diff options
Diffstat (limited to 'src')
| -rw-r--r-- | src/ChangeLog | 5 | ||||
| -rw-r--r-- | src/algebra/equation2.spad.pamphlet | 6 | ||||
| -rw-r--r-- | src/algebra/naalgc.spad.pamphlet | 2 | ||||
| -rw-r--r-- | src/algebra/stream.spad.pamphlet | 6 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 758 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1126 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1297 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8364 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 26180 |
9 files changed, 18869 insertions, 18875 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 482a3a0f..09a1fb3b 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,5 +1,9 @@ 2008-08-31 Gabriel Dos Reis <gdr@cs.tamu.edu> + * algebra/stream.spad.pamphlet (Stream): Remove duplicate of concat. + * algebra/naalgc.spad.pamphlet (FramedNonAssociativeAlgebra): + disambiguate coordinates. + * algebra/aggcat.spad.pamphlet (FiniteLinearAggregate): Remove duplicate definition of reverse. * algebra/algcat.spad.pamphlet (FramedAlgebra): Remove duplicate @@ -10,6 +14,7 @@ definition of asinhIfCan, acoshIfCan, asechIfCan, acshIfCan. * algebra/equation2.spad.pamphlet (Equation): Remove duplicate definition of *: (S,%) -> %. + Remove duplicate of factorAndSplit. * algebra/fortpak.spad.pamphlet (MultiVariableCalculusFunctions): Remove duplicate definition of jacobian. * algebra/tree.spad.pamphlet (BinaryTree): Remove duplicate diff --git a/src/algebra/equation2.spad.pamphlet b/src/algebra/equation2.spad.pamphlet index 7aad51f6..169df9ed 100644 --- a/src/algebra/equation2.spad.pamphlet +++ b/src/algebra/equation2.spad.pamphlet @@ -143,12 +143,6 @@ Equation(S: Type): public == private where Rep := Record(lhs: S, rhs: S) eq1,eq2: $ s : S - if S has IntegralDomain then - factorAndSplit eq == - (S has factor : S -> Factored S) => - eq0 := rightZero eq - [equation(rcf.factor,0) for rcf in factors factor lhs eq0] - [eq] l:S = r:S == [l, r] equation(l, r) == [l, r] -- hack! See comment above. lhs eqn == eqn.lhs diff --git a/src/algebra/naalgc.spad.pamphlet b/src/algebra/naalgc.spad.pamphlet index f6b470c1..2eee8450 100644 --- a/src/algebra/naalgc.spad.pamphlet +++ b/src/algebra/naalgc.spad.pamphlet @@ -1199,7 +1199,7 @@ FramedNonAssociativeAlgebra(R:CommutativeRing): rightDiscriminant() == rightDiscriminant basis() leftRegularRepresentation x == leftRegularRepresentation(x, basis()) rightRegularRepresentation x == rightRegularRepresentation(x, basis()) - coordinates x == coordinates(x, basis()) + coordinates(x: %) == coordinates(x, basis()) represents(v:Vector R):%== represents(v, basis()) coordinates(v:Vector %) == diff --git a/src/algebra/stream.spad.pamphlet b/src/algebra/stream.spad.pamphlet index ea503c3d..0879aad5 100644 --- a/src/algebra/stream.spad.pamphlet +++ b/src/algebra/stream.spad.pamphlet @@ -886,7 +886,7 @@ Stream(S): Exports == Implementation where concat(frst x,concat(rst x,s)) concat(x:%,y:%) == delay - empty? x => copy y + empty? x => y concat(frst x,concat(rst x, y)) concat l == delay @@ -1098,10 +1098,6 @@ Stream(S): Exports == Implementation where gen(f,s) == delay(ss:=f s; concat(ss, gen(f,ss))) generate(f,s)==concat(s,gen(f,s)) - concat(x:%,y:%) ==delay - empty? x => y - concat(frst x,concat(rst x,y)) - swhilee:(S -> Boolean,%) -> % swhilee(p,x) == delay empty? x => empty() diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 63fb62b1..61e51a5f 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2243771 . 3429202589) +(2243771 . 3429209006) (-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."))) -((-4271 . T) (-4270 . T) (-4102 . T)) +((-4271 . T) (-4270 . T) (-4087 . 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}."))) @@ -46,13 +46,13 @@ 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4267 . T) (-4265 . T) (-4264 . T) ((-4272 "*") . T) (-4263 . T) (-4268 . T) (-4262 . T) (-4102 . T)) +((-4267 . T) (-4265 . T) (-4264 . T) ((-4272 "*") . T) (-4263 . T) (-4268 . T) (-4262 . T) (-4087 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,{}x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,{}x,{}y,{}a..b,{}c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b,{} c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,{}x,{}y,{}xMin..xMax,{}yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) NIL NIL -(-31 R -1329) +(-31 R -1345) ((|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 -975) (QUOTE (-530))))) @@ -62,7 +62,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4270))) (-33) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) -((-4102 . T)) +((-4087 . T)) NIL (-34) ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\spad{acosh(x)} returns the hyperbolic arc-cosine of \\spad{x}."))) @@ -70,7 +70,7 @@ NIL NIL (-35 |Key| |Entry|) ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4270 . T) (-4271 . T) (-4102 . T)) +((-4270 . T) (-4271 . T) (-4087 . T)) NIL (-36 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#2|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) @@ -84,11 +84,11 @@ 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 -(-39 -1329 UP UPUP -1579) +(-39 -1345 UP UPUP -2113) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4263 |has| (-388 |#2|) (-344)) (-4268 |has| (-388 |#2|) (-344)) (-4262 |has| (-388 |#2|) (-344)) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| (-388 |#2|) (QUOTE (-138))) (|HasCategory| (-388 |#2|) (QUOTE (-140))) (|HasCategory| (-388 |#2|) (QUOTE (-330))) (-1450 (|HasCategory| (-388 |#2|) (QUOTE (-344))) (|HasCategory| (-388 |#2|) (QUOTE (-330)))) (|HasCategory| (-388 |#2|) (QUOTE (-344))) (|HasCategory| (-388 |#2|) (QUOTE (-349))) (-1450 (-12 (|HasCategory| (-388 |#2|) (QUOTE (-216))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (|HasCategory| (-388 |#2|) (QUOTE (-330)))) (-1450 (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-330))))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-349))) (-1450 (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (QUOTE (-216))) (|HasCategory| (-388 |#2|) (QUOTE (-344))))) -(-40 R -1329) +((|HasCategory| (-388 |#2|) (QUOTE (-138))) (|HasCategory| (-388 |#2|) (QUOTE (-140))) (|HasCategory| (-388 |#2|) (QUOTE (-330))) (-1476 (|HasCategory| (-388 |#2|) (QUOTE (-344))) (|HasCategory| (-388 |#2|) (QUOTE (-330)))) (|HasCategory| (-388 |#2|) (QUOTE (-344))) (|HasCategory| (-388 |#2|) (QUOTE (-349))) (-1476 (-12 (|HasCategory| (-388 |#2|) (QUOTE (-216))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (|HasCategory| (-388 |#2|) (QUOTE (-330)))) (-1476 (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-330))))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-349))) (-1476 (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (QUOTE (-216))) (|HasCategory| (-388 |#2|) (QUOTE (-344))))) +(-40 R -1345) ((|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 (-432))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|))))) @@ -107,7 +107,7 @@ NIL (-44 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) ((-4270 . T) (-4271 . T)) -((-1450 (-12 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-795))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2913) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1782) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2913) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1782) (|devaluate| |#2|))))))) (-1450 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-795))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-1450 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-795))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (-1450 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1450 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (-12 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2913) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1782) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) +((-1476 (-12 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-795))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1806) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1806) (|devaluate| |#2|))))))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-795))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-795))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (-12 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1806) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) (-45 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -140,7 +140,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-53 |Base| R -1329) +(-53 |Base| R -1345) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -150,7 +150,7 @@ NIL NIL (-55 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}a)} assign \\spad{a(i,{}j)} to \\spad{f(a(i,{}j))} for all \\spad{i,{} j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,{}a,{}b,{}r)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} when both \\spad{a(i,{}j)} and \\spad{b(i,{}j)} exist; else \\spad{c(i,{}j) = f(r,{} b(i,{}j))} when \\spad{a(i,{}j)} does not exist; else \\spad{c(i,{}j) = f(a(i,{}j),{}r)} when \\spad{b(i,{}j)} does not exist; otherwise \\spad{c(i,{}j) = f(r,{}r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i,{} j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = f(a(i,{}j))} for all \\spad{i,{} j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,{}j,{}v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,{}i,{}v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,{}r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,{}n,{}r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-4270 . T) (-4271 . T) (-4102 . T)) +((-4270 . T) (-4271 . T) (-4087 . T)) NIL (-56 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}."))) @@ -159,64 +159,64 @@ NIL (-57 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) ((-4271 . T) (-4270 . T)) -((-1450 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1450 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-1476 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-58 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) -(-59 -3890) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +(-59 -3901) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-60 -3890) +(-60 -3901) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-61 -3890) +(-61 -3901) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -3890) +(-62 -3901) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-63 -3890) +(-63 -3901) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct|) (|construct| (QUOTE X) (QUOTE HESS)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -3890) +(-64 -3901) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -3890) +(-65 -3901) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-66 -3890) +(-66 -3901) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-67 -3890) +(-67 -3901) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-68 -3890) +(-68 -3901) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-69 -3890) +(-69 -3901) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-70 -3890) +(-70 -3901) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-71 -3890) +(-71 -3901) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-72 -3890) +(-72 -3901) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -228,55 +228,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-75 -3890) +(-75 -3901) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-76 -3890) +(-76 -3901) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-77 -3890) +(-77 -3901) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-78 -3890) +(-78 -3901) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-79 -3890) +(-79 -3901) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -3890) +(-80 -3901) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -3890) +(-81 -3901) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-82 -3890) +(-82 -3901) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -3890) +(-83 -3901) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -3890) +(-84 -3901) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -3890) +(-85 -3901) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -3890) +(-86 -3901) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-87 -3890) +(-87 -3901) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -287,7 +287,7 @@ NIL (-89 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,{}y,{}...,{}z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-90 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -331,7 +331,7 @@ NIL (-100 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}."))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-101 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 @@ -346,12 +346,12 @@ NIL NIL (-104 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."))) -((-4271 . T) (-4102 . T)) +((-4271 . T) (-4087 . T)) NIL (-105) ((|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."))) ((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| (-530) (QUOTE (-850))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-530) (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-140))) (|HasCategory| (-530) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-530) (QUOTE (-960))) (|HasCategory| (-530) (QUOTE (-768))) (-1450 (|HasCategory| (-530) (QUOTE (-768))) (|HasCategory| (-530) (QUOTE (-795)))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-1075))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-530) (QUOTE (-216))) (|HasCategory| (-530) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-530) (LIST (QUOTE -491) (QUOTE (-1099)) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -291) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -268) (QUOTE (-530)) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-289))) (|HasCategory| (-530) (QUOTE (-515))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-530) (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (-1450 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (|HasCategory| (-530) (QUOTE (-138))))) +((|HasCategory| (-530) (QUOTE (-850))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-530) (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-140))) (|HasCategory| (-530) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-530) (QUOTE (-960))) (|HasCategory| (-530) (QUOTE (-768))) (-1476 (|HasCategory| (-530) (QUOTE (-768))) (|HasCategory| (-530) (QUOTE (-795)))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-1075))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-530) (QUOTE (-216))) (|HasCategory| (-530) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-530) (LIST (QUOTE -491) (QUOTE (-1099)) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -291) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -268) (QUOTE (-530)) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-289))) (|HasCategory| (-530) (QUOTE (-515))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-530) (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (|HasCategory| (-530) (QUOTE (-138))))) (-106) ((|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|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -380,7 +380,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|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 -(-113 -1329 UP) +(-113 -1345 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 @@ -391,14 +391,14 @@ NIL (-115 |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}."))) ((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| (-114 |#1|) (QUOTE (-850))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-114 |#1|) (QUOTE (-138))) (|HasCategory| (-114 |#1|) (QUOTE (-140))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-114 |#1|) (QUOTE (-960))) (|HasCategory| (-114 |#1|) (QUOTE (-768))) (-1450 (|HasCategory| (-114 |#1|) (QUOTE (-768))) (|HasCategory| (-114 |#1|) (QUOTE (-795)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-114 |#1|) (QUOTE (-1075))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| (-114 |#1|) (QUOTE (-216))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -491) (QUOTE (-1099)) (LIST (QUOTE -114) (|devaluate| |#1|)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -291) (LIST (QUOTE -114) (|devaluate| |#1|)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -268) (LIST (QUOTE -114) (|devaluate| |#1|)) (LIST (QUOTE -114) (|devaluate| |#1|)))) (|HasCategory| (-114 |#1|) (QUOTE (-289))) (|HasCategory| (-114 |#1|) (QUOTE (-515))) (|HasCategory| (-114 |#1|) (QUOTE (-795))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-114 |#1|) (QUOTE (-850)))) (-1450 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-114 |#1|) (QUOTE (-850)))) (|HasCategory| (-114 |#1|) (QUOTE (-138))))) +((|HasCategory| (-114 |#1|) (QUOTE (-850))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-114 |#1|) (QUOTE (-138))) (|HasCategory| (-114 |#1|) (QUOTE (-140))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-114 |#1|) (QUOTE (-960))) (|HasCategory| (-114 |#1|) (QUOTE (-768))) (-1476 (|HasCategory| (-114 |#1|) (QUOTE (-768))) (|HasCategory| (-114 |#1|) (QUOTE (-795)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-114 |#1|) (QUOTE (-1075))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| (-114 |#1|) (QUOTE (-216))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -491) (QUOTE (-1099)) (LIST (QUOTE -114) (|devaluate| |#1|)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -291) (LIST (QUOTE -114) (|devaluate| |#1|)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -268) (LIST (QUOTE -114) (|devaluate| |#1|)) (LIST (QUOTE -114) (|devaluate| |#1|)))) (|HasCategory| (-114 |#1|) (QUOTE (-289))) (|HasCategory| (-114 |#1|) (QUOTE (-515))) (|HasCategory| (-114 |#1|) (QUOTE (-795))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-114 |#1|) (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-114 |#1|) (QUOTE (-850)))) (|HasCategory| (-114 |#1|) (QUOTE (-138))))) (-116 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| (($ $) "\\spad{left(u)} returns the left child."))) NIL ((|HasAttribute| |#1| (QUOTE -4271))) (-117 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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."))) -((-4102 . T)) +((-4087 . T)) NIL (-118 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."))) @@ -407,14 +407,14 @@ NIL (-119 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"))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-120 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-121) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4271 . T) (-4270 . T) (-4102 . T)) +((-4271 . T) (-4270 . T) (-4087 . T)) NIL (-122 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -422,20 +422,20 @@ NIL NIL (-123 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4270 . T) (-4271 . T) (-4102 . T)) +((-4270 . T) (-4271 . T) (-4087 . T)) NIL (-124 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-125 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."))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-126) ((|constructor| (NIL "ByteArray provides datatype for fix-sized buffer of bytes."))) ((-4271 . T) (-4270 . T)) -((-1450 (-12 (|HasCategory| (-127) (QUOTE (-795))) (|HasCategory| (-127) (LIST (QUOTE -291) (QUOTE (-127))))) (-12 (|HasCategory| (-127) (QUOTE (-1027))) (|HasCategory| (-127) (LIST (QUOTE -291) (QUOTE (-127)))))) (-1450 (-12 (|HasCategory| (-127) (QUOTE (-1027))) (|HasCategory| (-127) (LIST (QUOTE -291) (QUOTE (-127))))) (|HasCategory| (-127) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-127) (LIST (QUOTE -572) (QUOTE (-506)))) (-1450 (|HasCategory| (-127) (QUOTE (-795))) (|HasCategory| (-127) (QUOTE (-1027)))) (|HasCategory| (-127) (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-127) (QUOTE (-1027))) (-12 (|HasCategory| (-127) (QUOTE (-1027))) (|HasCategory| (-127) (LIST (QUOTE -291) (QUOTE (-127))))) (|HasCategory| (-127) (LIST (QUOTE -571) (QUOTE (-804))))) +((-1476 (-12 (|HasCategory| (-127) (QUOTE (-795))) (|HasCategory| (-127) (LIST (QUOTE -291) (QUOTE (-127))))) (-12 (|HasCategory| (-127) (QUOTE (-1027))) (|HasCategory| (-127) (LIST (QUOTE -291) (QUOTE (-127)))))) (-1476 (-12 (|HasCategory| (-127) (QUOTE (-1027))) (|HasCategory| (-127) (LIST (QUOTE -291) (QUOTE (-127))))) (|HasCategory| (-127) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-127) (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| (-127) (QUOTE (-795))) (|HasCategory| (-127) (QUOTE (-1027)))) (|HasCategory| (-127) (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-127) (QUOTE (-1027))) (-12 (|HasCategory| (-127) (QUOTE (-1027))) (|HasCategory| (-127) (LIST (QUOTE -291) (QUOTE (-127))))) (|HasCategory| (-127) (LIST (QUOTE -571) (QUOTE (-804))))) (-127) ((|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 @@ -452,11 +452,11 @@ 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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4272 "*") . T)) NIL -(-131 |minix| -3004 S T$) +(-131 |minix| -3024 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-132 |minix| -3004 R) +(-132 |minix| -3024 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 @@ -467,7 +467,7 @@ NIL (-134) ((|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}."))) ((-4270 . T) (-4260 . T) (-4271 . T)) -((-1450 (-12 (|HasCategory| (-137) (QUOTE (-349))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137)))))) (|HasCategory| (-137) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-137) (QUOTE (-349))) (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-137) (QUOTE (-1027))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (|HasCategory| (-137) (LIST (QUOTE -571) (QUOTE (-804))))) +((-1476 (-12 (|HasCategory| (-137) (QUOTE (-349))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137)))))) (|HasCategory| (-137) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-137) (QUOTE (-349))) (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-137) (QUOTE (-1027))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (|HasCategory| (-137) (LIST (QUOTE -571) (QUOTE (-804))))) (-135 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 @@ -492,7 +492,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4267 . T)) NIL -(-141 -1329 UP UPUP) +(-141 -1345 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 @@ -506,7 +506,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasAttribute| |#1| (QUOTE -4270))) (-144 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."))) -((-4102 . T)) +((-4087 . T)) NIL (-145 |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."))) @@ -524,7 +524,7 @@ 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 -(-149 R -1329) +(-149 R -1345) ((|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 @@ -554,7 +554,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-941))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-993))) (|HasCategory| |#2| (QUOTE (-960))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (QUOTE (-344))) (|HasAttribute| |#2| (QUOTE -4266)) (|HasAttribute| |#2| (QUOTE -4269)) (|HasCategory| |#2| (QUOTE (-289))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-795)))) (-156 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})"))) -((-4263 -1450 (|has| |#1| (-522)) (-12 (|has| |#1| (-289)) (|has| |#1| (-850)))) (-4268 |has| |#1| (-344)) (-4262 |has| |#1| (-344)) (-4266 |has| |#1| (-6 -4266)) (-4269 |has| |#1| (-6 -4269)) (-4147 . T) (-4102 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4263 -1476 (|has| |#1| (-522)) (-12 (|has| |#1| (-289)) (|has| |#1| (-850)))) (-4268 |has| |#1| (-344)) (-4262 |has| |#1| (-344)) (-4266 |has| |#1| (-6 -4266)) (-4269 |has| |#1| (-6 -4269)) (-4136 . T) (-4087 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) NIL (-157 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."))) @@ -566,8 +566,8 @@ NIL NIL (-159 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}."))) -((-4263 -1450 (|has| |#1| (-522)) (-12 (|has| |#1| (-289)) (|has| |#1| (-850)))) (-4268 |has| |#1| (-344)) (-4262 |has| |#1| (-344)) (-4266 |has| |#1| (-6 -4266)) (-4269 |has| |#1| (-6 -4269)) (-4147 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-330))) (-1450 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-330)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-349))) (-1450 (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-330)))) (|HasCategory| |#1| (QUOTE (-216))) (-12 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -268) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530))))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099))))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-776)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-795)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-960)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-1121)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -572) 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T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-330))) (-1476 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-330)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-349))) (-1476 (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-330)))) (|HasCategory| |#1| (QUOTE (-216))) (-12 (|HasCategory| |#1| 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(QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -268) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-776))) (|HasCategory| |#1| (QUOTE (-993))) (-12 (|HasCategory| |#1| (QUOTE (-993))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-515))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-850))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-344)))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-216))) (-12 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasAttribute| |#1| (QUOTE -4266)) (|HasAttribute| |#1| (QUOTE -4269)) (-12 (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (QUOTE (-344)))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099))))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-330))))) (-160 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 @@ -616,7 +616,7 @@ 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|) $) "\\spad{constructorName c} returns the name of the constructor"))) NIL NIL -(-172 R -1329) +(-172 R -1345) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -724,19 +724,19 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} makes a database out of a list")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,{}start,{}end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,{}s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,{}q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,{}s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-199 -1329 UP UPUP R) +(-199 -1345 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 -(-200 -1329 FP) +(-200 -1345 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 (-201) ((|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."))) ((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| (-530) (QUOTE (-850))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-530) (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-140))) (|HasCategory| (-530) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-530) (QUOTE (-960))) (|HasCategory| (-530) (QUOTE (-768))) (-1450 (|HasCategory| (-530) (QUOTE (-768))) (|HasCategory| (-530) (QUOTE (-795)))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-1075))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-530) (QUOTE (-216))) (|HasCategory| (-530) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-530) (LIST (QUOTE -491) (QUOTE (-1099)) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -291) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -268) (QUOTE (-530)) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-289))) (|HasCategory| (-530) (QUOTE (-515))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-530) (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (-1450 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (|HasCategory| (-530) (QUOTE (-138))))) -(-202 R -1329) +((|HasCategory| (-530) (QUOTE (-850))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-530) (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-140))) (|HasCategory| (-530) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-530) (QUOTE (-960))) (|HasCategory| (-530) (QUOTE (-768))) (-1476 (|HasCategory| (-530) (QUOTE (-768))) (|HasCategory| (-530) (QUOTE (-795)))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-1075))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-530) (QUOTE (-216))) (|HasCategory| (-530) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-530) (LIST (QUOTE -491) (QUOTE (-1099)) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -291) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -268) (QUOTE (-530)) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-289))) (|HasCategory| (-530) (QUOTE (-515))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-530) (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (|HasCategory| (-530) (QUOTE (-138))))) +(-202 R -1345) ((|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 @@ -751,18 +751,18 @@ NIL (-205 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}."))