL NIL) (-591 1394138 1394162 1394203 "KOERCE" 1394265 NIL KOERCE (NIL T) -9 NIL NIL) (-590 1391872 1392632 1393025 "KERNEL" 1393777 NIL KERNEL (NIL T) -8 NIL NIL) (-589 1391374 1391455 1391585 "KERNEL2" 1391786 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-588 1385225 1389913 1389967 "KDAGG" 1390344 NIL KDAGG (NIL T T) -9 NIL 1390550) (-587 1384754 1384878 1385083 "KDAGG-" 1385088 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-586 1377929 1384415 1384570 "KAFILE" 1384632 NIL KAFILE (NIL T) -8 NIL NIL) (-585 1372384 1377440 1377668 "JORDAN" 1377750 NIL JORDAN (NIL T T) -8 NIL NIL) (-584 1371808 1372033 1372154 "JOINAST" 1372283 T JOINAST (NIL) -8 NIL NIL) (-583 1371537 1371596 1371683 "JAVACODE" 1371741 T JAVACODE (NIL) -8 NIL NIL) (-582 1367836 1369742 1369796 "IXAGG" 1370725 NIL IXAGG (NIL T T) -9 NIL 1371184) (-581 1366755 1367061 1367480 "IXAGG-" 1367485 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-580 1362335 1366677 1366736 "IVECTOR" 1366741 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-579 1361101 1361338 1361604 "ITUPLE" 1362102 NIL ITUPLE (NIL T) -8 NIL NIL) (-578 1359537 1359714 1360020 "ITRIGMNP" 1360923 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-577 1358282 1358486 1358769 "ITFUN3" 1359313 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-576 1357914 1357971 1358080 "ITFUN2" 1358219 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-575 1355751 1356776 1357075 "ITAYLOR" 1357648 NIL ITAYLOR (NIL T) -8 NIL NIL) (-574 1344745 1349897 1351057 "ISUPS" 1354624 NIL ISUPS (NIL T) -8 NIL NIL) (-573 1343849 1343989 1344225 "ISUMP" 1344592 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-572 1339113 1343650 1343729 "ISTRING" 1343802 NIL ISTRING (NIL NIL) -8 NIL NIL) (-571 1338633 1338834 1338926 "ISAST" 1339041 T ISAST (NIL) -8 NIL NIL) (-570 1337843 1337924 1338140 "IRURPK" 1338547 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-569 1336779 1336980 1337220 "IRSN" 1337623 T IRSN (NIL) -7 NIL NIL) (-568 1334808 1335163 1335599 "IRRF2F" 1336417 NIL IRRF2F (NIL T) -7 NIL NIL) (-567 1334555 1334593 1334669 "IRREDFFX" 1334764 NIL IRREDFFX (NIL T) -7 NIL NIL) (-566 1333170 1333429 1333728 "IROOT" 1334288 NIL IROOT (NIL T) -7 NIL NIL) (-565 1329802 1330854 1331546 "IR" 1332510 NIL IR (NIL T) -8 NIL NIL) (-564 1327415 1327910 1328476 "IR2" 1329280 NIL IR2 (NIL T T) -7 NIL NIL) (-563 1326487 1326600 1326821 "IR2F" 1327298 NIL IR2F (NIL T T) -7 NIL NIL) (-562 1326278 1326312 1326372 "IPRNTPK" 1326447 T IPRNTPK (NIL) -7 NIL NIL) (-561 1322897 1326167 1326236 "IPF" 1326241 NIL IPF (NIL NIL) -8 NIL NIL) (-560 1321260 1322822 1322879 "IPADIC" 1322884 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-559 1321024 1321164 1321192 "IOBCON" 1321197 T IOBCON (NIL) -9 NIL 1321218) (-558 1320521 1320579 1320769 "INVLAPLA" 1320960 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-557 1310170 1312523 1314909 "INTTR" 1318185 NIL INTTR (NIL T T) -7 NIL NIL) (-556 1306514 1307256 1308120 "INTTOOLS" 1309355 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-555 1306100 1306191 1306308 "INTSLPE" 1306417 T INTSLPE (NIL) -7 NIL NIL) (-554 1304095 1306023 1306082 "INTRVL" 1306087 NIL INTRVL (NIL T) -8 NIL NIL) (-553 1301697 1302209 1302784 "INTRF" 1303580 NIL INTRF (NIL T) -7 NIL NIL) (-552 1301108 1301205 1301347 "INTRET" 1301595 NIL INTRET (NIL T) -7 NIL NIL) (-551 1299105 1299494 1299964 "INTRAT" 1300716 NIL INTRAT (NIL T T) -7 NIL NIL) (-550 1296333 1296916 1297542 "INTPM" 1298590 NIL INTPM (NIL T T) -7 NIL NIL) (-549 1293036 1293635 1294380 "INTPAF" 1295719 NIL INTPAF (NIL T T T) -7 NIL NIL) (-548 1288215 1289177 1290228 "INTPACK" 1292005 T INTPACK (NIL) -7 NIL NIL) (-547 1285127 1287944 1288071 "INT" 1288108 T INT (NIL) -8 NIL NIL) (-546 1284379 1284531 1284739 "INTHERTR" 1284969 NIL INTHERTR (NIL T T) -7 NIL NIL) (-545 1283818 1283898 1284086 "INTHERAL" 1284293 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-544 1281664 1282107 1282564 "INTHEORY" 1283381 T INTHEORY (NIL) -7 NIL NIL) (-543 1272972 1274593 1276372 "INTG0" 1280016 NIL INTG0 (NIL T T T) -7 NIL NIL) (-542 1253545 1258335 1263145 "INTFTBL" 1268182 T INTFTBL (NIL) -8 NIL NIL) (-541 1252794 1252932 1253105 "INTFACT" 1253404 NIL INTFACT (NIL T) -7 NIL NIL) (-540 1250179 1250625 1251189 "INTEF" 1252348 NIL INTEF (NIL T T) -7 NIL NIL) (-539 1248681 1249386 1249414 "INTDOM" 1249715 T INTDOM (NIL) -9 NIL 1249922) (-538 1248050 1248224 1248466 "INTDOM-" 1248471 NIL INTDOM- (NIL T) -8 NIL NIL) (-537 1244583 1246469 1246523 "INTCAT" 1247322 NIL INTCAT (NIL T) -9 NIL 1247642) (-536 1244056 1244158 1244286 "INTBIT" 1244475 T INTBIT (NIL) -7 NIL NIL) (-535 1242727 1242881 1243195 "INTALG" 1243901 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-534 1242184 1242274 1242444 "INTAF" 1242631 NIL INTAF (NIL T T) -7 NIL NIL) (-533 1235638 1241994 1242134 "INTABL" 1242139 NIL INTABL (NIL T T T) -8 NIL NIL) (-532 1230693 1233364 1233392 "INS" 1234326 T INS (NIL) -9 NIL 1234990) (-531 1227933 1228704 1229678 "INS-" 1229751 NIL INS- (NIL T) -8 NIL NIL) (-530 1226708 1226935 1227233 "INPSIGN" 1227686 NIL INPSIGN (NIL T T) -7 NIL NIL) (-529 1225826 1225943 1226140 "INPRODPF" 1226588 NIL INPRODPF (NIL T T) -7 NIL NIL) (-528 1224720 1224837 1225074 "INPRODFF" 1225706 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-527 1223720 1223872 1224132 "INNMFACT" 1224556 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-526 1222917 1223014 1223202 "INMODGCD" 1223619 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-525 1221426 1221670 1221994 "INFSP" 1222662 NIL INFSP (NIL T T T) -7 NIL NIL) (-524 1220610 1220727 1220910 "INFPROD0" 1221306 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-523 1217492 1218675 1219190 "INFORM" 1220103 T INFORM (NIL) -8 NIL NIL) (-522 1217102 1217162 1217260 "INFORM1" 1217427 NIL INFORM1 (NIL T) -7 NIL NIL) (-521 1216625 1216714 1216828 "INFINITY" 1217008 T INFINITY (NIL) -7 NIL NIL) (-520 1215242 1215491 1215812 "INEP" 1216373 NIL INEP (NIL T T T) -7 NIL NIL) (-519 1214518 1215139 1215204 "INDE" 1215209 NIL INDE (NIL T) -8 NIL NIL) (-518 1214082 1214150 1214267 "INCRMAPS" 1214445 NIL INCRMAPS (NIL T) -7 NIL NIL) (-517 1209393 1210318 1211262 "INBFF" 1213170 NIL INBFF (NIL T) -7 NIL NIL) (-516 1209062 1209138 1209166 "INBCON" 1209299 T INBCON (NIL) -9 NIL 1209377) (-515 1208902 1208937 1209013 "INBCON-" 1209018 NIL INBCON- (NIL T) -8 NIL NIL) (-514 1208421 1208623 1208715 "INAST" 1208830 T INAST (NIL) -8 NIL NIL) (-513 1207892 1208100 1208206 "IMPTAST" 1208335 T IMPTAST (NIL) -8 NIL NIL) (-512 1204386 1207736 1207840 "IMATRIX" 1207845 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-511 1203098 1203221 1203536 "IMATQF" 1204242 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-510 1201318 1201545 1201882 "IMATLIN" 1202854 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-509 1195944 1201242 1201300 "ILIST" 1201305 NIL ILIST (NIL T NIL) -8 NIL NIL) (-508 1193897 1195804 1195917 "IIARRAY2" 1195922 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-507 1189330 1193808 1193872 "IFF" 1193877 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-506 1188721 1188947 1189063 "IFAST" 1189234 T IFAST (NIL) -8 NIL NIL) (-505 1183764 1188013 1188201 "IFARRAY" 1188578 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-504 1182971 1183668 1183741 "IFAMON" 1183746 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-503 1182555 1182620 1182674 "IEVALAB" 1182881 NIL IEVALAB (NIL T T) -9 NIL NIL) (-502 1182230 1182298 1182458 "IEVALAB-" 1182463 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-501 1181888 1182144 1182207 "IDPO" 1182212 NIL IDPO (NIL T T) -8 NIL NIL) (-500 1181165 1181777 1181852 "IDPOAMS" 1181857 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-499 1180499 1181054 1181129 "IDPOAM" 1181134 NIL IDPOAM (NIL T T) -8 NIL NIL) (-498 1179584 1179834 1179887 "IDPC" 1180300 NIL IDPC (NIL T T) -9 NIL 1180449) (-497 1179080 1179476 1179549 "IDPAM" 1179554 NIL IDPAM (NIL T T) -8 NIL NIL) (-496 1178483 1178972 1179045 "IDPAG" 1179050 NIL IDPAG (NIL T T) -8 NIL NIL) (-495 1178231 1178398 1178448 "IDENT" 1178453 T IDENT (NIL) -8 NIL NIL) (-494 1174486 1175334 1176229 "IDECOMP" 1177388 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-493 1167359 1168409 1169456 "IDEAL" 1173522 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-492 1166523 1166635 1166834 "ICDEN" 1167243 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-491 1165622 1166003 1166150 "ICARD" 1166396 T ICARD (NIL) -8 NIL NIL) (-490 1163682 1163995 1164400 "IBPTOOLS" 1165299 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-489 1159316 1163302 1163415 "IBITS" 1163601 NIL IBITS (NIL NIL) -8 NIL NIL) (-488 1156039 1156615 1157310 "IBATOOL" 1158733 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-487 1153819 1154280 1154813 "IBACHIN" 1155574 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-486 1151696 1153665 1153768 "IARRAY2" 1153773 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-485 1147849 1151622 1151679 "IARRAY1" 1151684 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-484 1141844 1146263 1146743 "IAN" 1147389 T IAN (NIL) -8 NIL NIL) (-483 1141355 1141412 1141585 "IALGFACT" 1141781 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-482 1140883 1140996 1141024 "HYPCAT" 1141231 T HYPCAT (NIL) -9 NIL NIL) (-481 1140421 1140538 1140724 "HYPCAT-" 1140729 NIL HYPCAT- (NIL T) -8 NIL NIL) (-480 1140043 1140216 1140299 "HOSTNAME" 1140358 T HOSTNAME (NIL) -8 NIL NIL) (-479 1136722 1138053 1138094 "HOAGG" 1139075 NIL HOAGG (NIL T) -9 NIL 1139754) (-478 1135316 1135715 1136241 "HOAGG-" 1136246 NIL HOAGG- (NIL T T) -8 NIL NIL) (-477 1129204 1134757 1134923 "HEXADEC" 1135170 T HEXADEC (NIL) -8 NIL NIL) (-476 1127952 1128174 1128437 "HEUGCD" 1128981 NIL HEUGCD (NIL T) -7 NIL NIL) (-475 1127055 1127789 1127919 "HELLFDIV" 1127924 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-474 1125283 1126832 1126920 "HEAP" 1126999 NIL HEAP (NIL T) -8 NIL NIL) (-473 1124591 1124835 1124969 "HEADAST" 1125169 T HEADAST (NIL) -8 NIL NIL) (-472 1118511 1124506 1124568 "HDP" 1124573 NIL HDP (NIL NIL T) -8 NIL NIL) (-471 1112262 1118146 1118298 "HDMP" 1118412 NIL HDMP (NIL NIL T) -8 NIL NIL) (-470 1111587 1111726 1111890 "HB" 1112118 T HB (NIL) -7 NIL NIL) (-469 1105084 1111433 1111537 "HASHTBL" 1111542 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-468 1104604 1104805 1104897 "HASAST" 1105012 T HASAST (NIL) -8 NIL NIL) (-467 1102418 1104228 1104409 "HACKPI" 1104443 T HACKPI (NIL) -8 NIL NIL) (-466 1098113 1102271 1102384 "GTSET" 1102389 NIL GTSET (NIL T T T T) -8 NIL NIL) (-465 1091639 1097991 1098089 "GSTBL" 1098094 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-464 1083952 1090670 1090935 "GSERIES" 1091430 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-463 1083119 1083510 1083538 "GROUP" 1083741 T GROUP (NIL) -9 NIL 1083875) (-462 1082485 1082644 1082895 "GROUP-" 1082900 NIL GROUP- (NIL T) -8 NIL NIL) (-461 1080854 1081173 1081560 "GROEBSOL" 1082162 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-460 1079794 1080056 1080107 "GRMOD" 1080636 NIL GRMOD (NIL T T) -9 NIL 1080804) (-459 1079562 1079598 1079726 "GRMOD-" 1079731 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-458 1074887 1075916 1076916 "GRIMAGE" 1078582 T GRIMAGE (NIL) -8 NIL NIL) (-457 1073354 1073614 1073938 "GRDEF" 1074583 T GRDEF (NIL) -7 NIL NIL) (-456 1072798 1072914 1073055 "GRAY" 1073233 T GRAY (NIL) -7 NIL NIL) (-455 1072029 1072409 1072460 "GRALG" 1072613 NIL GRALG (NIL T T) -9 NIL 1072706) (-454 1071690 1071763 1071926 "GRALG-" 1071931 NIL GRALG- (NIL T T T) -8 NIL NIL) (-453 1068494 1071275 1071453 "GPOLSET" 1071597 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-452 1067848 1067905 1068163 "GOSPER" 1068431 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-451 1063607 1064286 1064812 "GMODPOL" 1067547 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-450 1062612 1062796 1063034 "GHENSEL" 1063419 NIL GHENSEL (NIL T T) -7 NIL NIL) (-449 1056663 1057506 1058533 "GENUPS" 1061696 NIL GENUPS (NIL T T) -7 NIL NIL) (-448 1056360 1056411 1056500 "GENUFACT" 1056606 NIL GENUFACT (NIL T) -7 NIL NIL) (-447 1055772 1055849 1056014 "GENPGCD" 1056278 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-446 1055246 1055281 1055494 "GENMFACT" 1055731 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-445 1053814 1054069 1054376 "GENEEZ" 1054989 NIL GENEEZ (NIL T T) -7 NIL NIL) (-444 1047727 1053425 1053587 "GDMP" 1053737 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-443 1037104 1041498 1042604 "GCNAALG" 1046710 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-442 1035566 1036394 1036422 "GCDDOM" 1036677 T GCDDOM (NIL) -9 NIL 1036834) (-441 1035036 1035163 1035378 "GCDDOM-" 1035383 NIL GCDDOM- (NIL T) -8 NIL NIL) (-440 1033708 1033893 1034197 "GB" 1034815 NIL GB (NIL T T T T) -7 NIL NIL) (-439 1022328 1024654 1027046 "GBINTERN" 1031399 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-438 1020165 1020457 1020878 "GBF" 1022003 NIL GBF (NIL T T T T) -7 NIL NIL) (-437 1018946 1019111 1019378 "GBEUCLID" 1019981 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-436 1018295 1018420 1018569 "GAUSSFAC" 1018817 T GAUSSFAC (NIL) -7 NIL NIL) (-435 1016662 1016964 1017278 "GALUTIL" 1018014 NIL GALUTIL (NIL T) -7 NIL NIL) (-434 1014970 1015244 1015568 "GALPOLYU" 1016389 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-433 1012335 1012625 1013032 "GALFACTU" 1014667 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-432 1004141 1005640 1007248 "GALFACT" 1010767 NIL GALFACT (NIL T) -7 NIL NIL) (-431 1001529 1002187 1002215 "FVFUN" 1003371 T FVFUN (NIL) -9 NIL 1004091) (-430 1000795 1000977 1001005 "FVC" 1001296 T FVC (NIL) -9 NIL 1001479) (-429 1000437 1000592 1000673 "FUNCTION" 1000747 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-428 998107 998658 999147 "FT" 999968 T FT (NIL) -8 NIL NIL) (-427 996925 997408 997611 "FTEM" 997924 T FTEM (NIL) -8 NIL NIL) (-426 995181 995470 995874 "FSUPFACT" 996616 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-425 993578 993867 994199 "FST" 994869 T FST (NIL) -8 NIL NIL) (-424 992749 992855 993050 "FSRED" 993460 NIL FSRED (NIL T T) -7 NIL NIL) (-423 991428 991683 992037 "FSPRMELT" 992464 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-422 988513 988951 989450 "FSPECF" 990991 NIL FSPECF (NIL T T) -7 NIL NIL) (-421 970955 979397 979437 "FS" 983285 NIL FS (NIL T) -9 NIL 985574) (-420 959605 962595 966651 "FS-" 966948 NIL FS- (NIL T T) -8 NIL NIL) (-419 959119 959173 959350 "FSINT" 959546 NIL FSINT (NIL T T) -7 NIL NIL) (-418 957446 958112 958415 "FSERIES" 958898 NIL FSERIES (NIL T T) -8 NIL NIL) (-417 956460 956576 956807 "FSCINT" 957326 NIL FSCINT (NIL T T) -7 NIL NIL) (-416 952694 955404 955445 "FSAGG" 955815 NIL FSAGG (NIL T) -9 NIL 956074) (-415 950456 951057 951853 "FSAGG-" 951948 NIL FSAGG- (NIL T T) -8 NIL NIL) (-414 949498 949641 949868 "FSAGG2" 950309 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-413 947153 947432 947986 "FS2UPS" 949216 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-412 946735 946778 946933 "FS2" 947104 NIL FS2 (NIL T T T T) -7 NIL NIL) (-411 945592 945763 946072 "FS2EXPXP" 946560 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-410 945018 945133 945285 "FRUTIL" 945472 NIL FRUTIL (NIL T) -7 NIL NIL) (-409 936479 940517 941873 "FR" 943694 NIL FR (NIL T) -8 NIL NIL) (-408 931554 934197 934237 "FRNAALG" 935633 NIL FRNAALG (NIL T) -9 NIL 936240) (-407 927232 928303 929578 "FRNAALG-" 930328 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-406 926870 926913 927040 "FRNAAF2" 927183 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-405 925277 925724 926019 "FRMOD" 926682 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-404 923056 923660 923977 "FRIDEAL" 925068 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-403 922251 922338 922627 "FRIDEAL2" 922963 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-402 921493 921907 921948 "FRETRCT" 921953 NIL FRETRCT (NIL T) -9 NIL 922129) (-401 920605 920836 921187 "FRETRCT-" 921192 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-400 917855 919031 919090 "FRAMALG" 919972 NIL FRAMALG (NIL T T) -9 NIL 920264) (-399 915989 916444 917074 "FRAMALG-" 917297 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-398 909949 915464 915740 "FRAC" 915745 NIL FRAC (NIL T) -8 NIL NIL) (-397 909585 909642 909749 "FRAC2" 909886 NIL FRAC2 (NIL T T) -7 NIL NIL) (-396 909221 909278 909385 "FR2" 909522 NIL FR2 (NIL T T) -7 NIL NIL) (-395 903951 906799 906827 "FPS" 907946 T FPS (NIL) -9 NIL 908503) (-394 903400 903509 903673 "FPS-" 903819 NIL FPS- (NIL T) -8 NIL NIL) (-393 900906 902541 902569 "FPC" 902794 T FPC (NIL) -9 NIL 902936) (-392 900699 900739 900836 "FPC-" 900841 NIL FPC- (NIL T) -8 NIL NIL) (-391 899577 900187 900228 "FPATMAB" 900233 NIL FPATMAB (NIL T) -9 NIL 900385) (-390 897277 897753 898179 "FPARFRAC" 899214 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-389 892670 893169 893851 "FORTRAN" 896709 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-388 890386 890886 891425 "FORT" 892151 T FORT (NIL) -7 NIL NIL) (-387 888062 888624 888652 "FORTFN" 889712 T FORTFN (NIL) -9 NIL 890336) (-386 887826 887876 887904 "FORTCAT" 887963 T FORTCAT (NIL) -9 NIL 888025) (-385 885886 886369 886768 "FORMULA" 887447 T FORMULA (NIL) -8 NIL NIL) (-384 885674 885704 885773 "FORMULA1" 885850 NIL FORMULA1 (NIL T) -7 NIL NIL) (-383 885197 885249 885422 "FORDER" 885616 NIL FORDER (NIL T T T T) -7 NIL NIL) (-382 884293 884457 884650 "FOP" 885024 T FOP (NIL) -7 NIL NIL) (-381 882901 883573 883747 "FNLA" 884175 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-380 881569 881958 881986 "FNCAT" 882558 T FNCAT (NIL) -9 NIL 882851) (-379 881135 881528 881556 "FNAME" 881561 T FNAME (NIL) -8 NIL NIL) (-378 879833 880762 880790 "FMTC" 880795 T FMTC (NIL) -9 NIL 880831) (-377 876195 877356 877985 "FMONOID" 879237 NIL FMONOID (NIL T) -8 NIL NIL) (-376 875414 875937 876086 "FM" 876091 NIL FM (NIL T T) -8 NIL NIL) (-375 872838 873484 873512 "FMFUN" 874656 T FMFUN (NIL) -9 NIL 875364) (-374 872107 872288 872316 "FMC" 872606 T FMC (NIL) -9 NIL 872788) (-373 869319 870153 870207 "FMCAT" 871402 NIL FMCAT (NIL T T) -9 NIL 871897) (-372 868212 869085 869185 "FM1" 869264 NIL FM1 (NIL T T) -8 NIL NIL) (-371 865986 866402 866896 "FLOATRP" 867763 NIL FLOATRP (NIL T) -7 NIL NIL) (-370 859537 863642 864272 "FLOAT" 865376 T FLOAT (NIL) -8 NIL NIL) (-369 856975 857475 858053 "FLOATCP" 859004 NIL FLOATCP (NIL T) -7 NIL NIL) (-368 855804 856608 856649 "FLINEXP" 856654 NIL FLINEXP (NIL T) -9 NIL 856747) (-367 854958 855193 855521 "FLINEXP-" 855526 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-366 854034 854178 854402 "FLASORT" 854810 NIL FLASORT (NIL T T) -7 NIL NIL) (-365 851251 852093 852145 "FLALG" 853372 NIL FLALG (NIL T T) -9 NIL 853839) (-364 845035 848737 848778 "FLAGG" 850040 NIL FLAGG (NIL T) -9 NIL 850692) (-363 843761 844100 844590 "FLAGG-" 844595 NIL FLAGG- (NIL T T) -8 NIL NIL) (-362 842803 842946 843173 "FLAGG2" 843614 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-361 839816 840790 840849 "FINRALG" 841977 NIL FINRALG (NIL T T) -9 NIL 842485) (-360 838976 839205 839544 "FINRALG-" 839549 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-359 838382 838595 838623 "FINITE" 838819 T FINITE (NIL) -9 NIL 838926) (-358 830840 833001 833041 "FINAALG" 836708 NIL FINAALG (NIL T) -9 NIL 838161) (-357 826181 827222 828366 "FINAALG-" 829745 NIL FINAALG- (NIL T T) -8 NIL NIL) (-356 825576 825936 826039 "FILE" 826111 NIL FILE (NIL T) -8 NIL NIL) (-355 824260 824572 824626 "FILECAT" 825310 NIL FILECAT (NIL T T) -9 NIL 825526) (-354 822180 823674 823702 "FIELD" 823742 T FIELD (NIL) -9 NIL 823822) (-353 820800 821185 821696 "FIELD-" 821701 NIL FIELD- (NIL T) -8 NIL NIL) (-352 818678 819435 819782 "FGROUP" 820486 NIL FGROUP (NIL T) -8 NIL NIL) (-351 817768 817932 818152 "FGLMICPK" 818510 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-350 813635 817693 817750 "FFX" 817755 NIL FFX (NIL T NIL) -8 NIL NIL) (-349 813236 813297 813432 "FFSLPE" 813568 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-348 809229 810008 810804 "FFPOLY" 812472 NIL FFPOLY (NIL T) -7 NIL NIL) (-347 808733 808769 808978 "FFPOLY2" 809187 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-346 804619 808652 808715 "FFP" 808720 NIL FFP (NIL T NIL) -8 NIL NIL) (-345 800052 804530 804594 "FF" 804599 NIL FF (NIL NIL NIL) -8 NIL NIL) (-344 795213 799395 799585 "FFNBX" 799906 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-343 790187 794348 794606 "FFNBP" 795067 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-342 784855 789471 789682 "FFNB" 790020 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-341 783687 783885 784200 "FFINTBAS" 784652 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-340 779971 782146 782174 "FFIELDC" 782794 T FFIELDC (NIL) -9 NIL 783170) (-339 778634 779004 779501 "FFIELDC-" 779506 NIL FFIELDC- (NIL T) -8 NIL NIL) (-338 778204 778249 778373 "FFHOM" 778576 NIL FFHOM (NIL T T T) -7 NIL NIL) (-337 775902 776386 776903 "FFF" 777719 NIL FFF (NIL T) -7 NIL NIL) (-336 771555 775644 775745 "FFCGX" 775845 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-335 767222 771287 771394 "FFCGP" 771498 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-334 762440 766949 767057 "FFCG" 767158 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-333 744498 753534 753620 "FFCAT" 758785 NIL FFCAT (NIL T T T) -9 NIL 760236) (-332 739696 740743 742057 "FFCAT-" 743287 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-331 739107 739150 739385 "FFCAT2" 739647 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-330 728319 732079 733299 "FEXPR" 737959 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-329 727319 727754 727795 "FEVALAB" 727879 NIL FEVALAB (NIL T) -9 NIL 728140) (-328 726478 726688 727026 "FEVALAB-" 727031 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-327 725071 725861 726064 "FDIV" 726377 NIL FDIV (NIL T T T T) -8 NIL NIL) (-326 722137 722852 722967 "FDIVCAT" 724535 NIL FDIVCAT (NIL T T T T) -9 NIL 724972) (-325 721899 721926 722096 "FDIVCAT-" 722101 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-324 721119 721206 721483 "FDIV2" 721806 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-323 719805 720064 720353 "FCPAK1" 720850 T FCPAK1 (NIL) -7 NIL NIL) (-322 718933 719305 719446 "FCOMP" 719696 NIL FCOMP (NIL T) -8 NIL NIL) (-321 702568 705982 709543 "FC" 715392 T FC (NIL) -8 NIL NIL) (-320 695221 699202 699242 "FAXF" 701044 NIL FAXF (NIL T) -9 NIL 701736) (-319 692500 693155 693980 "FAXF-" 694445 NIL FAXF- (NIL T T) -8 NIL NIL) (-318 687600 691876 692052 "FARRAY" 692357 NIL FARRAY (NIL T) -8 NIL NIL) (-317 683007 685039 685092 "FAMR" 686115 NIL FAMR (NIL T T) -9 NIL 686575) (-316 681897 682199 682634 "FAMR-" 682639 NIL FAMR- (NIL T T T) -8 NIL NIL) (-315 681093 681819 681872 "FAMONOID" 681877 NIL FAMONOID (NIL T) -8 NIL NIL) (-314 678923 679607 679660 "FAMONC" 680601 NIL FAMONC (NIL T T) -9 NIL 680987) (-313 677615 678677 678814 "FAGROUP" 678819 NIL FAGROUP (NIL T) -8 NIL NIL) (-312 675410 675729 676132 "FACUTIL" 677296 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-311 674509 674694 674916 "FACTFUNC" 675220 NIL FACTFUNC (NIL T) -7 NIL NIL) (-310 666914 673760 673972 "EXPUPXS" 674365 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-309 664397 664937 665523 "EXPRTUBE" 666348 T EXPRTUBE (NIL) -7 NIL NIL) (-308 660591 661183 661920 "EXPRODE" 663736 NIL EXPRODE (NIL T T) -7 NIL NIL) (-307 645965 659246 659674 "EXPR" 660195 NIL EXPR (NIL T) -8 NIL NIL) (-306 640372 640959 641772 "EXPR2UPS" 645263 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-305 640008 640065 640172 "EXPR2" 640309 NIL EXPR2 (NIL T T) -7 NIL NIL) (-304 631415 639140 639437 "EXPEXPAN" 639845 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-303 631242 631372 631401 "EXIT" 631406 T EXIT (NIL) -8 NIL NIL) (-302 630766 630966 631057 "EXITAST" 631171 T EXITAST (NIL) -8 NIL NIL) (-301 630393 630455 630568 "EVALCYC" 630698 NIL EVALCYC (NIL T) -7 NIL NIL) (-300 629934 630052 630093 "EVALAB" 630263 NIL EVALAB (NIL T) -9 NIL 630367) (-299 629415 629537 629758 "EVALAB-" 629763 NIL EVALAB- (NIL T T) -8 NIL NIL) (-298 626918 628186 628214 "EUCDOM" 628769 T EUCDOM (NIL) -9 NIL 629119) (-297 625323 625765 626355 "EUCDOM-" 626360 NIL EUCDOM- (NIL T) -8 NIL NIL) (-296 612863 615621 618371 "ESTOOLS" 622593 T ESTOOLS (NIL) -7 NIL NIL) (-295 612495 612552 612661 "ESTOOLS2" 612800 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-294 612246 612288 612368 "ESTOOLS1" 612447 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-293 606171 607899 607927 "ES" 610695 T ES (NIL) -9 NIL 612104) (-292 601118 602405 604222 "ES-" 604386 NIL ES- (NIL T) -8 NIL NIL) (-291 597493 598253 599033 "ESCONT" 600358 T ESCONT (NIL) -7 NIL NIL) (-290 597238 597270 597352 "ESCONT1" 597455 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-289 596913 596963 597063 "ES2" 597182 NIL ES2 (NIL T T) -7 NIL NIL) (-288 596543 596601 596710 "ES1" 596849 NIL ES1 (NIL T T) -7 NIL NIL) (-287 595759 595888 596064 "ERROR" 596387 T ERROR (NIL) -7 NIL NIL) (-286 589262 595618 595709 "EQTBL" 595714 NIL EQTBL (NIL T T) -8 NIL NIL) (-285 581819 584576 586025 "EQ" 587846 NIL -3897 (NIL T) -8 NIL NIL) (-284 581451 581508 581617 "EQ2" 581756 NIL EQ2 (NIL T T) -7 NIL NIL) (-283 576743 577789 578882 "EP" 580390 NIL EP (NIL T) -7 NIL NIL) (-282 575325 575626 575943 "ENV" 576446 T ENV (NIL) -8 NIL NIL) (-281 574524 575044 575072 "ENTIRER" 575077 T ENTIRER (NIL) -9 NIL 575123) (-280 571026 572479 572849 "EMR" 574323 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-279 570170 570355 570409 "ELTAGG" 570789 NIL ELTAGG (NIL T T) -9 NIL 571000) (-278 569889 569951 570092 "ELTAGG-" 570097 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-277 569678 569707 569761 "ELTAB" 569845 NIL ELTAB (NIL T T) -9 NIL NIL) (-276 568804 568950 569149 "ELFUTS" 569529 NIL ELFUTS (NIL T T) -7 NIL NIL) (-275 568546 568602 568630 "ELEMFUN" 568735 T ELEMFUN (NIL) -9 NIL NIL) (-274 568416 568437 568505 "ELEMFUN-" 568510 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-273 563307 566516 566557 "ELAGG" 567497 NIL ELAGG (NIL T) -9 NIL 567960) (-272 561592 562026 562689 "ELAGG-" 562694 NIL ELAGG- (NIL T T) -8 NIL NIL) (-271 560249 560529 560824 "ELABEXPR" 561317 T ELABEXPR (NIL) -8 NIL NIL) (-270 553115 554916 555743 "EFUPXS" 559525 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-269 546565 548366 549176 "EFULS" 552391 NIL EFULS (NIL T T T) -8 NIL NIL) (-268 543987 544345 544824 "EFSTRUC" 546197 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-267 533059 534624 536184 "EF" 542502 NIL EF (NIL T T) -7 NIL NIL) (-266 532160 532544 532693 "EAB" 532930 T EAB (NIL) -8 NIL NIL) (-265 531369 532119 532147 "E04UCFA" 532152 T E04UCFA (NIL) -8 NIL NIL) (-264 530578 531328 531356 "E04NAFA" 531361 T E04NAFA (NIL) -8 NIL NIL) (-263 529787 530537 530565 "E04MBFA" 530570 T E04MBFA (NIL) -8 NIL NIL) (-262 528996 529746 529774 "E04JAFA" 529779 T E04JAFA (NIL) -8 NIL NIL) (-261 528207 528955 528983 "E04GCFA" 528988 T E04GCFA (NIL) -8 NIL NIL) (-260 527418 528166 528194 "E04FDFA" 528199 T E04FDFA (NIL) -8 NIL NIL) (-259 526627 527377 527405 "E04DGFA" 527410 T E04DGFA (NIL) -8 NIL NIL) (-258 520805 522152 523516 "E04AGNT" 525283 T E04AGNT (NIL) -7 NIL NIL) (-257 519529 520009 520049 "DVARCAT" 520524 NIL DVARCAT (NIL T) -9 NIL 520723) (-256 518733 518945 519259 "DVARCAT-" 519264 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-255 511633 518532 518661 "DSMP" 518666 NIL DSMP (NIL T T T) -8 NIL NIL) (-254 506443 507578 508646 "DROPT" 510585 T DROPT (NIL) -8 NIL NIL) (-253 506108 506167 506265 "DROPT1" 506378 NIL DROPT1 (NIL T) -7 NIL NIL) (-252 501223 502349 503486 "DROPT0" 504991 T DROPT0 (NIL) -7 NIL NIL) (-251 499568 499893 500279 "DRAWPT" 500857 T DRAWPT (NIL) -7 NIL NIL) (-250 494155 495078 496157 "DRAW" 498542 NIL DRAW (NIL T) -7 NIL NIL) (-249 493788 493841 493959 "DRAWHACK" 494096 NIL DRAWHACK (NIL T) -7 NIL NIL) (-248 492519 492788 493079 "DRAWCX" 493517 T DRAWCX (NIL) -7 NIL NIL) (-247 492035 492103 492254 "DRAWCURV" 492445 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-246 482506 484465 486580 "DRAWCFUN" 489940 T DRAWCFUN (NIL) -7 NIL NIL) (-245 479319 481201 481242 "DQAGG" 481871 NIL DQAGG (NIL T) -9 NIL 482144) (-244 467838 474535 474618 "DPOLCAT" 476470 NIL DPOLCAT (NIL T T T T) -9 NIL 477015) (-243 462677 464023 465981 "DPOLCAT-" 465986 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-242 455832 462538 462636 "DPMO" 462641 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-241 448890 455612 455779 "DPMM" 455784 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-240 448310 448513 448627 "DOMAIN" 448796 T DOMAIN (NIL) -8 NIL NIL) (-239 442061 447945 448097 "DMP" 448211 NIL DMP (NIL NIL T) -8 NIL NIL) (-238 441661 441717 441861 "DLP" 441999 NIL DLP (NIL T) -7 NIL NIL) (-237 435305 440762 440989 "DLIST" 441466 NIL DLIST (NIL T) -8 NIL NIL) (-236 432151 434160 434201 "DLAGG" 434751 NIL DLAGG (NIL T) -9 NIL 434980) (-235 431001 431631 431659 "DIVRING" 431751 T DIVRING (NIL) -9 NIL 431834) (-234 430238 430428 430728 "DIVRING-" 430733 NIL DIVRING- (NIL T) -8 NIL NIL) (-233 428340 428697 429103 "DISPLAY" 429852 T DISPLAY (NIL) -7 NIL NIL) (-232 422282 428254 428317 "DIRPROD" 428322 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-231 421130 421333 421598 "DIRPROD2" 422075 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-230 410668 416620 416673 "DIRPCAT" 417083 NIL DIRPCAT (NIL NIL T) -9 NIL 417923) (-229 407994 408636 409517 "DIRPCAT-" 409854 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-228 407281 407441 407627 "DIOSP" 407828 T DIOSP (NIL) -7 NIL NIL) (-227 403983 406193 406234 "DIOPS" 406668 NIL DIOPS (NIL T) -9 NIL 406897) (-226 403532 403646 403837 "DIOPS-" 403842 NIL DIOPS- (NIL T T) -8 NIL NIL) (-225 402444 403038 403066 "DIFRING" 403253 T DIFRING (NIL) -9 NIL 403363) (-224 402090 402167 402319 "DIFRING-" 402324 NIL DIFRING- (NIL T) -8 NIL NIL) (-223 399915 401153 401194 "DIFEXT" 401557 NIL DIFEXT (NIL T) -9 NIL 401851) (-222 398200 398628 399294 "DIFEXT-" 399299 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-221 395522 397732 397773 "DIAGG" 397778 NIL DIAGG (NIL T) -9 NIL 397798) (-220 394906 395063 395315 "DIAGG-" 395320 NIL DIAGG- (NIL T T) -8 NIL NIL) (-219 390371 393865 394142 "DHMATRIX" 394675 NIL DHMATRIX (NIL T) -8 NIL NIL) (-218 385983 386892 387902 "DFSFUN" 389381 T DFSFUN (NIL) -7 NIL NIL) (-217 380951 384798 385140 "DFLOAT" 385661 T DFLOAT (NIL) -8 NIL NIL) (-216 379179 379460 379856 "DFINTTLS" 380659 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-215 