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-206 |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}."))) ((-4267 . T)) NIL -(-207 R -1329) +(-207 R -1345) ((|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 (-208) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|hash| (((|Integer|) $) "\\spad{hash(x)} returns the hash key for \\spad{x}")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4137 . T) (-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4125 . T) (-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) NIL (-209) ((|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)}.}"))) @@ -771,14 +771,14 @@ NIL (-210 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}"))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-522))) (|HasAttribute| |#1| (QUOTE (-4272 "*"))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-522))) (|HasAttribute| |#1| (QUOTE (-4272 "*"))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-211 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 (-212 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."))) -((-4271 . T) (-4102 . T)) +((-4271 . T) (-4087 . T)) NIL (-213 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}."))) @@ -802,28 +802,28 @@ NIL ((|HasAttribute| |#1| (QUOTE -4270))) (-218 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}."))) -((-4271 . T) (-4102 . T)) +((-4271 . T) (-4087 . T)) NIL (-219) ((|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 -(-220 S -3004 R) +(-220 S -3024 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 (-344))) (|HasCategory| |#3| (QUOTE (-741))) (|HasCategory| |#3| (QUOTE (-793))) (|HasAttribute| |#3| (QUOTE -4267)) (|HasCategory| |#3| (QUOTE (-162))) (|HasCategory| |#3| (QUOTE (-349))) (|HasCategory| |#3| (QUOTE (-675))) (|HasCategory| |#3| (QUOTE (-128))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-984))) (|HasCategory| |#3| (QUOTE (-1027)))) -(-221 -3004 R) +(-221 -3024 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"))) -((-4264 |has| |#2| (-984)) (-4265 |has| |#2| (-984)) (-4267 |has| |#2| (-6 -4267)) ((-4272 "*") |has| |#2| (-162)) (-4270 . T) (-4102 . T)) +((-4264 |has| |#2| (-984)) (-4265 |has| |#2| (-984)) (-4267 |has| |#2| (-6 -4267)) ((-4272 "*") |has| |#2| (-162)) (-4270 . T) (-4087 . T)) NIL -(-222 -3004 A B) +(-222 -3024 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.")) 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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."))) ((-4264 |has| |#2| (-984)) (-4265 |has| |#2| (-984)) (-4267 |has| |#2| (-6 -4267)) ((-4272 "*") |has| |#2| (-162)) (-4270 . 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(QUOTE (-984))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099))))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530))))) (-1476 (|HasCategory| |#2| (QUOTE (-984))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (QUOTE (-1027)))) (|HasAttribute| |#2| (QUOTE -4267)) (|HasCategory| |#2| (QUOTE (-128))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (-224) ((|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 @@ -838,12 +838,12 @@ NIL NIL (-227 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."))) -((-4102 . T)) +((-4087 . T)) NIL (-228 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}"))) ((-4271 . T) (-4270 . T)) -((-1450 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1450 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-1476 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-229 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 @@ -851,19 +851,19 @@ NIL (-230 |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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T)) +((-1476 (-12 (|HasCategory| |#3| (QUOTE (-162))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-216))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-344))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-349))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-675))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-741))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-793))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-984))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1027))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|))) 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(|HasCategory| |#3| (QUOTE (-344))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (QUOTE (-349))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (QUOTE (-675))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (QUOTE (-741))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (QUOTE (-793))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (QUOTE (-984))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (QUOTE (-1027))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530)))))) (|HasCategory| (-530) (QUOTE (-795))) (-12 (|HasCategory| |#3| (QUOTE (-984))) (|HasCategory| |#3| (LIST (QUOTE -593) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (QUOTE (-984))) (|HasCategory| |#3| (LIST (QUOTE -841) (QUOTE (-1099))))) (-12 (|HasCategory| |#3| (QUOTE (-216))) (|HasCategory| |#3| (QUOTE (-984)))) (-1476 (-12 (|HasCategory| |#3| (QUOTE (-216))) (|HasCategory| |#3| (QUOTE (-984)))) (|HasCategory| |#3| (QUOTE (-675))) (-12 (|HasCategory| |#3| (QUOTE (-984))) (|HasCategory| |#3| (LIST (QUOTE -593) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (QUOTE (-984))) (|HasCategory| |#3| (LIST (QUOTE -841) (QUOTE (-1099)))))) (-1476 (|HasCategory| |#3| (QUOTE (-984))) (-12 (|HasCategory| |#3| (QUOTE (-1027))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530)))))) (-12 (|HasCategory| |#3| (QUOTE (-1027))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#3| (QUOTE (-1027)))) (-1476 (|HasAttribute| |#3| (QUOTE -4267)) (-12 (|HasCategory| |#3| (QUOTE (-216))) (|HasCategory| |#3| (QUOTE (-984)))) (-12 (|HasCategory| |#3| (QUOTE (-984))) (|HasCategory| |#3| (LIST (QUOTE -593) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (QUOTE (-984))) (|HasCategory| |#3| (LIST (QUOTE -841) (QUOTE (-1099)))))) (|HasCategory| |#3| (QUOTE (-128))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1027))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -571) (QUOTE (-804))))) (-234 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 @@ -874,7 +874,7 @@ NIL NIL (-236 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}."))) -((-4270 . T) (-4271 . T) (-4102 . T)) +((-4270 . T) (-4271 . T) (-4087 . T)) NIL (-237) ((|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."))) @@ -915,7 +915,7 @@ NIL (-246 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"))) (((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-850))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1450 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1450 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#3| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#3| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#3| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#3| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#3| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-344))) (-1450 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4268)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1450 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) +((|HasCategory| |#1| (QUOTE (-850))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#3| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#3| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#3| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#3| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#3| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4268)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) (-247 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 @@ -960,11 +960,11 @@ 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 -(-258 R -1329) +(-258 R -1345) ((|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 -(-259 R -1329) +(-259 R -1345) ((|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 @@ -986,7 +986,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027)))) (-264 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}."))) -((-4271 . T) (-4102 . T)) +((-4271 . T) (-4087 . T)) NIL (-265 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}."))) @@ -1012,7 +1012,7 @@ 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 -(-271 S R |Mod| -1810 -4067 |exactQuo|) +(-271 S R |Mod| -4004 -3842 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) NIL @@ -1034,21 +1034,21 @@ NIL NIL (-276 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) -((-4267 -1450 (|has| |#1| (-984)) (|has| |#1| (-453))) (-4264 |has| |#1| (-984)) (-4265 |has| |#1| (-984))) -((|HasCategory| |#1| (QUOTE (-344))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-984)))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-984))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (-1450 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-984)))) (-1450 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-984)))) (-1450 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-984)))) (-1450 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-675)))) (|HasCategory| |#1| (QUOTE (-453))) (-1450 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#1| (QUOTE (-984))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-1027)))) (-1450 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-284))) (-1450 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-453)))) (-1450 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-675)))) (-1450 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-984)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25)))) +((-4267 -1476 (|has| |#1| (-984)) (|has| |#1| (-453))) (-4264 |has| |#1| (-984)) (-4265 |has| |#1| (-984))) +((|HasCategory| |#1| (QUOTE (-344))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-984)))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-984))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-984)))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-984)))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-984)))) (-1476 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-675)))) (|HasCategory| |#1| (QUOTE (-453))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#1| (QUOTE (-984))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-1027)))) (-1476 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-284))) (-1476 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-453)))) (-1476 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-675)))) (-1476 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-984)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25)))) (-277 |Key| |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2913) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1782) (|devaluate| |#2|)))))) (-1450 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1450 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027))) (-1450 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1806) (|devaluate| |#2|)))))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) (-278) ((|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 -(-279 -1329 S) +(-279 -1345 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 -(-280 E -1329) +(-280 E -1345) ((|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 @@ -1096,7 +1096,7 @@ 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 -(-292 -1329) +(-292 -1345) ((|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 @@ -1107,7 +1107,7 @@ NIL (-294 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))}."))) ((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-850))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-140))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-960))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-768))) (-1450 (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-768))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-795)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-1075))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-216))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -491) (QUOTE (-1099)) (LIST (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -291) (LIST (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -268) (LIST (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-289))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-515))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-795))) (-12 (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-850))) (|HasCategory| $ (QUOTE (-138)))) (-1450 (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-138))) (-12 (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-850))) (|HasCategory| $ (QUOTE (-138)))))) +((|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-850))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-140))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-960))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-768))) (-1476 (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-768))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-795)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-1075))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-216))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -491) (QUOTE (-1099)) (LIST (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -291) (LIST (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -268) (LIST (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-289))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-515))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-795))) (-12 (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-850))) (|HasCategory| $ (QUOTE (-138)))) (-1476 (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-138))) (-12 (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-850))) (|HasCategory| $ (QUOTE (-138)))))) (-295 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 @@ -1118,9 +1118,9 @@ NIL NIL (-297 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."))) -((-4267 -1450 (-3314 (|has| |#1| (-984)) (|has| |#1| (-593 (-530)))) (-12 (|has| |#1| (-522)) (-1450 (-3314 (|has| |#1| (-984)) (|has| |#1| (-593 (-530)))) (|has| |#1| (-984)) (|has| |#1| (-453)))) (|has| |#1| (-984)) (|has| |#1| (-453))) (-4265 |has| |#1| (-162)) (-4264 |has| |#1| (-162)) ((-4272 "*") |has| |#1| (-522)) (-4263 |has| |#1| (-522)) (-4268 |has| 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(|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))))) (-1450 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-984)))) (-1450 (-12 (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| $ (QUOTE (-984))) (|HasCategory| $ (LIST (QUOTE -975) (QUOTE (-530))))) -(-298 R -1329) +((-4267 -1476 (-3340 (|has| |#1| (-984)) (|has| |#1| (-593 (-530)))) (-12 (|has| |#1| (-522)) (-1476 (-3340 (|has| |#1| (-984)) (|has| |#1| (-593 (-530)))) (|has| |#1| (-984)) (|has| |#1| (-453)))) (|has| |#1| (-984)) (|has| |#1| (-453))) (-4265 |has| |#1| (-162)) (-4264 |has| |#1| (-162)) ((-4272 "*") |has| |#1| (-522)) (-4263 |has| |#1| (-522)) 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(QUOTE (-984))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))))) (-1476 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-984)))) (-1476 (-12 (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| $ (QUOTE (-984))) (|HasCategory| $ (LIST (QUOTE -975) (QUOTE (-530))))) +(-298 R -1345) ((|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 @@ -1131,7 +1131,7 @@ NIL (-300 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."))) (((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-344)) (-4262 |has| |#1| (-344)) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|)))) (|HasCategory| (-388 (-530)) (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-344))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-1450 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasSignature| |#1| (LIST (QUOTE -2235) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1450 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -3700) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2562) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|)))) (|HasCategory| (-388 (-530)) (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-1476 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasSignature| |#1| (LIST (QUOTE -2258) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1476 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -1637) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2596) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|))))))) (-301 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 @@ -1163,12 +1163,12 @@ NIL (-308 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."))) ((-4271 . T) (-4270 . T)) -((-1450 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1450 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) -(-309 S -1329) +((-1476 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +(-309 S -1345) ((|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 (-349)))) -(-310 -1329) +(-310 -1345) ((|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."))) ((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) NIL @@ -1188,15 +1188,15 @@ 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 -(-315 S -1329 UP UPUP R) +(-315 S -1345 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 -(-316 -1329 UP UPUP R) +(-316 -1345 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 -(-317 -1329 UP UPUP R) +(-317 -1345 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 @@ -1216,26 +1216,26 @@ 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 -(-322 S -1329 UP UPUP) +(-322 S -1345 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.") (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-349))) (|HasCategory| |#2| (QUOTE (-344)))) -(-323 -1329 UP UPUP) +(-323 -1345 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.") (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) ((-4263 |has| (-388 |#2|) (-344)) (-4268 |has| (-388 |#2|) (-344)) (-4262 |has| (-388 |#2|) (-344)) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) NIL (-324 |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."))) ((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((-1450 (|HasCategory| (-851 |#1|) (QUOTE (-138))) (|HasCategory| (-851 |#1|) (QUOTE (-349)))) (|HasCategory| (-851 |#1|) (QUOTE (-140))) (|HasCategory| (-851 |#1|) (QUOTE (-349))) (|HasCategory| (-851 |#1|) (QUOTE (-138)))) +((-1476 (|HasCategory| (-851 |#1|) (QUOTE (-138))) (|HasCategory| (-851 |#1|) (QUOTE (-349)))) (|HasCategory| (-851 |#1|) (QUOTE (-140))) (|HasCategory| (-851 |#1|) (QUOTE (-349))) (|HasCategory| (-851 |#1|) (QUOTE (-138)))) (-325 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."))) ((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((-1450 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) +((-1476 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) (-326 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."))) ((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((-1450 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) +((-1476 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) (-327 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 @@ -1252,31 +1252,31 @@ 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."))) ((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) NIL -(-331 R UP -1329) +(-331 R UP -1345) ((|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 (-332 |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."))) ((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((-1450 (|HasCategory| (-851 |#1|) (QUOTE (-138))) (|HasCategory| (-851 |#1|) (QUOTE (-349)))) (|HasCategory| (-851 |#1|) (QUOTE (-140))) (|HasCategory| (-851 |#1|) (QUOTE (-349))) (|HasCategory| (-851 |#1|) (QUOTE (-138)))) +((-1476 (|HasCategory| (-851 |#1|) (QUOTE (-138))) (|HasCategory| (-851 |#1|) (QUOTE (-349)))) (|HasCategory| (-851 |#1|) (QUOTE (-140))) (|HasCategory| (-851 |#1|) (QUOTE (-349))) (|HasCategory| (-851 |#1|) (QUOTE (-138)))) (-333 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."))) ((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((-1450 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) +((-1476 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) (-334 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."))) ((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((-1450 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) +((-1476 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) (-335 |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}."))) ((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((-1450 (|HasCategory| (-851 |#1|) (QUOTE (-138))) (|HasCategory| (-851 |#1|) (QUOTE (-349)))) (|HasCategory| (-851 |#1|) (QUOTE (-140))) (|HasCategory| (-851 |#1|) (QUOTE (-349))) (|HasCategory| (-851 |#1|) (QUOTE (-138)))) +((-1476 (|HasCategory| (-851 |#1|) (QUOTE (-138))) (|HasCategory| (-851 |#1|) (QUOTE (-349)))) (|HasCategory| (-851 |#1|) (QUOTE (-140))) (|HasCategory| (-851 |#1|) (QUOTE (-349))) (|HasCategory| (-851 |#1|) (QUOTE (-138)))) (-336 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."))) ((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((-1450 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) -(-337 -1329 GF) +((-1476 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) +(-337 -1345 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 @@ -1284,14 +1284,14 @@ 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 -(-339 -1329 FP FPP) +(-339 -1345 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 (-340 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}."))) ((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((-1450 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) +((-1476 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) (-341 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 @@ -1346,7 +1346,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4271)) (|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027)))) (-354 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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4270 . T) (-4102 . T)) +((-4270 . T) (-4087 . T)) NIL (-355 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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."))) @@ -1370,7 +1370,7 @@ NIL NIL (-360) ((|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}."))) -((-4253 . T) (-4261 . T) (-4137 . T) (-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4253 . T) (-4261 . T) (-4125 . T) (-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) NIL (-361 |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}."))) @@ -1386,11 +1386,11 @@ NIL NIL (-364) ((|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}."))) -((-4102 . T)) +((-4087 . T)) NIL (-365) ((|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.}"))) -((-4102 . T)) +((-4087 . T)) NIL (-366 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."))) @@ -1420,7 +1420,7 @@ 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 -(-373 -1329 UP UPUP R) +(-373 -1345 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 @@ -1434,27 +1434,27 @@ NIL NIL (-376) ((|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."))) -((-4102 . T)) +((-4087 . T)) NIL (-377) ((|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.}"))) -((-4102 . T)) +((-4087 . T)) NIL (-378) ((|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 -(-379 -3890 |returnType| -2525 |symbols|) +(-379 -3901 |returnType| -2582 |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 -(-380 -1329 UP) +(-380 -1345 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL (-381 R) ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) -((-4102 . T)) +((-4087 . T)) NIL (-382 S) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) @@ -1470,7 +1470,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4253)) (|HasAttribute| |#1| (QUOTE -4261))) (-385) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) -((-4137 . T) (-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4125 . T) (-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) NIL (-386 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."))) @@ -1483,7 +1483,7 @@ NIL (-388 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."))) ((-4257 -12 (|has| |#1| (-6 -4268)) (|has| |#1| (-432)) (|has| |#1| (-6 -4257))) (-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (QUOTE (-768))) (-1450 (|HasCategory| |#1| (QUOTE (-768))) (|HasCategory| |#1| (QUOTE (-795)))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776)))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-1075))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (-1450 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776))))) (-1450 (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776))))) (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -268) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-515))) (-12 (|HasAttribute| |#1| (QUOTE -4268)) (|HasAttribute| |#1| (QUOTE -4257)) (|HasCategory| |#1| (QUOTE (-432)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1450 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) +((|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (QUOTE (-768))) (-1476 (|HasCategory| |#1| (QUOTE (-768))) (|HasCategory| |#1| (QUOTE (-795)))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776)))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-1075))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776))))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776))))) (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -268) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-515))) (-12 (|HasAttribute| |#1| (QUOTE -4268)) (|HasAttribute| |#1| (QUOTE -4257)) (|HasCategory| |#1| (QUOTE (-432)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) (-389 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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1504,11 +1504,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-394 R -1329 UP A) +(-394 R -1345 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4267 . T)) NIL -(-395 R -1329 UP A |ibasis|) +(-395 R -1345 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 -975) (|devaluate| |#2|)))) @@ -1527,7 +1527,7 @@ NIL (-399 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."))) ((-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -291) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -268) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-1139))) (-1450 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-1139)))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -268) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-432)))) +((|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -291) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -268) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-1139))) (-1476 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-1139)))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -268) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-432)))) (-400 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 @@ -1554,9 +1554,9 @@ NIL ((|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-349)))) (-406 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4270 . T) (-4260 . T) (-4271 . T) (-4102 . T)) +((-4270 . T) (-4260 . T) (-4271 . T) (-4087 . T)) NIL -(-407 R -1329) +(-407 R -1345) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1564,7 +1564,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) ((-4257 -12 (|has| |#1| (-6 -4257)) (|has| |#2| (-6 -4257))) (-4264 . T) (-4265 . T) (-4267 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4257)) (|HasAttribute| |#2| (QUOTE -4257)))) -(-409 R -1329) +(-409 R -1345) ((|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 @@ -1574,17 +1574,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (QUOTE (-984))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506))))) (-411 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}."))) -((-4267 -1450 (|has| |#1| (-984)) (|has| |#1| (-453))) (-4265 |has| |#1| (-162)) (-4264 |has| |#1| (-162)) ((-4272 "*") |has| |#1| (-522)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-522)) (-4262 |has| |#1| (-522)) (-4102 . T)) +((-4267 -1476 (|has| |#1| (-984)) (|has| |#1| (-453))) (-4265 |has| |#1| (-162)) (-4264 |has| |#1| (-162)) ((-4272 "*") |has| |#1| (-522)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-522)) (-4262 |has| |#1| (-522)) (-4087 . T)) NIL -(-412 R -1329) +(-412 R -1345) ((|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 -(-413 R -1329) +(-413 R -1345) ((|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)))) -(-414 R -1329) +(-414 R -1345) ((|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 @@ -1592,7 +1592,7 @@ 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 -(-416 R -1329 UP) +(-416 R -1345 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 -975) (QUOTE (-47))))) @@ -1610,17 +1610,17 @@ NIL NIL (-420) ((|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}."))) -((-4102 . T)) +((-4087 . T)) NIL (-421) ((|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.}"))) -((-4102 . T)) +((-4087 . T)) NIL (-422 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 -(-423 R UP -1329) +(-423 R UP -1345) ((|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 @@ -1667,7 +1667,7 @@ NIL (-434 |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"))) (((-4272 "*") |has| |#2| (-162)) (-4263 |has| |#2| (-522)) (-4268 |has| |#2| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#2| (QUOTE (-850))) (-1450 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1450 (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1450 (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-162))) (-1450 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-522)))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (QUOTE (-344))) (-1450 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#2| (QUOTE -4268)) (|HasCategory| |#2| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (-1450 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-138))))) +((|HasCategory| |#2| (QUOTE (-850))) (-1476 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1476 (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1476 (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-162))) (-1476 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-522)))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (QUOTE (-344))) (-1476 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#2| (QUOTE -4268)) (|HasCategory| |#2| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-138))))) (-435 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 @@ -1732,7 +1732,7 @@ 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 -(-451 |lv| -1329 R) +(-451 |lv| -1345 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 @@ -1747,11 +1747,11 @@ NIL (-454 |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."))) (((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-344)) (-4262 |has| |#1| (-344)) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|)))) (|HasCategory| (-388 (-530)) (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-344))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-1450 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasSignature| |#1| (LIST (QUOTE -2235) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1450 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -3700) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2562) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|)))) (|HasCategory| (-388 (-530)) (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-1476 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasSignature| |#1| (LIST (QUOTE -2258) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1476 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -1637) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2596) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|))))))) (-455 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) 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T)) -((-12 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2913) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1782) (|devaluate| |#2|)))))) (-1450 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1450 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-795))) (-1450 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1806) (|devaluate| |#2|)))))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-795))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) (-456 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)}"))) ((-4271 . T) (-4270 . T)) @@ -1763,7 +1763,7 @@ NIL (-458 |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."))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2913) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1782) (|devaluate| |#2|)))))) (-1450 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1450 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027))) (-1450 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1806) (|devaluate| |#2|)))))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) (-459) ((|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 @@ -1771,11 +1771,11 @@ NIL (-460 |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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(QUOTE (-216))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#2| (QUOTE (-349))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#2| (QUOTE (-675))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#2| (QUOTE (-741))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#2| (QUOTE (-793))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#2| (QUOTE (-984))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))))) (|HasCategory| (-530) (QUOTE (-795))) (-12 (|HasCategory| |#2| (QUOTE (-984))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530))))) (-12 (|HasCategory| |#2| (QUOTE (-216))) (|HasCategory| |#2| (QUOTE (-984)))) (-12 (|HasCategory| |#2| (QUOTE (-984))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099))))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530))))) (-1476 (|HasCategory| |#2| (QUOTE (-984))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (QUOTE (-1027)))) (|HasAttribute| |#2| (QUOTE -4267)) (|HasCategory| |#2| (QUOTE (-128))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (-462) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|Symbol|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Symbol|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|List| (|Symbol|))) "\\spad{headAst [f,{}x1,{}..,{}xn]} constructs a function definition header."))) NIL @@ -1783,8 +1783,8 @@ NIL (-463 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}."))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) -(-464 -1329 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +(-464 -1345 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1795,14 +1795,14 @@ NIL (-466) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion.")) (|coerce| (((|RadixExpansion| 16) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a radix expansion with base 16.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a rational number."))) ((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| (-530) (QUOTE (-850))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-530) (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-140))) (|HasCategory| (-530) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-530) (QUOTE (-960))) (|HasCategory| (-530) (QUOTE (-768))) (-1450 (|HasCategory| (-530) (QUOTE (-768))) (|HasCategory| (-530) (QUOTE (-795)))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-1075))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-530) (QUOTE (-216))) (|HasCategory| (-530) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-530) (LIST (QUOTE -491) (QUOTE (-1099)) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -291) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -268) (QUOTE (-530)) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-289))) (|HasCategory| (-530) (QUOTE (-515))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-530) (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (-1450 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (|HasCategory| (-530) (QUOTE (-138))))) +((|HasCategory| (-530) (QUOTE (-850))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-530) (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-140))) (|HasCategory| (-530) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-530) (QUOTE (-960))) (|HasCategory| (-530) (QUOTE (-768))) (-1476 (|HasCategory| (-530) (QUOTE (-768))) (|HasCategory| (-530) (QUOTE (-795)))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-1075))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-530) (QUOTE (-216))) (|HasCategory| (-530) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-530) (LIST (QUOTE -491) (QUOTE (-1099)) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -291) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -268) (QUOTE (-530)) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-289))) (|HasCategory| (-530) (QUOTE (-515))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-530) (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (|HasCategory| (-530) (QUOTE (-138))))) (-467 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL ((|HasAttribute| |#1| (QUOTE -4270)) (|HasAttribute| |#1| (QUOTE -4271)) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (-468 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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) -((-4102 . T)) +((-4087 . T)) NIL (-469) ((|constructor| (NIL "This domain represents hostnames on computer network.")) (|host| (($ (|String|)) "\\spad{host(n)} constructs a Hostname from the name \\spad{`n'}."))) @@ -1816,7 +1816,7 @@ 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 -(-472 -1329 UP |AlExt| |AlPol|) +(-472 -1345 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 @@ -1827,16 +1827,16 @@ NIL (-474 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4271 . T) (-4270 . T)) -((-1450 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1450 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-1476 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-475 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."))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-476 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 -(-477 R UP -1329) +(-477 R UP -1345) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1856,7 +1856,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-482 -1329 |Expon| |VarSet| |DPoly|) +(-482 -1345 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -572) (QUOTE (-1099))))) @@ -1903,19 +1903,19 @@ NIL (-493 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) ((-4271 . T) (-4270 . T)) -((-1450 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1450 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-1476 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-494 |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}."))) ((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((-1450 (|HasCategory| (-543 |#1|) (QUOTE (-138))) (|HasCategory| (-543 |#1|) (QUOTE (-349)))) (|HasCategory| (-543 |#1|) (QUOTE (-140))) (|HasCategory| (-543 |#1|) (QUOTE (-349))) (|HasCategory| (-543 |#1|) (QUOTE (-138)))) +((-1476 (|HasCategory| (-543 |#1|) (QUOTE (-138))) (|HasCategory| (-543 |#1|) (QUOTE (-349)))) (|HasCategory| (-543 |#1|) (QUOTE (-140))) (|HasCategory| (-543 |#1|) (QUOTE (-349))) (|HasCategory| (-543 |#1|) (QUOTE (-138)))) (-495 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}."))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-496 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."))) ((-4271 . T) (-4270 . T)) -((-1450 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1450 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-1476 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-497 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 @@ -1927,7 +1927,7 @@ NIL (-499 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."))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-522))) (|HasAttribute| |#1| (QUOTE (-4272 "*"))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-522))) (|HasAttribute| |#1| (QUOTE (-4272 "*"))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-500 GF) ((|constructor| (NIL "InnerNormalBasisFieldFunctions(\\spad{GF}) (unexposed): This package has functions used by every normal basis finite field extension domain.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{minimalPolynomial(x)} \\undocumented{} See \\axiomFunFrom{minimalPolynomial}{FiniteAlgebraicExtensionField}")) (|normalElement| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{normalElement(n)} \\undocumented{} See \\axiomFunFrom{normalElement}{FiniteAlgebraicExtensionField}")) (|basis| (((|Vector| (|Vector| |#1|)) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{} See \\axiomFunFrom{basis}{FiniteAlgebraicExtensionField}")) (|normal?| (((|Boolean|) (|Vector| |#1|)) "\\spad{normal?(x)} \\undocumented{} See \\axiomFunFrom{normal?}{FiniteAlgebraicExtensionField}")) (|lookup| (((|PositiveInteger|) (|Vector| |#1|)) "\\spad{lookup(x)} \\undocumented{} See \\axiomFunFrom{lookup}{Finite}")) (|inv| (((|Vector| |#1|) (|Vector| |#1|)) "\\spad{inv x} \\undocumented{} See \\axiomFunFrom{inv}{DivisionRing}")) (|trace| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{trace(x,{}n)} \\undocumented{} See \\axiomFunFrom{trace}{FiniteAlgebraicExtensionField}")) (|norm| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{norm(x,{}n)} \\undocumented{} See \\axiomFunFrom{norm}{FiniteAlgebraicExtensionField}")) (/ (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x/y} \\undocumented{} See \\axiomFunFrom{/}{Field}")) (* (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x*y} \\undocumented{} See \\axiomFunFrom{*}{SemiGroup}")) (** (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{x**n} \\undocumented{} See \\axiomFunFrom{\\spad{**}}{DivisionRing}")) (|qPot| (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{qPot(v,{}e)} computes \\spad{v**(q**e)},{} interpreting \\spad{v} as an element of normal basis field,{} \\spad{q} the size of the ground field. This is done by a cyclic \\spad{e}-shift of the vector \\spad{v}.")) (|expPot| (((|Vector| |#1|) (|Vector| |#1|) (|SingleInteger|) (|SingleInteger|)) "\\spad{expPot(v,{}e,{}d)} returns the sum from \\spad{i = 0} to \\spad{e - 1} of \\spad{v**(q**i*d)},{} interpreting \\spad{v} as an element of a normal basis field and where \\spad{q} is the size of the ground field. Note: for a description of the algorithm,{} see \\spad{T}.Itoh and \\spad{S}.Tsujii,{} \"A fast algorithm for computing multiplicative inverses in \\spad{GF}(2^m) using normal bases\",{} Information and Computation 78,{} \\spad{pp}.171-177,{} 1988.")) (|repSq| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|)) "\\spad{repSq(v,{}e)} computes \\spad{v**e} by repeated squaring,{} interpreting \\spad{v} as an element of a normal basis field.")) (|dAndcExp| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|) (|SingleInteger|)) "\\spad{dAndcExp(v,{}n,{}k)} computes \\spad{v**e} interpreting \\spad{v} as an element of normal basis field. A divide and conquer algorithm similar to the one from \\spad{D}.\\spad{R}.Stinson,{} \"Some observations on parallel Algorithms for fast exponentiation in \\spad{GF}(2^n)\",{} Siam \\spad{J}. Computation,{} Vol.19,{} No.4,{} \\spad{pp}.711-717,{} August 1990 is used. Argument \\spad{k} is a parameter of this algorithm.")) (|xn| (((|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|)) "\\spad{xn(n)} returns the polynomial \\spad{x**n-1}.")) (|pol| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{pol(v)} turns the vector \\spad{[v0,{}...,{}vn]} into the polynomial \\spad{v0+v1*x+ ... + vn*x**n}.")) (|index| (((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{index(n,{}m)} is a index function for vectors of length \\spad{n} over the ground field.")) (|random| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{random(n)} creates a vector over the ground field with random entries.")) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|) "\\spad{setFieldInfo(m,{}p)} initializes the field arithmetic,{} where \\spad{m} is the multiplication table and \\spad{p} is the respective normal element of the ground field \\spad{GF}."))) NIL @@ -1940,7 +1940,7 @@ 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 -(-503 K -1329 |Par|) +(-503 K -1345 |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 @@ -1960,7 +1960,7 @@ 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 -(-508 K -1329 |Par|) +(-508 K -1345 |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 @@ -1995,12 +1995,12 @@ NIL (-516 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2913) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1782) (|devaluate| |#2|)))))) (-1450 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1450 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027))) (-1450 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) -(-517 R -1329) +((-12 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1806) (|devaluate| |#2|)))))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) +(-517 R -1345) ((|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 -(-518 R0 -1329 UP UPUP R) +(-518 R0 -1345 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 @@ -2010,7 +2010,7 @@ NIL NIL (-520 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."))) -((-4137 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4125 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) NIL (-521 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."))) @@ -2020,7 +2020,7 @@ 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."))) ((-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) NIL -(-523 R -1329) +(-523 R -1345) ((|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 @@ -2032,7 +2032,7 @@ 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 -(-526 R -1329 L) +(-526 R -1345 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 -607) (|devaluate| |#2|)))) @@ -2040,11 +2040,11 @@ 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 -(-528 -1329 UP UPUP R) +(-528 -1345 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 -(-529 -1329 UP) +(-529 -1345 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 @@ -2056,15 +2056,15 @@ 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 -(-532 R -1329 L) +(-532 R -1345 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 -607) (|devaluate| |#2|)))) -(-533 R -1329) +(-533 R -1345) ((|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 -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-1063)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-583))))) -(-534 -1329 UP) +(-534 -1345 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 @@ -2072,27 +2072,27 @@ 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 -(-536 -1329) +(-536 -1345) ((|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 (-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 domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) -((-4137 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4125 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) NIL (-538) ((|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 -(-539 R -1329) +(-539 R -1345) ((|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 -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-266))) (|HasCategory| |#2| (QUOTE (-583))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-1099))))) (-12 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-266)))) (|HasCategory| |#1| (QUOTE (-522)))) -(-540 -1329 UP) +(-540 -1345 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 -(-541 R -1329) +(-541 R -1345) ((|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 @@ -2108,15 +2108,15 @@ 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 -(-545 R -1329) +(-545 R -1345) ((|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 -(-546 E -1329) +(-546 E -1345) ((|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 -(-547 -1329) +(-547 -1345) ((|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}."))) ((-4265 . T) (-4264 . T)) ((|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-1099))))) @@ -2143,7 +2143,7 @@ NIL (-553 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) ((-4271 . T) (-4270 . T)) -((-1450 (-12 (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137)))))) (-1450 (|HasCategory| (-137) (LIST (QUOTE -571) (QUOTE (-804)))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137)))))) (|HasCategory| (-137) (LIST (QUOTE -572) (QUOTE (-506)))) (-1450 (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-137) (QUOTE (-1027)))) (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-137) (QUOTE (-1027))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (|HasCategory| (-137) (LIST (QUOTE -571) (QUOTE (-804))))) +((-1476 (-12 (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137)))))) (-1476 (|HasCategory| (-137) (LIST (QUOTE -571) (QUOTE (-804)))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137)))))) (|HasCategory| (-137) (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-137) (QUOTE (-1027)))) (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-137) (QUOTE (-1027))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (|HasCategory| (-137) (LIST (QUOTE -571) (QUOTE (-804))))) (-554 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 @@ -2151,7 +2151,7 @@ NIL (-555 |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}."))) (((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-530)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-530)) (|devaluate| |#1|)))) (|HasCategory| (-530) (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-344))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -2235) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-530)))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-530)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-530)) (|devaluate| |#1|)))) (|HasCategory| (-530) (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-344))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -2258) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-530)))))) (-556 |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.}"))) ((-4265 |has| |#1| (-522)) (-4264 |has| |#1| (-522)) ((-4272 "*") |has| |#1| (-522)) (-4263 |has| |#1| (-522)) (-4267 . T)) @@ -2164,7 +2164,7 @@ 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 -(-559 R -1329 FG) +(-559 R -1345 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 @@ -2175,14 +2175,14 @@ NIL (-561 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4271 . T) (-4270 . T)) -((-1450 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1450 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#1| (QUOTE (-984))) (-12 (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-984)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-1476 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#1| (QUOTE (-984))) (-12 (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-984)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-562 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 -4271)) (|HasCategory| |#2| (QUOTE (-795))) (|HasAttribute| |#1| (QUOTE -4270)) (|HasCategory| |#3| (QUOTE (-1027)))) (-563 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) -((-4102 . T)) +((-4087 . T)) NIL (-564) ((|constructor| (NIL "\\indented{1}{This domain defines the datatype for the Java} Virtual Machine byte codes.")) (|coerce| (($ (|Byte|)) "\\spad{coerce(x)} the numerical byte value into a \\spad{JVM} bytecode."))) @@ -2190,19 +2190,19 @@ NIL NIL (-565 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)."))) -((-4267 -1450 (-3314 (|has| |#2| (-348 |#1|)) (|has| |#1| (-522))) (-12 (|has| |#2| (-398 |#1|)) (|has| |#1| (-522)))) (-4265 . T) (-4264 . T)) -((-1450 (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|)))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|)))) +((-4267 -1476 (-3340 (|has| |#2| (-348 |#1|)) (|has| |#1| (-522))) (-12 (|has| |#2| (-398 |#1|)) (|has| |#1| (-522)))) (-4265 . T) (-4264 . T)) +((-1476 (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|)))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|)))) (-566 |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."))