376244 377200 377600 "DERHAM" 378845 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-214 374093 376019 376108 "DEQUEUE" 376188 NIL DEQUEUE (NIL T) -8 NIL NIL) (-213 373308 373441 373637 "DEGRED" 373955 NIL DEGRED (NIL T T) -7 NIL NIL) (-212 369703 370448 371301 "DEFINTRF" 372536 NIL DEFINTRF (NIL T) -7 NIL NIL) (-211 367230 367699 368298 "DEFINTEF" 369222 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-210 366596 366829 366951 "DEFAST" 367128 T DEFAST (NIL) -8 NIL NIL) (-209 360484 366037 366203 "DECIMAL" 366450 T DECIMAL (NIL) -8 NIL NIL) (-208 357996 358454 358960 "DDFACT" 360028 NIL DDFACT (NIL T T) -7 NIL NIL) (-207 357592 357635 357786 "DBLRESP" 357947 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-206 355302 355636 356005 "DBASE" 357350 NIL DBASE (NIL T) -8 NIL NIL) (-205 354571 354782 354928 "DATABUF" 355201 NIL DATABUF (NIL NIL T) -8 NIL NIL) (-204 353704 354530 354558 "D03FAFA" 354563 T D03FAFA (NIL) -8 NIL NIL) (-203 352838 353663 353691 "D03EEFA" 353696 T D03EEFA (NIL) -8 NIL NIL) (-202 350788 351254 351743 "D03AGNT" 352369 T D03AGNT (NIL) -7 NIL NIL) (-201 350104 350747 350775 "D02EJFA" 350780 T D02EJFA (NIL) -8 NIL NIL) (-200 349420 350063 350091 "D02CJFA" 350096 T D02CJFA (NIL) -8 NIL NIL) (-199 348736 349379 349407 "D02BHFA" 349412 T D02BHFA (NIL) -8 NIL NIL) (-198 348052 348695 348723 "D02BBFA" 348728 T D02BBFA (NIL) -8 NIL NIL) (-197 341250 342838 344444 "D02AGNT" 346466 T D02AGNT (NIL) -7 NIL NIL) (-196 339019 339541 340087 "D01WGTS" 340724 T D01WGTS (NIL) -7 NIL NIL) (-195 338114 338978 339006 "D01TRNS" 339011 T D01TRNS (NIL) -8 NIL NIL) (-194 337209 338073 338101 "D01GBFA" 338106 T D01GBFA (NIL) -8 NIL NIL) (-193 336304 337168 337196 "D01FCFA" 337201 T D01FCFA (NIL) -8 NIL NIL) (-192 335399 336263 336291 "D01ASFA" 336296 T D01ASFA (NIL) -8 NIL NIL) (-191 334494 335358 335386 "D01AQFA" 335391 T D01AQFA (NIL) -8 NIL NIL) (-190 333589 334453 334481 "D01APFA" 334486 T D01APFA (NIL) -8 NIL NIL) (-189 332684 333548 333576 "D01ANFA" 333581 T D01ANFA (NIL) -8 NIL NIL) (-188 331779 332643 332671 "D01AMFA" 332676 T D01AMFA (NIL) -8 NIL NIL) (-187 330874 331738 331766 "D01ALFA" 331771 T D01ALFA (NIL) -8 NIL NIL) (-186 329969 330833 330861 "D01AKFA" 330866 T D01AKFA (NIL) -8 NIL NIL) (-185 329064 329928 329956 "D01AJFA" 329961 T D01AJFA (NIL) -8 NIL NIL) (-184 322361 323912 325473 "D01AGNT" 327523 T D01AGNT (NIL) -7 NIL NIL) (-183 321698 321826 321978 "CYCLOTOM" 322229 T CYCLOTOM (NIL) -7 NIL NIL) (-182 318433 319146 319873 "CYCLES" 320991 T CYCLES (NIL) -7 NIL NIL) (-181 317745 317879 318050 "CVMP" 318294 NIL CVMP (NIL T) -7 NIL NIL) (-180 315516 315774 316150 "CTRIGMNP" 317473 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-179 315027 315216 315315 "CTORCALL" 315437 T CTORCALL (NIL) -8 NIL NIL) (-178 314401 314500 314653 "CSTTOOLS" 314924 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-177 310200 310857 311615 "CRFP" 313713 NIL CRFP (NIL T T) -7 NIL NIL) (-176 309247 309432 309660 "CRAPACK" 310004 NIL CRAPACK (NIL T) -7 NIL NIL) (-175 308631 308732 308936 "CPMATCH" 309123 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-174 308356 308384 308490 "CPIMA" 308597 NIL CPIMA (NIL T T T) -7 NIL NIL) (-173 304720 305392 306110 "COORDSYS" 307691 NIL COORDSYS (NIL T) -7 NIL NIL) (-172 304104 304233 304383 "CONTOUR" 304590 T CONTOUR (NIL) -8 NIL NIL) (-171 300030 302107 302599 "CONTFRAC" 303644 NIL CONTFRAC (NIL T) -8 NIL NIL) (-170 299910 299931 299959 "CONDUIT" 299996 T CONDUIT (NIL) -9 NIL NIL) (-169 299103 299623 299651 "COMRING" 299656 T COMRING (NIL) -9 NIL 299708) (-168 298184 298461 298645 "COMPPROP" 298939 T COMPPROP (NIL) -8 NIL NIL) (-167 297845 297880 298008 "COMPLPAT" 298143 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-166 287904 297654 297763 "COMPLEX" 297768 NIL COMPLEX (NIL T) -8 NIL NIL) (-165 287540 287597 287704 "COMPLEX2" 287841 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-164 287258 287293 287391 "COMPFACT" 287499 NIL COMPFACT (NIL T T) -7 NIL NIL) (-163 271656 281872 281912 "COMPCAT" 282916 NIL COMPCAT (NIL T) -9 NIL 284311) (-162 261171 264095 267722 "COMPCAT-" 268078 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-161 260900 260928 261031 "COMMUPC" 261137 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-160 260695 260728 260787 "COMMONOP" 260861 T COMMONOP (NIL) -7 NIL NIL) (-159 260278 260446 260533 "COMM" 260628 T COMM (NIL) -8 NIL NIL) (-158 259899 260082 260157 "COMMAAST" 260223 T COMMAAST (NIL) -8 NIL NIL) (-157 259148 259342 259370 "COMBOPC" 259708 T COMBOPC (NIL) -9 NIL 259883) (-156 258044 258254 258496 "COMBINAT" 258938 NIL COMBINAT (NIL T) -7 NIL NIL) (-155 254242 254815 255455 "COMBF" 257466 NIL COMBF (NIL T T) -7 NIL NIL) (-154 253028 253358 253593 "COLOR" 254027 T COLOR (NIL) -8 NIL NIL) (-153 252548 252749 252841 "COLONAST" 252956 T COLONAST (NIL) -8 NIL NIL) (-152 252188 252235 252360 "CMPLXRT" 252495 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-151 247690 248718 249798 "CLIP" 251128 T CLIP (NIL) -7 NIL NIL) (-150 246072 246796 247035 "CLIF" 247517 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-149 242294 244218 244259 "CLAGG" 245188 NIL CLAGG (NIL T) -9 NIL 245724) (-148 240716 241173 241756 "CLAGG-" 241761 NIL CLAGG- (NIL T T) -8 NIL NIL) (-147 240260 240345 240485 "CINTSLPE" 240625 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-146 237761 238232 238780 "CHVAR" 239788 NIL CHVAR (NIL T T T) -7 NIL NIL) (-145 237024 237544 237572 "CHARZ" 237577 T CHARZ (NIL) -9 NIL 237592) (-144 236778 236818 236896 "CHARPOL" 236978 NIL CHARPOL (NIL T) -7 NIL NIL) (-143 235925 236478 236506 "CHARNZ" 236553 T CHARNZ (NIL) -9 NIL 236609) (-142 233950 234615 234950 "CHAR" 235610 T CHAR (NIL) -8 NIL NIL) (-141 233676 233737 233765 "CFCAT" 233876 T CFCAT (NIL) -9 NIL NIL) (-140 232921 233032 233214 "CDEN" 233560 NIL CDEN (NIL T T T) -7 NIL NIL) (-139 228913 232074 232354 "CCLASS" 232661 T CCLASS (NIL) -8 NIL NIL) (-138 228832 228858 228893 "CATEGORY" 228898 T -10 (NIL) -8 NIL NIL) (-137 228323 228532 228631 "CATAST" 228753 T CATAST (NIL) -8 NIL NIL) (-136 227843 228044 228136 "CASEAST" 228251 T CASEAST (NIL) -8 NIL NIL) (-135 222895 223872 224625 "CARTEN" 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150128 150241 150267 "ATRIG" 150468 T ATRIG (NIL) -9 NIL NIL) (-93 149937 149978 150065 "ATRIG-" 150070 NIL ATRIG- (NIL T) -8 NIL NIL) (-92 149662 149805 149831 "ASTCAT" 149836 T ASTCAT (NIL) -9 NIL 149866) (-91 149459 149502 149594 "ASTCAT-" 149599 NIL ASTCAT- (NIL T) -8 NIL NIL) (-90 147656 149235 149323 "ASTACK" 149402 NIL ASTACK (NIL T) -8 NIL NIL) (-89 146161 146458 146823 "ASSOCEQ" 147338 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-88 145193 145820 145944 "ASP9" 146068 NIL ASP9 (NIL NIL) -8 NIL NIL) (-87 144957 145141 145180 "ASP8" 145185 NIL ASP8 (NIL NIL) -8 NIL NIL) (-86 143826 144562 144704 "ASP80" 144846 NIL ASP80 (NIL NIL) -8 NIL NIL) (-85 142725 143461 143593 "ASP7" 143725 NIL ASP7 (NIL NIL) -8 NIL NIL) (-84 141679 142402 142520 "ASP78" 142638 NIL ASP78 (NIL NIL) -8 NIL NIL) (-83 140648 141359 141476 "ASP77" 141593 NIL ASP77 (NIL NIL) -8 NIL NIL) (-82 139560 140286 140417 "ASP74" 140548 NIL ASP74 (NIL NIL) -8 NIL NIL) (-81 138460 139195 139327 "ASP73" 139459 NIL ASP73 (NIL NIL) -8 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\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index b79e175e..322b855b 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,114 +1,572 @@ -(732944 . 3430960044) -(((*1 *2 *2) - (-12 (-4 *3 (-592 (-861 *3))) (-4 *3 (-855 *3)) - (-4 *3 (-13 (-821) (-442))) (-5 *1 (-1163 *3 *2)) - (-4 *2 (-592 (-861 *3))) (-4 *2 (-855 *3)) - (-4 *2 (-13 (-421 *3) (-1157)))))) -(((*1 *2 *3) - (|partial| -12 (-5 *3 (-1118)) (-5 *2 (-370)) (-5 *1 (-760))))) -(((*1 *2 *1) - (-12 (-4 *1 (-244 *3 *4 *5 *6)) (-4 *3 (-1016)) (-4 *4 (-821)) - (-4 *5 (-257 *4)) (-4 *6 (-767)) (-5 *2 (-112))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-619 (-619 (-619 *4)))) (-5 *3 (-619 *4)) (-4 *4 (-821)) - (-5 *1 (-1143 *4))))) -(((*1 *2 *3 *3 *4 *4 *4 *3) - (-12 (-5 *3 (-547)) (-5 *4 (-663 (-217))) (-5 *2 (-1004)) - (-5 *1 (-731))))) -(((*1 *2 *2 *3) - (|partial| -12 (-5 *3 (-1135)) - (-4 *4 (-13 (-442) (-821) (-145) (-1007 (-547)) 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(-114)) (-5 *1 (-808 *2)) (-4 *2 (-1016))))) +(((*1 *2 *2 *1) + (-12 (-4 *1 (-1165 *3 *4 *5 *2)) (-4 *3 (-539)) (-4 *4 (-767)) + (-4 *5 (-821)) (-4 *2 (-1030 *3 *4 *5))))) +(((*1 *2 *3 *4 *3 *3 *3 *3 *4 *3) + (-12 (-5 *3 (-547)) (-5 *4 (-663 (-166 (-217)))) (-5 *2 (-1004)) + (-5 *1 (-731))))) +(((*1 *2 *2 *2 *2) + (-12 (-4 *2 (-13 (-354) (-10 -8 (-15 ** ($ $ (-398 (-547))))))) + (-5 *1 (-1090 *3 *2)) (-4 *3 (-1194 *2))))) +(((*1 *2 *3 *4 *3) + (-12 (-5 *3 (-547)) (-5 *4 (-663 (-217))) (-5 *2 (-1004)) + (-5 *1 (-722))))) +(((*1 *2) (-12 (-5 *2 (-1107 (-1118))) (-5 *1 (-382))))) (((*1 *2 *3) (-12 (-5 *3 (-743)) (-5 *2 - (-2 (|:| -4283 (-370)) (|:| -2464 (-1118)) + (-2 (|:| -4170 (-370)) (|:| -2465 (-1118)) (|:| |explanations| (-619 (-1118))) (|:| |extra| (-1004)))) (-5 *1 (-548)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-743)) (-5 *4 (-1028)) (-5 *2 - (-2 (|:| -4283 (-370)) (|:| -2464 (-1118)) + (-2 (|:| -4170 (-370)) (|:| -2465 (-1118)) (|:| |explanations| (-619 (-1118))) (|:| |extra| (-1004)))) (-5 *1 (-548)))) ((*1 *2 *3 *4) (-12 (-4 *1 (-761)) (-5 *3 (-1028)) (-5 *4 (-2 (|:| |fn| (-307 (-217))) - (|:| -2693 (-619 (-1058 (-814 (-217))))) (|:| |abserr| (-217)) + (|:| -2905 (-619 (-1058 (-814 (-217))))) (|:| |abserr| (-217)) (|:| |relerr| (-217)))) (-5 *2 - (-2 (|:| -4283 (-370)) (|:| |explanations| (-1118)) + (-2 (|:| -4170 (-370)) (|:| |explanations| (-1118)) (|:| |extra| (-1004)))))) ((*1 *2 *3 *4) (-12 (-4 *1 (-761)) (-5 *3 (-1028)) (-5 *4 (-2 (|:| |var| (-1135)) (|:| |fn| (-307 (-217))) - (|:| -2693 (-1058 (-814 (-217)))) (|:| |abserr| (-217)) + (|:| -2905 (-1058 (-814 (-217)))) (|:| |abserr| (-217)) (|:| |relerr| (-217)))) (-5 *2 - (-2 (|:| -4283 (-370)) (|:| |explanations| (-1118)) + (-2 (|:| -4170 (-370)) (|:| |explanations| (-1118)) (|:| |extra| (-1004)))))) ((*1 *2 *3 *4) (-12 (-4 *1 (-774)) (-5 *3 (-1028)) @@ -117,41 +575,41 @@ (|:| |fn| (-1218 (-307 (-217)))) (|:| |yinit| (-619 (-217))) (|:| |intvals| (-619 (-217))) (|:| |g| (-307 (-217))) (|:| |abserr| (-217)) (|:| |relerr| (-217)))) - (-5 *2 (-2 (|:| -4283 (-370)) (|:| |explanations| (-1118)))))) + (-5 *2 (-2 (|:| -4170 (-370)) (|:| |explanations| (-1118)))))) ((*1 *2 *3) (-12 (-5 *3 (-782)) (-5 *2 - (-2 (|:| -4283 (-370)) (|:| -2464 (-1118)) + (-2 (|:| -4170 (-370)) (|:| -2465 (-1118)) (|:| |explanations| (-619 (-1118))))) (-5 *1 (-779)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-782)) (-5 *4 (-1028)) (-5 *2 - (-2 (|:| -4283 (-370)) (|:| -2464 (-1118)) + (-2 (|:| -4170 (-370)) (|:| -2465 (-1118)) (|:| |explanations| (-619 (-1118))))) (-5 *1 (-779)))) ((*1 *2 *3 *4) (-12 (-4 *1 (-810)) (-5 *3 (-1028)) (-5 *4 - (-2 (|:| |lfn| (-619 (-307 (-217)))) (|:| -3045 (-619 (-217))))) - (-5 *2 (-2 (|:| -4283 (-370)) (|:| |explanations| (-1118)))))) + (-2 (|:| |lfn| (-619 (-307 (-217)))) (|:| -3046 (-619 (-217))))) + (-5 *2 (-2 (|:| -4170 (-370)) (|:| |explanations| (-1118)))))) ((*1 *2 *3 *4) (-12 (-4 *1 (-810)) (-5 *3 (-1028)) (-5 *4 - (-2 (|:| |fn| (-307 (-217))) (|:| -3045 (-619 (-217))) + (-2 (|:| |fn| (-307 (-217))) (|:| -3046 (-619 (-217))) (|:| |lb| (-619 (-814 (-217)))) (|:| |cf| (-619 (-307 (-217)))) (|:| |ub| (-619 (-814 (-217)))))) - (-5 *2 (-2 (|:| -4283 (-370)) (|:| |explanations| (-1118)))))) + (-5 *2 (-2 (|:| -4170 (-370)) (|:| |explanations| (-1118)))))) ((*1 *2 *3) (-12 (-5 *3 (-812)) (-5 *2 - (-2 (|:| -4283 (-370)) (|:| -2464 (-1118)) + (-2 (|:| -4170 (-370)) (|:| -2465 (-1118)) (|:| |explanations| (-619 (-1118))))) (-5 *1 (-811)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-812)) (-5 *4 (-1028)) (-5 *2 - (-2 (|:| -4283 (-370)) (|:| -2464 (-1118)) + (-2 (|:| -4170 (-370)) (|:| -2465 (-1118)) (|:| |explanations| (-619 (-1118))))) (-5 *1 (-811)))) ((*1 *2 *3 *4) @@ -165,31 +623,270 @@ (|:| |dStart| (-663 (-217))) (|:| |dFinish| (-663 (-217)))))) (|:| |f| (-619 (-619 (-307 (-217))))) (|:| |st| (-1118)) (|:| |tol| (-217)))) - (-5 *2 (-2 (|:| -4283 (-370)) (|:| |explanations| (-1118)))))) + (-5 *2 (-2 (|:| -4170 (-370)) (|:| |explanations| (-1118)))))) ((*1 *2 *3) (-12 (-5 *3 (-867)) (-5 *2 - 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*2)) (-4 *2 (-821)))) ((*1 *1 *1) (-12 (-5 *1 (-651 *2)) (-4 *2 (-821)))) @@ -2295,9 +2245,9 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-819) (-354))) (-5 *1 (-1026 *2 *3)) (-4 *3 (-1194 *2))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-354)) (-5 *1 (-741 *2 *3)) (-4 *2 (-683 *3)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-823 *2)) (-4 *2 (-1016)) (-4 *2 (-354))))) +(((*1 *2) + (-12 (-5 *2 (-2 (|:| -3554 (-619 *3)) (|:| -1949 (-619 *3)))) + (-5 *1 (-1173 *3)) (-4 *3 (-1063))))) (((*1 *1 *2) (-12 (-4 *1 (-38 *2)) (-4 *2 (-169)))) ((*1 *1 *2) (-12 (-5 *2 (-1218 *3)) (-4 *3 (-354)) (-14 *6 (-1218 (-663 *3))) @@ -2305,69 +2255,69 @@ ((*1 *1 *2) (-12 (-5 *2 (-1087 (-547) (-590 (-48)))) (-5 *1 (-48)))) ((*1 *2 *3) (-12 (-5 *2 (-52)) (-5 *1 (-51 *3)) (-4 *3 (-1172)))) ((*1 *1 *2) - (-12 (-5 *2 (-1218 (-330 (-3841 'JINT 'X 'ELAM) (-3841) (-673)))) + (-12 (-5 *2 (-1218 (-330 (-3843 'JINT 'X 'ELAM) (-3843) (-673)))) (-5 *1 (-60 *3)) (-14 *3 (-1135)))) ((*1 *1 *2) - (-12 (-5 *2 (-1218 (-330 (-3841) (-3841 'XC) (-673)))) + 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(-85 *3)) (-14 *3 (-1135)))) ((*1 *1 *2) - (-12 (-5 *2 (-663 (-330 (-3841 'XL 'XR 'ELAM) (-3841) (-673)))) + (-12 (-5 *2 (-663 (-330 (-3843 'XL 'XR 'ELAM) (-3843) (-673)))) (-5 *1 (-86 *3)) (-14 *3 (-1135)))) ((*1 *1 *2) - (-12 (-5 *2 (-330 (-3841 'X) (-3841 '-2647) (-673))) (-5 *1 (-88 *3)) + (-12 (-5 *2 (-330 (-3843 'X) (-3843 '-2648) (-673))) (-5 *1 (-88 *3)) (-14 *3 (-1135)))) ((*1 *2 *1) (-12 (-5 *2 (-973 2)) (-5 *1 (-107)))) ((*1 *2 *1) (-12 (-5 *2 (-398 (-547))) (-5 *1 (-107)))) @@ -2391,8 +2341,8 @@ (-12 (-5 *2 (-619 *3)) (-4 *3 (-13 (-821) - (-10 -8 (-15 -3329 ((-1118) $ (-1135))) (-15 -2683 ((-1223) $)) - (-15 -3617 ((-1223) $))))) + (-10 -8 (-15 -3330 ((-1118) $ (-1135))) (-15 -2684 ((-1223) $)) + (-15 -1884 ((-1223) $))))) (-5 *1 (-206 *3)))) ((*1 *2 *1) (-12 (-5 *2 (-973 10)) (-5 *1 (-209)))) ((*1 *2 *1) (-12 (-5 *2 (-398 (-547))) (-5 *1 (-209)))) @@ -2433,14 +2383,14 @@ ((*1 *1 *2) (-12 (-4 *1 (-365 *2 *3)) (-4 *2 (-821)) (-4 *3 (-169)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 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(-1139)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1139)) (|:| -2087 (-619 (-321))))) + (-5 *2 (-2 (|:| |localSymbols| (-1139)) (|:| -2088 (-619 (-321))))) (-5 *1 (-389 *3 *4 *5 *6)) (-14 *3 (-1135)) - (-14 *4 (-3 (|:| |fst| (-425)) (|:| -2887 "void"))) + (-14 *4 (-3 (|:| |fst| (-425)) (|:| -2888 "void"))) (-14 *5 (-619 (-1135))) (-14 *6 (-1139)))) ((*1 *1 *2) (-12 (-5 *2 (-619 (-321))) (-5 *1 (-389 *3 *4 *5 *6)) - (-14 *3 (-1135)) (-14 *4 (-3 (|:| |fst| (-425)) (|:| -2887 "void"))) + (-14 *3 (-1135)) (-14 *4 (-3 (|:| |fst| (-425)) (|:| -2888 "void"))) (-14 *5 (-619 (-1135))) (-14 *6 (-1139)))) ((*1 *1 *2) (-12 (-5 *2 (-321)) (-5 *1 (-389 *3 *4 *5 *6)) (-14 *3 (-1135)) - (-14 *4 (-3 (|:| |fst| (-425)) (|:| -2887 "void"))) + (-14 *4 (-3 (|:| |fst| (-425)) (|:| -2888 "void"))) (-14 *5 (-619 (-1135))) (-14 *6 (-1139)))) ((*1 *1 *2) (-12 (-5 *2 (-322 *4)) (-4 *4 (-13 (-821) (-21))) @@ -2542,14 +2492,14 @@ ((*1 *2 *1) (-12 (-5 *2 (-832)) (-5 *1 (-428)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1139)) (|:| -2087 (-619 (-321))))) + (-5 *2 (-2 (|:| |localSymbols| (-1139)) (|:| -2088 (-619 (-321))))) (-4 *1 (-430)))) ((*1 *1 *2) (-12 (-5 *2 (-321)) (-4 *1 (-430)))) ((*1 *1 *2) (-12 (-5 *2 (-619 (-321))) (-4 *1 (-430)))) ((*1 *1 *2) (-12 (-5 *2 (-1218 (-673))) (-4 *1 (-430)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1139)) (|:| -2087 (-619 (-321))))) + (-5 *2 (-2 (|:| |localSymbols| (-1139)) (|:| -2088 (-619 (-321))))) (-4 *1 (-431)))) ((*1 *1 *2) (-12 (-5 *2 (-321)) (-4 *1 (-431)))) ((*1 *1 *2) (-12 (-5 *2 (-619 (-321))) (-4 *1 (-431)))) @@ -2621,18 +2571,18 @@ ((*1 *1 *2) (-12 (-4 *3 (-1016)) (-5 *1 (-687 *3 *2)) (-4 *2 (-1194 *3)))) ((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| -3479 *3) (|:| -4248 *4))) + (-12 (-5 *2 (-2 (|:| -3481 *3) (|:| -1973 *4))) (-5 *1 (-688 *3 *4 *5)) (-4 *3 (-821)) (-4 *4 (-1063)) (-14 *5 (-1 (-112) *2 *2)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| -3479 *3) (|:| -4248 *4))) (-4 *3 (-821)) + (-12 (-5 *2 (-2 (|:| -3481 *3) (|:| -1973 *4))) (-4 *3 (-821)) (-4 *4 (-1063)) (-5 *1 (-688 *3 *4 *5)) (-14 *5 (-1 (-112) *2 *2)))) ((*1 *2 *1) (-12 (-4 *2 (-169)) (-5 *1 (-690 *2 *3 *4 *5 *6)) (-4 *3 (-23)) (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-619 (-2 (|:| -1557 *3) (|:| -3513 *4)))) + (-12 (-5 *2 (-619 (-2 (|:| -1558 *3) (|:| -3514 *4)))) (-4 *3 (-1016)) (-4 *4 (-701)) (-5 *1 (-710 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-547)) (-4 *1 (-738)))) ((*1 *1 *2) @@ -2641,25 +2591,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1135)) (|:| |fn| (-307 (-217))) - (|:| -2693 (-1058 (-814 (-217)))) (|:| |abserr| (-217)) + (|:| -2905 (-1058 (-814 (-217)))) (|:| |abserr| (-217)) (|:| |relerr| (-217)))) (|:| |mdnia| (-2 (|:| |fn| (-307 (-217))) - (|:| -2693 (-619 (-1058 (-814 (-217))))) + (|:| -2905 (-619 (-1058 (-814 (-217))))) (|:| |abserr| (-217)) (|:| |relerr| (-217)))))) (-5 *1 (-743)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-307 (-217))) - (|:| -2693 (-619 (-1058 (-814 (-217))))) (|:| |abserr| (-217)) + (|:| -2905 (-619 (-1058 (-814 (-217))))) (|:| |abserr| (-217)) (|:| |relerr| (-217)))) (-5 *1 (-743)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1135)) (|:| |fn| (-307 (-217))) - (|:| -2693 (-1058 (-814 (-217)))) (|:| |abserr| (-217)) + (|:| -2905 (-1058 (-814 (-217)))) (|:| |abserr| (-217)) (|:| |relerr| (-217)))) (-5 *1 (-743)))) ((*1 *2 *1) (-12 (-5 *2 (-832)) (-5 *1 (-743)))) @@ -2685,23 +2635,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-307 (-217))) (|:| -3045 (-619 (-217))) + (-2 (|:| |fn| (-307 (-217))) (|:| -3046 (-619 (-217))) (|:| |lb| (-619 (-814 (-217)))) (|:| |cf| (-619 (-307 (-217)))) (|:| |ub| (-619 (-814 (-217)))))) (|:| |lsa| (-2 (|:| |lfn| (-619 (-307 (-217)))) - (|:| -3045 (-619 (-217))))))) + (|:| -3046 (-619 (-217))))))) (-5 *1 (-812)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-619 (-307 (-217)))) (|:| -3045 (-619 (-217))))) + (-2 (|:| |lfn| (-619 (-307 (-217)))) (|:| -3046 (-619 (-217))))) (-5 *1 (-812)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-307 (-217))) (|:| -3045 (-619 (-217))) + (-2 (|:| |fn| (-307 (-217))) (|:| -3046 (-619 (-217))) (|:| |lb| (-619 (-814 (-217)))) (|:| |cf| (-619 (-307 (-217)))) (|:| |ub| (-619 (-814 (-217)))))) (-5 *1 (-812)))) @@ -2864,36 +2814,94 @@ (-5 *1 (-1238 *3 *4)))) ((*1 *1 *2) (-12 (-5 *1 (-1241 *3 *2)) (-4 *3 (-1016)) (-4 *2 (-817))))) -(((*1 *2 *3) - (-12 (-5 *2 (-409 (-1131 *1))) (-5 *1 (-307 *4)) (-5 *3 (-1131 *1)) - (-4 *4 (-442)) (-4 *4 (-539)) (-4 *4 (-821)))) - ((*1 *2 *3) - (-12 (-4 *1 (-878)) (-5 *2 (-409 (-1131 *1))) (-5 *3 (-1131 *1))))) -(((*1 *2 *2 *1) (-12 (-4 *1 (-245 *2)) (-4 *2 (-1172))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-354) (-10 -8 (-15 ** ($ $ (-398 (-547))))))) - (-5 *2 (-619 *4)) (-5 *1 (-1090 *3 *4)) (-4 *3 (-1194 *4)))) - ((*1 *2 *3 *3 *3 *3 *3) - (-12 (-4 *3 (-13 (-354) (-10 -8 (-15 ** ($ $ (-398 (-547))))))) - (-5 *2 (-619 *3)) (-5 *1 (-1090 *4 *3)) (-4 *4 (-1194 *3))))) -(((*1 *2 *1 *2) (-12 (-5 *2 (-619 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*1 (-938 *4 *3)) + (-4 *3 (-1194 *4))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-217)) (-5 *4 (-547)) (-5 *2 (-1004)) (-5 *1 (-733))))) +(((*1 *1 *2) + (-12 + (-5 *2 + (-619 + (-2 + (|:| -3327 + (-2 (|:| |var| (-1135)) (|:| |fn| (-307 (-217))) + (|:| -2905 (-1058 (-814 (-217)))) (|:| |abserr| (-217)) + (|:| |relerr| (-217)))) + (|:| -1778 + (-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| (-1116 (-217))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -2905 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated")))))))) + (-5 *1 (-542))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-745)) (-5 *3 (-912 *4)) (-4 *1 (-1096 *4)) + (-4 *4 (-1016)))) + ((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-745)) (-5 *4 (-912 (-217))) (-5 *2 (-1223)) + (-5 *1 (-1220))))) (((*1 *1 *1) (-5 *1 (-112)))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-619 (-2 (|:| |val| (-619 *8)) (|:| -1965 *9)))) + (-12 (-5 *3 (-619 (-2 (|:| |val| (-619 *8)) (|:| -1966 *9)))) (-5 *4 (-745)) (-4 *8 (-1030 *5 *6 *7)) (-4 *9 (-1036 *5 *6 *7 *8)) (-4 *5 (-442)) (-4 *6 (-767)) (-4 *7 (-821)) (-5 *2 (-1223)) (-5 *1 (-1034 *5 *6 *7 *8 *9)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-619 (-2 (|:| |val| (-619 *8)) (|:| -1965 *9)))) + (-12 (-5 *3 (-619 (-2 (|:| |val| (-619 *8)) (|:| -1966 *9)))) (-5 *4 (-745)) (-4 *8 (-1030 *5 *6 *7)) (-4 *9 (-1072 *5 *6 *7 *8)) (-4 *5 (-442)) (-4 *6 (-767)) (-4 *7 (-821)) (-5 *2 (-1223)) (-5 *1 (-1105 *5 *6 *7 *8 *9))))) 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(-145))) + (-4 *4 (-13 (-29 *6) (-1157) (-928))) + (-5 *2 (-2 (|:| |particular| *4) (|:| -1352 (-619 *4)))) + (-5 *1 (-775 *6 *4 *3)) (-4 *3 (-630 *4))))) +(((*1 *2 *1) + (-12 + (-5 *2 + (-619 + (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *3) + (|:| |xpnt| (-547))))) + (-5 *1 (-409 *3)) (-4 *3 (-539)))) + ((*1 *2 *3 *4 *4 *4) + (-12 (-5 *4 (-745)) (-4 *3 (-340)) (-4 *5 (-1194 *3)) + (-5 *2 (-619 (-1131 *3))) (-5 *1 (-487 *3 *5 *6)) + (-4 *6 (-1194 *5))))) (((*1 *2 *1) (-12 (-4 *1 (-1066 *3 *4 *5 *6 *7)) (-4 *3 (-1063)) (-4 *4 (-1063)) (-4 *5 (-1063)) (-4 *6 (-1063)) (-4 *7 (-1063)) (-5 *2 (-112))))) +(((*1 *1 *1 *1) (-5 *1 (-832)))) +(((*1 *2 *1) + (-12 (-4 *1 (-1030 *3 *4 *5)) (-4 *3 (-1016)) (-4 *4 (-767)) + (-4 *5 (-821)) (-5 *2 (-112))))) +(((*1 *2 *2) + (-12 (-5 *2 (-1116 *3)) (-4 *3 (-1016)) (-5 *1 (-1120 *3)))) + ((*1 *1 *1) + (-12 (-5 *1 (-1210 *2 *3 *4)) (-4 *2 (-1016)) (-14 *3 (-1135)) + (-14 *4 *2)))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-619 *2)) (-5 *4 (-1 (-112) *2 *2)) (-5 *1 (-1173 *2)) + (-4 *2 (-1063)))) + ((*1 *2 *3) + (-12 (-5 *3 (-619 *2)) (-4 *2 (-1063)) (-4 *2 (-821)) + (-5 *1 (-1173 *2))))) +(((*1 *1 *1 *1) + (-12 (-4 *1 (-661 *2 *3 *4)) (-4 *2 (-1016)) (-4 *3 (-364 *2)) + (-4 *4 (-364 *2))))) +(((*1 *2 *3) + (-12 (-4 *4 (-539)) (-5 *2 (-619 *3)) (-5 *1 (-43 *4 *3)) + (-4 *3 (-408 *4))))) (((*1 *2 *3 *4 *4 *5 *6) (-12 (-5 *3 (-619 (-619 (-912 (-217))))) (-5 *4 (-843)) (-5 *5 (-890)) (-5 *6 (-619 (-254))) (-5 *2 (-1219)) @@ -3330,46 +3317,7 @@ ((*1 *2 *3 *4) (-12 (-5 *3 (-619 (-619 (-912 (-217))))) (-5 *4 (-619 (-254))) (-5 *2 (-1219)) (-5 *1 (-1222))))) -(((*1 *1 *2) (-12 (-5 *2 (-398 (-547))) (-5 *1 (-107)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-619 (-523))) (-5 *1 (-523))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-547)) (-5 *1 (-470))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1218 *1)) (-4 *1 (-361 *4 *5)) (-4 *4 (-169)) - (-4 *5 (-1194 *4)) (-5 *2 (-663 *4)))) - ((*1 *2) - (-12 (-4 *4 (-169)) (-4 *5 (-1194 *4)) (-5 *2 (-663 *4)) - (-5 *1 (-399 *3 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*3 (-1063))))) +(((*1 *1 *2) (-12 (-5 *2 (-547)) (-5 *1 (-832))))) (((*1 *1 *1) (-12 (-5 *1 (-651 *2)) (-4 *2 (-821)))) ((*1 *1 *1) (-12 (-5 *1 (-793 *2)) (-4 *2 (-821)))) ((*1 *1 *1) (-12 (-5 *1 (-862 *2)) (-4 *2 (-821)))) @@ -3744,39 +3725,35 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-745)) (-4 *1 (-1206 *3)) (-4 *3 (-1172)))) ((*1 *1 *1) (-12 (-4 *1 (-1206 *2)) (-4 *2 (-1172))))) -(((*1 *2 *3) - (-12 (-4 *4 (-821)) (-5 *2 (-1144 (-619 *4))) (-5 *1 (-1143 *4)) - (-5 *3 (-619 *4))))) -(((*1 *1 *1) (-4 *1 (-1025))) - ((*1 *1 *1 *2 *2) - (-12 (-4 *1 (-1196 *3 *2)) (-4 *3 (-1016)) (-4 *2 (-766)))) - ((*1 *1 *1 *2) - (-12 (-4 *1 (-1196 *3 *2)) (-4 *3 (-1016)) (-4 *2 (-766))))) (((*1 *2 *1) (-12 (-4 *3 (-1063)) (-4 *4 (-13 (-1016) (-855 *3) (-821) (-592 *2))) (-5 *2 (-861 *3)) (-5 *1 (-1039 *3 *4 *5)) (-4 *5 (-13 (-421 *4) (-855 *3) (-592 *2)))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-619 (-834 *5))) (-14 *5 (-619 (-1135))) (-4 *6 (-442)) - (-5 *2 - (-2 (|:| |dpolys| (-619 (-239 *5 *6))) - (|:| |coords| (-619 (-547))))) - (-5 *1 (-461 *5 *6 *7)) (-5 *3 (-619 (-239 *5 *6))) (-4 *7 (-442))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1096 *3)) (-4 *3 (-1016)) (-5 *2 (-1124 3 *3)))) + ((*1 *1) (-12 (-5 *1 (-1124 *2 *3)) (-14 *2 (-890)) (-4 *3 (-1016)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-1095 (-217))) (-5 *1 (-1220)))) + ((*1 *2 *1) (-12 (-5 *2 (-1095 (-217))) (-5 *1 (-1220))))) +(((*1 *1 *1 *2) + (-12 (-5 *1 (-574 *2)) (-4 *2 (-38 (-398 (-547)))) (-4 *2 (-1016))))) +(((*1 *2 *3) (-12 (-5 *3 (-398 (-547))) (-5 *2 (-217)) (-5 *1 (-296))))) +(((*1 *2 *3) (-12 (-5 *3 (-745)) (-5 *2 (-370)) (-5 *1 (-1009))))) +(((*1 *2 *2 *1) (-12 (-4 *1 (-245 *2)) (-4 *2 (-1172))))) (((*1 *2 *3) - (-12 (-5 *2 (-1131 (-547))) (-5 *1 (-911)) (-5 *3 (-547))))) -(((*1 *2 *3 *3 *3 *3 *4 *4 *4 *5) - (-12 (-5 *3 (-217)) (-5 *4 (-547)) - (-5 *5 (-3 (|:| |fn| (-379)) (|:| |fp| (-63 -1409)))) - (-5 *2 (-1004)) (-5 *1 (-723))))) -(((*1 *2 *3) (-12 (-5 *3 (-370)) (-5 *2 (-1118)) (-5 *1 (-296))))) + (-12 (-5 *3 (-1135)) (-5 *2 (-1 *6 *5)) (-5 *1 (-681 *4 *5 *6)) + (-4 *4 (-592 (-523))) (-4 *5 (-1172)) (-4 *6 (-1172))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-890)) (-5 *3 (-619 (-254))) (-5 *1 (-252)))) + ((*1 *1 *2) (-12 (-5 *2 (-890)) (-5 *1 (-254))))) (((*1 *2 *1) - (-12 (-4 *3 (-354)) (-4 *4 (-1194 *3)) (-4 *5 (-1194 (-398 *4))) - (-5 *2 (-1218 *6)) (-5 *1 (-327 *3 *4 *5 *6)) - (-4 *6 (-333 *3 *4 *5))))) -(((*1 *1 *1) - (-12 (-4 *1 (-661 *2 *3 *4)) (-4 *2 (-1016)) (-4 *3 (-364 *2)) - (-4 *4 (-364 *2))))) -(((*1 *2 *1) (-12 (-5 *2 (-1118)) (-5 *1 (-523))))) + (-12 (-5 *2 (-619 (-2 (|:| |k| (-1135)) (|:| |c| (-1240 *3))))) + (-5 *1 (-1240 *3)) (-4 *3 (-1016)))) + ((*1 *2 *1) + (-12 (-5 *2 (-619 (-2 (|:| |k| *3) (|:| |c| (-1242 *3 *4))))) + (-5 *1 (-1242 *3 *4)) (-4 *3 (-821)) (-4 *4 (-1016))))) +(((*1 *1 *1) (-12 (-4 *1 (-964 *2)) (-4 *2 (-1172))))) +(((*1 *2 *3) (-12 (-5 *3 (-370)) (-5 *2 (-217)) (-5 *1 (-1221)))) + ((*1 *2) (-12 (-5 *2 (-217)) (-5 *1 (-1221))))) (((*1 *2 *1) (-12 (-4 *1 (-582 *3 *2)) (-4 *3 (-1063)) (-4 *3 (-821)) (-4 *2 (-1172)))) @@ -3791,37 +3768,57 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-745)) (-4 *1 (-1206 *3)) (-4 *3 (-1172)))) ((*1 *2 *1) (-12 (-4 *1 (-1206 *2)) (-4 *2 (-1172))))) -(((*1 *2 *1) (-12 (-5 *2 (-1223)) (-5 *1 (-796))))) -(((*1 *2 *1) - (-12 (-5 *2 (-619 (-52))) (-5 *1 (-861 *3)) (-4 *3 (-1063))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-663 (-398 (-921 (-547))))) + (-5 *2 (-619 (-663 (-307 (-547))))) (-5 *1 (-1000)) + (-5 *3 (-307 (-547)))))) (((*1 *2 *3) - (-12 (-5 *2 (-166 *4)) (-5 *1 (-177 *4 *3)) - (-4 *4 (-13 (-354) (-819))) (-4 *3 (-1194 *2))))) -(((*1 *2 *3 *3 *4 *5) - (-12 (-5 *3 (-1118)) (-4 *6 (-442)) (-4 *7 (-767)) (-4 *8 (-821)) - (-4 *4 (-1030 *6 *7 *8)) (-5 *2 (-1223)) - (-5 *1 (-750 *6 *7 *8 *4 *5)) (-4 *5 (-1036 *6 *7 *8 *4))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-425))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-1191 *5 *4)) (-4 *4 (-794)) (-14 *5 (-1135)) - (-5 *2 (-547)) (-5 *1 (-1077 *4 *5))))) -(((*1 *2 *3) (-12 (-5 *3 (-832)) (-5 *2 (-1223)) (-5 *1 (-1098)))) + (-12 (-5 *3 (-1218 *1)) (-4 *1 (-358 *4)) (-4 *4 (-169)) + (-5 *2 (-619 (-921 *4))))) + ((*1 *2) + (-12 (-4 *4 (-169)) (-5 *2 (-619 (-921 *4))) (-5 *1 (-407 *3 *4)) + (-4 *3 (-408 *4)))) + ((*1 *2) + (-12 (-4 *1 (-408 *3)) (-4 *3 (-169)) (-5 *2 (-619 (-921 *3))))) + ((*1 *2) + (-12 (-5 *2 (-619 (-921 *3))) (-5 *1 (-443 *3 *4 *5 *6)) + (-4 *3 (-539)) (-4 *3 (-169)) (-14 *4 (-890)) + (-14 *5 (-619 (-1135))) (-14 *6 (-1218 (-663 *3))))) ((*1 *2 *3) - (-12 (-5 *3 (-619 (-832))) (-5 *2 (-1223)) (-5 *1 (-1098))))) + (-12 (-5 *3 (-1218 (-443 *4 *5 *6 *7))) (-5 *2 (-619 (-921 *4))) + (-5 *1 (-443 *4 *5 *6 *7)) (-4 *4 (-539)) (-4 *4 (-169)) + (-14 *5 (-890)) (-14 *6 (-619 (-1135))) (-14 *7 (-1218 (-663 *4)))))) +(((*1 *2 *2) + (-12 (-5 *2 (-619 (-619 *3))) (-4 *3 (-821)) (-5 *1 (-1143 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-565 *3)) (-4 *3 (-354))))) +(((*1 *2 *1) + (-12 (-14 *3 (-619 (-1135))) (-4 *4 (-169)) + (-14 *6 + (-1 (-112) (-2 (|:| -3481 *5) (|:| -1973 *2)) + (-2 (|:| -3481 *5) (|:| -1973 *2)))) + (-4 *2 (-230 (-3764 *3) (-745))) (-5 *1 (-451 *3 *4 *5 *2 *6 *7)) + (-4 *5 (-821)) (-4 *7 (-918 *4 *2 (-834 *3)))))) +(((*1 *2 *3) + (-12 (-4 *4 (-340)) (-5 *2 (-409 (-1131 (-1131 *4)))) + (-5 *1 (-1170 *4)) (-5 *3 (-1131 (-1131 *4)))))) (((*1 *2 *1) (-12 (-4 *3 (-1063)) (-4 *4 (-13 (-1016) (-855 *3) (-821) (-592 (-861 *3)))) (-5 *2 (-619 (-1039 *3 *4 *5))) (-5 *1 (-1040 *3 *4 *5)) (-4 *5 (-13 (-421 *4) (-855 *3) (-592 (-861 *3))))))) -(((*1 *2 *2) (-12 (-5 *2 (-619 *3)) (-4 *3 (-819)) (-5 *1 (-294 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-745)) (-5 *2 (-1 (-1116 (-921 *4)) (-1116 (-921 *4)))) - (-5 *1 (-1226 *4)) (-4 *4 (-354))))) (((*1 *2 *1) - (-12 (-4 *1 (-945 *3 *4 *5 *6)) (-4 *3 (-1016)) (-4 *4 (-767)) - (-4 *5 (-821)) (-4 *6 (-1030 *3 *4 *5)) (-5 *2 (-619 *5))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-952 *2)) (-4 *2 (-1157))))) -(((*1 *2 *1) (-12 (-4 *1 (-245 *2)) (-4 *2 (-1172))))) + (-12 (-5 *2 (-1116 (-547))) (-5 *1 (-973 *3)) (-14 *3 (-547))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-619 *5)) (-5 *4 (-890)) (-4 *5 (-821)) + (-5 *2 (-58 (-619 (-646 *5)))) (-5 *1 (-646 *5))))) +(((*1 *2 *2) (-12 (-5 *2 (-547)) (-5 *1 (-536))))) +(((*1 *2 *3 *3 *3 *4 *5 *3 *6) + (-12 (-5 *3 (-547)) (-5 *4 (-663 (-217))) (-5 *5 (-217)) + (-5 *6 (-3 (|:| |fn| (-379)) (|:| |fp| (-73 FCN)))) (-5 *2 (-1004)) + (-5 *1 (-721))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-821) (-539))) (-5 *1 (-267 *3 *2)) + (-4 *2 (-13 (-421 *3) (-971)))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-821) (-539))) (-5 *1 (-267 *3 *2)) (-4 *2 (-13 (-421 *3) (-971))))) @@ -3834,7 +3831,7 @@ ((*1 *1 *1) (-4 *1 (-275))) ((*1 *2 *3) (-12 (-5 *3 (-409 *4)) (-4 *4 (-539)) - (-5 *2 (-619 (-2 (|:| -1557 (-745)) (|:| |logand| *4)))) + (-5 *2 (-619 (-2 (|:| -1558 (-745)) (|:| |logand| *4)))) (-5 *1 (-311 *4)))) ((*1 *1 *1) (-12 (-5 *1 (-330 *2 *3 *4)) (-14 *2 (-619 (-1135))) @@ -3854,80 +3851,62 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-745)) (-5 *1 (-1238 *3 *4)) (-4 *4 (-692 (-398 (-547)))) (-4 *3 (-821)) (-4 *4 (-169))))) -(((*1 *2 *1) (-12 (-5 *2 (-1118)) (-5 *1 (-1153))))) -(((*1 *2 *3 *3 *3 *4 *5 *5 *3) - (-12 (-5 *3 (-547)) (-5 *5 (-663 (-217))) (-5 *4 (-217)) - (-5 *2 (-1004)) (-5 *1 (-727))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-890)) (-5 *2 (-1223)) (-5 *1 (-206 *4)) - (-4 *4 - (-13 (-821) - (-10 -8 (-15 -3329 ((-1118) $ (-1135))) (-15 -2683 (*2 $)) - (-15 -3617 (*2 $))))))) - ((*1 *2 *1) - (-12 (-5 *2 (-1223)) (-5 *1 (-206 *3)) - (-4 *3 - (-13 (-821) - (-10 -8 (-15 -3329 ((-1118) $ (-1135))) (-15 -2683 (*2 $)) - (-15 -3617 (*2 $))))))) - ((*1 *2 *1) (-12 (-5 *2 (-1223)) (-5 *1 (-491))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-217)) (-5 *4 (-547)) (-5 *2 (-1004)) (-5 *1 (-733))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1118)) (-5 *2 (-1223)) (-5 *1 (-1220))))) (((*1 *2 *3) - (-12 (-4 *4 (-38 (-398 (-547)))) - (-5 *2 (-2 (|:| -1624 (-1116 *4)) (|:| -1635 (-1116 *4)))) - (-5 *1 (-1122 *4)) (-5 *3 (-1116 *4))))) + (-12 (-5 *2 (-1116 (-547))) (-5 *1 (-1120 *4)) (-4 *4 (-1016)) + (-5 *3 (-547))))) +(((*1 *1 *2) (-12 (-5 *2 (-619 (-832))) (-5 *1 (-832)))) + ((*1 *1 *1 *1) (-5 *1 (-832)))) (((*1 *2 *2) - (-12 (-4 *3 (-13 (-298) (-145))) (-4 *4 (-13 (-821) (-592 (-1135)))) - (-4 *5 (-767)) (-5 *1 (-893 *3 *4 *5 *2)) (-4 *2 (-918 *3 *5 *4))))) -(((*1 *2 *2) (-12 (-5 *2 (-547)) (-5 *1 (-544))))) -(((*1 *2 *2 *3 *3) - (|partial| -12 (-5 *3 (-1135)) - (-4 *4 (-13 (-298) (-821) (-145) (-1007 (-547)) (-615 (-547)))) - (-5 *1 (-558 *4 *2)) - (-4 *2 (-13 (-1157) (-928) (-1099) (-29 *4)))))) -(((*1 *1) (-5 *1 (-797)))) -(((*1 *2 *3) - (-12 (-5 *3 (-663 (-307 (-217)))) (-5 *2 (-370)) (-5 *1 (-197))))) + (-12 (-4 *2 (-13 (-354) (-819))) (-5 *1 (-177 *2 *3)) + (-4 *3 (-1194 (-166 *2)))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1201 *3 *4)) (-4 *3 (-1016)) (-4 *4 (-1178 *3)) + (-5 *2 (-398 (-547)))))) (((*1 *2 *3) - (-12 (-5 *2 (-547)) (-5 *1 (-435 *3)) (-4 *3 (-395)) (-4 *3 (-1016))))) -(((*1 *1 *2 *3 *4) - (-12 (-14 *5 (-619 (-1135))) (-4 *2 (-169)) - (-4 *4 (-230 (-3763 *5) (-745))) - (-14 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(-5 *1 (-733))))) +(((*1 *2 *3 *4 *4) + (-12 (-5 *4 (-745)) (-4 *5 (-340)) (-4 *6 (-1194 *5)) + (-5 *2 + (-619 + (-2 (|:| -1352 (-663 *6)) (|:| |basisDen| *6) + (|:| |basisInv| (-663 *6))))) + (-5 *1 (-487 *5 *6 *7)) + (-5 *3 + (-2 (|:| -1352 (-663 *6)) (|:| |basisDen| *6) + (|:| |basisInv| (-663 *6)))) + (-4 *7 (-1194 *6))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1030 *3 *4 *5)) (-4 *3 (-1016)) (-4 *4 (-767)) + (-4 *5 (-821)) (-5 *2 (-745))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-547)) (-5 *1 (-544)))) ((*1 *2 *3) - (-12 (-5 *3 (-619 *2)) (-4 *2 (-918 *6 *4 *5)) - (-5 *1 (-885 *4 *5 *6 *2)) (-4 *4 (-767)) (-4 *5 (-821)) - (-4 *6 (-298))))) -(((*1 *2 *3 *4 *5 *6 *5 *3 *7) - (-12 (-5 *4 (-547)) - (-5 *6 - (-2 (|:| |try| (-370)) (|:| |did| (-370)) (|:| -3027 (-370)))) - (-5 *7 (-1 (-1223) (-1218 *5) (-1218 *5) (-370))) - (-5 *3 (-1218 (-370))) (-5 *5 (-370)) (-5 *2 (-1223)) - (-5 *1 (-762)))) - ((*1 *2 *3 *4 *5 *6 *5 *3 *7 *3 *3 *3 *3 *3 *3 *3) - (-12 (-5 *4 (-547)) - (-5 *6 - (-2 (|:| |try| (-370)) (|:| |did| (-370)) (|:| -3027 (-370)))) - (-5 *7 (-1 (-1223) (-1218 *5) (-1218 *5) (-370))) - (-5 *3 (-1218 (-370))) (-5 *5 (-370)) (-5 *2 (-1223)) - (-5 *1 (-762))))) -(((*1 *2 *3 *1) - (-12 (-4 *4 (-442)) (-4 *5 (-767)) (-4 *6 (-821)) - (-4 *3 (-1030 *4 *5 *6)) (-5 *2 (-3 (-112) (-619 *1))) - (-4 *1 (-1036 *4 *5 *6 *3))))) + (-12 (-5 *2 (-1131 (-398 (-547)))) (-5 *1 (-911)) (-5 *3 (-547))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-1135)) (-5 *2 (-1 (-217) (-217))) (-5 *1 (-678 *3)) + (-4 *3 (-592 (-523))))) + ((*1 *2 *3 *4 *4) + (-12 (-5 *4 (-1135)) (-5 *2 (-1 (-217) (-217) (-217))) + (-5 *1 (-678 *3)) (-4 *3 (-592 (-523)))))) +(((*1 *2 *3) + (-12 (-4 *4 (-539)) (-4 *5 (-767)) (-4 *6 (-821)) (-5 *2 (-112)) + (-5 *1 (-946 *4 *5 *6 *3)) (-4 *3 (-1030 *4 *5 *6))))) +(((*1 *1 *2) + (-12 (-5 *2 (-619 (-619 *3))) (-4 *3 (-1063)) (-5 *1 (-1144 *3))))) +(((*1 *1 *1 *1 *2 *3) + (-12 (-5 *2 (-912 *5)) (-5 *3 (-745)) (-4 *5 (-1016)) + (-5 *1 (-1124 *4 *5)) (-14 *4 (-890))))) (((*1 *2) (-12 (-14 *4 *2) 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(-1172))))) +(((*1 *1 *1 *1 *2) + (-12 (-4 *1 (-918 *3 *4 *2)) (-4 *3 (-1016)) (-4 *4 (-767)) + (-4 *2 (-821)) (-4 *3 (-169)))) + ((*1 *2 *3 *3) + (-12 (-4 *2 (-539)) (-5 *1 (-938 *2 *3)) (-4 *3 (-1194 *2)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1030 *2 *3 *4)) (-4 *2 (-1016)) (-4 *3 (-767)) + (-4 *4 (-821)) (-4 *2 (-539)))) + ((*1 *2 *1 *1) + (-12 (-4 *1 (-1194 *2)) (-4 *2 (-1016)) (-4 *2 (-169))))) (((*1 *2 *1) - (-12 (-4 *3 (-354)) (-4 *4 (-767)) (-4 *5 (-821)) (-5 *2 (-112)) - (-5 *1 (-493 *3 *4 *5 *6)) (-4 *6 (-918 *3 *4 *5))))) -(((*1 *2 *2 *3) - (-12 (-4 *3 (-354)) (-5 *1 (-276 *3 *2)) (-4 *2 (-1209 *3))))) + (-12 (-5 *2 (-1065 (-1065 *3))) (-5 *1 (-873 *3)) (-4 *3 (-1063))))) (((*1 *2 *3 *4 *5) (-12 (-5 *5 (-1058 *3)) (-4 *3 (-918 *7 *6 *4)) (-4 *6 (-767)) (-4 *4 (-821)) (-4 *7 (-539)) @@ -8120,99 +8021,63 @@ (-12 (-5 *4 (-1056 (-398 (-921 *5)))) (-5 *3 (-398 (-921 *5))) (-4 *5 (-13 (-539) (-821) (-1007 (-547)))) (-5 *2 (-3 *3 (-307 *5))) (-5 *1 (-1128 *5))))) -(((*1 *2 *1 *1) - 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+ (-12 + (-5 *3 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1116 (-217))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -2905 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))) + (-5 *2 (-1004)) (-5 *1 (-296))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-1 *5 *6 *5)) (-5 *4 (-58 *6)) (-4 *6 (-1172)) + (-4 *5 (-1172)) (-5 *2 (-58 *5)) (-5 *1 (-57 *6 *5)))) + ((*1 *2 *3 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*2 *1 *3) (-12 (-4 *1 (-1196 *2 *3)) (-4 *3 (-766)) - (|has| *2 (-15 ** (*2 *2 *3))) (|has| *2 (-15 -3834 (*2 (-1135)))) + (|has| *2 (-15 ** (*2 *2 *3))) (|has| *2 (-15 -3835 (*2 (-1135)))) (-4 *2 (-1016))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1030 *3 *4 *5)) (-4 *3 (-1016)) (-4 *4 (-767)) - (-4 *5 (-821)) (-5 *2 (-745))))) +(((*1 *1 *1) (-12 (-5 *1 (-883 *2)) (-4 *2 (-298))))) (((*1 *2 *3) (-12 (-5 *3 (-52)) (-5 *1 (-51 *2)) (-4 *2 (-1172)))) ((*1 *1 *2) (-12 (-5 *2 (-921 (-370))) (-5 *1 (-330 *3 *4 *5)) @@ -9431,11 +9509,11 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1135)) (|:| |fn| (-307 (-217))) - (|:| -2693 (-1058 (-814 (-217)))) (|:| |abserr| (-217)) + (|:| -2905 (-1058 (-814 (-217)))) (|:| |abserr| (-217)) (|:| |relerr| (-217)))) (|:| |mdnia| (-2 (|:| |fn| (-307 (-217))) - (|:| -2693 (-619 (-1058 (-814 (-217))))) + (|:| -2905 (-619 (-1058 (-814 (-217))))) (|:| |abserr| (-217)) (|:| |relerr| (-217)))))) (-5 *1 (-743)))) ((*1 *2 *1) @@ -9451,13 +9529,13 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| 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- (|:| -2483 (-619 (-2 (|:| |irr| *3) (|:| -1889 (-547))))))) - (-5 *1 (-208 *5 *3)) (-4 *3 (-1194 *5))))) +(((*1 *1 *1) (-5 *1 (-1028)))) +(((*1 *2 *3) + (-12 (-5 *3 (-890)) (-5 *2 (-1131 *4)) (-5 *1 (-348 *4)) + (-4 *4 (-340))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1058 (-814 (-217)))) (-5 *2 (-217)) (-5 *1 (-184)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1058 (-814 (-217)))) (-5 *2 (-217)) (-5 *1 (-291)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1058 (-814 (-217)))) (-5 *2 (-217)) (-5 *1 (-296))))) (((*1 *2 *1) (-12 (-5 *2 (-1140)) (-5 *1 (-31)))) ((*1 *2 *1) (-12 (-5 *2 (-1140)) (-5 *1 (-49)))) ((*1 *2 *1) (-12 (-5 *2 (-619 (-1140))) (-5 *1 (-132)))) @@ -10449,47 +10522,34 @@ ((*1 *2 *1) (-12 (-5 *2 (-1140)) (-5 *1 (-650)))) ((*1 *2 *1) (-12 (-5 *2 (-1140)) (-5 *1 (-988)))) ((*1 *2 *1) (-12 (-5 *2 (-1140)) (-5 *1 (-1031))))) -(((*1 *2 *3 *3 *3 *4 *4 *3) - (-12 (-5 *3 (-547)) (-5 *4 (-663 (-217))) (-5 *2 (-1004)) - (-5 *1 (-730))))) -(((*1 *2 *3) - (-12 (-4 *4 (-539)) (-4 *5 (-767)) (-4 *6 (-821)) - (-4 *7 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*2) (-12 (-5 *2 (-1223)) (-5 *1 (-1221))))) (((*1 *1 *1 *1) (-4 *1 (-25))) ((*1 *1 *1 *1) (-5 *1 (-154))) ((*1 *1 *1 *1) (-12 (-5 *1 (-206 *2)) (-4 *2 (-13 (-821) - (-10 -8 (-15 -3329 ((-1118) $ (-1135))) (-15 -2683 ((-1223) $)) - (-15 -3617 ((-1223) $))))))) + (-10 -8 (-15 -3330 ((-1118) $ (-1135))) (-15 -2684 ((-1223) $)) + (-15 -1884 ((-1223) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-285 *2)) (-4 *2 (-25)) (-4 *2 (-1172)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-285 *2)) (-4 *2 (-25)) (-4 *2 (-1172)))) ((*1 *1 *2 *1) @@ -10512,65 +10572,26 @@ (-12 (-5 *2 (-1116 *3)) (-4 *3 (-1016)) (-5 *1 (-1120 *3)))) ((*1 *2 *2 *2) (-12 (-5 *2 (-912 (-217))) (-5 *1 (-1168)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1216 *2)) (-4 *2 (-1172)) (-4 *2 (-25))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1165 *3 *4 *5 *6)) (-4 *3 (-539)) (-4 *4 (-767)) - (-4 *5 (-821)) (-4 *6 (-1030 *3 *4 *5)) (-5 *2 (-112)))) - ((*1 *2 *3 *1) - (-12 (-4 *1 (-1165 *4 *5 *6 *3)) (-4 *4 (-539)) (-4 *5 (-767)) - (-4 *6 (-821)) (-4 *3 (-1030 *4 *5 *6)) (-5 *2 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(-4 *7 (-821)) + (-4 *8 (-1030 *5 *6 *7)) (-5 *2 (-112)) + (-5 *1 (-570 *5 *6 *7 *8 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-619 (-619 (-217)))) (-5 *1 (-895))))) (((*1 *1 *1) (-12 (-4 *1 (-244 *2 *3 *4 *5)) (-4 *2 (-1016)) (-4 *3 (-821)) (-4 *4 (-257 *3)) (-4 *5 (-767))))) -(((*1 *2 *2) (-12 (-5 *2 (-217)) (-5 *1 (-218)))) - ((*1 *2 *2) (-12 (-5 *2 (-166 (-217))) (-5 *1 (-218))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1218 *6)) (-5 *4 (-1218 (-547))) (-5 *5 (-547)) - (-4 *6 (-1063)) (-5 *2 (-1 *6)) (-5 *1 (-986 *6))))) -(((*1 *2) - (-12 (-4 *3 (-539)) (-5 *2 (-619 *4)) (-5 *1 (-43 *3 *4)) - (-4 *4 (-408 *3))))) (((*1 *2 *1 *3 *3 *2) (-12 (-5 *3 (-547)) (-4 *1 (-56 *2 *4 *5)) (-4 *2 (-1172)) (-4 *4 (-364 *2)) (-4 *5 (-364 *2)))) @@ -11724,78 +11739,51 @@ ((*1 *2 *1 *3 *2) (-12 (-5 *3 "first") (|has| *1 (-6 -4329)) (-4 *1 (-1206 *2)) (-4 *2 (-1172))))) -(((*1 *2 *3 *2 *4) - (|partial| -12 (-5 *4 (-1 (-3 (-547) "failed") *5)) (-4 *5 (-1016)) - (-5 *2 (-547)) (-5 *1 (-530 *5 *3)) (-4 *3 (-1194 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(-354)) (-14 *5 (-962 *4 *2)))) ((*1 *1 *2 *3) (-12 (-5 *3 (-688 *5 *6 *7)) (-4 *5 (-821)) - (-4 *6 (-230 (-3763 *4) (-745))) + (-4 *6 (-230 (-3764 *4) (-745))) (-14 *7 - (-1 (-112) (-2 (|:| -3479 *5) (|:| -4248 *6)) - (-2 (|:| -3479 *5) (|:| -4248 *6)))) + (-1 (-112) (-2 (|:| -3481 *5) (|:| -1973 *6)) + (-2 (|:| -3481 *5) (|:| -1973 *6)))) (-14 *4 (-619 (-1135))) (-4 *2 (-169)) (-5 *1 (-451 *4 *2 *5 *6 *7 *8)) (-4 *8 (-918 *2 *6 (-834 *4))))) ((*1 *1 *2 *3) @@ -11836,205 +11824,150 @@ ((*1 *1 *1 *2 *3) (-12 (-4 *1 (-942 *4 *3 *2)) (-4 *4 (-1016)) (-4 *3 (-766)) (-4 *2 (-821))))) -(((*1 *2 *1) (-12 (-4 *1 (-771 *2)) (-4 *2 (-169)))) - ((*1 *2 *1) (-12 (-4 *1 (-966 *2)) (-4 *2 (-169))))) -(((*1 *2 *3) - (-12 (-5 *3 (-619 *4)) (-4 *4 (-354)) (-5 *2 (-663 *4)) - (-5 *1 (-788 *4 *5)) (-4 *5 (-630 *4)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-619 *5)) (-5 *4 (-745)) (-4 *5 (-354)) - (-5 *2 (-663 *5)) (-5 *1 (-788 *5 *6)) (-4 *6 (-630 *5))))) -(((*1 *2 *3 *3) - (|partial| -12 (-4 *4 (-539)) - (-5 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(-821) (-1007 (-547)))) (-5 *2 (-307 *4)) @@ -12319,63 +12193,89 @@ ((*1 *2 *2) (-12 (-4 *3 (-13 (-442) (-821) (-1007 (-547)) (-615 (-547)))) (-5 *1 (-1161 *3 *2)) (-4 *2 (-13 (-27) (-1157) (-421 *3)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-890)) (-5 *2 (-1131 *4)) (-5 *1 (-348 *4)) - (-4 *4 (-340))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-1 (-112) *7 (-619 *7))) (-4 *1 (-1165 *4 *5 *6 *7)) - (-4 *4 (-539)) (-4 *5 (-767)) (-4 *6 (-821)) - (-4 *7 (-1030 *4 *5 *6)) (-5 *2 (-112))))) -(((*1 *2 *3 *4 *4) - (-12 (-5 *4 (-1135)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-676 *3 *5 *6 *7)) - (-4 *3 (-592 (-523))) (-4 *5 (-1172)) (-4 *6 (-1172)) - (-4 *7 (-1172)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-1135)) (-5 *2 (-1 *6 *5)) (-5 *1 (-681 *3 *5 *6)) - (-4 *3 (-592 (-523))) (-4 *5 (-1172)) (-4 *6 (-1172))))) -(((*1 *2 *2 *3 *4) - (|partial| -12 (-5 *4 (-1 *3)) (-4 *3 (-821)) (-4 *5 (-767)) - (-4 *6 (-539)) (-4 *7 (-918 *6 *5 *3)) - (-5 *1 (-452 *5 *3 *6 *7 *2)) - (-4 *2 - (-13 (-1007 (-398 (-547))) (-354) - (-10 -8 (-15 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(-12 (-4 *3 (-13 (-354) (-359) (-592 (-547)))) (-4 *4 (-1194 *3)) + (-4 *5 (-699 *3 *4)) (-5 *1 (-528 *3 *4 *5 *2)) (-4 *2 (-1209 *5)))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-354) (-359) (-592 (-547)))) (-5 *1 (-529 *3 *2)) + (-4 *2 (-1209 *3)))) + ((*1 *2 *2) + (-12 (-5 *2 (-1116 *3)) (-4 *3 (-13 (-539) (-145))) + (-5 *1 (-1112 *3))))) +(((*1 *2 *2 *2) + (-12 (-4 *3 (-354)) (-5 *1 (-741 *2 *3)) (-4 *2 (-683 *3)))) + ((*1 *1 *1 *1) (-12 (-4 *1 (-823 *2)) (-4 *2 (-1016)) (-4 *2 (-354))))) +(((*1 *2 *3) (-12 (-5 *3 (-912 *2)) (-5 *1 (-951 *2)) (-4 *2 (-1016))))) (((*1 *2 *1) (-12 (-4 *1 (-163 *2)) (-4 *2 (-169)))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-539) (-821) (-1007 (-547)))) (-5 *2 (-307 *4)) @@ -12385,36 +12285,35 @@ ((*1 *2 *2) (-12 (-4 *3 (-13 (-442) (-821) (-1007 (-547)) (-615 (-547)))) (-5 *1 (-1161 *3 *2)) (-4 *2 (-13 (-27) (-1157) (-421 *3)))))) -(((*1 *2 *1) - (-12 (-4 *1 (-373 *3 *4)) (-4 *3 (-1016)) (-4 *4 (-1063)) - (-5 *2 (-2 (|:| |k| *4) (|:| |c| *3)))))) -(((*1 *2) - (-12 (-4 *3 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(-1131 *1)) + (-4 *4 (-442)) (-4 *4 (-539)) (-4 *4 (-821)))) + ((*1 *2 *3) + (-12 (-4 *1 (-878)) (-5 *2 (-409 (-1131 *1))) (-5 *3 (-1131 *1))))) (((*1 *1 *1) (-12 (-5 *1 (-330 *2 *3 *4)) (-14 *2 (-619 (-1135))) (-14 *3 (-619 (-1135))) (-4 *4 (-378)))) @@ -12424,38 +12323,57 @@ ((*1 *1 *2) (-12 (-5 *2 (-398 (-547))) (-4 *1 (-981)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-981)) (-5 *2 (-890)))) ((*1 *1 *1) (-4 *1 (-981)))) -(((*1 *2) (-12 (-5 *2 (-1135)) (-5 *1 (-1138))))) -(((*1 *2 *1) (-12 (-4 *1 (-771 *2)) (-4 *2 (-169)))) - ((*1 *2 *1) (-12 (-4 *1 (-966 *2)) (-4 *2 (-169))))) -(((*1 *2 *3 *3 *4 *4) - (-12 (-5 *3 (-663 (-217))) (-5 *4 (-547)) (-5 *2 (-1004)) - (-5 *1 (-723))))) -(((*1 *2 *2) - (-12 (-5 *2 (-912 *3)) (-4 *3 (-13 (-354) (-1157) (-971))) - (-5 *1 (-173 *3))))) -(((*1 *2 *3 *4 *5 *6 *3 *3 *3 *3 *6 *3 *7 *8) - (-12 (-5 *3 (-547)) (-5 *4 (-663 (-217))) (-5 *5 (-112)) - (-5 *6 (-217)) (-5 *7 (-3 (|:| |fn| (-379)) (|:| |fp| (-67 APROD)))) - (-5 *8 (-3 (|:| |fn| (-379)) (|:| |fp| (-72 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*4 (-1 *7 *7)) + (-5 *5 + (-1 (-2 (|:| |ans| *6) (|:| -3837 *6) (|:| |sol?