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 |#1|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 |#1|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2913) (QUOTE (-1082))) (LIST (QUOTE |:|) (QUOTE -1782) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 |#1|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| (-1082) (QUOTE (-795))) (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 |#1|)) (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 |#1|)) (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (QUOTE (-1082))) (LIST (QUOTE |:|) (QUOTE -1806) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| (-1082) (QUOTE (-795))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (LIST (QUOTE -571) (QUOTE (-804))))) (-567 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 (-568 |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}."))) -((-4271 . T) (-4102 . T)) +((-4271 . T) (-4087 . T)) NIL (-569 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"))) @@ -2220,7 +2220,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-573 -1329 UP) +(-573 -1345 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2236,7 +2236,7 @@ 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}."))) ((-4264 . T) (-4265 . T) (-4267 . T)) ((|HasCategory| |#1| (QUOTE (-793)))) -(-577 R -1329) +(-577 R -1345) ((|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 @@ -2264,18 +2264,18 @@ 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 -(-584 R -1329) +(-584 R -1345) ((|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 -(-585 |lv| -1329) +(-585 |lv| -1345) ((|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 (-586) ((|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."))) ((-4271 . T)) -((-12 (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 (-51))) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2913) (QUOTE (-1082))) (LIST (QUOTE |:|) (QUOTE -1782) (QUOTE (-51))))))) (-1450 (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 (-51))) (QUOTE (-1027))) (|HasCategory| (-51) (QUOTE (-1027)))) (-1450 (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 (-51))) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -291) (QUOTE (-51))))) (|HasCategory| (-1082) (QUOTE (-795))) (-1450 (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 (-51))) (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (QUOTE (-1082))) (LIST (QUOTE |:|) (QUOTE -1806) (QUOTE (-51))))))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-51) (QUOTE (-1027)))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -291) (QUOTE (-51))))) (|HasCategory| (-1082) (QUOTE (-795))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) (LIST (QUOTE -571) (QUOTE (-804))))) (-587 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2286,8 +2286,8 @@ NIL NIL (-589 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4267 -1450 (-3314 (|has| |#2| (-348 |#1|)) (|has| |#1| (-522))) (-12 (|has| |#2| (-398 |#1|)) (|has| |#1| (-522)))) (-4265 . T) (-4264 . T)) -((-1450 (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|)))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|)))) +((-4267 -1476 (-3340 (|has| |#2| (-348 |#1|)) (|has| |#1| (-522))) (-12 (|has| |#2| (-398 |#1|)) (|has| |#1| (-522)))) (-4265 . T) (-4264 . T)) +((-1476 (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|)))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|)))) (-590 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 @@ -2299,7 +2299,7 @@ NIL (-592 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,{}...,{}vn])} returns \\spad{[c1,{}...,{}cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-3659 (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-344)))) +((-3694 (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-344)))) (-593 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A,{} v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4267 . T)) @@ -2319,11 +2319,11 @@ NIL (-597 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) ((-4271 . T) (-4270 . T)) -((-1450 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1450 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-776))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-1476 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-776))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-598 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|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-599 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2338,9 +2338,9 @@ NIL ((|HasAttribute| |#1| (QUOTE -4271))) (-602 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})}."))) -((-4102 . T)) +((-4087 . T)) NIL -(-603 R -1329 L) +(-603 R -1345 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 @@ -2360,11 +2360,11 @@ 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}."))) ((-4264 . T) (-4265 . T) (-4267 . T)) NIL -(-608 -1329 UP) +(-608 -1345 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)))) -(-609 A -2847) +(-609 A -3955) ((|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}}"))) ((-4264 . T) (-4265 . T) (-4267 . T)) ((|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-344)))) @@ -2398,13 +2398,13 @@ NIL NIL (-617 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}."))) -((-4271 . T) (-4270 . T) (-4102 . T)) +((-4271 . T) (-4270 . T) (-4087 . T)) NIL -(-618 -1329) +(-618 -1345) ((|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 -(-619 -1329 |Row| |Col| M) +(-619 -1345 |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 @@ -2415,7 +2415,7 @@ NIL (-621 |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."))) ((-4267 . T) (-4270 . T) (-4264 . T) (-4265 . T)) -((|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-216))) (|HasAttribute| |#2| (QUOTE (-4272 "*"))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (-1450 (-12 (|HasCategory| |#2| (QUOTE (-216))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))))) (|HasCategory| |#2| (QUOTE (-289))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-522))) (-1450 (|HasAttribute| |#2| (QUOTE (-4272 "*"))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-216)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-162)))) +((|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-216))) (|HasAttribute| |#2| (QUOTE (-4272 "*"))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (-1476 (-12 (|HasCategory| |#2| (QUOTE (-216))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))))) (|HasCategory| |#2| (QUOTE (-289))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-522))) (-1476 (|HasAttribute| |#2| (QUOTE (-4272 "*"))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-216)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-162)))) (-622 |VarSet|) ((|constructor| (NIL "Lyndon words over arbitrary (ordered) symbols: see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). A Lyndon word is a word which is smaller than any of its right factors \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering. If \\axiom{a} and \\axiom{\\spad{b}} are two Lyndon words such that \\axiom{a < \\spad{b}} holds \\spad{w}.\\spad{r}.\\spad{t} lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule: \\axiom{[[a,{}\\spad{b}],{}\\spad{c}]} is a Lyndon word iff \\axiom{a*b < \\spad{c} \\spad{<=} \\spad{b}} holds. Lyndon words are internally represented by binary trees using the \\spadtype{Magma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic. \\newline Author : Michel Petitot (petitot@lifl.\\spad{fr}).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(\\spad{vl},{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList1(\\spad{vl},{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{\\spad{x}}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) NIL @@ -2426,12 +2426,12 @@ NIL NIL (-624 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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)]}."))) -((-4102 . T)) +((-4087 . T)) NIL (-625 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 -((-1450 (-12 (|HasCategory| |#1| (QUOTE (-984))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1027))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (QUOTE (-984))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-1476 (-12 (|HasCategory| |#1| (QUOTE (-984))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (QUOTE (-984))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-626 |VarSet|) ((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{\\spad{y*z}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}} by removing parentheses.")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}."))) NIL @@ -2470,7 +2470,7 @@ NIL ((|HasAttribute| |#2| (QUOTE (-4272 "*"))) (|HasCategory| |#2| (QUOTE (-289))) (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-522)))) (-635 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"))) -((-4270 . T) (-4271 . T) (-4102 . T)) +((-4270 . T) (-4271 . T) (-4087 . T)) NIL (-636 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."))) @@ -2479,7 +2479,7 @@ NIL (-637 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."))) ((-4270 . T) (-4271 . T)) -((-1450 (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1027))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-522))) (|HasAttribute| |#1| (QUOTE (-4272 "*"))) (|HasCategory| |#1| (QUOTE (-344))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-1476 (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-522))) (|HasAttribute| |#1| (QUOTE (-4272 "*"))) (|HasCategory| |#1| (QUOTE (-344))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-638 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 @@ -2488,7 +2488,7 @@ 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 -(-640 S -1329 FLAF FLAS) +(-640 S -1345 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 @@ -2498,11 +2498,11 @@ NIL NIL (-642) ((|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"))) -((-4263 . T) (-4268 |has| (-647) (-344)) (-4262 |has| (-647) (-344)) (-4147 . 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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}."))) -((-4271 . T) (-4102 . T)) +((-4271 . T) (-4087 . T)) NIL (-644 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}."))) @@ -2512,13 +2512,13 @@ 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 -(-646 OV E -1329 PG) +(-646 OV E -1345 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 (-647) ((|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}"))) -((-4137 . T) (-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4125 . T) (-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) NIL (-648 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."))) @@ -2548,7 +2548,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,{}b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-655 S -3260 I) +(-655 S -3286 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr,{} x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) NIL NIL @@ -2568,14 +2568,14 @@ 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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(LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-1075))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-330))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasCategory| |#1| (QUOTE (-216))) (|HasAttribute| |#1| (QUOTE -4268)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) (-662 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| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2584,7 +2584,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4265 |has| |#1| (-162)) (-4264 |has| |#1| (-162)) (-4267 . T)) ((|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140)))) -(-664 R |Mod| -1810 -4067 |exactQuo|) +(-664 R |Mod| -4004 -3842 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4267 . T)) NIL @@ -2596,7 +2596,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4265 . T) (-4264 . T)) NIL -(-667 -1329) +(-667 -1345) ((|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]]}."))) ((-4267 . T)) NIL @@ -2632,7 +2632,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (^ (($ $ (|NonNegativeInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-676 -1329 UP) +(-676 -1345 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 @@ -2651,7 +2651,7 @@ NIL (-680 |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."))) (((-4272 "*") |has| |#2| (-162)) (-4263 |has| |#2| (-522)) (-4268 |has| |#2| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#2| (QUOTE (-850))) (-1450 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1450 (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1450 (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-162))) (-1450 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-522)))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (QUOTE (-344))) (-1450 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#2| (QUOTE -4268)) (|HasCategory| |#2| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (-1450 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-138))))) +((|HasCategory| |#2| (QUOTE (-850))) (-1476 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1476 (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1476 (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-162))) (-1476 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-522)))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (QUOTE (-344))) (-1476 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#2| (QUOTE -4268)) (|HasCategory| |#2| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-138))))) (-681 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2670,7 +2670,7 @@ NIL ((-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#2| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#2| (QUOTE (-795)))) (-685 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4260 . T) (-4271 . T) (-4102 . T)) +((-4260 . T) (-4271 . T) (-4087 . T)) NIL (-686 S) ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|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}."))) @@ -2784,15 +2784,15 @@ 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 -(-714 -1329) +(-714 -1345) ((|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 -(-715 P -1329) +(-715 P -1345) ((|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 -(-716 UP -1329) +(-716 UP -1345) ((|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 @@ -2808,7 +2808,7 @@ 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."))) (((-4272 "*") . T)) NIL -(-720 R -1329) +(-720 R -1345) ((|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 @@ -2828,7 +2828,7 @@ 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 -(-725 -1329 |ExtF| |SUEx| |ExtP| |n|) +(-725 -1345 |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 @@ -2843,7 +2843,7 @@ NIL (-728 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."))) (((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-850))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1450 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1450 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) 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(QUOTE -37) (QUOTE (-530))))) (-3694 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-1099)))) (-3694 (|HasCategory| |#1| (LIST (QUOTE -932) (QUOTE (-530))))))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4268)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) (-729 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 @@ -2851,14 +2851,14 @@ NIL (-730 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)}"))) (((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4266 |has| |#1| (-344)) (-4268 |has| |#1| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1450 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1450 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-1075))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (-1450 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasCategory| |#1| (QUOTE (-216))) (|HasAttribute| |#1| (QUOTE -4268)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1450 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) +((|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-1075))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasCategory| |#1| (QUOTE (-216))) (|HasAttribute| |#1| (QUOTE -4268)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) (-731 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL ((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-732 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.}"))) -((-4271 . T) (-4270 . T) (-4102 . T)) +((-4271 . T) (-4270 . T) (-4087 . T)) NIL (-733 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}."))) @@ -2912,23 +2912,23 @@ 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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4264 . T) (-4265 . T) (-4267 . T)) NIL -(-746 -1450 R OS S) +(-746 -1476 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-747 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -268) (|devaluate| |#1|) (|devaluate| |#1|))) (-1450 (|HasCategory| (-938 |#1|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1450 (|HasCategory| (-938 |#1|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-993))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| (-938 |#1|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-938 |#1|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) +((|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -268) (|devaluate| |#1|) (|devaluate| |#1|))) (-1476 (|HasCategory| (-938 |#1|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1476 (|HasCategory| (-938 |#1|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-993))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| (-938 |#1|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-938 |#1|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (-748) ((|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 -(-749 R -1329 L) +(-749 R -1345 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 -(-750 R -1329) +(-750 R -1345) ((|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 @@ -2936,7 +2936,7 @@ 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 -(-752 R -1329) +(-752 R -1345) ((|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 @@ -2944,11 +2944,11 @@ 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 -(-754 -1329 UP UPUP R) +(-754 -1345 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 -(-755 -1329 UP L LQ) +(-755 -1345 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 @@ -2956,38 +2956,38 @@ 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 -(-757 -1329 UP L LQ) +(-757 -1345 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 -(-758 -1329 UP) +(-758 -1345 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 -(-759 -1329 L UP A LO) +(-759 -1345 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 -(-760 -1329 UP) +(-760 -1345 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)))) -(-761 -1329 LO) +(-761 -1345 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 -(-762 -1329 LODO) +(-762 -1345 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) 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(QUOTE (-984))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099))))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530))))) (-1476 (|HasCategory| |#2| (QUOTE (-984))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (QUOTE (-1027)))) (|HasAttribute| |#2| (QUOTE -4267)) (|HasCategory| |#2| (QUOTE (-128))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (-764 R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-850))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1450 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1450 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| (-766 (-1099)) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-766 (-1099)) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-766 (-1099)) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-766 (-1099)) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-766 (-1099)) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-344))) (-1450 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4268)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1450 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) +((|HasCategory| |#1| (QUOTE (-850))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| (-766 (-1099)) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-766 (-1099)) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-766 (-1099)) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-766 (-1099)) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-766 (-1099)) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4268)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) (-765 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable.")) (|coerce| ((|#2| $) "\\spad{coerce(p)} views \\spad{p} as a valie in the partial differential ring.") (($ |#2|) "\\spad{coerce(r)} views \\spad{r} as a value in the ordinary differential ring."))) (((-4272 "*") |has| |#2| (-344)) (-4263 |has| |#2| (-344)) (-4268 |has| |#2| (-344)) (-4262 |has| |#2| (-344)) (-4267 . T) (-4265 . T) (-4264 . T)) @@ -3042,7 +3042,7 @@ NIL NIL (-778 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4270 . T) (-4260 . T) (-4271 . T) (-4102 . T)) +((-4270 . T) (-4260 . T) (-4271 . T) (-4087 . T)) NIL (-779) ((|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."))) @@ -3055,7 +3055,7 @@ NIL (-781 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."))) ((-4267 |has| |#1| (-793))) -((|HasCategory| |#1| (QUOTE (-793))) (-1450 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-793)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-515))) (-1450 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-793))) (-1476 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-793)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-515))) (-1476 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-21)))) (-782 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) ((-4265 |has| |#1| (-162)) (-4264 |has| |#1| (-162)) (-4267 . T)) @@ -3083,12 +3083,12 @@ NIL (-788 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."))) ((-4267 |has| |#1| (-793))) -((|HasCategory| |#1| (QUOTE (-793))) (-1450 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-793)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-515))) (-1450 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-793))) (-1476 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-793)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-515))) (-1476 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-21)))) (-789) ((|constructor| (NIL "Ordered finite sets."))) NIL NIL -(-790 -3004 S) +(-790 -3024 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 @@ -3124,11 +3124,11 @@ 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 (-344))) (|HasCategory| |#1| (QUOTE (-522)))) -(-799 R |sigma| -2013) +(-799 R |sigma| -1535) ((|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."))) ((-4264 . T) (-4265 . T) (-4267 . T)) ((|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-344)))) -(-800 |x| R |sigma| -2013) +(-800 |x| R |sigma| -1535) ((|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."))) ((-4264 . T) (-4265 . T) (-4267 . T)) ((|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-344)))) @@ -3179,15 +3179,15 @@ NIL (-812 |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)."))) ((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| (-811 |#1|) (QUOTE (-850))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-811 |#1|) (QUOTE (-138))) (|HasCategory| (-811 |#1|) (QUOTE (-140))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-811 |#1|) (QUOTE (-960))) (|HasCategory| (-811 |#1|) (QUOTE (-768))) (-1450 (|HasCategory| (-811 |#1|) (QUOTE (-768))) (|HasCategory| (-811 |#1|) (QUOTE (-795)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-811 |#1|) (QUOTE (-1075))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| (-811 |#1|) (QUOTE (-216))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -491) (QUOTE (-1099)) (LIST (QUOTE -811) (|devaluate| |#1|)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -291) (LIST (QUOTE -811) (|devaluate| |#1|)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -268) (LIST (QUOTE -811) (|devaluate| |#1|)) (LIST (QUOTE -811) (|devaluate| |#1|)))) (|HasCategory| (-811 |#1|) (QUOTE (-289))) (|HasCategory| (-811 |#1|) (QUOTE (-515))) (|HasCategory| (-811 |#1|) (QUOTE (-795))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-811 |#1|) (QUOTE (-850)))) (-1450 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-811 |#1|) (QUOTE (-850)))) (|HasCategory| (-811 |#1|) (QUOTE (-138))))) +((|HasCategory| (-811 |#1|) (QUOTE (-850))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-811 |#1|) (QUOTE (-138))) (|HasCategory| (-811 |#1|) (QUOTE (-140))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-811 |#1|) (QUOTE (-960))) (|HasCategory| (-811 |#1|) (QUOTE (-768))) (-1476 (|HasCategory| (-811 |#1|) (QUOTE (-768))) (|HasCategory| (-811 |#1|) (QUOTE (-795)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-811 |#1|) (QUOTE (-1075))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| (-811 |#1|) (QUOTE (-216))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -491) (QUOTE (-1099)) (LIST (QUOTE -811) (|devaluate| |#1|)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -291) (LIST (QUOTE -811) (|devaluate| |#1|)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -268) (LIST (QUOTE -811) (|devaluate| |#1|)) (LIST (QUOTE -811) (|devaluate| |#1|)))) (|HasCategory| (-811 |#1|) (QUOTE (-289))) (|HasCategory| (-811 |#1|) (QUOTE (-515))) (|HasCategory| (-811 |#1|) (QUOTE (-795))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-811 |#1|) (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-811 |#1|) (QUOTE (-850)))) (|HasCategory| (-811 |#1|) (QUOTE (-138))))) (-813 |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)}."))) ((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#2| (QUOTE (-850))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (QUOTE (-960))) (|HasCategory| |#2| (QUOTE (-768))) (-1450 (|HasCategory| |#2| (QUOTE (-768))) (|HasCategory| |#2| (QUOTE (-795)))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-1075))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-216))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#2| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -268) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-289))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-795))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (-1450 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-138))))) +((|HasCategory| |#2| (QUOTE (-850))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (QUOTE (-960))) (|HasCategory| |#2| (QUOTE (-768))) (-1476 (|HasCategory| |#2| (QUOTE (-768))) (|HasCategory| |#2| (QUOTE (-795)))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-1075))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-216))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#2| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -268) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-289))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-795))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-138))))) (-814 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 (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))))) (-815) ((|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 @@ -3243,7 +3243,7 @@ NIL (-828 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,{}...,{}en],{} pat)} matches the pattern pat on the list of expressions \\spad{[e1,{}...,{}en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,{}...,{}en],{} pat)} tests if the list of expressions \\spad{[e1,{}...,{}en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr,{} pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((-12 (-3659 (|HasCategory| |#2| (QUOTE (-984)))) (-3659 (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-1099)))))) (-12 (|HasCategory| |#2| (QUOTE (-984))) (-3659 (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-1099)))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-1099))))) +((-12 (-3694 (|HasCategory| |#2| (QUOTE (-984)))) (-3694 (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-1099)))))) (-12 (|HasCategory| |#2| (QUOTE (-984))) (-3694 (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-1099)))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-1099))))) (-829 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f,{} [(v1,{}a1),{}...,{}(vn,{}an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL @@ -3252,7 +3252,7 @@ NIL ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-831 R -3260) +(-831 R -3286) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,{}...,{}vn],{} p)} returns \\spad{f(v1,{}...,{}vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v,{} p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p,{} [a1,{}...,{}an],{} f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p,{} [f1,{}...,{}fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p,{} f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3276,7 +3276,7 @@ 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 -(-837 UP -1329) +(-837 UP -1345) ((|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 @@ -3299,7 +3299,7 @@ NIL (-842 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 (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-843 |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 @@ -3315,7 +3315,7 @@ NIL (-846 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."))) ((-4267 . T)) -((-1450 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-795)))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-795)))) +((-1476 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-795)))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-795)))) (-847 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 @@ -3336,7 +3336,7 @@ 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."))) ((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) ((|HasCategory| $ (QUOTE (-140))) (|HasCategory| $ (QUOTE (-138))) (|HasCategory| $ (QUOTE (-349)))) -(-852 R0 -1329 UP UPUP R) +(-852 R0 -1345 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 @@ -3364,7 +3364,7 @@ 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 -(-859 -1329) +(-859 -1345) ((|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 @@ -3380,11 +3380,11 @@ 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}."))) (((-4272 "*") . T)) NIL -(-863 -1329 P) +(-863 -1345 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-864 |xx| -1329) +(-864 |xx| -1345) ((|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 @@ -3408,7 +3408,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-870 R -1329) +(-870 R -1345) ((|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 @@ -3420,7 +3420,7 @@ 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 -(-873 S R -1329) +(-873 S R -1345) ((|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 @@ -3440,11 +3440,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -827) (|devaluate| |#1|)))) -(-878 R -1329 -3260) +(-878 R -1345 -3286) ((|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 -(-879 -3260) +(-879 -3286) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL @@ -3467,7 +3467,7 @@ NIL (-884 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4271 . T) (-4270 . T)) -((-1450 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1450 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#1| (QUOTE (-984))) (-12 (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-984)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-1476 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#1| (QUOTE (-984))) (-12 (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-984)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-885 |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 @@ -3492,7 +3492,7 @@ 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}."))) (((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) NIL -(-891 E V R P -1329) +(-891 E V R P -1345) ((|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 @@ -3503,8 +3503,8 @@ NIL (-893 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}."))) (((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-850))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1450 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1450 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-344))) (-1450 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4268)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1450 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) -(-894 E V R P -1329) +((|HasCategory| |#1| (QUOTE (-850))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4268)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) +(-894 E V R P -1345) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-432)))) @@ -3527,12 +3527,12 @@ NIL (-899 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4271 . T) (-4270 . T)) -((-1450 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1450 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-1476 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-900) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -(-901 -1329) +(-901 -1345) ((|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 @@ -3547,11 +3547,11 @@ NIL (-904 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}"))) (((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-6 -4268)) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-128)))) (-1450 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4268))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-128)))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4268))) (-905 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"))) ((-4267 -12 (|has| |#2| (-453)) (|has| |#1| (-453)))) -((-1450 (-12 (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-741)))) (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-795))))) (-12 (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-741)))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-128))) (|HasCategory| |#2| (QUOTE (-128)))) (-12 (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-741))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-128))) (|HasCategory| |#2| (QUOTE (-128)))) (-12 (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-741))))) (-12 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-453)))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-453)))) (-12 (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#2| (QUOTE (-675))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#2| (QUOTE (-349)))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-128))) (|HasCategory| |#2| (QUOTE (-128)))) (-12 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-453)))) (-12 (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#2| (QUOTE (-675)))) (-12 (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-741))))) (-12 (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#2| (QUOTE (-675)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-128))) (|HasCategory| |#2| (QUOTE (-128)))) (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-795))))) +((-1476 (-12 (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-741)))) (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-795))))) (-12 (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-741)))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-128))) (|HasCategory| |#2| (QUOTE (-128)))) (-12 (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-741))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-128))) (|HasCategory| |#2| (QUOTE (-128)))) (-12 (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-741))))) (-12 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-453)))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-453)))) (-12 (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#2| (QUOTE (-675))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#2| (QUOTE (-349)))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-128))) (|HasCategory| |#2| (QUOTE (-128)))) (-12 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-453)))) (-12 (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#2| (QUOTE (-675)))) (-12 (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-741))))) (-12 (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#2| (QUOTE (-675)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-128))) (|HasCategory| |#2| (QUOTE (-128)))) (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-795))))) (-906) ((|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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3566,7 +3566,7 @@ NIL NIL (-909 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4270 . T) (-4271 . T) (-4102 . T)) +((-4270 . T) (-4271 . T) (-4087 . T)) NIL (-910 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}}"))) @@ -3594,7 +3594,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-522)))) (-916 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."))) -((-4270 . T) (-4102 . T)) +((-4270 . T) (-4087 . T)) NIL (-917 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."))) @@ -3610,7 +3610,7 @@ NIL NIL (-920 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}."))) -((-4271 . T) (-4270 . T) (-4102 . T)) +((-4271 . T) (-4270 . T) (-4087 . T)) NIL (-921 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3628,7 +3628,7 @@ 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 -(-925 K R UP -1329) +(-925 K R UP -1345) ((|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 @@ -3658,7 +3658,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-289))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (QUOTE (-960))) (|HasCategory| |#2| (QUOTE (-768))) (|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-1075)))) (-932 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}."))) -((-4102 . T) (-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4087 . T) (-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) NIL (-933 |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}."))) @@ -3666,7 +3666,7 @@ NIL NIL (-934 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."))) -((-4270 . T) (-4271 . T) (-4102 . T)) +((-4270 . T) (-4271 . T) (-4087 . T)) NIL (-935 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}."))) @@ -3683,11 +3683,11 @@ NIL (-938 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.}"))) ((-4263 |has| |#1| (-272)) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-344))) (-1450 (|HasCategory| |#1| (QUOTE (-272))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-272))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -268) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-993))) (|HasCategory| |#1| (QUOTE (-515))) (-1450 (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-344))))) +((|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (|HasCategory| |#1| (QUOTE (-272))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-272))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -268) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-993))) (|HasCategory| |#1| (QUOTE (-515))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-344))))) (-939 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}."))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-940 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3696,14 +3696,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-942 -1329 UP UPUP |radicnd| |n|) +(-942 -1345 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4263 |has| (-388 |#2|) (-344)) (-4268 |has| (-388 |#2|) (-344)) (-4262 |has| (-388 |#2|) (-344)) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| (-388 |#2|) (QUOTE (-138))) (|HasCategory| (-388 |#2|) (QUOTE (-140))) (|HasCategory| (-388 |#2|) (QUOTE (-330))) (-1450 (|HasCategory| (-388 |#2|) (QUOTE (-344))) (|HasCategory| (-388 |#2|) (QUOTE (-330)))) (|HasCategory| (-388 |#2|) (QUOTE (-344))) (|HasCategory| (-388 |#2|) (QUOTE (-349))) (-1450 (-12 (|HasCategory| (-388 |#2|) (QUOTE (-216))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (|HasCategory| (-388 |#2|) (QUOTE (-330)))) (-1450 (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-330))))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-349))) (-1450 (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (QUOTE (-216))) (|HasCategory| (-388 |#2|) (QUOTE (-344))))) +((|HasCategory| (-388 |#2|) (QUOTE (-138))) (|HasCategory| (-388 |#2|) (QUOTE (-140))) (|HasCategory| (-388 |#2|) (QUOTE (-330))) (-1476 (|HasCategory| (-388 |#2|) (QUOTE (-344))) (|HasCategory| (-388 |#2|) (QUOTE (-330)))) (|HasCategory| (-388 |#2|) (QUOTE (-344))) (|HasCategory| (-388 |#2|) (QUOTE (-349))) (-1476 (-12 (|HasCategory| (-388 |#2|) (QUOTE (-216))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (|HasCategory| (-388 |#2|) (QUOTE (-330)))) (-1476 (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-330))))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-349))) (-1476 (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (QUOTE (-216))) (|HasCategory| (-388 |#2|) (QUOTE (-344))))) (-943 |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."))) ((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| (-530) (QUOTE (-850))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-530) (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-140))) (|HasCategory| (-530) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-530) (QUOTE (-960))) (|HasCategory| (-530) (QUOTE (-768))) (-1450 (|HasCategory| (-530) (QUOTE (-768))) (|HasCategory| (-530) (QUOTE (-795)))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-1075))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-530) (QUOTE (-216))) (|HasCategory| (-530) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-530) (LIST (QUOTE -491) (QUOTE (-1099)) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -291) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -268) (QUOTE (-530)) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-289))) (|HasCategory| (-530) (QUOTE (-515))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-530) (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (-1450 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (|HasCategory| (-530) (QUOTE (-138))))) +((|HasCategory| (-530) (QUOTE (-850))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-530) (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-140))) (|HasCategory| (-530) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-530) (QUOTE (-960))) (|HasCategory| (-530) (QUOTE (-768))) (-1476 (|HasCategory| (-530) (QUOTE (-768))) (|HasCategory| (-530) (QUOTE (-795)))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-1075))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-530) (QUOTE (-216))) (|HasCategory| (-530) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-530) (LIST (QUOTE -491) (QUOTE (-1099)) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -291) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -268) (QUOTE (-530)) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-289))) (|HasCategory| (-530) (QUOTE (-515))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-530) (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (|HasCategory| (-530) (QUOTE (-138))))) (-944) ((|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 @@ -3726,7 +3726,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4271)) (|HasCategory| |#2| (QUOTE (-1027)))) (-949 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}."))) -((-4102 . T)) +((-4087 . T)) NIL (-950 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}}"))) @@ -3736,19 +3736,19 @@ 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}}"))) ((-4263 . T) (-4268 . T) (-4262 . T) (-4265 . T) (-4264 . T) ((-4272 "*") . T) (-4267 . T)) NIL -(-952 R -1329) +(-952 R -1345) ((|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 -(-953 R -1329) +(-953 R -1345) ((|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 -(-954 -1329 UP) +(-954 -1345 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 -(-955 -1329 UP) +(-955 -1345 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 @@ -3779,8 +3779,8 @@ NIL (-962 |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"))) ((-4263 . T) (-4268 . T) (-4262 . T) (-4265 . T) (-4264 . T) ((-4272 "*") . T) (-4267 . T)) -((-1450 (|HasCategory| (-388 (-530)) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-388 (-530)) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-388 (-530)) (LIST (QUOTE -975) (QUOTE (-530))))) -(-963 -1329 L) +((-1476 (|HasCategory| (-388 (-530)) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-388 (-530)) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-388 (-530)) (LIST (QUOTE -975) (QUOTE (-530))))) +(-963 -1345 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 @@ -3816,14 +3816,14 @@ 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 -(-972 -1329 |Expon| |VarSet| |FPol| |LFPol|) +(-972 -1345 |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"))) (((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) NIL (-973) ((|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.}"))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| (-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2913) (QUOTE (-1099))) (LIST (QUOTE |:|) (QUOTE -1782) (QUOTE (-51))))))) (-1450 (|HasCategory| (-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) (QUOTE (-1027))) (|HasCategory| (-51) (QUOTE (-1027)))) (-1450 (|HasCategory| (-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -291) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) (QUOTE (-1027))) (|HasCategory| (-1099) (QUOTE (-795))) (|HasCategory| (-51) (QUOTE (-1027))) (-1450 (|HasCategory| (-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (QUOTE (-1099))) (LIST (QUOTE |:|) (QUOTE -1806) (QUOTE (-51))))))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-51) (QUOTE (-1027)))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -291) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-1099) (QUOTE (-795))) (|HasCategory| (-51) (QUOTE (-1027))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (LIST (QUOTE -571) (QUOTE (-804))))) (-974 A S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#2| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#2| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} transforms a into an element of \\%."))) NIL @@ -3868,7 +3868,7 @@ 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."))) ((-4267 . T)) NIL -(-985 |xx| -1329) +(-985 |xx| -1345) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -3878,12 +3878,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-289))) (|HasCategory| |#4| (QUOTE (-344))) (|HasCategory| |#4| (QUOTE (-522))) (|HasCategory| |#4| (QUOTE (-162)))) (-987 |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"))) -((-4270 . T) (-4102 . T) (-4265 . T) (-4264 . T)) +((-4270 . T) (-4087 . T) (-4265 . T) (-4264 . T)) NIL (-988 |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}."))) ((-4270 . T) (-4265 . T) (-4264 . T)) -((-1450 (-12 (|HasCategory| |#3| (QUOTE (-162))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-344))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1027))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -572) (QUOTE (-506)))) (-1450 (|HasCategory| |#3| (QUOTE (-162))) (|HasCategory| |#3| (QUOTE (-344)))) (|HasCategory| |#3| (QUOTE (-344))) (|HasCategory| |#3| (QUOTE (-1027))) (|HasCategory| |#3| (QUOTE (-289))) (|HasCategory| |#3| (QUOTE (-522))) (|HasCategory| |#3| (QUOTE (-162))) (|HasCategory| |#3| (LIST (QUOTE -571) (QUOTE (-804)))) (-12 (|HasCategory| |#3| (QUOTE (-1027))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|))))) +((-1476 (-12 (|HasCategory| |#3| (QUOTE (-162))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-344))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1027))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#3| (QUOTE (-162))) (|HasCategory| |#3| (QUOTE (-344)))) (|HasCategory| |#3| (QUOTE (-344))) (|HasCategory| |#3| (QUOTE (-1027))) (|HasCategory| |#3| (QUOTE (-289))) (|HasCategory| |#3| (QUOTE (-522))) (|HasCategory| |#3| (QUOTE (-162))) (|HasCategory| |#3| (LIST (QUOTE -571) (QUOTE (-804)))) (-12 (|HasCategory| |#3| (QUOTE (-1027))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|))))) (-989 |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 @@ -3915,7 +3915,7 @@ NIL (-996) ((|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}"))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| (-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2913) (QUOTE (-1099))) (LIST (QUOTE |:|) (QUOTE -1782) (QUOTE (-51))))))) (-1450 (|HasCategory| (-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) (QUOTE (-1027))) (|HasCategory| (-51) (QUOTE (-1027)))) (-1450 (|HasCategory| (-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -291) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) (QUOTE (-1027))) (|HasCategory| (-1099) (QUOTE (-795))) (|HasCategory| (-51) (QUOTE (-1027))) (-1450 (|HasCategory| (-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (QUOTE (-1099))) (LIST (QUOTE |:|) (QUOTE -1806) (QUOTE (-51))))))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-51) (QUOTE (-1027)))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -291) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-1099) (QUOTE (-795))) (|HasCategory| (-51) (QUOTE (-1027))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (LIST (QUOTE -571) (QUOTE (-804))))) (-997 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 @@ -3942,7 +3942,7 @@ NIL NIL (-1003 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}."))) -((-4271 . T) (-4270 . T) (-4102 . T)) +((-4271 . T) (-4270 . T) (-4087 . T)) NIL (-1004 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."))) @@ -3952,11 +3952,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1006 |Base| R -1329) +(-1006 |Base| R -1345) ((|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 -(-1007 |Base| R -1329) +(-1007 |Base| R -1345) ((|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 @@ -3971,7 +3971,7 @@ NIL (-1010 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."))) ((-4263 |has| |#1| (-344)) (-4268 |has| |#1| (-344)) (-4262 |has| |#1| (-344)) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-330))) (-1450 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-330)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-349))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-330)))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099))))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099))))) (-1450 (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-344)))) (-12 (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (QUOTE (-344))))) +((|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-330))) (-1476 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-330)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-349))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-330)))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099))))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099))))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-344)))) (-12 (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (QUOTE (-344))))) (-1011 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 @@ -3995,7 +3995,7 @@ NIL (-1016 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"))) (((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-850))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1450 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1450 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| (-1017 (-1099)) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-1017 (-1099)) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-1017 (-1099)) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-1017 (-1099)) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-1017 (-1099)) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-344))) (-1450 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4268)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1450 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) +((|HasCategory| |#1| (QUOTE (-850))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| (-1017 (-1099)) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-1017 (-1099)) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-1017 (-1099)) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-1017 (-1099)) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-1017 (-1099)) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4268)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) (-1017 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 @@ -4014,7 +4014,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-1027)))) (-1021 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."))) -((-4102 . T)) +((-4087 . T)) NIL (-1022 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) @@ -4022,7 +4022,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#1| (QUOTE (-1027)))) (-1023 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| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}."))) -((-4102 . T)) +((-4087 . T)) NIL (-1024 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) @@ -4030,7 +4030,7 @@ NIL NIL (-1025 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) -((-4260 . T) (-4102 . T)) +((-4260 . T) (-4087 . T)) NIL (-1026 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}."))) @@ -4047,7 +4047,7 @@ NIL (-1029 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)}}"))) ((-4270 . T) (-4260 . T) (-4271 . T)) -((-1450 (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-795))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-1476 (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-795))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-1030 |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 @@ -4074,7 +4074,7 @@ NIL NIL (-1036 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.}"))) -((-4271 . T) (-4270 . T) (-4102 . T)) +((-4271 . T) (-4270 . T) (-4087 . T)) NIL (-1037) ((|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."))) @@ -4091,12 +4091,12 @@ NIL (-1040 |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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-975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#3| (QUOTE (-741)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#3| (QUOTE (-793)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#3| (QUOTE (-984)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#3| (QUOTE (-1027))))) (-1476 (-12 (|HasCategory| |#3| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (QUOTE (-128))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (QUOTE (-162))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (QUOTE (-216))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (QUOTE (-344))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (QUOTE (-349))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (QUOTE (-675))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (QUOTE (-741))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (QUOTE (-793))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (QUOTE (-984))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (QUOTE (-1027))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530)))))) (|HasCategory| (-530) (QUOTE (-795))) (-12 (|HasCategory| |#3| (QUOTE (-984))) (|HasCategory| |#3| (LIST (QUOTE -593) (QUOTE (-530))))) (-12 (|HasCategory| |#3| (QUOTE (-216))) (|HasCategory| |#3| (QUOTE (-984)))) (-12 (|HasCategory| |#3| (QUOTE (-984))) (|HasCategory| |#3| (LIST (QUOTE -841) (QUOTE (-1099))))) (-12 (|HasCategory| |#3| (QUOTE (-1027))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530))))) (-1476 (|HasCategory| |#3| (QUOTE (-984))) (-12 (|HasCategory| |#3| (QUOTE (-1027))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#3| (QUOTE (-1027)))) (|HasAttribute| |#3| (QUOTE -4267)) (|HasCategory| |#3| (QUOTE (-128))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1027))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -571) (QUOTE (-804))))) (-1041 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 (-432)))) -(-1042 R -1329) +(-1042 R -1345) ((|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 @@ -4118,7 +4118,7 @@ NIL NIL (-1047 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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4270 . T) (-4271 . T) (-4102 . T)) +((-4270 . T) (-4271 . T) (-4087 . T)) NIL (-1048 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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."))) @@ -4126,7 +4126,7 @@ NIL ((|HasCategory| |#3| (QUOTE (-344))) (|HasAttribute| |#3| (QUOTE (-4272 "*"))) (|HasCategory| |#3| (QUOTE (-162)))) (-1049 |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."))) -((-4102 . T) (-4270 . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4087 . T) (-4270 . T) (-4264 . T) (-4265 . T) (-4267 . T)) NIL (-1050 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}."))) @@ -4135,16 +4135,16 @@ NIL (-1051 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."))) (((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-850))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1450 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1450 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-344))) (-1450 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4268)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1450 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) +((|HasCategory| |#1| (QUOTE (-850))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4268)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) (-1052 |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}."))) (((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-344)))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-344)))) (-1053 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}"))) -((-4271 . T) (-4270 . T) (-4102 . T)) +((-4271 . T) (-4270 . T) (-4087 . T)) NIL -(-1054 UP -1329) +(-1054 UP -1345) ((|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 @@ -4191,18 +4191,18 @@ NIL (-1065 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."))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| (-1064 |#1| |#2|) (LIST (QUOTE -291) (LIST (QUOTE -1064) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1064 |#1| |#2|) (QUOTE (-1027)))) (|HasCategory| (-1064 |#1| |#2|) (QUOTE (-1027))) (-1450 (|HasCategory| (-1064 |#1| |#2|) (LIST (QUOTE -571) (QUOTE (-804)))) (-12 (|HasCategory| (-1064 |#1| |#2|) (LIST (QUOTE -291) (LIST (QUOTE -1064) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1064 |#1| |#2|) (QUOTE (-1027))))) (|HasCategory| (-1064 |#1| |#2|) (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| (-1064 |#1| |#2|) (LIST (QUOTE -291) (LIST (QUOTE -1064) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1064 |#1| |#2|) (QUOTE (-1027)))) (|HasCategory| (-1064 |#1| |#2|) (QUOTE (-1027))) (-1476 (|HasCategory| (-1064 |#1| |#2|) (LIST (QUOTE -571) (QUOTE (-804)))) (-12 (|HasCategory| (-1064 |#1| |#2|) (LIST (QUOTE -291) (LIST (QUOTE -1064) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1064 |#1| |#2|) (QUOTE (-1027))))) (|HasCategory| (-1064 |#1| |#2|) (LIST (QUOTE -571) (QUOTE (-804))))) (-1066 |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}."))) ((-4267 . T) (-4259 |has| |#2| (-6 (-4272 "*"))) (-4270 . T) (-4264 . T) (-4265 . T)) -((|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-216))) (|HasAttribute| |#2| (QUOTE (-4272 "*"))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (-1450 (-12 (|HasCategory| |#2| (QUOTE (-216))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (QUOTE (-289))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-344))) (-1450 (|HasAttribute| |#2| (QUOTE (-4272 "*"))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-216)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-162)))) +((|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-216))) (|HasAttribute| |#2| (QUOTE (-4272 "*"))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (-1476 (-12 (|HasCategory| |#2| (QUOTE (-216))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (QUOTE (-289))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-344))) (-1476 (|HasAttribute| |#2| (QUOTE (-4272 "*"))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-216)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-162)))) (-1067 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1068) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-4271 . T) (-4270 . T) (-4102 . T)) +((-4271 . T) (-4270 . T) (-4087 . T)) NIL (-1069 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,{}E,{}V,{}P,{}TS)} and \\spad{RSETGCD(R,{}E,{}V,{}P,{}TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) @@ -4215,19 +4215,19 @@ NIL (-1071 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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}."))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-1072 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 (-1073 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})}."))) -((-4102 . T)) +((-4087 . T)) NIL (-1074 |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."))) ((-4271 . T)) -((-12 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2913) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1782) (|devaluate| |#2|)))))) (-1450 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1450 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-795))) (-1450 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1806) (|devaluate| |#2|)))))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-795))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) (-1075) ((|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 @@ -4251,19 +4251,19 @@ NIL (-1080 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."))) ((-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-1081) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4271 . T) (-4270 . T) (-4102 . T)) +((-4271 . T) (-4270 . T) (-4087 . T)) NIL (-1082) NIL ((-4271 . T) (-4270 . T)) -((-1450 (-12 (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137)))))) (|HasCategory| (-137) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-137) (QUOTE (-1027))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (|HasCategory| (-137) (LIST (QUOTE -571) (QUOTE (-804))))) +((-1476 (-12 (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137)))))) (|HasCategory| (-137) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-137) (QUOTE (-1027))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (|HasCategory| (-137) (LIST (QUOTE -571) (QUOTE (-804))))) (-1083 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 |#1|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 |#1|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2913) (QUOTE (-1082))) (LIST (QUOTE |:|) (QUOTE -1782) (|devaluate| |#1|)))))) (-1450 (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 |#1|)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-1027)))) (-1450 (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 |#1|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 |#1|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 |#1|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 |#1|)) (QUOTE (-1027))) (|HasCategory| (-1082) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-1450 (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 |#1|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2913 (-1082)) (|:| -1782 |#1|)) (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (QUOTE (-1082))) (LIST (QUOTE |:|) (QUOTE -1806) (|devaluate| |#1|)))))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-1027)))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (QUOTE (-1027))) (|HasCategory| (-1082) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (LIST (QUOTE -571) (QUOTE (-804))))) (-1084 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 @@ -4290,9 +4290,9 @@ NIL NIL (-1090 |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. 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 Laurent series."))) -(((-4272 "*") -1450 (-3314 (|has| |#1| (-344)) (|has| (-1097 |#1| |#2| |#3|) (-768))) (|has| |#1| (-162)) (-3314 (|has| |#1| (-344)) (|has| (-1097 |#1| |#2| |#3|) (-850)))) (-4263 -1450 (-3314 (|has| |#1| (-344)) (|has| (-1097 |#1| |#2| |#3|) (-768))) (|has| |#1| (-522)) (-3314 (|has| |#1| (-344)) (|has| (-1097 |#1| |#2| |#3|) (-850)))) (-4268 |has| |#1| (-344)) (-4262 |has| |#1| (-344)) (-4264 . T) (-4265 . T) (-4267 . 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T)) -((|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE 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(-850)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-1075))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasCategory| |#1| (QUOTE (-216))) (|HasAttribute| |#1| (QUOTE -4268)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) (-1096 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|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."))) (((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-344)) (-4262 |has| |#1| (-344)) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|)))) (|HasCategory| (-388 (-530)) (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-344))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-1450 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasSignature| |#1| (LIST (QUOTE -2235) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1450 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -3700) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2562) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|)))) (|HasCategory| (-388 (-530)) (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-1476 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasSignature| |#1| (LIST (QUOTE -2258) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1476 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -1637) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2596) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|))))))) (-1097 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|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}."))) (((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-719)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-719)) (|devaluate| |#1|)))) (|HasCategory| (-719) (QUOTE (-1039))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-719))))) (|HasSignature| |#1| (LIST (QUOTE -2235) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-719))))) (|HasCategory| |#1| (QUOTE (-344))) (-1450 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -3700) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2562) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-719)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-719)) (|devaluate| |#1|)))) (|HasCategory| (-719) (QUOTE (-1039))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-719))))) (|HasSignature| |#1| (LIST (QUOTE -2258) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-719))))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -1637) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2596) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|))))))) (-1098) ((|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 @@ -4335,7 +4335,7 @@ NIL (-1101 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-6 -4268)) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| (-911) (QUOTE (-128))) (|HasCategory| |#1| (QUOTE (-522)))) (-1450 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4268))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| (-911) (QUOTE (-128))) (|HasCategory| |#1| (QUOTE (-522)))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4268))) (-1102) ((|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 @@ -4367,7 +4367,7 @@ NIL (-1109 |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}"))) ((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2913) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1782) (|devaluate| |#2|)))))) (-1450 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1450 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027))) (-1450 (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1806) (|devaluate| |#2|)))))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) (-1110 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 @@ -4378,7 +4378,7 @@ NIL NIL (-1112 |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})}."))) -((-4271 . T) (-4102 . T)) +((-4271 . T) (-4087 . T)) NIL (-1113 |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."))) @@ -4419,7 +4419,7 @@ NIL (-1122 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4271 . T) (-4270 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-1123 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4428,7 +4428,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1125 R -1329) +(-1125 R -1345) ((|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 @@ -4436,7 +4436,7 @@ 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 -(-1127 R -1329) +(-1127 R -1345) ((|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 -572) (LIST (QUOTE -833) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -827) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -827) (|devaluate| |#1|))))) @@ -4446,12 +4446,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-349)))) (-1129 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4271 . T) (-4270 . T) (-4102 . T)) +((-4271 . T) (-4270 . T) (-4087 . T)) NIL (-1130 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) (((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-344)))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-344)))) (-1131 |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 @@ -4464,13 +4464,13 @@ 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 (-1027))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) -(-1134 -1329) +(-1134 -1345) ((|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 (-1135) ((|constructor| (NIL "The fundamental Type."))) -((-4102 . T)) +((-4087 . T)) NIL (-1136 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}.}"))) @@ -4502,16 +4502,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-344)))) (-1143 |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|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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(QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1476 (-12 (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-768))) (|HasCategory| |#1| (QUOTE (-344)))) (-12 (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-162)))) (-12 (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-344)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-344)))) (-12 (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-138))))) (-1146 ZP) ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4547,7 +4547,7 @@ NIL (-1154 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} converts the variable \\spad{x} to a univariate polynomial."))) (((-4272 "*") |has| |#2| (-162)) (-4263 |has| |#2| (-522)) (-4266 |has| |#2| (-344)) (-4268 |has| |#2| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#2| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-162))) (-1450 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-522)))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (-1450 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1450 (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1450 (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-1075))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (-1450 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasCategory| |#2| (QUOTE (-216))) (|HasAttribute| |#2| (QUOTE -4268)) (|HasCategory| |#2| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (-1450 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-138))))) +((|HasCategory| |#2| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-162))) (-1476 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-522)))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (-1476 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1476 (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1476 (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-1075))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (-1476 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasCategory| |#2| (QUOTE (-216))) (|HasAttribute| |#2| (QUOTE -4268)) (|HasCategory| |#2| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-138))))) (-1155 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 @@ -4563,7 +4563,7 @@ NIL (-1158 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 -841) (QUOTE (-1099)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1039))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2235) (LIST (|devaluate| |#2|) (QUOTE (-1099)))))) +((|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1039))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2258) (LIST (|devaluate| |#2|) (QUOTE (-1099)))))) (-1159 |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."))) (((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4264 . T) (-4265 . T) (-4267 . T)) @@ -4591,22 +4591,22 @@ NIL (-1165 |Coef| ULS) ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. Univariate Puiseux series are represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}."))) (((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-344)) (-4262 |has| |#1| (-344)) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|)))) (|HasCategory| (-388 (-530)) (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-344))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-1450 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasSignature| |#1| (LIST (QUOTE -2235) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1450 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -3700) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2562) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) +((|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|)))) (|HasCategory| (-388 (-530)) (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-1476 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasSignature| |#1| (LIST (QUOTE -2258) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1476 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -1637) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2596) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1166 |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."))) (((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-344)) (-4262 |has| |#1| (-344)) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|)))) (|HasCategory| (-388 (-530)) (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-344))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-1450 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasSignature| |#1| (LIST (QUOTE -2235) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1450 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -3700) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2562) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|)))) (|HasCategory| (-388 (-530)) (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-1476 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasSignature| |#1| (LIST (QUOTE -2258) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1476 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -1637) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2596) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|))))))) (-1167 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))}."))) (((-4272 "*") |has| (-1166 |#2| |#3| |#4|) (-162)) (-4263 |has| (-1166 |#2| |#3| |#4|) (-522)) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| (-1166 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-140))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-162))) (|HasCategory| (-1166 |#2| |#3| |#4|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-1166 |#2| |#3| |#4|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-344))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-432))) (-1450 (|HasCategory| (-1166 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-1166 |#2| |#3| |#4|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-522)))) +((|HasCategory| (-1166 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-140))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-162))) (|HasCategory| (-1166 |#2| |#3| |#4|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-1166 |#2| |#3| |#4|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-344))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-432))) (-1476 (|HasCategory| (-1166 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-1166 |#2| |#3| |#4|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-522)))) (-1168 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL ((|HasAttribute| |#1| (QUOTE -4271))) (-1169 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) -((-4102 . T)) +((-4087 . T)) NIL (-1170 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) @@ -4615,7 +4615,7 @@ NIL (-1171 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-900))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasSignature| |#2| (LIST (QUOTE -2562) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3700) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1099))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (QUOTE (-344)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-900))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasSignature| |#2| (LIST (QUOTE -2596) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1637) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1099))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (QUOTE (-344)))) (-1172 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#1|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) (((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4264 . T) (-4265 . T) (-4267 . T)) @@ -4623,18 +4623,18 @@ NIL (-1173 |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}."))) (((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (-1450 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-719)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-719)) (|devaluate| |#1|)))) (|HasCategory| (-719) (QUOTE (-1039))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-719))))) (|HasSignature| |#1| (LIST (QUOTE -2235) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-719))))) (|HasCategory| |#1| (QUOTE (-344))) (-1450 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -3700) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2562) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-719)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-719)) (|devaluate| |#1|)))) (|HasCategory| (-719) (QUOTE (-1039))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-719))))) (|HasSignature| |#1| (LIST (QUOTE -2258) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-719))))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -1637) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2596) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|))))))) (-1174 |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,{}f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,{}y[1],{}y[2],{}...,{}y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,{}cl)} is the solution to \\spad{y<n>=f(y,{}y',{}..,{}y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,{}c0,{}c1)} is the solution to \\spad{y'' = f(y,{}y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,{}c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,{}g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1175 -1329 UP L UTS) +(-1175 -1345 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 (-522)))) (-1176) ((|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."))) -((-4102 . T)) +((-4087 . T)) NIL (-1177 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) @@ -4646,7 +4646,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-941))) (|HasCategory| |#2| (QUOTE (-984))) (|HasCategory| |#2| (QUOTE (-675))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1179 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4271 . T) (-4270 . T) (-4102 . T)) +((-4271 . T) (-4270 . T) (-4087 . T)) NIL (-1180 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -4655,7 +4655,7 @@ NIL (-1181 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) ((-4271 . T) (-4270 . T)) -((-1450 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1450 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1450 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#1| (QUOTE (-984))) (-12 (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-984)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-1476 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#1| (QUOTE (-984))) (-12 (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-984)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-1182) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\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 @@ -4688,7 +4688,7 @@ 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 -(-1190 K R UP -1329) +(-1190 K R UP -1345) ((|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 @@ -4716,11 +4716,11 @@ 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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4263 |has| |#2| (-6 -4263)) (-4265 . T) (-4264 . T) (-4267 . T)) NIL -(-1197 S -1329) +(-1197 S -1345) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-349))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-140)))) -(-1198 -1329) +(-1198 -1345) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index ed7c9091..3afc9f26 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,14 +1,14 @@ -(143433 . 3429202594) -(((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) ((#0=(-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) #0#) |has| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (-291 (-2 (|:| -2913 |#1|) (|:| -1782 |#2|))))) +(143433 . 3429209011) +(((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) ((#0=(-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) #0#) |has| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (-291 (-2 (|:| -2940 |#1|) (|:| -1806 |#2|))))) (((|#2| |#2|) . T)) ((((-530)) . T)) -((($ $) -1450 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) ((|#2| |#2|) . T) ((#0=(-388 (-530)) #0#) |has| |#2| (-37 (-388 (-530))))) +((($ $) -1476 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) ((|#2| |#2|) . T) ((#0=(-388 (-530)) #0#) |has| |#2| (-37 (-388 (-530))))) ((($) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) (((|#2|) . T)) -((($) -1450 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) ((|#2|) . T) (((-388 (-530))) |has| |#2| (-37 (-388 (-530))))) +((($) -1476 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) ((|#2|) . T) (((-388 (-530))) |has| |#2| (-37 (-388 (-530))))) (|has| |#1| (-850)) ((((-804)) . T)) ((((-804)) . T)) @@ -23,28 +23,28 @@ ((((-208)) . T) (((-804)) . T)) (((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (((|#1|) . T)) -(-1450 (|has| |#1| (-21)) (|has| |#1| (-793))) -((($ $) . T) ((#0=(-388 (-530)) #0#) -1450 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1| |#1|) . T)) -(-1450 (|has| |#1| (-768)) (|has| |#1| (-795))) +(-1476 (|has| |#1| (-21)) (|has| |#1| (-793))) +((($ $) . T) ((#0=(-388 (-530)) #0#) -1476 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1| |#1|) . T)) +(-1476 (|has| |#1| (-768)) (|has| |#1| (-795))) ((((-388 (-530))) |has| |#1| (-975 (-388 (-530)))) (((-530)) |has| |#1| (-975 (-530))) ((|#1|) . T)) ((((-804)) . T)) ((((-804)) . T)) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) (|has| |#1| (-793)) (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (((|#1| |#2| |#3|) . T)) (((|#4|) . T)) -((($) . T) (((-388 (-530))) -1450 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1|) . T)) +((($) . T) (((-388 (-530))) -1476 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1|) . T)) ((((-804)) . T)) ((((-804)) |has| |#1| (-1027))) (((|#1|) . T) ((|#2|) . T)) (((|#1|) . T) (((-530)) |has| |#1| (-975 (-530))) (((-388 (-530))) |has| |#1| (-975 (-388 (-530))))) -(-1450 (|has| |#2| (-162)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) -(-1450 (|has| |#1| (-162)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) -(((|#2| (-461 (-2144 |#1|) (-719))) . T)) +(-1476 (|has| |#2| (-162)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) +(-1476 (|has| |#1| (-162)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) +(((|#2| (-461 (-2167 |#1|) (-719))) . T)) (((|#1| (-502 (-1099))) . T)) (((#0=(-811 |#1|) #0#) . T) ((#1=(-388 (-530)) #1#) . T) (($ $) . T)) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) (|has| |#4| (-349)) (|has| |#3| (-349)) (((|#1|) . T)) @@ -54,10 +54,10 @@ (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-522)) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-522))) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) ((($) . T)) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) ((((-506)) |has| |#1| (-572 (-506)))) ((($) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530)))) ((|#1|) . T)) ((($) . T)) @@ -66,59 +66,59 @@ ((((-804)) . T)) ((((-804)) . T)) ((((-388 (-530))) . T) (($) . T)) -((((-388 (-530))) -1450 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (((-1173 |#1| |#2| |#3|)) |has| |#1| (-344)) (($) . T) ((|#1|) . T)) +((((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (((-1173 |#1| |#2| |#3|)) |has| |#1| (-344)) (($) . T) ((|#1|) . T)) ((((-804)) . 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T)) (((|#1|) . T)) ((((-388 (-530))) |has| |#1| (-975 (-388 (-530)))) (((-530)) |has| |#1| (-975 (-530))) ((|#1|) . T)) (((|#1|) . T) (((-530)) |has| |#1| (-593 (-530)))) -(((|#2|) . T) (((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -2913 (-1082)) (|:| -1782 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) . T)) (|has| |#1| (-522)) (|has| |#1| (-522)) (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) -(-1450 (|has| |#1| (-795)) (|has| |#1| (-1027))) +(-1476 (|has| |#1| (-795)) (|has| |#1| (-1027))) (((|#1|) . T)) (|has| |#1| (-522)) (|has| |#1| (-522)) @@ -218,11 +218,11 @@ (((|#2|) . T) (($) . T) (((-388 (-530))) . T)) (-12 (|has| |#1| (-1027)) (|has| |#2| (-1027))) ((($) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530)))) ((|#1|) . 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T) (((-208)) . T) (((-360)) . T) (((-833 (-360))) . T)) ((((-804)) . T)) -(-1450 (|has| |#1| (-21)) (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-841 (-1099))) (|has| |#1| (-984))) +(-1476 (|has| |#1| (-21)) (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-841 (-1099))) (|has| |#1| (-984))) (((|#1|) |has| |#1| (-162))) (((|#1| $) |has| |#1| (-268 |#1| |#1|))) ((((-804)) . T)) @@ -256,15 +256,15 @@ (|has| |#1| (-795)) (|has| |#1| (-1027)) (((|#1|) . T)) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) ((((-506)) |has| |#1| (-572 (-506)))) ((((-127)) . 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T)) (((|#1| (-911)) . T)) (((#0=(-811 |#1|) $) |has| #0# (-268 #0# #0#))) @@ -273,7 +273,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1075)) -((((-2 (|:| -2913 (-1082)) (|:| -1782 |#1|))) . T)) +((((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) . T)) (|has| (-1167 |#1| |#2| |#3| |#4|) (-138)) (|has| (-1167 |#1| |#2| |#3| |#4|) (-140)) (|has| |#1| (-138)) @@ -290,20 +290,20 @@ ((($) . T) ((|#1|) . T)) (((|#2|) |has| |#2| (-984))) ((((-804)) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) ((#0=(-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) #0#) |has| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (-291 (-2 (|:| -2913 |#1|) (|:| -1782 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) ((#0=(-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) #0#) |has| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (-291 (-2 (|:| -2940 |#1|) (|:| -1806 |#2|))))) (((|#1|) . 