| (-112))) (-547) + *6)) + (-4 *6 (-354)) (-4 *7 (-1194 *6)) + (-5 *2 (-2 (|:| |answer| (-565 (-398 *7))) (|:| |a0| *6))) + (-5 *1 (-557 *6 *7)) (-5 *3 (-398 *7))))) +(((*1 *2 *2 *3 *2) + (-12 (-5 *3 (-745)) (-4 *4 (-340)) (-5 *1 (-208 *4 *2)) + (-4 *2 (-1194 *4))))) +(((*1 *1 *2) + (-12 (-5 *2 (-1233 (-1135) *3)) (-4 *3 (-1016)) (-5 *1 (-1240 *3)))) + ((*1 *1 *2) + (-12 (-5 *2 (-1233 *3 *4)) (-4 *3 (-821)) (-4 *4 (-1016)) + (-5 *1 (-1242 *3 *4))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1102 *4 *2)) (-14 *4 (-890)) + (-4 *2 (-13 (-1016) (-10 -7 (-6 (-4330 "*"))))) + (-5 *1 (-871 *4 *2))))) +(((*1 *2 *1) (-12 (-5 *2 (-619 (-1140))) (-5 *1 (-1054))))) +(((*1 *2 *3 *4 *5 *6 *7 *7 *8) + (-12 + (-5 *3 + (-2 (|:| |det| *12) (|:| |rows| (-619 (-547))) + (|:| |cols| (-619 (-547))))) + (-5 *4 (-663 *12)) (-5 *5 (-619 (-398 (-921 *9)))) + (-5 *6 (-619 (-619 *12))) (-5 *7 (-745)) (-5 *8 (-547)) + (-4 *9 (-13 (-298) (-145))) (-4 *12 (-918 *9 *11 *10)) + (-4 *10 (-13 (-821) (-592 (-1135)))) (-4 *11 (-767)) + (-5 *2 + (-2 (|:| |eqzro| (-619 *12)) (|:| |neqzro| (-619 *12)) + (|:| |wcond| (-619 (-921 *9))) + (|:| |bsoln| + (-2 (|:| |partsol| (-1218 (-398 (-921 *9)))) + (|:| -1352 (-619 (-1218 (-398 (-921 *9))))))))) + (-5 *1 (-893 *9 *10 *11 *12))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-547)) (|has| *1 (-6 -4329)) (-4 *1 (-1206 *3)) + (-4 *3 (-1172))))) +(((*1 *2 *3) + (-12 (-4 *4 (-13 (-354) (-1007 (-398 *2)))) (-5 *2 (-547)) + (-5 *1 (-115 *4 *3)) (-4 *3 (-1194 *4))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-547)) (-4 *1 (-1057 *3)) (-4 *3 (-1172))))) (((*1 *2 *3 *4) @@ -12506,8 +12424,8 @@ (-12 (-4 *4 (-13 (-821) - (-10 -8 (-15 -2829 ((-1135) $)) - (-15 -2995 ((-3 $ "failed") (-1135)))))) + (-10 -8 (-15 -2830 ((-1135) $)) + (-15 -2996 ((-3 $ "failed") (-1135)))))) (-4 *5 (-767)) (-4 *7 (-539)) (-5 *2 (-409 *3)) (-5 *1 (-446 *4 *5 *6 *7 *3)) (-4 *6 (-539)) (-4 *3 (-918 *7 *5 *4)))) @@ -12556,13 +12474,13 @@ (-12 (-4 *4 (-767)) 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(-1099)))) (((*1 *2 *2) - (-12 (-4 *3 (-539)) (-5 *1 (-41 *3 *2)) - (-4 *2 - (-13 (-354) (-293) - (-10 -8 (-15 -1382 ((-1087 *3 (-590 $)) $)) - (-15 -1392 ((-1087 *3 (-590 $)) $)) - (-15 -3834 ($ (-1087 *3 (-590 $)))))))))) -(((*1 *1 *1) (-12 (-4 *1 (-245 *2)) (-4 *2 (-1172)))) - ((*1 *1 *1) - (-12 (|has| *1 (-6 -4329)) (-4 *1 (-364 *2)) (-4 *2 (-1172)))) - ((*1 *1 *1) - (-12 (-5 *1 (-623 *2 *3 *4)) (-4 *2 (-1063)) (-4 *3 (-23)) - (-14 *4 *3)))) + (-12 (-5 *2 (-912 *3)) (-4 *3 (-13 (-354) (-1157) (-971))) + (-5 *1 (-173 *3))))) +(((*1 *2 *3 *3 *4 *3) + (-12 (-5 *3 (-547)) (-5 *4 (-663 (-217))) (-5 *2 (-1004)) + (-5 *1 (-730))))) +(((*1 *2 *3) (-12 (-5 *3 (-795)) (-5 *2 (-52)) (-5 *1 (-805))))) (((*1 *2 *3) - (-12 (-5 *3 (-1218 *1)) (-4 *1 (-358 *4)) (-4 *4 (-169)) - (-5 *2 (-663 *4)))) - ((*1 *2) - (-12 (-4 *4 (-169)) (-5 *2 (-663 *4)) (-5 *1 (-407 *3 *4)) - (-4 *3 (-408 *4)))) - ((*1 *2) (-12 (-4 *1 (-408 *3)) (-4 *3 (-169)) (-5 *2 (-663 *3))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-952 *2)) (-4 *2 (-1157))))) -(((*1 *2 *1) - (-12 (-4 *2 (-13 (-819) (-354))) (-5 *1 (-1026 *2 *3)) - (-4 *3 (-1194 *2))))) -(((*1 *2 *2 *2 *2) - (-12 (-5 *2 (-663 *3)) (-4 *3 (-1016)) (-5 *1 (-664 *3))))) + (-12 + (-5 *3 + (-2 (|:| |lfn| (-619 (-307 (-217)))) (|:| -3046 (-619 (-217))))) + (-5 *2 (-370)) (-5 *1 (-258)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1218 (-307 (-217)))) (-5 *2 (-370)) (-5 *1 (-296))))) (((*1 *2 *3) (-12 (-5 *2 (-166 (-370))) (-5 *1 (-759 *3)) (-4 *3 (-592 (-370))))) ((*1 *2 *3 *4) @@ -13309,10 +12936,9 @@ (-12 (-5 *3 (-307 (-166 *5))) (-5 *4 (-890)) (-4 *5 (-539)) (-4 *5 (-821)) (-4 *5 (-592 (-370))) (-5 *2 (-166 (-370))) (-5 *1 (-759 *5))))) -(((*1 *2 *2 *1 *3 *4) - (-12 (-5 *2 (-619 *8)) (-5 *3 (-1 *8 *8 *8)) - (-5 *4 (-1 (-112) *8 *8)) (-4 *1 (-1165 *5 *6 *7 *8)) (-4 *5 (-539)) - (-4 *6 (-767)) (-4 *7 (-821)) (-4 *8 (-1030 *5 *6 *7))))) +(((*1 *2 *3) + (-12 (-4 *4 (-13 (-539) (-145))) (-5 *2 (-619 *3)) + (-5 *1 (-1188 *4 *3)) (-4 *3 (-1194 *4))))) (((*1 *2 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *3 (-766)) (-4 *2 (-1016)))) ((*1 *2 *1) (-12 (-4 *2 (-1016)) (-5 *1 (-50 *2 *3)) (-14 *3 (-619 (-1135))))) @@ -13322,10 +12948,10 @@ ((*1 *2 *1) (-12 (-4 *1 (-373 *2 *3)) (-4 *3 (-1063)) (-4 *2 (-1016)))) ((*1 *2 *1) - (-12 (-14 *3 (-619 (-1135))) (-4 *5 (-230 (-3763 *3) (-745))) + (-12 (-14 *3 (-619 (-1135))) (-4 *5 (-230 (-3764 *3) (-745))) (-14 *6 - (-1 (-112) (-2 (|:| -3479 *4) (|:| -4248 *5)) - (-2 (|:| -3479 *4) (|:| -4248 *5)))) + (-1 (-112) (-2 (|:| -3481 *4) (|:| -1973 *5)) + (-2 (|:| -3481 *4) (|:| -1973 *5)))) (-4 *2 (-169)) (-5 *1 (-451 *3 *2 *4 *5 *6 *7)) (-4 *4 (-821)) (-4 *7 (-918 *2 *5 (-834 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-498 *2 *3)) (-4 *3 (-821)) (-4 *2 (-1063)))) @@ -13342,12 +12968,6 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-1030 *3 *4 *2)) (-4 *3 (-1016)) (-4 *4 (-767)) (-4 *2 (-821))))) -(((*1 *2 *3) - (-12 (-4 *4 (-1016)) (-5 *2 (-112)) (-5 *1 (-434 *4 *3)) - (-4 *3 (-1194 *4)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1030 *3 *4 *5)) (-4 *3 (-1016)) (-4 *4 (-767)) - (-4 *5 (-821)) (-5 *2 (-112))))) (((*1 *1 *1 *2) (|partial| -12 (-4 *1 (-163 *2)) (-4 *2 (-169)) (-4 *2 (-539)))) ((*1 *1 *1 *2) @@ -13369,28 +12989,22 @@ (-4 *5 (-230 *4 *2)) (-4 *6 (-230 *3 *2)) (-4 *2 (-539)))) ((*1 *2 *2 *2) (|partial| -12 (-5 *2 (-1116 *3)) (-4 *3 (-1016)) (-5 *1 (-1120 *3))))) -(((*1 *2 *1 *3) (-12 (-4 *1 (-34)) (-5 *3 (-745)) (-5 *2 (-112)))) - ((*1 *2 *3 *3) - (|partial| -12 (-5 *2 (-112)) (-5 *1 (-1173 *3)) (-4 *3 (-1063)))) - ((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-1 (-112) *3 *3)) (-4 *3 (-1063)) (-5 *2 (-112)) - (-5 *1 (-1173 *3))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1030 *3 *4 *5)) (-4 *3 (-1016)) (-4 *4 (-767)) - (-4 *5 (-821)) (-5 *2 (-112))))) -(((*1 *2 *3 *3 *3 *4) - (-12 (-5 *3 (-217)) (-5 *4 (-547)) (-5 *2 (-1004)) (-5 *1 (-733))))) -(((*1 *2 *3 *4 *5 *6 *7 *6) - (|partial| -12 - (-5 *5 - (-2 (|:| |contp| *3) - (|:| -2483 (-619 (-2 (|:| |irr| *10) (|:| -1889 (-547))))))) - (-5 *6 (-619 *3)) (-5 *7 (-619 *8)) (-4 *8 (-821)) (-4 *3 (-298)) - (-4 *10 (-918 *3 *9 *8)) (-4 *9 (-767)) - (-5 *2 - (-2 (|:| |polfac| (-619 *10)) (|:| |correct| *3) - (|:| |corrfact| (-619 (-1131 *3))))) - (-5 *1 (-601 *8 *9 *3 *10)) (-5 *4 (-619 (-1131 *3)))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-2 (|:| |totdeg| (-745)) (|:| -3528 *4))) (-5 *5 (-745)) + (-4 *4 (-918 *6 *7 *8)) (-4 *6 (-442)) (-4 *7 (-767)) (-4 *8 (-821)) + (-5 *2 + (-2 (|:| |lcmfij| *7) (|:| |totdeg| *5) (|:| |poli| *4) + (|:| |polj| *4))) + (-5 *1 (-439 *6 *7 *8 *4))))) +(((*1 *2 *3 *4 *5 *5 *5 *6 *4 *4 *4 *5 *4 *5 *7) + (-12 (-5 *3 (-1118)) (-5 *5 (-663 (-217))) (-5 *6 (-217)) + (-5 *7 (-663 (-547))) (-5 *4 (-547)) (-5 *2 (-1004)) (-5 *1 (-727))))) +(((*1 *2 *3 *3 *1) + (|partial| -12 (-5 *3 (-1135)) (-5 *2 (-1067)) (-5 *1 (-282))))) +(((*1 *1 *1 *2 *2) + (-12 (-5 *2 (-547)) (-4 *1 (-661 *3 *4 *5)) (-4 *3 (-1016)) + (-4 *4 (-364 *3)) (-4 *5 (-364 *3))))) +(((*1 *2 *2) (-12 (-5 *2 (-307 (-217))) (-5 *1 (-202))))) (((*1 *2 *3 *2) (-12 (-5 *2 (-619 (-370))) (-5 *3 (-619 (-254))) (-5 *1 (-252)))) ((*1 *2 *1 *2) (-12 (-5 *2 (-619 (-370))) (-5 *1 (-458)))) @@ -13399,35 +13013,33 @@ (-12 (-5 *3 (-890)) (-5 *4 (-843)) (-5 *2 (-1223)) (-5 *1 (-1219)))) ((*1 *2 *1 *3 *4) (-12 (-5 *3 (-890)) (-5 *4 (-1118)) (-5 *2 (-1223)) (-5 *1 (-1219))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-890)) (-5 *2 (-1131 *3)) (-5 *1 (-1146 *3)) - (-4 *3 (-354))))) -(((*1 *2 *3) (-12 (-5 *2 (-112)) (-5 *1 (-566 *3)) (-4 *3 (-532))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1118)) (-5 *2 (-1223)) (-5 *1 (-1220))))) (((*1 *2 *3) - (-12 (-4 *1 (-333 *4 *3 *5)) (-4 *4 (-1176)) (-4 *3 (-1194 *4)) - (-4 *5 (-1194 (-398 *3))) (-5 *2 (-112)))) - ((*1 *2 *3) - (-12 (-4 *1 (-333 *3 *4 *5)) (-4 *3 (-1176)) (-4 *4 (-1194 *3)) - (-4 *5 (-1194 (-398 *4))) (-5 *2 (-112))))) + (-12 (-5 *3 (-745)) (-5 *2 (-663 (-921 *4))) (-5 *1 (-997 *4)) + (-4 *4 (-1016))))) (((*1 *2 *3) - (-12 (-5 *3 (-1 *6 *4)) (-4 *4 (-1063)) (-4 *6 (-1063)) - (-5 *2 (-1 *6 *4 *5)) (-5 *1 (-658 *4 *5 *6)) (-4 *5 (-1063))))) -(((*1 *2 *3 *4 *5) - (|partial| 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*1) - (-12 (-5 *2 (-912 *4)) (-5 *1 (-1124 *3 *4)) (-14 *3 (-890)) - (-4 *4 (-1016))))) + (-12 (-5 *2 (-1 (-912 *3) (-912 *3))) (-5 *1 (-173 *3)) + (-4 *3 (-13 (-354) (-1157) (-971)))))) (((*1 *2 *3) - (-12 (-14 *4 (-619 (-1135))) (-14 *5 (-745)) + (-12 (-5 *3 (-890)) (-5 *2 - (-619 - (-493 (-398 (-547)) (-232 *5 (-745)) (-834 *4) - (-239 *4 (-398 (-547)))))) - (-5 *1 (-494 *4 *5)) - (-5 *3 - (-493 (-398 (-547)) (-232 *5 (-745)) (-834 *4) - (-239 *4 (-398 (-547)))))))) + (-3 (-1131 *4) + (-1218 (-619 (-2 (|:| -4152 *4) (|:| -3481 (-1082))))))) + (-5 *1 (-337 *4)) (-4 *4 (-340))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-1131 *3)) (-4 *3 (-359)) (-4 *1 (-320 *3)) + (-4 *3 (-354))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1118)) (-5 *2 (-1223)) (-5 *1 (-1220))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-821) (-539))) (-5 *1 (-267 *3 *2)) @@ -14852,43 +14363,77 @@ ((*1 *2 *2) (-12 (-5 *2 (-1116 *3)) (-4 *3 (-38 (-398 (-547)))) (-5 *1 (-1122 *3))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1 *5 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(-12 (-5 *2 (-547)) (-5 *1 (-117 *3)) (-14 *3 *2))) + ((*1 *1 *1) (-12 (-5 *1 (-117 *2)) (-14 *2 (-547)))) + ((*1 *1 *2 *1) (-12 (-5 *2 (-547)) (-5 *1 (-840 *3)) (-14 *3 *2))) + ((*1 *1 *1) (-12 (-5 *1 (-840 *2)) (-14 *2 (-547)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-547)) (-14 *3 *2) (-5 *1 (-841 *3 *4)) + (-4 *4 (-838 *3)))) ((*1 *1 *1) - (-12 (-5 *1 (-1241 *2 *3)) (-4 *2 (-1016)) (-4 *3 (-817))))) -(((*1 *2) (-12 (-5 *2 (-1118)) (-5 *1 (-734))))) + (-12 (-14 *2 (-547)) (-5 *1 (-841 *2 *3)) (-4 *3 (-838 *2)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-547)) (-4 *1 (-1180 *3 *4)) (-4 *3 (-1016)) + (-4 *4 (-1209 *3)))) + ((*1 *1 *1) + (-12 (-4 *1 (-1180 *2 *3)) (-4 *2 (-1016)) (-4 *3 (-1209 *2))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-821) (-442))) (-5 *1 (-1163 *3 *2)) (-4 *2 (-13 (-421 *3) (-1157)))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5) - (-12 (-5 *3 (-1 (-370) (-370))) (-5 *4 (-370)) - (-5 *2 - (-2 (|:| -4152 *4) (|:| -3026 *4) (|:| |totalpts| (-547)) - (|:| |success| (-112)))) - (-5 *1 (-763)) (-5 *5 (-547))))) -(((*1 *1 *2) (-12 (-5 *2 (-398 (-547))) (-5 *1 (-209))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-821) (-539))) (-5 *1 (-267 *3 *2)) @@ -14905,63 +14450,81 @@ ((*1 *2 *2) (-12 (-5 *2 (-1116 *3)) (-4 *3 (-38 (-398 (-547)))) (-5 *1 (-1122 *3))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-539)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3772 *4))) - (-5 *1 (-938 *4 *3)) (-4 *3 (-1194 *4))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *4) - (-12 (-5 *3 (-1118)) (-5 *4 (-547)) (-5 *5 (-663 (-166 (-217)))) - (-5 *2 (-1004)) (-5 *1 (-729))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-912 (-217))) (-5 *2 (-1223)) (-5 *1 (-458))))) -(((*1 *2 *3 *3 *3 *4 *5 *3 *6 *6 *3) - (-12 (-5 *3 (-547)) (-5 *5 (-112)) (-5 *6 (-663 (-217))) - (-5 *4 (-217)) (-5 *2 (-1004)) (-5 *1 (-730))))) -(((*1 *1 *2) (-12 (-5 *2 (-843)) (-5 *1 (-254)))) - ((*1 *1 *2) (-12 (-5 *2 (-370)) (-5 *1 (-254))))) -(((*1 *1 *2) - (-12 (-5 *2 (-619 (-493 *3 *4 *5 *6))) (-4 *3 (-354)) (-4 *4 (-767)) - (-4 *5 (-821)) (-5 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(-217)) (-217))) (-5 *3 (-1058 (-217))) - (-5 *1 (-895)))) - ((*1 *1 *2 *3 *3 *3) - (-12 (-5 *2 (-1 (-912 (-217)) (-217))) (-5 *3 (-1058 (-217))) - (-5 *1 (-896)))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-1 (-912 (-217)) (-217))) (-5 *3 (-1058 (-217))) - (-5 *1 (-896))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-1218 *5)) (-4 *5 (-766)) (-5 *2 (-112)) - (-5 *1 (-816 *4 *5)) (-14 *4 (-745))))) +(((*1 *2 *3 *3 *3) + (|partial| -12 (-4 *4 (-13 (-354) (-145) (-1007 (-547)))) + (-4 *5 (-1194 *4)) (-5 *2 (-619 (-398 *5))) (-5 *1 (-985 *4 *5)) + (-5 *3 (-398 *5))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-823 *2)) (-4 *2 (-1016)) (-4 *2 (-354))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *2 *2)) (-4 *2 (-1209 *4)) (-5 *1 (-1211 *4 *2)) - (-4 *4 (-38 (-398 (-547))))))) -(((*1 *2 *1) - (-12 (-5 *2 (-842 (-935 *3) (-935 *3))) (-5 *1 (-935 *3)) - (-4 *3 (-936))))) + (-12 (-5 *4 (-1 (-619 *5) *6)) + (-4 *5 (-13 (-354) (-145) (-1007 (-398 (-547))))) (-4 *6 (-1194 *5)) + (-5 *2 (-619 (-2 (|:| -2574 *5) (|:| -2637 *3)))) + (-5 *1 (-783 *5 *6 *3 *7)) (-4 *3 (-630 *6)) + (-4 *7 (-630 (-398 *6)))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-821) (-539))) (-5 *1 (-267 *3 *2)) + (-4 *2 (-13 (-421 *3) (-971)))))) +(((*1 *1 *2 *1) (-12 (-4 *1 (-106 *2)) (-4 *2 (-1172)))) + ((*1 *1 *2 *1) (-12 (-5 *1 (-121 *2)) (-4 *2 (-821)))) + ((*1 *1 *2 *1) (-12 (-5 *1 (-126 *2)) (-4 *2 (-821)))) + ((*1 *1 *1 *1 *2) + (-12 (-5 *2 (-547)) (-4 *1 (-273 *3)) (-4 *3 (-1172)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-547)) (-4 *1 (-273 *2)) (-4 *2 (-1172)))) + ((*1 *1 *2) + (-12 + (-5 *2 + (-2 + (|:| -3327 + (-2 (|:| |var| (-1135)) (|:| |fn| (-307 (-217))) + (|:| -2905 (-1058 (-814 (-217)))) (|:| |abserr| (-217)) + (|:| |relerr| (-217)))) + (|:| -1778 + (-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| (-1116 (-217))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -2905 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))))) + (-5 *1 (-542)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-745)) (-4 *1 (-669 *2)) (-4 *2 (-1063)))) + ((*1 *1 *2) + (-12 + (-5 *2 + (-2 + (|:| -3327 + (-2 (|:| |xinit| (-217)) (|:| |xend| (-217)) + (|:| |fn| (-1218 (-307 (-217)))) (|:| |yinit| (-619 (-217))) + (|:| |intvals| (-619 (-217))) (|:| |g| (-307 (-217))) + (|:| |abserr| (-217)) (|:| |relerr| (-217)))) + (|:| -1778 + (-2 (|:| |stiffness| (-370)) (|:| |stability| (-370)) + (|:| |expense| (-370)) (|:| |accuracy| (-370)) + (|:| |intermediateResults| (-370)))))) + (-5 *1 (-777)))) + ((*1 *2 *3 *4) + (-12 (-5 *2 (-1223)) (-5 *1 (-1149 *3 *4)) (-4 *3 (-1063)) + (-4 *4 (-1063))))) +(((*1 *2 *1) (-12 (-5 *2 (-619 (-1135))) (-5 *1 (-799))))) +(((*1 *2 *1) (-12 (-4 *1 (-771 *2)) (-4 *2 (-169))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-821) (-539))) (-5 *1 (-267 *3 *2)) @@ -14978,81 +14541,60 @@ ((*1 *2 *2) (-12 (-5 *2 (-1116 *3)) (-4 *3 (-38 (-398 (-547)))) (-5 *1 (-1122 *3))))) -(((*1 *1 *2) - (-12 (-5 *2 (-398 (-547))) (-4 *1 (-537 *3)) - (-4 *3 (-13 (-395) (-1157))))) - ((*1 *1 *2) (-12 (-4 *1 (-537 *2)) (-4 *2 (-13 (-395) (-1157))))) - ((*1 *1 *2 *2) (-12 (-4 *1 (-537 *2)) (-4 *2 (-13 (-395) (-1157)))))) -(((*1 *1 *2) - (-12 (-5 *2 (-619 *1)) (-4 *1 (-1096 *3)) (-4 *3 (-1016)))) - ((*1 *2 *2 *1) - (|partial| -12 (-5 *2 (-398 *1)) (-4 *1 (-1194 *3)) (-4 *3 (-1016)) - (-4 *3 (-539)))) - ((*1 *1 *1 *1) - (|partial| -12 (-4 *1 (-1194 *2)) (-4 *2 (-1016)) (-4 *2 (-539))))) -(((*1 *1 *2) - (-12 (-5 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(-298) (-145) (-991))) + (-5 *2 (-619 (-619 (-993 (-398 *4))))) (-5 *1 (-1244 *4 *5 *6)) + (-14 *5 (-619 (-1135))) (-14 *6 (-619 (-1135)))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-821) (-539))) (-5 *1 (-267 *3 *2)) (-4 *2 (-13 (-421 *3) (-971))))) @@ -15235,42 +14763,48 @@ ((*1 *2 *2) (-12 (-5 *2 (-1116 *3)) (-4 *3 (-38 (-398 (-547)))) (-5 *1 (-1122 *3))))) -(((*1 *2 *1) - (-12 (-5 *2 (-619 (-547))) (-5 *1 (-973 *3)) (-14 *3 (-547))))) -(((*1 *2 *2 *3) - (-12 - (-5 *2 - (-2 (|:| |partsol| (-1218 (-398 (-921 *4)))) - (|:| -4013 (-619 (-1218 (-398 (-921 *4))))))) - (-5 *3 (-619 *7)) (-4 *4 (-13 (-298) (-145))) - (-4 *7 (-918 *4 *6 *5)) (-4 *5 (-13 (-821) (-592 (-1135)))) - (-4 *6 (-767)) (-5 *1 (-893 *4 *5 *6 *7))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-619 (-239 *4 *5))) (-5 *2 (-239 *4 *5)) - (-14 *4 (-619 (-1135))) (-4 *5 (-442)) (-5 *1 (-607 *4 *5))))) -(((*1 *1 *1 *1) (-5 *1 (-832)))) -(((*1 *2 *3 *3) - (-12 (-4 *3 (-298)) (-4 *3 (-169)) (-4 *4 (-364 *3)) - (-4 *5 (-364 *3)) (-5 *2 (-2 (|:| 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(-5 *2 (-890)) (-5 *1 (-319 *3 *4)) + (-4 *3 (-320 *4)))) + ((*1 *2) + (-12 (-4 *4 (-354)) (-5 *2 (-807 (-890))) (-5 *1 (-319 *3 *4)) + (-4 *3 (-320 *4)))) + ((*1 *2) (-12 (-4 *1 (-320 *3)) (-4 *3 (-354)) (-5 *2 (-890)))) + ((*1 *2) + (-12 (-4 *1 (-1237 *3)) (-4 *3 (-354)) (-5 *2 (-807 (-890)))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-1194 *2)) (-4 *2 (-1016))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-821) (-539))) (-5 *1 (-267 *3 *2)) (-4 *2 (-13 (-421 *3) (-971))))) @@ -15287,61 +14821,53 @@ ((*1 *2 *2) (-12 (-5 *2 (-1116 *3)) (-4 *3 (-38 (-398 (-547)))) (-5 *1 (-1122 *3))))) -(((*1 *1 *2 *3) (-12 (-5 *2 (-1131 *1)) (-5 *3 (-1135)) (-4 *1 (-27)))) - ((*1 *1 *2) (-12 (-5 *2 (-1131 *1)) (-4 *1 (-27)))) - ((*1 *1 *2) (-12 (-5 *2 (-921 *1)) (-4 *1 (-27)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-1135)) (-4 *1 (-29 *3)) (-4 *3 (-13 (-821) (-539))))) - ((*1 *1 *1) (-12 (-4 *1 (-29 *2)) (-4 *2 (-13 (-821) (-539))))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-1131 *2)) (-5 *4 (-1135)) (-4 *2 (-421 *5)) - (-5 *1 (-32 *5 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(|:| |b| (-398 *6)) (|:| |c| (-398 *6)) + (|:| -2617 *6))) + (-5 *1 (-984 *5 *6)) (-5 *3 (-398 *6))))) +(((*1 *2 *3 *4 *4 *4 *4) + (-12 (-5 *3 (-663 (-217))) (-5 *4 (-547)) (-5 *2 (-1004)) + (-5 *1 (-730))))) +(((*1 *2) (-12 (-5 *2 (-1118)) (-5 *1 (-1142))))) +(((*1 *1 *1 *2 *3 *1) + (-12 (-4 *1 (-317 *2 *3)) (-4 *2 (-1016)) (-4 *3 (-766))))) +(((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 (-547))) (-4 *3 (-1016)) (-5 *1 (-574 *3)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 (-547))) (-4 *1 (-1178 *3)) (-4 *3 (-1016)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 (-547))) (-4 *1 (-1209 *3)) (-4 *3 (-1016))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-821) (-539))) (-5 *1 (-267 *3 *2)) (-4 *2 (-13 (-421 *3) (-971))))) @@ -15361,9 +14887,6 @@ ((*1 *2 *2) (-12 (-5 *2 (-1116 *3)) (-4 *3 (-38 (-398 (-547)))) (-5 *1 (-1122 *3))))) -(((*1 *1 *1) - (-12 (-4 *2 (-340)) (-4 *2 (-1016)) (-5 *1 (-687 *2 *3)) - (-4 *3 (-1194 *2))))) (((*1 *1 *2 *1) (-12 (-4 *1 (-21)) (-5 *2 (-547)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-745)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-25)) (-5 *2 (-890)))) @@ -15395,10 +14918,10 @@ ((*1 *1 *2 *1) (-12 (-5 *1 (-377 *2)) (-4 *2 (-1063)))) ((*1 *1 *2 *1) (-12 (-14 *3 (-619 (-1135))) (-4 *4 (-169)) - (-4 *6 (-230 (-3763 *3) (-745))) + (-4 *6 (-230 (-3764 *3) (-745))) (-14 *7 - (-1 (-112) (-2 (|:| -3479 *5) (|:| -4248 *6)) - (-2 (|:| -3479 *5) (|:| -4248 *6)))) + (-1 (-112) (-2 (|:| -3481 *5) (|:| -1973 *6)) + (-2 (|:| -3481 *5) (|:| -1973 *6)))) (-5 *1 (-451 *3 *4 *5 *6 *7 *2)) (-4 *5 (-821)) (-4 *2 (-918 *4 *6 (-834 *3))))) ((*1 *1 *1 *2) @@ -15477,45 +15000,77 @@ (-12 (-4 *1 (-1235 *3 *2)) (-4 *3 (-821)) (-4 *2 (-1016)))) ((*1 *1 *1 *2) (-12 (-5 *1 (-1241 *2 *3)) (-4 *2 (-1016)) (-4 *3 (-817))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-217)) (-5 *1 (-218)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-166 (-217))) (-5 *1 (-218)))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-13 (-821) (-539))) (-5 *1 (-422 *3 *2)) - (-4 *2 (-421 *3)))) - ((*1 *1 *1 *1) (-4 *1 (-1099)))) +(((*1 *2 *1) + (-12 (-4 *3 (-1016)) (-4 *4 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(-4 *2 (-13 (-27) (-1157) (-421 *3))))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-1135)) + (-4 *4 (-13 (-442) (-821) (-1007 (-547)) (-615 (-547)))) + (-5 *1 (-1161 *4 *2)) (-4 *2 (-13 (-27) (-1157) (-421 *4)))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-821) (-539))) (-5 *1 (-267 *3 *2)) (-4 *2 (-13 (-421 *3) (-971))))) @@ -15535,51 +15090,93 @@ ((*1 *2 *2) (-12 (-5 *2 (-1116 *3)) (-4 *3 (-38 (-398 (-547)))) (-5 *1 (-1122 *3))))) -(((*1 *2 *3 *2) - (|partial| -12 (-5 *2 (-1218 *4)) (-5 *3 (-663 *4)) (-4 *4 (-354)) - (-5 *1 (-641 *4)))) - ((*1 *2 *3 *2) - (|partial| -12 (-4 *4 (-354)) - (-4 *5 (-13 (-364 *4) (-10 -7 (-6 -4329)))) - (-4 *2 (-13 (-364 *4) (-10 -7 (-6 -4329)))) - (-5 *1 (-642 *4 *5 *2 *3)) (-4 *3 (-661 *4 *5 *2)))) - ((*1 *2 *3 *2 *4 *5) - (|partial| -12 (-5 *4 (-619 *2)) (-5 *5 (-1 *2 *2)) (-4 *2 (-354)) - (-5 *1 (-788 *2 *3)) (-4 *3 (-630 *2)))) - ((*1 *2 *3) - (-12 (-4 *2 (-13 (-354) (-10 -8 (-15 ** ($ $ (-398 (-547))))))) - (-5 *1 (-1090 *3 *2)) (-4 *3 (-1194 *2))))) +(((*1 *2 *1) + 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(-1016)) (-4 *4 (-766)) + (-5 *2 (-112)))) + ((*1 *2 *1) + (-12 (-4 *1 (-373 *3 *4)) (-4 *3 (-1016)) (-4 *4 (-1063)) + (-5 *2 (-112)))) + ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-574 *3)) (-4 *3 (-1016)))) + ((*1 *2 *1) + (-12 (-4 *3 (-539)) (-5 *2 (-112)) (-5 *1 (-599 *3 *4)) + (-4 *4 (-1194 *3)))) + ((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-710 *3 *4)) (-4 *3 (-1016)) + (-4 *4 (-701)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1235 *3 *4)) (-4 *3 (-821)) (-4 *4 (-1016)) + (-5 *2 (-112))))) +(((*1 *2 *1) (-12 (-4 *1 (-1206 *3)) (-4 *3 (-1172)) (-5 *2 (-745))))) (((*1 *1 *1) (-4 *1 (-94))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-821) (-539))) (-5 *1 (-267 *3 *2)) @@ -15992,20 +15588,21 @@ ((*1 *2 *2) (-12 (-5 *2 (-1116 *3)) (-4 *3 (-38 (-398 (-547)))) (-5 *1 (-1122 *3))))) -(((*1 *2 *1) - (-12 (-5 *2 (-995 (-814 (-547)))) (-5 *1 (-574 *3)) (-4 *3 (-1016))))) -(((*1 *2 *3 *2 *2) - (-12 (-5 *2 (-619 (-471 *4 *5))) (-5 *3 (-834 *4)) - (-14 *4 (-619 (-1135))) (-4 *5 (-442)) (-5 *1 (-607 *4 *5))))) -(((*1 *2 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(-4 *1 (-365 *4 *2)) (-4 *4 (-821)) (-4 *2 (-169)))) @@ -16016,30 +15613,21 @@ (-4 *2 (-1016)))) ((*1 *2 *1 *3) (-12 (-4 *2 (-1016)) (-5 *1 (-1241 *2 *3)) (-4 *3 (-817))))) +(((*1 *2 *2 *3 *4) + (|partial| -12 (-5 *3 (-745)) (-4 *4 (-13 (-539) (-145))) + (-5 *1 (-1188 *4 *2)) (-4 *2 (-1194 *4))))) +(((*1 *1 *1 *1) + (-12 (|has| *1 (-6 -4329)) (-4 *1 (-236 *2)) (-4 *2 (-1172))))) +(((*1 *2 *3) + (-12 (-4 *4 (-539)) (-5 *2 (-1218 (-663 *4))) (-5 *1 (-89 *4 *5)) + (-5 *3 (-663 *4)) (-4 *5 (-630 *4))))) (((*1 *2 *1) - (|partial| -12 - (-4 *3 (-13 (-821) (-1007 (-547)) (-615 (-547)) (-442))) - (-5 *2 - (-2 - (|:| |%term| - (-2 (|:| |%coef| (-1203 *4 *5 *6)) - (|:| |%expon| (-310 *4 *5 *6)) - (|:| |%expTerms| - (-619 (-2 (|:| |k| (-398 (-547))) (|:| |c| *4)))))) - (|:| |%type| (-1118)))) - (-5 *1 (-1204 *3 *4 *5 *6)) (-4 *4 (-13 (-27) (-1157) (-421 *3))) - (-14 *5 (-1135)) (-14 *6 *4)))) + (-12 (-4 *4 (-1063)) (-5 *2 (-112)) (-5 *1 (-854 *3 *4 *5)) + (-4 *3 (-1063)) (-4 *5 (-640 *4)))) + ((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-858 *3 *4)) (-4 *3 (-1063)) + (-4 *4 (-1063))))) (((*1 *2 *1) (-12 (-5 *2 (-1223)) (-5 *1 (-796))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-442)) (-4 *6 (-767)) (-4 *7 (-821)) - (-4 *3 (-1030 *5 *6 *7)) (-5 *2 (-619 *4)) - (-5 *1 (-1071 *5 *6 *7 *3 *4)) (-4 *4 (-1036 *5 *6 *7 *3))))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-1118)) (-5 *2 (-303)) (-5 *1 (-803))))) -(((*1 *2 *3 *4) - (-12 (-5 *2 (-2 (|:| |part1| *3) (|:| |part2| *4))) - (-5 *1 (-680 *3 *4)) (-4 *3 (-1172)) (-4 *4 (-1172))))) -(((*1 *2) (-12 (-5 *2 (-843)) (-5 *1 (-1221)))) - ((*1 *2 *2) (-12 (-5 *2 (-843)) (-5 *1 (-1221))))) (((*1 *1 *1) (-4 *1 (-94))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-821) (-539))) (-5 *1 (-267 *3 *2)) @@ -16059,44 +15647,68 @@ ((*1 *2 *2) (-12 (-5 *2 (-1116 *3)) (-4 *3 (-38 (-398 (-547)))) (-5 *1 (-1122 *3))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1066 *3 *4 *5 *6 *7)) (-4 *3 (-1063)) (-4 *4 (-1063)) + (-4 *5 (-1063)) (-4 *6 (-1063)) (-4 *7 (-1063)) (-5 *2 (-112))))) +(((*1 *2 *1) + (|partial| -12 (-4 *1 (-918 *3 *4 *2)) (-4 *3 (-1016)) (-4 *4 (-767)) + (-4 *2 (-821)))) + ((*1 *2 *3) + (|partial| -12 (-4 *4 (-767)) (-4 *5 (-1016)) (-4 *6 (-918 *5 *4 *2)) + (-4 *2 (-821)) (-5 *1 (-919 *4 *2 *5 *6 *3)) + (-4 *3 + (-13 (-354) + (-10 -8 (-15 -3835 ($ *6)) (-15 -1384 (*6 $)) + (-15 -1394 (*6 $))))))) + ((*1 *2 *3) + (|partial| -12 (-5 *3 (-398 (-921 *4))) (-4 *4 (-539)) + (-5 *2 (-1135)) (-5 *1 (-1012 *4))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *5 *4)) (-4 *4 (-1063)) (-4 *5 (-1063)) - (-5 *2 (-1 *5)) (-5 *1 (-657 *4 *5))))) -(((*1 *2 *3) - (-12 (-5 *2 (-1 (-912 *3) (-912 *3))) (-5 *1 (-173 *3)) - (-4 *3 (-13 (-354) (-1157) (-971))))) - ((*1 *2) - (|partial| -12 (-4 *4 (-1176)) (-4 *5 (-1194 (-398 *2))) - (-4 *2 (-1194 *4)) (-5 *1 (-332 *3 *4 *2 *5)) - (-4 *3 (-333 *4 *2 *5)))) - ((*1 *2) - (|partial| -12 (-4 *1 (-333 *3 *2 *4)) (-4 *3 (-1176)) - (-4 *4 (-1194 (-398 *2))) (-4 *2 (-1194 *3))))) + (-12 (-5 *2 (-2 (|:| |part1| *3) (|:| |part2| *4))) + (-5 *1 (-680 *3 *4)) (-4 *3 (-1172)) (-4 *4 (-1172))))) (((*1 *2 *3) (-12 (-5 *3 (-619 (-307 (-217)))) (-5 *2 (-112)) (-5 *1 (-258))))) -(((*1 *1 *1 *1) (-5 *1 (-832)))) -(((*1 *2 *2 *3 *3) - (-12 (-5 *2 (-663 *3)) (-4 *3 (-298)) (-5 *1 (-674 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-1140)) (-5 *1 (-1228))))) +(((*1 *2 *1 *3 *3 *4) + (-12 (-5 *3 (-1 (-832) (-832) (-832))) (-5 *4 (-547)) (-5 *2 (-832)) + (-5 *1 (-623 *5 *6 *7)) (-4 *5 (-1063)) (-4 *6 (-23)) (-14 *7 *6))) + ((*1 *2 *1 *2) + (-12 (-5 *2 (-832)) (-5 *1 (-825 *3 *4 *5)) (-4 *3 (-1016)) + (-14 *4 (-98 *3)) (-14 *5 (-1 *3 *3)))) + ((*1 *1 *2) (-12 (-5 *2 (-217)) (-5 *1 (-832)))) + ((*1 *1 *2) (-12 (-5 *2 (-1118)) (-5 *1 (-832)))) + ((*1 *1 *2) (-12 (-5 *2 (-1135)) (-5 *1 (-832)))) + ((*1 *1 *2) (-12 (-5 *2 (-547)) (-5 *1 (-832)))) + ((*1 *2 *1 *2) + (-12 (-5 *2 (-832)) (-5 *1 (-1131 *3)) (-4 *3 (-1016))))) (((*1 *2 *3) - (-12 (-4 *4 (-539)) (-4 *5 (-767)) (-4 *6 (-821)) - (-4 *7 (-1030 *4 *5 *6)) - (-5 *2 (-2 (|:| |goodPols| (-619 *7)) (|:| |badPols| (-619 *7)))) - (-5 *1 (-946 *4 *5 *6 *7)) (-5 *3 (-619 *7))))) -(((*1 *2 *1 *3) - (|partial| -12 (-5 *3 (-861 *4)) (-4 *4 (-1063)) (-5 *2 (-112)) - (-5 *1 (-858 *4 *5)) (-4 *5 (-1063)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-861 *5)) (-4 *5 (-1063)) (-5 *2 (-112)) - (-5 *1 (-859 *5 *3)) (-4 *3 (-1172)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-619 *6)) (-5 *4 (-861 *5)) (-4 *5 (-1063)) - (-4 *6 (-1172)) (-5 *2 (-112)) (-5 *1 (-859 *5 *6))))) -(((*1 *2 *3 *3 *3 *4 *4 *4 *3) - (-12 (-5 *3 (-547)) (-5 *4 (-663 (-217))) (-5 *2 (-1004)) - (-5 *1 (-727))))) -(((*1 *2 *1) - (-12 (-4 *2 (-1063)) (-5 *1 (-933 *2 *3)) (-4 *3 (-1063))))) -(((*1 *2 *2) (-12 (-5 *2 (-1131 *3)) (-4 *3 (-340)) (-5 *1 (-348 *3))))) + (-12 (-5 *3 (-1118)) (-5 *2 (-1223)) (-5 *1 (-1149 *4 *5)) + (-4 *4 (-1063)) (-4 *5 (-1063))))) +(((*1 *2 *3 *4 *5 *5) + (-12 (-5 *5 (-745)) (-4 *6 (-1063)) (-4 *7 (-869 *6)) + (-5 *2 (-663 *7)) (-5 *1 (-666 *6 *7 *3 *4)) (-4 *3 (-364 *7)) + (-4 *4 (-13 (-364 *6) (-10 -7 (-6 -4328))))))) +(((*1 *2 *3 *1) + (-12 (-5 *3 (-425)) + (-5 *2 + (-619 + (-3 (|:| -2465 (-1135)) + (|:| -2112 (-619 (-3 (|:| S (-1135)) (|:| P (-921 (-547))))))))) + (-5 *1 (-1139))))) +(((*1 *2 *3 *3 *3 *3 *4 *3 *3 *3 *3 *3 *3 *5 *5 *4 *3 *6 *7) + (-12 (-5 *3 (-547)) (-5 *5 (-663 (-217))) + (-5 *6 (-3 (|:| |fn| (-379)) (|:| |fp| (-74 FCN JACOBF JACEPS)))) + (-5 *7 (-3 (|:| |fn| (-379)) (|:| |fp| (-75 G JACOBG JACGEP)))) + (-5 *4 (-217)) (-5 *2 (-1004)) (-5 *1 (-724))))) +(((*1 *2 *3) (-12 (-5 *3 (-1118)) (-5 *2 (-370)) (-5 *1 (-96)))) + ((*1 *2 *3 *3) (-12 (-5 *3 (-1118)) (-5 *2 (-370)) (-5 *1 (-96))))) +(((*1 *1 *2 *3 *4) + (-12 (-5 *2 (-1 (-1088 *4 *3 *5))) (-4 *4 (-38 (-398 (-547)))) + (-4 *4 (-1016)) (-4 *3 (-821)) (-5 *1 (-1088 *4 *3 *5)) + (-4 *5 (-918 *4 (-519 *3) *3)))) + ((*1 *1 *2 *3 *4) + (-12 (-5 *2 (-1 (-1166 *4))) (-5 *3 (-1135)) (-5 *1 (-1166 *4)) + (-4 *4 (-38 (-398 (-547)))) (-4 *4 (-1016))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-821) (-539))) (-5 *1 (-267 *3 *2)) (-4 *2 (-13 (-421 *3) (-971))))) @@ -16113,58 +15725,31 @@ (-12 (-5 *2 (-1116 *3)) (-4 *3 (-38 (-398 (-547)))) (-5 *1 (-1122 *3)))) ((*1 *1 *1) (-4 *1 (-1160)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-619 *6)) (-5 *4 (-619 (-1116 *7))) (-4 *6 (-821)) - (-4 *7 (-918 *5 (-519 *6) *6)) (-4 *5 (-1016)) - (-5 *2 (-1 (-1116 *7) *7)) (-5 *1 (-1088 *5 *6 *7))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-663 *8)) (-4 *8 (-918 *5 *7 *6)) - (-4 *5 (-13 (-298) (-145))) (-4 *6 (-13 (-821) (-592 (-1135)))) - (-4 *7 (-767)) - (-5 *2 - (-619 - (-2 (|:| -3107 (-745)) - (|:| |eqns| - (-619 - (-2 (|:| |det| *8) (|:| |rows| (-619 (-547))) - (|:| |cols| (-619 (-547)))))) - (|:| |fgb| (-619 *8))))) - (-5 *1 (-893 *5 *6 *7 *8)) (-5 *4 (-745))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-307 (-547))) (|:| -1409 (-307 (-370))) + (-3 (|:| I (-307 (-547))) (|:| -1410 (-307 (-370))) (|:| CF (-307 (-166 (-370)))) (|:| |switch| (-1134)))) (-5 *1 (-1134))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-217)) (-5 *1 (-218)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-166 (-217))) (-5 *1 (-218)))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-13 (-821) (-539))) (-5 *1 (-422 *3 *2)) - (-4 *2 (-421 *3)))) - ((*1 *1 *1 *1) (-4 *1 (-1099)))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-619 *1)) (|has| *1 (-6 -4329)) (-4 *1 (-979 *3)) - (-4 *3 (-1172))))) -(((*1 *1 *1) (-5 *1 (-217))) ((*1 *1 *1) (-5 *1 (-370))) - ((*1 *1) (-5 *1 (-370)))) -(((*1 *2 *3) (-12 (-5 *3 (-745)) (-5 *2 (-1 (-370))) (-5 *1 (-1009))))) -(((*1 *2 *3 *4) - (|partial| -12 (-5 *4 (-1135)) (-4 *5 (-592 (-861 (-547)))) - (-4 *5 (-855 (-547))) - (-4 *5 (-13 (-821) (-1007 (-547)) (-442) (-615 (-547)))) - (-5 *2 (-2 (|:| |special| *3) (|:| |integrand| *3))) - (-5 *1 (-550 *5 *3)) (-4 *3 (-605)) - (-4 *3 (-13 (-27) (-1157) (-421 *5))))) - ((*1 *2 *2 *3 *4 *4) - (|partial| -12 (-5 *3 (-1135)) (-5 *4 (-814 *2)) (-4 *2 (-1099)) - (-4 *2 (-13 (-27) (-1157) (-421 *5))) - (-4 *5 (-592 (-861 (-547)))) (-4 *5 (-855 (-547))) - (-4 *5 (-13 (-821) (-1007 (-547)) (-442) (-615 (-547)))) - (-5 *1 (-550 *5 *2))))) -(((*1 *2 *3) - (-12 (-4 *4 (-1016)) (-5 *2 (-547)) (-5 *1 (-433 *4 *3 *5)) - (-4 *3 (-1194 *4)) - (-4 *5 (-13 (-395) (-1007 *4) (-354) (-1157) (-275)))))) +(((*1 *1 *1 *1) (-5 *1 (-832)))) +(((*1 *2 *3 *4 *4 *4 *3 *4 *3) + (-12 (-5 *3 (-547)) (-5 *4 (-663 (-217))) (-5 *2 (-1004)) + (-5 *1 (-726))))) +(((*1 *2 *3 *4 *4 *4 *4 *5 *5) + (-12 (-5 *3 (-1 (-370) (-370))) (-5 *4 (-370)) + (-5 *2 + (-2 (|:| -4152 *4) (|:| -3027 *4) (|:| |totalpts| (-547)) + (|:| |success| (-112)))) + (-5 *1 (-763)) (-5 *5 (-547))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *3 (-1 (-619 *2) *2 *2 *2)) (-4 *2 (-1063)) + (-5 *1 (-102 *2)))) + ((*1 *1 *1 *2 *3) + (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1063)) (-5 *1 (-102 *2))))) +(((*1 *1 *1) (-4 *1 (-1104)))) +(((*1 *2 *1) (-12 (-5 *2 (-1140)) (-5 *1 (-514))))) +(((*1 *2 *1) (-12 (-4 *1 (-340)) (-5 *2 (-745)))) + ((*1 *2 *1 *1) (|partial| -12 (-4 *1 (-393)) (-5 *2 (-745))))) (((*1 *2 *3 *4 *5) (-12 (-5 *3 (-848 (-1 (-217) (-217)))) (-5 *4 (-1058 (-370))) (-5 *5 (-619 (-254))) (-5 *2 (-1095 (-217))) (-5 *1 (-246)))) @@ -16218,17 +15803,10 @@ (-12 (-5 *3 (-851 *5)) (-5 *4 (-1056 (-370))) (-4 *5 (-13 (-592 (-523)) (-1063))) (-5 *2 (-1095 (-217))) (-5 *1 (-250 *5))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-1135)) - (-4 *4 (-13 (-821) (-298) (-1007 (-547)) (-615 (-547)) (-145))) - (-5 *1 (-778 *4 *2)) (-4 *2 (-13 (-29 *4) (-1157) (-928))))) - ((*1 *1 *1 *1 *1) (-5 *1 (-832))) ((*1 *1 *1 *1) (-5 *1 (-832))) - ((*1 *1 *1) (-5 *1 (-832))) - ((*1 *2 *3) - (-12 (-5 *2 (-1116 *3)) (-5 *1 (-1120 *3)) (-4 *3 (-1016))))) (((*1 *2 *3) - (-12 (-5 *3 (-745)) (-5 *2 (-1131 *4)) (-5 *1 (-517 *4)) - (-4 *4 (-340))))) + (-12 (-5 *3 (-471 *4 *5)) (-14 *4 (-619 (-1135))) (-4 *5 (-1016)) + (-5 *2 (-239 *4 *5)) (-5 *1 (-913 *4 *5))))) +(((*1 *2 *1) (-12 (-5 *2 (-1223)) (-5 *1 (-796))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-821) (-539))) (-5 *1 (-267 *3 *2)) (-4 *2 (-13 (-421 *3) (-971))))) @@ -16245,52 +15823,43 @@ (-12 (-5 *2 (-1116 *3)) (-4 *3 (-38 (-398 (-547)))) (-5 *1 (-1122 *3)))) ((*1 *1 *1) (-4 *1 (-1160)))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-398 (-547))) (-5 *1 (-993 *3)) - (-4 *3 (-13 (-819) (-354) (-991))))) - ((*1 *2 *3 *1 *2) - (-12 (-4 *2 (-13 (-819) (-354))) (-5 *1 (-1026 *2 *3)) - (-4 *3 (-1194 *2)))) - ((*1 *2 *3 *1 *2) - (-12 (-4 *1 (-1033 *2 *3)) (-4 *2 (-13 (-819) (-354))) - (-4 *3 (-1194 *2))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-322 *3)) (-4 *3 (-821))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-307 (-547))) (|:| -1409 (-307 (-370))) + (-3 (|:| I (-307 (-547))) (|:| -1410 (-307 (-370))) (|:| CF (-307 (-166 (-370)))) (|:| |switch| (-1134)))) (-5 *1 (-1134))))) +(((*1 *2 *2 *3 *3) + (-12 (-5 *2 (-663 *3)) (-4 *3 (-298)) (-5 *1 (-674 *3))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-547)) (-4 *1 (-56 *4 *3 *5)) (-4 *4 (-1172)) + (-4 *3 (-364 *4)) (-4 *5 (-364 *4))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1118)) (-5 *2 (-1223)) (-5 *1 (-796))))) +(((*1 *2 *3 *3 *4 *5 *5 *5 *3) + (-12 (-5 *3 (-547)) (-5 *4 (-1118)) (-5 *5 (-663 (-217))) + (-5 *2 (-1004)) (-5 *1 (-722))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-217)) (-5 *4 (-547)) (-5 *2 (-1004)) (-5 *1 (-733))))) -(((*1 *2 *3 *3 *3 *4 *3) - (-12 (-5 *3 (-547)) (-5 *4 (-663 (-166 (-217)))) (-5 *2 (-1004)) - (-5 *1 (-729))))) -(((*1 *2 *3 *1) (-12 (-5 *3 (-1135)) (-5 *2 (-1139)) (-5 *1 (-1138))))) + (-12 (-4 *5 (-442)) (-4 *6 (-767)) (-4 *7 (-821)) + (-4 *3 (-1030 *5 *6 *7)) (-5 *2 (-619 *4)) + (-5 *1 (-1071 *5 *6 *7 *3 *4)) (-4 *4 (-1036 *5 *6 *7 *3))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-442)) (-4 *6 (-767)) (-4 *7 (-821)) + (-4 *3 (-1030 *5 *6 *7)) + (-5 *2 (-619 (-2 (|:| |val| *3) (|:| -1966 *4)))) + (-5 *1 (-1037 *5 *6 *7 *3 *4)) (-4 *4 (-1036 *5 *6 *7 *3))))) (((*1 *2 *1) - (-12 (-4 *1 (-582 *3 *4)) (-4 *3 (-1063)) (-4 *4 (-1172)) - (-5 *2 (-619 *3))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-745)) (-4 *1 (-630 *3)) (-4 *3 (-1016)) (-4 *3 (-354)))) - ((*1 *2 *2 *3 *4) - (-12 (-5 *3 (-745)) (-5 *4 (-1 *5 *5)) (-4 *5 (-354)) - (-5 *1 (-633 *5 *2)) (-4 *2 (-630 *5))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-821) (-539))) (-5 *1 (-267 *3 *2)) - (-4 *2 (-13 (-421 *3) (-971)))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-821) (-442))) (-5 *1 (-1163 *3 *2)) - (-4 *2 (-13 (-421 *3) (-1157)))))) + (-12 (-4 *1 (-333 *3 *4 *5)) (-4 *3 (-1176)) (-4 *4 (-1194 *3)) + (-4 *5 (-1194 (-398 *4))) + (-5 *2 (-2 (|:| |num| (-1218 *4)) (|:| |den| *4)))))) (((*1 *2 *1) (-12 (-5 *2 (-1067)) (-5 *1 (-52))))) -(((*1 *2 *3 *2) - (-12 (-5 *3 (-745)) (-5 *1 (-757 *2)) (-4 *2 (-38 (-398 (-547)))) - (-4 *2 (-169))))) -(((*1 *2 *3) - (-12 (-5 *3 (-285 (-921 (-547)))) - (-5 *2 - (-2 (|:| |varOrder| (-619 (-1135))) - (|:| |inhom| (-3 (-619 (-1218 (-745))) "failed")) - (|:| |hom| (-619 (-1218 (-745)))))) - (-5 *1 (-228))))) +(((*1 *2) (-12 (-5 *2 (-1223)) (-5 *1 (-734))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-1 *7 *7)) + (-5 *5 (-1 (-3 (-619 *6) "failed") (-547) *6 *6)) (-4 *6 (-354)) + (-4 *7 (-1194 *6)) + (-5 *2 (-2 (|:| |answer| (-565 (-398 *7))) (|:| |a0| *6))) + (-5 *1 (-557 *6 *7)) (-5 *3 (-398 *7))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-821) (-539))) (-5 *1 (-267 *3 *2)) (-4 *2 (-13 (-421 *3) (-971))))) @@ -16313,37 +15882,42 @@ (-4 *5 (-1063)) (-4 *6 (-1063)) (-4 *2 (-1063)))) ((*1 *1 *2) (-12 (-5 *2 (-547)) (-4 *1 (-1117)))) ((*1 *2 *1) (-12 (-5 *2 (-1118)) (-5 *1 (-1135))))) +(((*1 *2 *1 *1 *3) + (-12 (-4 *4 (-1016)) (-4 *5 (-767)) (-4 *3 (-821)) + (-5 *2 (-2 (|:| -1558 *1) (|:| |gap| (-745)) (|:| -2374 *1))) + (-4 *1 (-1030 *4 *5 *3)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-1016)) (-4 *4 (-767)) (-4 *5 (-821)) + (-5 *2 (-2 (|:| -1558 *1) (|:| |gap| (-745)) (|:| -2374 *1))) + (-4 *1 (-1030 *3 *4 *5))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-547)) (-5 *2 (-1223)) (-5 *1 (-873 *4)) + (-4 *4 (-1063)))) + ((*1 *2 *1) (-12 (-5 *2 (-1223)) (-5 *1 (-873 *3)) (-4 *3 (-1063))))) (((*1 *1 *1) (-5 *1 (-1134))) ((*1 *1 *2) (-12 (-5 *2 - (-3 (|:| I (-307 (-547))) (|:| -1409 (-307 (-370))) + (-3 (|:| I (-307 (-547))) (|:| -1410 (-307 (-370))) (|:| CF (-307 (-166 (-370)))) (|:| |switch| (-1134)))) (-5 *1 (-1134))))) -(((*1 *2 *3) (-12 (-5 *3 (-832)) (-5 *2 (-1118)) (-5 *1 (-685))))) (((*1 *2 *3) - (-12 (-5 *3 (-619 (-619 (-912 (-217))))) (-5 *2 (-619 (-217))) - (-5 *1 (-458))))) + (-12 (-4 *4 (-539)) (-4 *5 (-767)) (-4 *6 (-821)) + (-4 *7 (-1030 *4 *5 *6)) + (-5 *2 (-2 (|:| |goodPols| (-619 *7)) (|:| |badPols| (-619 *7)))) + (-5 *1 (-946 *4 *5 *6 *7)) (-5 *3 (-619 *7))))) +(((*1 *1) + (-12 (-5 *1 (-623 *2 *3 *4)) (-4 *2 (-1063)) (-4 *3 (-23)) + (-14 *4 *3)))) +(((*1 *2 *2 *2) + (-12 + (-5 *2 + (-2 (|:| -1352 (-663 *3)) (|:| |basisDen| *3) + (|:| |basisInv| (-663 *3)))) + (-4 *3 (-13 (-298) (-10 -8 (-15 -2925 ((-409 $) $))))) + (-4 *4 (-1194 *3)) (-5 *1 (-488 *3 *4 *5)) (-4 *5 (-400 *3 *4))))) (((*1 *2 *1) - (-12 (-4 *3 (-13 (-354) (-145))) - (-5 *2 (-619 (-2 (|:| -4248 (-745)) (|:| -2582 *4) (|:| |num| *4)))) - (-5 *1 (-390 *3 *4)) (-4 *4 (-1194 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-627 (-398 *2))) (-4 *2 (-1194 *4)) (-5 *1 (-784 *4 *2)) - (-4 *4 (-13 (-354) (-145) (-1007 (-547)) (-1007 (-398 (-547))))))) - ((*1 *2 *3) - (-12 (-5 *3 (-628 *2 (-398 *2))) (-4 *2 (-1194 *4)) - (-5 *1 (-784 *4 *2)) - (-4 *4 (-13 (-354) (-145) (-1007 (-547)) (-1007 (-398 (-547)))))))) -(((*1 *2 *3) - (-12 (-5 *3 (-547)) (-4 *4 (-767)) (-4 *5 (-821)) (-4 *2 (-1016)) - (-5 *1 (-312 *4 *5 *2 *6)) (-4 *6 (-918 *2 *4 *5))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-745)) (-4 *1 (-365 *3 *4)) (-4 *3 (-821)) - (-4 *4 (-169)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-745)) (-4 *1 (-1239 *3 *4)) (-4 *3 (-821)) - (-4 *4 (-1016))))) + (-12 (-4 *3 (-1016)) (-5 *2 (-619 *1)) (-4 *1 (-1096 *3))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-812)) (-5 *4 (-1028)) (-5 *2 (-1004)) (-5 *1 (-811)))) ((*1 *2 *3) (-12 (-5 *3 (-812)) (-5 *2 (-1004)) (-5 *1 (-811)))) @@ -16360,27 +15934,27 @@ ((*1 *2 *3 *4) (-12 (-5 *3 (-619 (-307 (-370)))) (-5 *4 (-619 (-370))) (-5 *2 (-1004)) (-5 *1 (-811))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-807 *3)) (-4 *3 (-1063)))) - ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-814 *3)) (-4 *3 (-1063))))) -(((*1 *2) - (-12 (-5 *2 (-927 (-1082))) (-5 *1 (-334 *3 *4)) (-14 *3 (-890)) - (-14 *4 (-890)))) - ((*1 *2) - (-12 (-5 *2 (-927 (-1082))) (-5 *1 (-335 *3 *4)) (-4 *3 (-340)) - (-14 *4 (-1131 *3)))) - ((*1 *2) - (-12 (-5 *2 (-927 (-1082))) (-5 *1 (-336 *3 *4)) (-4 *3 (-340)) - (-14 *4 (-890))))) -(((*1 *1 *1) (-5 *1 (-1028)))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-619 *6)) (-4 *1 (-918 *4 *5 *6)) (-4 *4 (-1016)) - (-4 *5 (-767)) (-4 *6 (-821)) (-5 *2 (-745)))) - ((*1 *2 *1) - (-12 (-4 *1 (-918 *3 *4 *5)) (-4 *3 (-1016)) (-4 *4 (-767)) - (-4 *5 (-821)) (-5 *2 (-745))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1165 *3 *4 *5 *6)) (-4 *3 (-539)) (-4 *4 (-767)) - (-4 *5 (-821)) (-4 *6 (-1030 *3 *4 *5)) (-5 *2 (-619 *6))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-1 (-619 *5) *6)) + (-4 *5 (-13 (-354) (-145) (-1007 (-398 (-547))))) (-4 *6 (-1194 *5)) + (-5 *2 (-619 (-2 (|:| |poly| *6) (|:| -2637 *3)))) + (-5 *1 (-783 *5 *6 *3 *7)) (-4 *3 (-630 *6)) + (-4 *7 (-630 (-398 *6))))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-1 (-619 *5) *6)) + (-4 *5 (-13 (-354) (-145) (-1007 (-547)) (-1007 (-398 (-547))))) + (-4 *6 (-1194 *5)) + (-5 *2 (-619 (-2 (|:| |poly| *6) (|:| -2637 (-628 *6 (-398 *6)))))) + (-5 *1 (-786 *5 *6)) (-5 *3 (-628 *6 (-398 *6)))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-217)) (-5 *4 (-547)) (-5 *2 (-1004)) (-5 *1 (-733))))) +(((*1 *1 *1) + (-12 (-4 *1 (-1165 *2 *3 *4 *5)) (-4 *2 (-539)) (-4 *3 (-767)) + (-4 *4 (-821)) (-4 *5 (-1030 *2 *3 *4))))) +(((*1 *2 *1 *1) + (-12 (-4 *3 (-354)) (-4 *3 (-1016)) + (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -4240 *1))) + (-4 *1 (-823 *3))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-821) (-539))) (-5 *1 (-267 *3 *2)) (-4 *2 (-13 (-421 *3) (-971))))) @@ -16401,31 +15975,52 @@ (-5 *1 (-1122 *3)))) ((*1 *1 *1) (-4 *1 (-1160)))) (((*1 *2 *1) - (-12 (-5 *2 (-832)) (-5 *1 (-381 *3 *4 *5)) (-14 *3 (-745)) - (-14 *4 (-745)) (-4 *5 (-169))))) -(((*1 *2 *3) - (-12 (-5 *2 (-1 (-912 *3) (-912 *3))) (-5 *1 (-173 *3)) - (-4 *3 (-13 (-354) (-1157) (-971)))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-539)) (-5 *2 (-2 (|:| 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(-619 (-1135))) (-14 *5 (-745)) (-5 *2 (-112)) - (-5 *1 (-494 *4 *5))))) + (-12 (-5 *2 (-1218 *1)) (-4 *1 (-333 *3 *4 *5)) (-4 *3 (-1176)) + (-4 *4 (-1194 *3)) (-4 *5 (-1194 (-398 *4)))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-547)) (-4 *1 (-314 *4 *2)) (-4 *4 (-1063)) + (-4 *2 (-130))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-1131 *1)) (-4 *1 (-442)))) + ((*1 *2 *2 *2) + (-12 (-5 *2 (-1131 *6)) (-4 *6 (-918 *5 *3 *4)) (-4 *3 (-767)) + (-4 *4 (-821)) (-4 *5 (-878)) (-5 *1 (-447 *3 *4 *5 *6)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-1131 *1)) (-4 *1 (-878))))) +(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-318 *3)) (-4 *3 (-1172)))) + ((*1 *2 *2) + (-12 (-5 *2 (-112)) (-5 *1 (-505 *3 *4)) (-4 *3 (-1172)) + (-14 *4 (-547))))) +(((*1 *2 *2) (-12 (-5 *2 (-370)) (-5 *1 (-1220)))) + ((*1 *2) (-12 (-5 *2 (-370)) (-5 *1 (-1220))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-821) (-539))) (-5 *1 (-267 *3 *2)) (-4 *2 (-13 (-421 *3) (-971))))) @@ -16446,49 +16041,43 @@ (-12 (-5 *2 (-1116 *3)) (-4 *3 (-38 (-398 (-547)))) (-5 *1 (-1122 *3)))) ((*1 *1 *1) (-4 *1 (-1160)))) -(((*1 *2 *1) (-12 (-5 *2 (-1067)) (-5 *1 (-1139))))) -(((*1 *1 *1 *1) (-5 *1 (-832)))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-619 (-619 (-619 *4)))) (-5 *2 (-619 (-619 *4))) + (-4 *4 (-821)) (-5 *1 (-1143 *4))))) (((*1 *2 *1) - (-12 (-5 *2 (-619 (-2 (|:| |val| *3) (|:| -1965 *4)))) + (-12 (-5 *2 (-619 (-2 (|:| |val| *3) (|:| -1966 *4)))) (-5 *1 (-1101 *3 *4)) (-4 *3 (-13 (-1063) (-34))) (-4 *4 (-13 (-1063) (-34)))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-539)) - (-5 *2 (-2 (|:| -1557 *4) (|:| -2225 *3) (|:| -3856 *3))) - (-5 *1 (-938 *4 *3)) (-4 *3 (-1194 *4)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-1016)) (-4 *4 (-767)) (-4 *5 (-821)) - (-5 *2 (-2 (|:| -2225 *1) (|:| -3856 *1))) (-4 *1 (-1030 *3 *4 *5)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-539)) (-4 *3 (-1016)) - (-5 *2 (-2 (|:| -1557 *3) (|:| -2225 *1) (|:| -3856 *1))) - (-4 *1 (-1194 *3))))) +(((*1 *2 *3 *3 *3 *4 *4 *4 *3) + (-12 (-5 *3 (-547)) (-5 *4 (-663 (-217))) (-5 *2 (-1004)) + (-5 *1 (-727))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-285 (-398 (-921 *5)))) (-5 *4 (-1135)) - (-4 *5 (-13 (-298) (-821) (-145))) - (-5 *2 (-1125 (-619 (-307 *5)) (-619 (-285 (-307 *5))))) - (-5 *1 (-1091 *5)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-398 (-921 *5))) (-5 *4 (-1135)) - (-4 *5 (-13 (-298) (-821) (-145))) - (-5 *2 (-1125 (-619 (-307 *5)) (-619 (-285 (-307 *5))))) - (-5 *1 (-1091 *5))))) -(((*1 *1 *1 *1 *1) (-4 *1 (-532)))) + (-12 (-5 *3 (-398 (-547))) (-4 *5 (-767)) (-4 *6 (-821)) + (-4 *7 (-539)) (-4 *8 (-918 *7 *5 *6)) + (-5 *2 (-2 (|:| -1973 (-745)) (|:| -1558 *9) (|:| |radicand| *9))) + (-5 *1 (-922 *5 *6 *7 *8 *9)) (-5 *4 (-745)) + (-4 *9 + (-13 (-354) + (-10 -8 (-15 -1384 (*8 $)) (-15 -1394 (*8 $)) (-15 -3835 ($ *8)))))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-619 (-754 *5 (-834 *6)))) (-5 *4 (-112)) (-4 *5 (-442)) + (-14 *6 (-619 (-1135))) (-5 *2 (-619 (-1013 *5 *6))) + (-5 *1 (-604 *5 *6))))) +(((*1 *2 *3) (-12 (-5 *3 (-1135)) (-5 *2 (-1223)) (-5 *1 (-1138)))) + ((*1 *2) (-12 (-5 *2 (-1223)) (-5 *1 (-1138))))) (((*1 *2 *1) (-12 (-5 *2 (-547)) (-5 *1 (-302)))) ((*1 *2 *1) (-12 (-5 *2 (-745)) (-5 *1 (-1124 *3 *4)) (-14 *3 (-890)) (-4 *4 (-1016))))) -(((*1 *2 *3 *3 *3 *3 *4) - (-12 (-5 *3 (-217)) (-5 *4 (-547)) (-5 *2 (-1004)) (-5 *1 (-733))))) -(((*1 *2 *3 *3 *3 *3 *4 *5) - (-12 (-5 *3 (-217)) (-5 *4 (-547)) - (-5 *5 (-3 (|:| |fn| (-379)) (|:| |fp| (-63 -1409)))) - (-5 *2 (-1004)) (-5 *1 (-721))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-619 *3)) (-4 *3 (-1072 *5 *6 *7 *8)) - (-4 *5 (-13 (-298) (-145))) (-4 *6 (-767)) (-4 *7 (-821)) - (-4 *8 (-1030 *5 *6 *7)) (-5 *2 (-112)) - (-5 *1 (-570 *5 *6 *7 *8 *3))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-547)) (-4 *1 (-56 *4 *2 *5)) (-4 *4 (-1172)) + (-4 *5 (-364 *4)) (-4 *2 (-364 *4)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-547)) (-4 *1 (-1019 *4 *5 *6 *2 *7)) (-4 *6 (-1016)) + (-4 *7 (-230 *4 *6)) (-4 *2 (-230 *5 *6))))) +(((*1 *2 *2) + (-12 (-5 *2 (-619 *6)) (-4 *6 (-1030 *3 *4 *5)) (-4 *3 (-539)) + (-4 *4 (-767)) (-4 *5 (-821)) (-5 *1 (-946 *3 *4 *5 *6))))) (((*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 (-217) (-217))) (-5 *4 (-1058 (-370))) (-5 *5 (-619 (-254))) (-5 *2 (-1219)) (-5 *1 (-246)))) @@ -16598,10 +16187,7 @@ (-4 *5 (-767)) (-4 *3 (-821)) (-4 *2 (-1030 *4 *5 *3)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-745)) (-5 *1 (-1169 *2)) (-4 *2 (-1172))))) -(((*1 *2) - (-12 (-4 *4 (-169)) (-5 *2 (-112)) (-5 *1 (-357 *3 *4)) - (-4 *3 (-358 *4)))) - ((*1 *2) (-12 (-4 *1 (-358 *3)) (-4 *3 (-169)) (-5 *2 (-112))))) +(((*1 *2 *1) (-12 (-4 *1 (-245 *2)) (-4 *2 (-1172))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-619 (-254))) (-5 *1 (-1219)))) ((*1 *2 *1) (-12 (-5 *2 (-619 (-254))) (-5 *1 (-1219)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-619 (-254))) (-5 *1 (-1220)))) @@ -16627,102 +16213,98 @@ (-5 *1 (-1122 *3)))) ((*1 *1 *1) (-4 *1 (-1160)))) (((*1 *2 *1) (-12 (-5 *2 (-619 (-1118))) (-5 *1 (-1152))))) -(((*1 *1 *2) - (-12 (-5 *2 (-619 (-547))) (-5 *1 (-973 *3)) (-14 *3 (-547))))) -(((*1 *2 *1 *1) - (-12 +(((*1 *2 *3 *4) + (-12 (-5 *3 (-663 *8)) (-5 *4 (-745)) (-4 *8 (-918 *5 *7 *6)) + (-4 *5 (-13 (-298) (-145))) (-4 *6 (-13 (-821) (-592 (-1135)))) + (-4 *7 (-767)) (-5 *2 - (-2 (|:| |lm| (-377 *3)) (|:| |mm| (-377 *3)) (|:| |rm| (-377 *3)))) - (-5 *1 (-377 *3)) (-4 *3 (-1063)))) - ((*1 *2 *1 *1) + (-619 + (-2 (|:| |det| *8) (|:| |rows| (-619 (-547))) + (|:| |cols| (-619 (-547)))))) + (-5 *1 (-893 *5 *6 *7 *8))))) +(((*1 *2 *1) + (-12 (-4 *2 (-1063)) (-5 *1 (-933 *2 *3)) (-4 *3 (-1063))))) +(((*1 *2 *3 *3 *3 *3 *4 *5 *5 *6 *7 *8 *8 *3) + (-12 (-5 *6 (-619 (-112))) (-5 *7 (-663 (-217))) + (-5 *8 (-663 (-547))) (-5 *3 (-547)) (-5 *4 (-217)) (-5 *5 (-112)) + (-5 *2 (-1004)) (-5 *1 (-729))))) +(((*1 *2 *2) + (-12 (-4 *3 (-442)) (-4 *4 (-767)) (-4 *5 (-821)) + (-4 *6 (-1030 *3 *4 *5)) (-5 *1 (-600 *3 *4 *5 *6 *7 *2)) + (-4 *7 (-1036 *3 *4 *5 *6)) (-4 *2 (-1072 *3 *4 *5 *6))))) +(((*1 *1 *1) + (-12 (-4 *1 (-244 *2 *3 *4 *5)) (-4 *2 (-1016)) (-4 *3 (-821)) + (-4 *4 (-257 *3)) (-4 *5 (-767))))) +(((*1 *2 *2) (-12 (-5 *2 - (-2 (|:| |lm| (-793 *3)) (|:| |mm| (-793 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