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T) ((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530))))) +((($ $) -1476 (|has| |#1| (-162)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1| |#1|) . T) ((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530))))) ((($) . T)) ((($) . T)) ((($) . T)) -((($) -1450 (|has| |#1| (-162)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) +((($) -1476 (|has| |#1| (-162)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) ((((-804)) . T)) ((((-804)) . T)) (|has| (-1166 |#2| |#3| |#4|) (-140)) @@ -314,16 +314,16 @@ ((((-804)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-1450 (|has| |#1| (-21)) (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-841 (-1099))) (|has| |#1| (-984))) +(-1476 (|has| |#1| (-21)) (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-841 (-1099))) (|has| |#1| (-984))) (((|#1|) . T)) ((((-530) |#1|) . 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T)) ((((-388 (-530))) |has| |#1| (-37 (-388 (-530)))) ((|#1|) |has| |#1| (-162)) (($) |has| |#1| (-522))) (|has| |#1| (-344)) -(-1450 (-12 (|has| (-1173 |#1| |#2| |#3|) (-216)) (|has| |#1| (-344))) (|has| |#1| (-15 * (|#1| (-530) |#1|)))) +(-1476 (-12 (|has| (-1173 |#1| |#2| |#3|) (-216)) (|has| |#1| (-344))) (|has| |#1| (-15 * (|#1| (-530) |#1|)))) (|has| |#1| (-15 * (|#1| (-388 (-530)) |#1|))) (|has| |#1| (-344)) ((((-530)) . T)) @@ -347,31 +347,31 @@ (((|#1|) . T)) ((((-530) |#1|) . T)) (((|#2|) . T)) -(-1450 (|has| |#2| (-344)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) -(-1450 (|has| |#2| (-741)) (|has| |#2| (-793))) -(-1450 (|has| |#2| (-741)) (|has| |#2| (-793))) +(-1476 (|has| |#2| (-344)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) +(-1476 (|has| |#2| (-741)) (|has| |#2| (-793))) +(-1476 (|has| |#2| (-741)) (|has| |#2| (-793))) (((|#1|) . 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T)) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) (|has| |#1| (-349)) (|has| |#1| (-349)) (|has| |#1| (-349)) ((((-804)) . T)) (((|#1|) . T)) -(-1450 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) +(-1476 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) (|has| |#1| (-349)) -(-1450 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) +(-1476 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((((-530)) . T)) ((((-530)) . T)) -(-1450 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) +(-1476 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) ((((-804)) . T)) ((((-804)) . T)) (-12 (|has| |#2| (-216)) (|has| |#2| (-984))) @@ -422,10 +422,10 @@ ((((-530) |#4|) . T)) ((((-530) |#3|) . T)) (((|#1|) . T) (((-530)) |has| |#1| (-593 (-530)))) -(-1450 (|has| |#2| (-162)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1476 (|has| |#2| (-162)) (|has| |#2| (-793)) (|has| |#2| (-984))) ((((-1167 |#1| |#2| |#3| |#4|)) . T)) ((((-388 (-530))) . T) (((-530)) . T)) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) @@ -454,38 +454,38 @@ ((($) . T)) ((($ $) . T) ((#0=(-1099) $) . T) ((#0# |#1|) . 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T)) (|has| (-388 |#2|) (-140)) (|has| (-388 |#2|) (-138)) @@ -688,22 +688,22 @@ (|has| |#1| (-522)) (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-37 (-388 (-530)))) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) ((((-804)) . T)) -((((-2 (|:| -2913 (-1082)) (|:| -1782 |#1|))) . T)) +((((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) . T)) (|has| |#1| (-37 (-388 (-530)))) -((((-369) (-2 (|:| -2913 (-1082)) (|:| -1782 |#1|))) . T)) +((((-369) (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) . T)) (|has| |#1| (-37 (-388 (-530)))) (|has| |#2| (-1075)) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-522))) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) (((|#1|) . T)) ((((-369) (-1082)) . T)) (|has| |#1| (-522)) ((((-114 |#1|)) . T)) ((((-127)) . T)) ((((-530) |#1|) . T)) -(-1450 (|has| |#1| (-162)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) +(-1476 (|has| |#1| (-162)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) (((|#2|) . T)) ((((-804)) . T)) ((((-767 |#1|)) . T)) @@ -716,7 +716,7 @@ (((|#1|) |has| |#1| (-162))) ((((-804)) . T)) ((((-506)) |has| |#1| (-572 (-506)))) -(-1450 (|has| |#1| (-795)) (|has| |#1| (-1027))) +(-1476 (|has| |#1| (-795)) (|has| |#1| (-1027))) (((|#2|) |has| |#2| (-291 |#2|))) (((#0=(-530) #0#) . T) ((#1=(-388 (-530)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -726,7 +726,7 @@ (((#0=(-530) #0#) . T) ((#1=(-388 (-530)) #1#) . T) (($ $) . T)) ((($) . T) (((-530)) . T) (((-388 (-530))) . T)) (|has| |#2| (-349)) -(-1450 (|has| |#1| (-795)) (|has| |#1| (-1027))) +(-1476 (|has| |#1| (-795)) (|has| |#1| (-1027))) (((|#1|) . T) (((-388 (-530))) . T) (($) . T)) (((|#1|) . T) (((-388 (-530))) . T) (($) . T)) (((|#1|) . T) (((-388 (-530))) . T) (($) . T)) @@ -737,9 +737,9 @@ ((((-1097 |#1| |#2| |#3|) $) -12 (|has| (-1097 |#1| |#2| |#3|) (-268 (-1097 |#1| |#2| |#3|) (-1097 |#1| |#2| |#3|))) (|has| |#1| (-344))) (($ $) . T)) ((((-804)) . T)) ((((-804)) . T)) -((($) . T) (((-388 (-530))) -1450 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1|) . T)) +((($) . T) (((-388 (-530))) -1476 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1|) . T)) ((((-506)) |has| |#1| (-572 (-506)))) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) ((($ $) . T)) ((($ $) . T)) ((((-804)) . T)) @@ -749,12 +749,12 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((($) -1450 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) +((($) -1476 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) ((((-388 (-530))) . T) (((-530)) . T)) ((((-530) (-137)) . T)) ((((-137)) . T)) (((|#1|) . T)) -(-1450 (|has| |#1| (-21)) (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-522)) (|has| |#1| (-984))) +(-1476 (|has| |#1| (-21)) (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-522)) (|has| |#1| (-984))) ((((-110)) . T)) (((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) ((((-110)) . T)) @@ -762,38 +762,38 @@ ((((-506)) |has| |#1| (-572 (-506))) (((-208)) . #0=(|has| |#1| (-960))) (((-360)) . #0#)) ((((-804)) . T)) (|has| |#1| (-768)) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) (|has| |#1| (-795)) -(-1450 (|has| |#1| (-162)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-162)) (|has| |#1| (-522))) (|has| |#1| (-522)) (|has| |#1| (-850)) (((|#1|) . T)) (|has| |#1| (-1027)) ((((-804)) . T)) -(-1450 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-522))) -(-1450 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-522))) -(-1450 (|has| |#1| (-162)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-162)) (|has| |#1| (-522))) ((((-804)) . T)) ((((-804)) . T)) ((((-804)) . T)) (((|#1| (-1181 |#1|) (-1181 |#1|)) . T)) ((((-530) (-137)) . T)) ((($) . T)) -(-1450 (|has| |#4| (-162)) (|has| |#4| (-793)) (|has| |#4| (-984))) -(-1450 (|has| |#3| (-162)) (|has| |#3| (-793)) (|has| |#3| (-984))) +(-1476 (|has| |#4| (-162)) (|has| |#4| (-793)) (|has| |#4| (-984))) +(-1476 (|has| |#3| (-162)) (|has| |#3| (-793)) (|has| |#3| (-984))) ((((-804)) . T)) (|has| |#1| (-1027)) (((|#1| (-911)) . T)) (((|#1| |#1|) . T)) ((($) . T)) -(-1450 (|has| |#2| (-741)) (|has| |#2| (-793))) -(-1450 (|has| |#2| (-741)) (|has| |#2| (-793))) +(-1476 (|has| |#2| (-741)) (|has| |#2| (-793))) +(-1476 (|has| |#2| (-741)) (|has| |#2| (-793))) (-12 (|has| |#1| (-453)) (|has| |#2| (-453))) -(-1450 (|has| |#2| (-162)) (|has| |#2| (-675)) (|has| |#2| (-793)) (|has| |#2| (-984))) -(-1450 (-12 (|has| |#1| (-453)) (|has| |#2| (-453))) (-12 (|has| |#1| (-675)) (|has| |#2| (-675)))) +(-1476 (|has| |#2| (-162)) (|has| |#2| (-675)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1476 (-12 (|has| |#1| (-453)) (|has| |#2| (-453))) (-12 (|has| |#1| (-675)) (|has| |#2| (-675)))) (((|#1|) . T)) (|has| |#2| (-741)) -(-1450 (|has| |#2| (-741)) (|has| |#2| (-793))) +(-1476 (|has| |#2| (-741)) (|has| |#2| (-793))) (((|#1| |#2|) . T)) (((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (|has| |#2| (-793)) @@ -808,7 +808,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-388 (-530))) . T) (($) . T)) -((($) . T) (((-388 (-530))) -1450 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) ((|#1|) . T)) +((($) . T) (((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) ((|#1|) . T)) (|has| |#1| (-776)) ((((-388 (-530))) |has| |#1| (-975 (-388 (-530)))) (((-530)) |has| |#1| (-975 (-530))) ((|#1|) . T)) (|has| |#1| (-1027)) @@ -819,8 +819,8 @@ (((|#3|) |has| |#3| (-1027))) (|has| |#3| (-349)) (((|#1|) . T) (((-804)) . T)) -((((-388 (-530))) -1450 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1450 (|has| |#1| (-344)) (|has| |#1| (-522))) (((-1173 |#1| |#2| |#3|)) |has| |#1| (-344)) ((|#1|) |has| |#1| (-162))) -(((|#1|) |has| |#1| (-162)) (((-388 (-530))) -1450 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1450 (|has| |#1| (-344)) (|has| |#1| (-522)))) +((((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1476 (|has| |#1| (-344)) (|has| |#1| (-522))) (((-1173 |#1| |#2| |#3|)) |has| |#1| (-344)) ((|#1|) |has| |#1| (-162))) +(((|#1|) |has| |#1| (-162)) (((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1476 (|has| |#1| (-344)) (|has| |#1| (-522)))) ((((-804)) . T)) ((($) |has| |#1| (-522)) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) (((|#2|) . T)) @@ -830,30 +830,30 @@ (((|#1|) . T)) (((|#1|) |has| |#1| (-162))) ((((-388 (-530))) . T) (((-530)) . T)) -((($ $) -1450 (|has| |#1| (-162)) (|has| |#1| (-522))) ((|#1| |#1|) . T) ((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530))))) -((($) -1450 (|has| |#1| (-162)) (|has| |#1| (-522))) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) +((($ $) -1476 (|has| |#1| (-162)) (|has| |#1| (-522))) ((|#1| |#1|) . T) ((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530))))) +((($) -1476 (|has| |#1| (-162)) (|has| |#1| (-522))) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) (((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) ((((-137)) . T)) (((|#1|) . T)) ((((-137)) . T)) -((($) -1450 (|has| |#2| (-162)) (|has| |#2| (-793)) (|has| |#2| (-984))) ((|#2|) -1450 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-984)))) +((($) -1476 (|has| |#2| (-162)) (|has| |#2| (-793)) (|has| |#2| (-984))) ((|#2|) -1476 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-984)))) ((((-137)) . T)) (((|#1| |#2| |#3|) . T)) -(-1450 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-522)) (|has| |#1| (-984))) +(-1476 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-522)) (|has| |#1| (-984))) (|has| $ (-140)) (|has| $ (-140)) (|has| |#1| (-1027)) ((((-804)) . T)) (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-37 (-388 (-530)))) -(-1450 (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-453)) (|has| |#1| (-522)) (|has| |#1| (-984)) (|has| |#1| (-1039))) +(-1476 (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-453)) (|has| |#1| (-522)) (|has| |#1| (-984)) (|has| |#1| (-1039))) ((($ $) |has| |#1| (-268 $ $)) ((|#1| $) |has| |#1| (-268 |#1| |#1|))) (((|#1| (-388 (-530))) . T)) (((|#1|) . T)) ((((-1099)) . T)) (|has| |#1| (-522)) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-522))) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) (|has| |#1| (-522)) (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-37 (-388 (-530)))) @@ -864,7 +864,7 @@ (|has| |#1| (-140)) (|has| |#1| (-138)) (|has| |#4| (-793)) -(((|#2| (-223 (-2144 |#1|) (-719)) (-806 |#1|)) . T)) +(((|#2| (-223 (-2167 |#1|) (-719)) (-806 |#1|)) . T)) (|has| |#3| (-793)) (((|#1| (-502 |#3|) |#3|) . T)) (|has| |#1| (-140)) @@ -878,21 +878,21 @@ (|has| |#1| (-138)) ((((-388 (-530))) |has| |#2| (-344)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) -(-1450 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) -(-1450 (|has| |#1| (-330)) (|has| |#1| (-349))) +(-1476 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) +(-1476 (|has| |#1| (-330)) (|has| |#1| (-349))) ((((-1066 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-162)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-216)) (|has| |#2| (-984))) -(((|#2|) . T) (((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) -(-1450 (|has| |#3| (-741)) (|has| |#3| (-793))) -(-1450 (|has| |#3| (-741)) (|has| |#3| (-793))) +(((|#2|) . T) (((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +(-1476 (|has| |#3| (-741)) (|has| |#3| (-793))) +(-1476 (|has| |#3| (-741)) (|has| |#3| (-793))) ((((-804)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) (((|#1|) . T) (($) . T)) ((((-647)) . T)) -(-1450 (|has| |#2| (-162)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1476 (|has| |#2| (-162)) (|has| |#2| (-793)) (|has| |#2| (-984))) (|has| |#1| (-522)) (((|#1|) . T)) (((|#1|) . T)) @@ -914,10 +914,10 @@ (((|#1| (-388 (-530))) . T)) (((|#3|) . T) (((-570 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) ((($ $) . T) ((|#2| $) . T)) (((|#1|) . T) (((-388 (-530))) . T) (($) . T)) (((#0=(-1097 |#1| |#2| |#3|) #0#) -12 (|has| (-1097 |#1| |#2| |#3|) (-291 (-1097 |#1| |#2| |#3|))) (|has| |#1| (-344))) (((-1099) #0#) -12 (|has| (-1097 |#1| |#2| |#3|) (-491 (-1099) (-1097 |#1| |#2| |#3|))) (|has| |#1| (-344)))) @@ -925,8 +925,8 @@ ((((-804)) . T)) ((((-804)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) (((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) |has| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (-291 (-2 (|:| -2913 |#1|) (|:| -1782 |#2|))))) -(((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027))) (((-2 (|:| -2913 (-1082)) (|:| -1782 |#1|))) |has| (-2 (|:| -2913 (-1082)) (|:| -1782 |#1|)) (-291 (-2 (|:| -2913 (-1082)) (|:| -1782 |#1|))))) +(((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) (((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) |has| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (-291 (-2 (|:| -2940 |#1|) (|:| -1806 |#2|))))) +(((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027))) (((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) |has| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (-291 (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))))) ((((-804)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -937,10 +937,10 @@ ((($ $) . T) ((#0=(-806 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-776)) (|has| |#1| (-1027)) -(((|#2| |#2|) -1450 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-984))) (($ $) |has| |#2| (-162))) -(((|#2|) -1450 (|has| |#2| (-162)) (|has| |#2| (-344)))) -((((-530) (-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -1450 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-984))) (($) |has| |#2| (-162))) +(((|#2| |#2|) -1476 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-984))) (($ $) |has| |#2| (-162))) +(((|#2|) -1476 (|has| |#2| (-162)) (|has| |#2| (-344)))) +((((-530) (-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -1476 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-984))) (($) |has| |#2| (-162))) ((((-719)) . T)) ((((-530)) . T)) (|has| |#1| (-522)) @@ -953,29 +953,29 @@ ((((-114 |#1|)) . T)) (((|#1|) . 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T)) -((($) -1450 (|has| |#1| (-289)) (|has| |#1| (-344)) (|has| |#1| (-330)) (|has| |#1| (-522))) (((-388 (-530))) -1450 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1|) . T)) +((($) -1476 (|has| |#1| (-289)) (|has| |#1| (-344)) (|has| |#1| (-330)) (|has| |#1| (-522))) (((-388 (-530))) -1476 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1|) . T)) ((((-530) |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) @@ -983,37 +983,37 @@ (-12 (|has| |#1| (-349)) (|has| |#2| (-349))) ((((-804)) . T)) ((((-1099) |#1|) |has| |#1| (-491 (-1099) |#1|)) ((|#1| |#1|) |has| |#1| (-291 |#1|))) -(-1450 (|has| |#1| (-138)) (|has| |#1| (-349))) -(-1450 (|has| |#1| (-138)) (|has| |#1| (-349))) -(-1450 (|has| |#1| (-138)) (|has| |#1| (-349))) +(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) +(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) +(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) (((|#1|) . 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T)) (((|#1|) |has| |#1| (-291 |#1|))) (|has| |#1| (-349)) @@ -1021,31 +1021,31 @@ (|has| |#1| (-349)) ((((-1099) $) |has| |#1| (-491 (-1099) $)) (($ $) |has| |#1| (-291 $)) ((|#1| |#1|) |has| |#1| (-291 |#1|)) (((-1099) |#1|) |has| |#1| (-491 (-1099) |#1|))) ((((-1099)) |has| |#1| (-841 (-1099)))) -(-1450 (-12 (|has| |#1| (-216)) (|has| |#1| (-344))) (|has| |#1| (-330))) +(-1476 (-12 (|has| |#1| (-216)) (|has| |#1| (-344))) (|has| |#1| (-330))) ((((-369) (-1046)) . T)) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-369) |#1|) . T)) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-330))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-330))) (|has| |#1| (-1027)) ((((-804)) . T)) ((((-804)) . T)) ((((-851 |#1|)) . 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T)) ((((-804)) . T)) ((((-804)) . T)) @@ -1072,14 +1072,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-793)) (|has| |#1| (-793)) -((($) . T) (((-388 (-530))) -1450 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1|) . T)) -(-1450 (|has| |#1| (-162)) (|has| |#1| (-522))) -(((#0=(-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) #0#) |has| (-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) (-291 (-2 (|:| -2913 (-1099)) (|:| -1782 (-51)))))) +((($) . T) (((-388 (-530))) -1476 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1|) . T)) +(-1476 (|has| |#1| (-162)) (|has| |#1| (-522))) +(((#0=(-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) #0#) |has| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (-291 (-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))))) ((($) . T)) (|has| |#2| (-795)) ((($) . 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T)) ((((-530)) |has| |#1| (-827 (-530))) (((-360)) |has| |#1| (-827 (-360)))) -((((-388 (-530))) -1450 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1450 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-522))) ((|#1|) . T)) +((((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-522))) ((|#1|) . T)) (((|#1|) . T)) ((((-597 |#4|)) . T) (((-804)) . T)) ((((-506)) |has| |#4| (-572 (-506)))) @@ -1152,17 +1152,17 @@ (((|#1|) . T)) (((|#2|) . T)) ((((-1099)) |has| (-388 |#2|) (-841 (-1099)))) -(((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) ((#0=(-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) #0#) |has| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (-291 (-2 (|:| -2913 |#1|) (|:| -1782 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) ((#0=(-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) #0#) |has| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (-291 (-2 (|:| -2940 |#1|) (|:| -1806 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) -((((-804)) -1450 (|has| |#3| (-25)) (|has| |#3| (-128)) (|has| |#3| (-571 (-804))) (|has| |#3| (-162)) (|has| |#3| (-344)) (|has| |#3| (-349)) (|has| |#3| (-675)) (|has| |#3| (-741)) (|has| |#3| (-793)) (|has| |#3| (-984)) (|has| |#3| (-1027))) (((-1181 |#3|)) . T)) +((((-804)) -1476 (|has| |#3| (-25)) (|has| |#3| (-128)) (|has| |#3| (-571 (-804))) (|has| |#3| (-162)) (|has| |#3| (-344)) (|has| |#3| (-349)) (|has| |#3| (-675)) (|has| |#3| (-741)) (|has| |#3| (-793)) (|has| |#3| (-984)) (|has| |#3| (-1027))) (((-1181 |#3|)) . T)) ((((-530) |#2|) . T)) -(-1450 (|has| |#1| (-795)) (|has| |#1| (-1027))) -(((|#2| |#2|) -1450 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-984))) (($ $) |has| |#2| (-162))) +(-1476 (|has| |#1| (-795)) (|has| |#1| (-1027))) +(((|#2| |#2|) -1476 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-984))) (($ $) |has| |#2| (-162))) ((((-804)) . T)) ((((-804)) . T)) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T) ((|#2|) . T)) ((((-804)) . T)) ((((-804)) . T)) ((((-1082) (-1099) (-530) (-208) (-804)) . T)) @@ -1197,8 +1197,8 @@ (|has| |#1| (-37 (-388 (-530)))) ((((-804)) . T)) ((((-506)) |has| |#1| (-572 (-506)))) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) -(((|#2|) -1450 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-984))) (($) |has| |#2| (-162))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +(((|#2|) -1476 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-984))) (($) |has| |#2| (-162))) (|has| $ (-140)) ((((-388 |#2|)) . T)) ((((-388 (-530))) |has| #0=(-388 |#2|) (-975 (-388 (-530)))) (((-530)) |has| #0# (-975 (-530))) ((#0#) . T)) @@ -1209,11 +1209,11 @@ (((|#3|) |has| |#3| (-162))) (|has| |#1| (-140)) (|has| |#1| (-138)) -(-1450 (|has| |#1| (-138)) (|has| |#1| (-349))) +(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) (|has| |#1| (-140)) -(-1450 (|has| |#1| (-138)) (|has| |#1| (-349))) +(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) (|has| |#1| (-140)) -(-1450 (|has| |#1| (-138)) (|has| |#1| (-349))) +(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) (|has| |#1| (-140)) (((|#1|) . T)) (((|#2|) . T)) @@ -1244,7 +1244,7 @@ ((((-938 |#1|)) . T) ((|#1|) . T)) ((((-804)) . T)) ((((-804)) . T)) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) ((((-388 (-530))) . T) (((-388 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1095 |#1|)) . T)) ((((-530)) . T) (($) . T) (((-388 (-530))) . T)) @@ -1252,9 +1252,9 @@ (|has| |#1| (-795)) (((|#2|) . T)) ((((-530)) . T) (($) . T) (((-388 (-530))) . T)) -((((-2 (|:| -2913 (-1082)) (|:| -1782 |#1|))) . T)) +((((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) . T)) ((((-530) |#2|) . T)) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) (((|#2|) . T)) ((((-530) |#3|) . T)) (((|#2|) . T)) @@ -1269,7 +1269,7 @@ (((|#3|) -12 (|has| |#3| (-291 |#3|)) (|has| |#3| (-1027)))) (((|#2|) . T)) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) ((#0=(-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) #0#) |has| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (-291 (-2 (|:| -2913 |#1|) (|:| -1782 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) ((#0=(-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) #0#) |has| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (-291 (-2 (|:| -2940 |#1|) (|:| -1806 |#2|))))) (((|#2| |#2|) . T)) (|has| |#2| (-344)) (((|#2|) . T) (((-530)) |has| |#2| (-975 (-530))) (((-388 (-530))) |has| |#2| (-975 (-388 (-530))))) @@ -1299,19 +1299,19 @@ (((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (((|#1| |#2|) . T)) ((((-530) (-137)) . T)) -(((#0=(-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) #0#) |has| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (-291 (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) -((($) -1450 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) +(((#0=(-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) #0#) |has| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (-291 (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) +((($) -1476 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) (|has| |#1| (-795)) (((|#2| (-719) (-1012)) . T)) (((|#1| |#2|) . T)) -(-1450 (|has| |#1| (-162)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-162)) (|has| |#1| (-522))) (|has| |#1| (-739)) (((|#1|) |has| |#1| (-162))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-1450 (|has| |#1| (-140)) (-12 (|has| |#1| (-344)) (|has| |#2| (-140)))) -(-1450 (|has| |#1| (-138)) (-12 (|has| |#1| (-344)) (|has| |#2| (-138)))) +(-1476 (|has| |#1| (-140)) (-12 (|has| |#1| (-344)) (|has| |#2| (-140)))) +(-1476 (|has| |#1| (-138)) (-12 (|has| |#1| (-344)) (|has| |#2| (-138)))) (((|#4|) . T)) (|has| |#1| (-138)) ((((-1082) |#1|) . T)) @@ -1324,10 +1324,10 @@ (((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (((|#3|) . T)) ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-344))) -(-1450 (|has| |#1| (-795)) (|has| |#1| (-1027))) +(-1476 (|has| |#1| (-795)) (|has| |#1| (-1027))) (((|#1|) . T)) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027))) (((-899 |#1|)) . T)) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027))) (((-899 |#1|)) . T)) (|has| |#1| (-793)) (|has| |#1| (-793)) (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) @@ -1340,8 +1340,8 @@ ((($) . T)) ((((-369) (-1082)) . T)) ((($) |has| |#1| (-522)) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) -((((-804)) -1450 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-571 (-804))) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) (((-1181 |#2|)) . T)) -(((#0=(-51)) . T) (((-2 (|:| -2913 (-1082)) (|:| -1782 #0#))) . T)) +((((-804)) -1476 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-571 (-804))) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) (((-1181 |#2|)) . T)) +(((#0=(-51)) . T) (((-2 (|:| -2940 (-1082)) (|:| -1806 #0#))) . T)) (((|#1|) . T)) ((((-804)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) @@ -1349,7 +1349,7 @@ (|has| |#2| (-138)) (|has| |#2| (-140)) (|has| |#1| (-453)) -(-1450 (|has| |#1| (-453)) (|has| |#1| (-675)) (|has| |#1| (-841 (-1099))) (|has| |#1| (-984))) +(-1476 (|has| |#1| (-453)) (|has| |#1| (-675)) (|has| |#1| (-841 (-1099))) (|has| |#1| (-984))) (|has| |#1| (-344)) ((((-804)) . T)) (|has| |#1| (-37 (-388 (-530)))) @@ -1358,8 +1358,8 @@ (|has| |#1| (-793)) (|has| |#1| (-793)) ((((-804)) . T)) -((((-388 (-530))) -1450 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1450 (|has| |#1| (-344)) (|has| |#1| (-522))) (((-1173 |#1| |#2| |#3|)) |has| |#1| (-344)) ((|#1|) |has| |#1| (-162))) -(((|#1|) |has| |#1| (-162)) (((-388 (-530))) -1450 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1450 (|has| |#1| (-344)) (|has| |#1| (-522)))) +((((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1476 (|has| |#1| (-344)) (|has| |#1| (-522))) (((-1173 |#1| |#2| |#3|)) |has| |#1| (-344)) ((|#1|) |has| |#1| (-162))) +(((|#1|) |has| |#1| (-162)) (((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1476 (|has| |#1| (-344)) (|has| |#1| (-522)))) ((($) |has| |#1| (-522)) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) (((|#1| |#2|) . T)) ((((-1099)) |has| |#1| (-841 (-1099)))) @@ -1367,7 +1367,7 @@ ((((-804)) . T)) ((((-804)) . T)) (|has| |#1| (-1027)) -(((|#2| (-461 (-2144 |#1|) (-719)) (-806 |#1|)) . T)) +(((|#2| (-461 (-2167 |#1|) (-719)) (-806 |#1|)) . T)) ((((-388 (-530))) . #0=(|has| |#2| (-344))) (($) . #0#)) (((|#1| (-502 (-1099)) (-1099)) . T)) (((|#1|) . T)) @@ -1387,16 +1387,16 @@ (|has| |#1| (-140)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2913 (-1082)) (|:| -1782 |#1|))) . T)) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) -((((-2 (|:| -2913 (-1099)) (|:| -1782 (-51)))) . T)) +(((|#1|) . T) (((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))) . T)) ((((-1097 |#1| |#2| |#3|)) |has| |#1| (-344))) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) ((((-1099) (-51)) . T)) ((($ $) . T)) (((|#1| (-530)) . T)) ((((-851 |#1|)) . T)) -(((|#1|) -1450 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-984))) (($) -1450 (|has| |#1| (-841 (-1099))) (|has| |#1| (-984)))) +(((|#1|) -1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-984))) (($) -1476 (|has| |#1| (-841 (-1099))) (|has| |#1| (-984)))) (((|#1|) . T) (((-530)) |has| |#1| (-975 (-530))) (((-388 (-530))) |has| |#1| (-975 (-388 (-530))))) (|has| |#1| (-795)) (|has| |#1| (-795)) @@ -1411,13 +1411,13 @@ (((|#4| |#4|) -12 (|has| |#4| (-291 |#4|)) (|has| |#4| (-1027)))) (((|#1|) |has| |#1| (-162))) (((|#4| |#4|) -12 (|has| |#4| (-291 |#4|)) (|has| |#4| (-1027)))) -(((|#3|) -1450 (|has| |#3| (-162)) (|has| |#3| (-344)))) +(((|#3|) -1476 (|has| |#3| (-162)) (|has| |#3| (-344)))) (|has| |#2| (-795)) (|has| |#1| (-795)) -(-1450 (|has| |#2| (-344)) (|has| |#2| (-432)) (|has| |#2| (-850))) +(-1476 (|has| |#2| (-344)) (|has| |#2| (-432)) (|has| |#2| (-850))) ((($ $) . T) ((#0=(-388 (-530)) #0#) . T)) ((((-530) |#2|) . T)) -(((|#2|) -1450 (|has| |#2| (-162)) (|has| |#2| (-344)))) +(((|#2|) -1476 (|has| |#2| (-162)) (|has| |#2| (-344)))) (|has| |#1| (-330)) (((|#3| |#3|) -12 (|has| |#3| (-291 |#3|)) (|has| |#3| (-1027)))) ((($) . T) (((-388 (-530))) . T)) @@ -1425,7 +1425,7 @@ (|has| |#1| (-768)) (|has| |#1| (-768)) (((|#1|) . T)) -(-1450 (|has| |#1| (-289)) (|has| |#1| (-344)) (|has| |#1| (-330))) +(-1476 (|has| |#1| (-289)) (|has| |#1| (-344)) (|has| |#1| (-330))) (|has| |#1| (-793)) (|has| |#1| (-793)) (|has| |#1| (-793)) @@ -1434,13 +1434,13 @@ ((((-530)) . T) (($) . T) (((-388 (-530))) . T)) (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-37 (-388 (-530)))) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-330))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-330))) (|has| |#1| (-37 (-388 (-530)))) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) ((((-1099)) |has| |#1| (-841 (-1099))) (((-1012)) . T)) (((|#1|) . T)) (|has| |#1| (-793)) -(((#0=(-2 (|:| -2913 (-1082)) (|:| -1782 (-51))) #0#) |has| (-2 (|:| -2913 (-1082)) (|:| -1782 (-51))) (-291 (-2 (|:| -2913 (-1082)) (|:| -1782 (-51)))))) +(((#0=(-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) #0#) |has| (-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) (-291 (-2 (|:| -2940 (-1082)) (|:| -1806 (-51)))))) (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (|has| |#1| (-1027)) (((|#1|) . T)) @@ -1459,7 +1459,7 @@ (((|#1|) . T)) ((((-137)) . T)) (((|#2|) |has| |#2| (-162))) -(-1450 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) +(-1476 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) (((|#1|) . T)) (|has| |#1| (-138)) (|has| |#1| (-140)) @@ -1481,32 +1481,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (((|#1|) . T)) (((|#1| |#2|) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027))) ((#0=(-2 (|:| -2913 (-1082)) (|:| -1782 |#1|)) #0#) |has| (-2 (|:| -2913 (-1082)) (|:| -1782 |#1|)) (-291 (-2 (|:| -2913 (-1082)) (|:| -1782 |#1|))))) -(-1450 (|has| |#2| (-432)) (|has| |#2| (-850))) -(-1450 (|has| |#1| (-432)) (|has| |#1| (-850))) +(((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027))) ((#0=(-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) #0#) |has| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (-291 (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))))) +(-1476 (|has| |#2| (-432)) (|has| |#2| (-850))) +(-1476 (|has| |#1| (-432)) (|has| |#1| (-850))) (((|#1|) . T) (($) . T)) (((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) (((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(((|#3|) -1450 (|has| |#3| (-162)) (|has| |#3| (-344)))) +(((|#3|) -1476 (|has| |#3| (-162)) (|has| |#3| (-344)))) (|has| |#1| (-795)) (|has| |#1| (-522)) ((((-543 |#1|)) . T)) ((($) . T)) (((|#2|) . T)) -(-1450 (-12 (|has| |#1| (-344)) (|has| |#2| (-768))) (-12 (|has| |#1| (-344)) (|has| |#2| (-795)))) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1476 (-12 (|has| |#1| (-344)) (|has| |#2| (-768))) (-12 (|has| |#1| (-344)) (|has| |#2| (-795)))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) ((((-851 |#1|)) . T)) (((|#1| (-474 |#1| |#3|) (-474 |#1| |#2|)) . T)) (((|#1| |#4| |#5|) . T)) (((|#1| (-719)) . 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T)) +((((-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))) . T)) ((((-388 |#2|)) . T) (((-388 (-530))) . T) (($) . T)) ((((-622 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1514,17 +1514,17 @@ ((((-804)) . T)) (((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) ((((-804)) . T)) -((((-388 (-530))) |has| |#2| (-37 (-388 (-530)))) ((|#2|) |has| |#2| (-162)) (($) -1450 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850)))) +((((-388 (-530))) |has| |#2| (-37 (-388 (-530)))) ((|#2|) |has| |#2| (-162)) (($) -1476 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850)))) ((((-804)) . T)) ((((-804)) . T)) ((((-804)) . T)) (((|#2|) . T)) -(-1450 (|has| |#3| (-25)) (|has| |#3| (-128)) (|has| |#3| (-162)) (|has| |#3| (-344)) (|has| |#3| (-349)) (|has| |#3| (-675)) (|has| |#3| (-741)) (|has| |#3| (-793)) (|has| |#3| (-984)) (|has| |#3| (-1027))) -(-1450 (|has| |#2| (-162)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1476 (|has| |#3| (-25)) (|has| |#3| (-128)) (|has| |#3| (-162)) (|has| |#3| (-344)) (|has| |#3| (-349)) (|has| |#3| (-675)) (|has| |#3| (-741)) (|has| |#3| (-793)) (|has| |#3| (-984)) (|has| |#3| (-1027))) +(-1476 (|has| |#2| (-162)) (|has| |#2| (-793)) (|has| |#2| (-984))) ((((-388 (-530))) |has| |#1| (-975 (-388 (-530)))) (((-530)) |has| |#1| (-975 (-530))) ((|#1|) . T)) (|has| |#1| (-1121)) (|has| |#1| (-1121)) -(-1450 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) +(-1476 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) (|has| |#1| (-1121)) (|has| |#1| (-1121)) (((|#3| |#3|) . T)) @@ -1537,43 +1537,43 @@ (((|#1|) . T) (((-388 (-530))) . T) (($) . T)) ((((-1082) (-51)) . T)) (|has| |#1| (-1027)) -(-1450 (|has| |#2| (-768)) (|has| |#2| (-795))) +(-1476 (|has| |#2| (-768)) (|has| |#2| (-795))) (((|#1|) . T)) -((($) -1450 (|has| |#1| (-344)) (|has| |#1| (-330))) (((-388 (-530))) -1450 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1|) . T)) +((($) -1476 (|has| |#1| (-344)) (|has| |#1| (-330))) (((-388 (-530))) -1476 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1|) . T)) (((|#1|) |has| |#1| (-162)) (($) . T)) ((($) . T)) ((((-1097 |#1| |#2| |#3|)) -12 (|has| (-1097 |#1| |#2| |#3|) (-291 (-1097 |#1| |#2| |#3|))) (|has| |#1| (-344)))) ((((-804)) . T)) -(-1450 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) +(-1476 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) ((($) . T)) -(-1450 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) +(-1476 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) ((((-804)) . 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T)) (((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) ((($ $) . T)) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) ((($ $) . T)) ((((-530) (-110)) . T)) ((($) . T)) (((|#1|) . T)) ((((-530)) . T)) ((((-110)) . T)) -(-1450 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-522))) (|has| |#1| (-37 (-388 (-530)))) (((|#1| (-530)) . T)) ((($) . T)) @@ -1595,7 +1595,7 @@ (((|#1| (-1145 |#1| |#2| |#3|)) . T)) (((|#1| (-719)) . T)) (((|#1|) . T)) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) ((((-804)) . T)) (|has| |#1| (-1027)) ((((-1082) |#1|) . T)) @@ -1615,18 +1615,18 @@ (((|#1|) . T)) ((((-530)) . T)) ((((-804)) . T)) -(-1450 (|has| |#1| (-138)) (|has| |#1| (-330))) +(-1476 (|has| |#1| (-138)) (|has| |#1| (-330))) (|has| |#1| (-140)) ((((-804)) . T)) (((|#3|) . T)) -(-1450 (|has| |#3| (-162)) (|has| |#3| (-793)) (|has| |#3| (-984))) +(-1476 (|has| |#3| (-162)) (|has| |#3| (-793)) (|has| |#3| (-984))) ((((-804)) . T)) ((((-1166 |#2| |#3| |#4|)) . T) (((-1167 |#1| |#2| |#3| |#4|)) . T)) ((((-804)) . T)) -((((-47)) -12 (|has| |#1| (-522)) (|has| |#1| (-975 (-530)))) (((-570 $)) . T) ((|#1|) . T) (((-530)) |has| |#1| (-975 (-530))) (((-388 (-530))) -1450 (-12 (|has| |#1| (-522)) (|has| |#1| (-975 (-530)))) (|has| |#1| (-975 (-388 (-530))))) (((-388 (-893 |#1|))) |has| |#1| (-522)) (((-893 |#1|)) |has| |#1| (-984)) (((-1099)) . T)) +((((-47)) -12 (|has| |#1| (-522)) (|has| |#1| (-975 (-530)))) (((-570 $)) . T) ((|#1|) . T) (((-530)) |has| |#1| (-975 (-530))) (((-388 (-530))) -1476 (-12 (|has| |#1| (-522)) (|has| |#1| (-975 (-530)))) (|has| |#1| (-975 (-388 (-530))))) (((-388 (-893 |#1|))) |has| |#1| (-522)) (((-893 |#1|)) |has| |#1| (-984)) (((-1099)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-719)) . T)) -((($) -1450 (|has| |#1| (-344)) (|has| |#1| (-522))) (((-388 (-530))) -1450 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) ((|#1|) |has| |#1| (-162))) +((($) -1476 (|has| |#1| (-344)) (|has| |#1| (-522))) (((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) ((|#1|) |has| |#1| (-162))) (((|#1|) |has| |#1| (-291 |#1|))) ((((-1167 |#1| |#2| |#3| |#4|)) . T)) ((((-530)) |has| |#1| (-827 (-530))) (((-360)) |has| |#1| (-827 (-360)))) @@ -1634,14 +1634,14 @@ (|has| |#1| (-522)) (((|#1|) . T)) ((((-804)) . T)) -(((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) (((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) |has| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (-291 (-2 (|:| -2913 |#1|) (|:| -1782 |#2|))))) +(((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) (((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) |has| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (-291 (-2 (|:| -2940 |#1|) (|:| -1806 |#2|))))) (((|#1|) |has| |#1| (-162))) ((($) |has| |#1| (-522)) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) (((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) (((|#1|) . T)) (((|#3|) |has| |#3| (-1027))) -(((|#2|) -1450 (|has| |#2| (-162)) (|has| |#2| (-344)))) +(((|#2|) -1476 (|has| |#2| (-162)) (|has| |#2| (-344)))) ((((-1166 |#2| |#3| |#4|)) . T)) ((((-110)) . T)) (|has| |#1| (-768)) @@ -1651,8 +1651,8 @@ (|has| |#1| (-793)) (|has| |#1| (-793)) (((|#1| (-530) (-1012)) . T)) -(-1450 (|has| |#1| (-841 (-1099))) (|has| |#1| (-984))) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +(-1476 (|has| |#1| (-841 (-1099))) (|has| |#1| (-984))) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) (((|#1| (-388 (-530)) (-1012)) . T)) (((|#1| (-719) (-1012)) . T)) (|has| |#1| (-795)) @@ -1668,28 +1668,28 @@ (((|#1|) . T)) (|has| |#1| (-1027)) ((((-530)) -12 (|has| |#1| (-344)) (|has| |#2| (-593 (-530)))) ((|#2|) |has| |#1| (-344))) -(-1450 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) +(-1476 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) (((|#2|) |has| |#2| (-162))) (((|#1|) |has| |#1| (-162))) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) -((((-2 (|:| -2913 (-1082)) (|:| -1782 |#1|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) . T)) ((((-804)) . T)) (|has| |#3| (-793)) ((((-804)) . T)) ((((-1166 |#2| |#3| |#4|) (-300 |#2| |#3| |#4|)) . T)) ((((-804)) . T)) -(((|#1| |#1|) -1450 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-984)))) +(((|#1| |#1|) -1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-984)))) (((|#1|) . T)) ((((-530)) . T)) ((((-530)) . T)) -(((|#1|) -1450 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-984)))) +(((|#1|) -1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-984)))) (((|#2|) |has| |#2| (-344))) ((($) . T) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-344))) (|has| |#1| (-795)) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -2913 (-1099)) (|:| -1782 (-51)))) |has| (-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) (-291 (-2 (|:| -2913 (-1099)) (|:| -1782 (-51)))))) -(-1450 (|has| |#1| (-432)) (|has| |#1| (-850))) +((((-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))) |has| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (-291 (-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))))) +(-1476 (|has| |#1| (-432)) (|has| |#1| (-850))) (((|#2|) . T) (((-530)) |has| |#2| (-593 (-530)))) ((((-804)) . T)) ((((-804)) . T)) @@ -1725,18 +1725,18 @@ (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-37 (-388 (-530)))) (((|#1|) . T)) -(-1450 (|has| |#2| (-162)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1476 (|has| |#2| (-162)) (|has| |#2| (-793)) (|has| |#2| (-984))) (((|#1| |#1|) . T) ((#0=(-388 (-530)) #0#) . T) (($ $) . T)) ((((-804)) . T)) (((|#1|) . T) (((-388 (-530))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) (|has| |#1| (-344)) (|has| |#1| (-344)) (|has| (-388 |#2|) (-216)) (|has| |#1| (-850)) (((|#2|) |has| |#2| (-984))) -(((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) (((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) |has| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (-291 (-2 (|:| -2913 |#1|) (|:| -1782 |#2|))))) +(((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) (((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) |has| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (-291 (-2 (|:| -2940 |#1|) (|:| -1806 |#2|))))) (|has| |#1| (-344)) (((|#1|) |has| |#1| (-162))) (((|#1| |#1|) . T)) @@ -1761,7 +1761,7 @@ (((|#1| (-388 (-530)) (-1012)) . T)) (((|#1| (-719) (-1012)) . T)) (((#0=(-388 |#2|) #0#) . T) ((#1=(-388 (-530)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-530)) -1450 (|has| (-388 (-530)) (-975 (-530))) (|has| |#1| (-975 (-530)))) (((-388 (-530))) . T)) +(((|#1|) . T) (((-530)) -1476 (|has| (-388 (-530)) (-975 (-530))) (|has| |#1| (-975 (-530)))) (((-388 (-530))) . T)) (((|#1| (-561 |#1| |#3|) (-561 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-162))) (((|#1|) . T)) @@ -1780,24 +1780,24 @@ ((((-647)) . T)) (((|#2|) |has| |#2| (-162))) (|has| |#2| (-793)) -((((-110)) |has| |#1| (-1027)) (((-804)) -1450 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-453)) (|has| |#1| (-675)) (|has| |#1| (-841 (-1099))) (|has| |#1| (-984)) (|has| |#1| (-1039)) (|has| |#1| (-1027)))) +((((-110)) |has| |#1| (-1027)) (((-804)) -1476 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-453)) (|has| |#1| (-675)) (|has| |#1| (-841 (-1099))) (|has| |#1| (-984)) (|has| |#1| (-1039)) (|has| |#1| (-1027)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2913 (-1082)) (|:| -1782 (-51)))) . T)) +((((-2 (|:| -2940 (-1082)) (|:| -1806 (-51)))) . T)) ((((-804)) . T)) ((((-530) |#1|) . T)) ((((-647)) . T) (((-388 (-530))) . T) (((-530)) . T)) (((|#1| |#1|) |has| |#1| (-162))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) (((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) |has| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (-291 (-2 (|:| -2913 |#1|) (|:| -1782 |#2|))))) +(((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) (((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) |has| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (-291 (-2 (|:| -2940 |#1|) (|:| -1806 |#2|))))) ((((-360)) . T)) ((((-647)) . T)) ((((-388 (-530))) . #0=(|has| |#2| (-344))) (($) . #0#)) (((|#1|) |has| |#1| (-162))) ((((-388 (-893 |#1|))) . T)) (((|#2| |#2|) . T)) -(-1450 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) -(-1450 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) +(-1476 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) +(-1476 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) (((|#2|) . T)) (|has| |#2| (-795)) (((|#3|) |has| |#3| (-984))) @@ -1807,14 +1807,14 @@ (|has| |#1| (-795)) ((((-1099)) |has| |#2| (-841 (-1099)))) ((((-804)) . T)) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) ((((-388 (-530))) . T) (($) . T)) (|has| |#1| (-453)) (|has| |#1| (-349)) (|has| |#1| (-349)) (|has| |#1| (-349)) (|has| |#1| (-344)) -(-1450 (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-453)) (|has| |#1| (-522)) (|has| |#1| (-984)) (|has| |#1| (-1039))) +(-1476 (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-453)) (|has| |#1| (-522)) (|has| |#1| (-984)) (|has| |#1| (-1039))) (|has| |#1| (-37 (-388 (-530)))) ((((-114 |#1|)) . T)) ((((-114 |#1|)) . T)) @@ -1835,11 +1835,11 @@ (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-795)) -((((-2 (|:| -2913 (-1082)) (|:| -1782 |#1|))) . T)) +((((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-140)) (|has| |#1| (-138)) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) |has| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (-291 (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)))) ((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) |has| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (-291 (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)))) ((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) (((|#2|) . T)) (((|#3|) . T)) ((((-114 |#1|)) . T)) @@ -1857,11 +1857,11 @@ ((((-506)) |has| |#1| (-572 (-506))) (((-833 (-530))) |has| |#1| (-572 (-833 (-530)))) (((-833 (-360))) |has| |#1| (-572 (-833 (-360)))) (((-360)) . #0=(|has| |#1| (-960))) (((-208)) . #0#)) (((|#1|) |has| |#1| (-344))) ((((-804)) . T)) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) ((($ $) . T) (((-570 $) $) . T)) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) ((($) . T) (((-1167 |#1| |#2| |#3| |#4|)) . T) (((-388 (-530))) . T)) -((($) -1450 (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-522)) (|has| |#1| (-984))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-522))) +((($) -1476 (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-522)) (|has| |#1| (-984))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-522))) (|has| |#1| (-344)) (|has| |#1| (-344)) (|has| |#1| (-344)) @@ -1872,11 +1872,11 @@ ((((-360)) . T)) (((|#3|) -12 (|has| |#3| (-291 |#3|)) (|has| |#3| (-1027)))) ((((-804)) . T)) -(-1450 (|has| |#2| (-432)) (|has| |#2| (-850))) +(-1476 (|has| |#2| (-432)) (|has| |#2| (-850))) (((|#1|) . T)) (|has| |#1| (-795)) (|has| |#1| (-795)) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) ((((-506)) |has| |#1| (-572 (-506)))) (((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) (|has| |#1| (-1027)) @@ -1885,13 +1885,13 @@ (|has| |#1| (-138)) (|has| |#1| (-140)) ((((-530)) . T)) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-522))) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) (((#0=(-1166 |#2| |#3| |#4|)) . T) (((-388 (-530))) |has| #0# (-37 (-388 (-530)))) (($) . T)) ((((-530)) . T)) (|has| |#1| (-344)) -(-1450 (-12 (|has| (-1173 |#1| |#2| |#3|) (-140)) (|has| |#1| (-344))) (|has| |#1| (-140))) -(-1450 (-12 (|has| (-1173 |#1| |#2| |#3|) (-138)) (|has| |#1| (-344))) (|has| |#1| (-138))) +(-1476 (-12 (|has| (-1173 |#1| |#2| |#3|) (-140)) (|has| |#1| (-344))) (|has| |#1| (-140))) +(-1476 (-12 (|has| (-1173 |#1| |#2| |#3|) (-138)) (|has| |#1| (-344))) (|has| |#1| (-138))) (|has| |#1| (-344)) (|has| |#1| (-138)) (|has| |#1| (-140)) @@ -1908,18 +1908,18 @@ (((|#1| |#2|) . T)) (((|#1|) . T) (((-530)) |has| |#1| (-593 (-530)))) (((|#3|) |has| |#3| (-162))) -(-1450 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) +(-1476 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) ((((-530)) . T)) (((|#1| $) |has| |#1| (-268 |#1| |#1|))) ((((-388 (-530))) . T) (($) . T) (((-388 |#1|)) . T) ((|#1|) . T)) ((((-804)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -1450 (|has| |#1| (-272)) (|has| |#1| (-344))) ((#0=(-388 (-530)) #0#) |has| |#1| (-344))) -((((-2 (|:| -2913 (-1099)) (|:| -1782 (-51)))) . T)) +(((|#1| |#1|) . T) (($ $) -1476 (|has| |#1| (-272)) (|has| |#1| (-344))) ((#0=(-388 (-530)) #0#) |has| |#1| (-344))) +((((-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))) . T)) ((($) . T)) ((((-530) |#1|) . T)) ((((-1099)) |has| (-388 |#2|) (-841 (-1099)))) -(((|#1|) . T) (($) -1450 (|has| |#1| (-272)) (|has| |#1| (-344))) (((-388 (-530))) |has| |#1| (-344))) +(((|#1|) . T) (($) -1476 (|has| |#1| (-272)) (|has| |#1| (-344))) (((-388 (-530))) |has| |#1| (-344))) ((((-506)) |has| |#2| (-572 (-506)))) ((((-637 |#2|)) . T) (((-804)) . T)) (((|#1|) . T)) @@ -1927,8 +1927,8 @@ (((|#4|) -12 (|has| |#4| (-291 |#4|)) (|has| |#4| (-1027)))) ((((-811 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) -(-1450 (|has| |#4| (-741)) (|has| |#4| (-793))) -(-1450 (|has| |#3| (-741)) (|has| |#3| (-793))) +(-1476 (|has| |#4| (-741)) (|has| |#4| (-793))) +(-1476 (|has| |#3| (-741)) (|has| |#3| (-793))) ((((-804)) . T)) ((((-804)) . T)) (((|#4|) -12 (|has| |#4| (-291 |#4|)) (|has| |#4| (-1027)))) @@ -1944,17 +1944,17 @@ ((((-388 (-530))) . T) (($) . T)) ((((-388 (-530))) . T) (($) . T)) ((((-388 (-530))) . T) (($) . T)) -(-1450 (|has| |#1| (-432)) (|has| |#1| (-1139))) +(-1476 (|has| |#1| (-432)) (|has| |#1| (-1139))) ((($) . T)) ((((-388 (-530))) |has| #0=(-388 |#2|) (-975 (-388 (-530)))) (((-530)) |has| #0# (-975 (-530))) ((#0#) . T)) (((|#2|) . T) (((-530)) |has| |#2| (-593 (-530)))) (((|#1| (-719)) . T)) (|has| |#1| (-795)) (((|#1|) . T) (((-530)) |has| |#1| (-593 (-530)))) -((($) -1450 (|has| |#1| (-344)) (|has| |#1| (-330))) (((-388 (-530))) -1450 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1|) . T)) +((($) -1476 (|has| |#1| (-344)) (|has| |#1| (-330))) (((-388 (-530))) -1476 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1|) . T)) ((((-530)) . T)) (|has| |#1| (-37 (-388 (-530)))) -((((-2 (|:| -2913 (-1082)) (|:| -1782 (-51)))) |has| (-2 (|:| -2913 (-1082)) (|:| -1782 (-51))) (-291 (-2 (|:| -2913 (-1082)) (|:| -1782 (-51)))))) +((((-2 (|:| -2940 (-1082)) (|:| -1806 (-51)))) |has| (-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) (-291 (-2 (|:| -2940 (-1082)) (|:| -1806 (-51)))))) (((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (|has| |#1| (-793)) (|has| |#1| (-37 (-388 (-530)))) @@ -1979,24 +1979,24 @@ (((|#1| |#2|) . T)) ((((-137)) . T)) ((((-728 |#1| (-806 |#2|))) . T)) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) (|has| |#1| (-1121)) (((|#1|) . T)) -(-1450 (|has| |#3| (-25)) (|has| |#3| (-128)) (|has| |#3| (-162)) (|has| |#3| (-344)) (|has| |#3| (-349)) (|has| |#3| (-675)) (|has| |#3| (-741)) (|has| |#3| (-793)) (|has| |#3| (-984)) (|has| |#3| (-1027))) +(-1476 (|has| |#3| (-25)) (|has| |#3| (-128)) (|has| |#3| (-162)) (|has| |#3| (-344)) (|has| |#3| (-349)) (|has| |#3| (-675)) (|has| |#3| (-741)) (|has| |#3| (-793)) (|has| |#3| (-984)) (|has| |#3| (-1027))) ((((-1099) |#1|) |has| |#1| (-491 (-1099) |#1|))) (((|#2|) . T)) -((($ $) -1450 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1| |#1|) . T) ((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530))))) -((($) -1450 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) +((($ $) -1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1| |#1|) . T) ((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530))))) +((($) -1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) ((((-851 |#1|)) . T)) ((($) . T)) ((((-388 (-893 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) ((((-506)) |has| |#4| (-572 (-506)))) ((((-804)) . T) (((-597 |#4|)) . T)) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-793)) -(((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027))) (((-2 (|:| -2913 (-1082)) (|:| -1782 |#1|))) |has| (-2 (|:| -2913 (-1082)) (|:| -1782 |#1|)) (-291 (-2 (|:| -2913 (-1082)) (|:| -1782 |#1|))))) +(((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027))) (((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) |has| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (-291 (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))))) (|has| |#1| (-1027)) (|has| |#1| (-344)) (|has| |#1| (-795)) @@ -2004,16 +2004,16 @@ (((|#1|) . T)) (((|#1|) . T)) ((($) . T) (((-388 (-530))) . T)) -((($) -1450 (|has| |#1| (-344)) (|has| |#1| (-522))) (((-388 (-530))) -1450 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) ((|#1|) |has| |#1| (-162))) +((($) -1476 (|has| |#1| (-344)) (|has| |#1| (-522))) (((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) ((|#1|) |has| |#1| (-162))) (|has| |#1| (-138)) (|has| |#1| (-140)) -(-1450 (-12 (|has| (-1097 |#1| |#2| |#3|) (-140)) (|has| |#1| (-344))) (|has| |#1| (-140))) -(-1450 (-12 (|has| (-1097 |#1| |#2| |#3|) (-138)) (|has| |#1| (-344))) (|has| |#1| (-138))) +(-1476 (-12 (|has| (-1097 |#1| |#2| |#3|) (-140)) (|has| |#1| (-344))) (|has| |#1| (-140))) +(-1476 (-12 (|has| (-1097 |#1| |#2| |#3|) (-138)) (|has| |#1| (-344))) (|has| |#1| (-138))) (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-140)) (|has| |#1| (-138)) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-344))) (|has| |#1| (-793)) (((|#1| |#2|) . T)) @@ -2036,9 +2036,9 @@ ((((-804)) . T)) ((((-804)) . T)) ((((-506)) |has| |#1| (-572 (-506)))) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) ((((-1099) |#1|) |has| |#1| (-491 (-1099) |#1|)) ((|#1| |#1|) |has| |#1| (-291 |#1|))) -(((|#1|) -1450 (|has| |#1| (-162)) (|has| |#1| (-344)))) +(((|#1|) -1476 (|has| |#1| (-162)) (|has| |#1| (-344)))) ((((-297 |#1|)) . T)) (((|#2|) |has| |#2| (-344))) (((|#2|) . T)) @@ -2059,13 +2059,13 @@ (|has| |#1| (-138)) (|has| |#1| (-140)) ((($ $) . T)) -(-1450 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-453)) (|has| |#1| (-675)) (|has| |#1| (-841 (-1099))) (|has| |#1| (-984)) (|has| |#1| (-1039)) (|has| |#1| (-1027))) +(-1476 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-453)) (|has| |#1| (-675)) (|has| |#1| (-841 (-1099))) (|has| |#1| (-984)) (|has| |#1| (-1039)) (|has| |#1| (-1027))) (|has| |#1| (-522)) (((|#2|) . T)) ((((-530)) . T)) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) (((|#1|) . T)) -(-1450 (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-522)) (|has| |#1| (-984))) +(-1476 (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-522)) (|has| |#1| (-984))) ((((-543 |#1|)) . T)) ((($) . T)) (((|#1| (-57 |#1|) (-57 |#1|)) . T)) @@ -2091,12 +2091,12 @@ (((|#1| |#2|) . T)) ((((-1099) |#1|) . T)) (((|#4|) . T)) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-330))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-330))) ((((-1099) (-51)) . T)) ((((-1166 |#2| |#3| |#4|) (-300 |#2| |#3| |#4|)) . T)) ((((-388 (-530))) |has| |#1| (-975 (-388 (-530)))) (((-530)) |has| |#1| (-975 (-530))) ((|#1|) . T)) ((((-804)) . T)) -(-1450 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) +(-1476 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) (((#0=(-1167 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-388 (-530)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-162)) ((#0=(-388 (-530)) #0#) |has| |#1| (-522)) (($ $) |has| |#1| (-522))) (((|#1|) . T) (($) . T) (((-388 (-530))) . T)) @@ -2115,14 +2115,14 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) (((|#2| |#3|) . T)) -(-1450 (|has| |#2| (-344)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) +(-1476 (|has| |#2| (-344)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) (((|#1| (-502 |#2|)) . T)) (((|#1| (-719)) . T)) (((|#1| (-502 (-1017 (-1099)))) . T)) (((|#1|) |has| |#1| (-162))) (((|#1|) . T)) (|has| |#2| (-850)) -(-1450 (|has| |#2| (-741)) (|has| |#2| (-793))) +(-1476 (|has| |#2| (-741)) (|has| |#2| (-793))) ((((-804)) . T)) ((($ $) . T) ((#0=(-1166 |#2| |#3| |#4|) #0#) . T) ((#1=(-388 (-530)) #1#) |has| #0# (-37 (-388 (-530))))) ((((-851 |#1|)) . T)) @@ -2131,13 +2131,13 @@ ((($) . T)) ((($) . T)) (|has| |#1| (-344)) -(-1450 (|has| |#1| (-289)) (|has| |#1| (-344)) (|has| |#1| (-330)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-289)) (|has| |#1| (-344)) (|has| |#1| (-330)) (|has| |#1| (-522))) (|has| |#1| (-344)) ((($) . T) ((#0=(-1166 |#2| |#3| |#4|)) . T) (((-388 (-530))) |has| #0# (-37 (-388 (-530))))) (((|#1| |#2|) . T)) ((((-1097 |#1| |#2| |#3|)) |has| |#1| (-344))) -(-1450 (-12 (|has| |#1| (-289)) (|has| |#1| (-850))) (|has| |#1| (-344)) (|has| |#1| (-330))) -(-1450 (|has| |#1| (-841 (-1099))) (|has| |#1| (-984))) +(-1476 (-12 (|has| |#1| (-289)) (|has| |#1| (-850))) (|has| |#1| (-344)) (|has| |#1| (-330))) +(-1476 (|has| |#1| (-841 (-1099))) (|has| |#1| (-984))) ((((-530)) |has| |#1| (-593 (-530))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-804)) . T)) @@ -2169,27 +2169,27 @@ (((|#1|) |has| |#1| (-162))) ((((-804)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-291 |#4|)) (|has| |#4| (-1027)))) -(((|#2|) -1450 (|has| |#2| (-6 (-4272 "*"))) (|has| |#2| (-162)))) -(-1450 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) -(-1450 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) +(((|#2|) -1476 (|has| |#2| (-6 (-4272 "*"))) (|has| |#2| (-162)))) +(-1476 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) +(-1476 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) (|has| |#2| (-795)) (|has| |#2| (-850)) (|has| |#1| (-850)) (((|#2|) |has| |#2| (-162))) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-344))) ((((-804)) . T)) ((((-804)) . T)) ((((-506)) . T) (((-530)) . T) (((-833 (-530))) . T) (((-360)) . T) (((-208)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) -((((-2 (|:| -2913 (-1082)) (|:| -1782 (-51)))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -2940 (-1082)) (|:| -1806 (-51)))) . T)) (((|#1|) . T)) ((((-804)) . T)) (((|#1| |#2|) . T)) (((|#1| (-388 (-530))) . T)) (((|#1|) . T)) -(-1450 (|has| |#1| (-272)) (|has| |#1| (-344))) +(-1476 (|has| |#1| (-272)) (|has| |#1| (-344))) ((((-137)) . T)) ((((-388 |#2|)) . T) (((-388 (-530))) . T) (($) . T)) (|has| |#1| (-793)) @@ -2204,7 +2204,7 @@ ((((-388 (-530))) . T) (($) . T)) ((((-804)) . T)) ((((-804)) . T)) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-804)) . T)) ((((-804)) . T)) @@ -2215,7 +2215,7 @@ (((|#1|) . T)) ((((-597 (-137))) . T) (((-1082)) . T)) ((((-804)) . T)) -((((-2 (|:| -2913 (-1082)) (|:| -1782 |#1|))) . T)) +((((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) . T)) ((((-1099) |#1|) |has| |#1| (-491 (-1099) |#1|)) ((|#1| |#1|) |has| |#1| (-291 |#1|))) (|has| |#1| (-795)) ((((-804)) . T)) @@ -2227,16 +2227,16 @@ ((((-804)) . T) (((-597 |#4|)) . T)) (((|#2|) . T)) ((((-851 |#1|)) . T) (((-388 (-530))) . T) (($) . T)) -(-1450 (|has| |#4| (-162)) (|has| |#4| (-675)) (|has| |#4| (-793)) (|has| |#4| (-984))) -(-1450 (|has| |#3| (-162)) (|has| |#3| (-675)) (|has| |#3| (-793)) (|has| |#3| (-984))) +(-1476 (|has| |#4| (-162)) (|has| |#4| (-675)) (|has| |#4| (-793)) (|has| |#4| (-984))) +(-1476 (|has| |#3| (-162)) (|has| |#3| (-675)) (|has| |#3| (-793)) (|has| |#3| (-984))) ((((-1099) (-51)) . T)) -(-1450 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) +(-1476 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-1450 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) -(-1450 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1476 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1476 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-793)) (|has| |#2| (-984))) (|has| |#1| (-850)) (|has| |#1| (-850)) (((|#2|) . T)) @@ -2251,12 +2251,12 @@ (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-37 (-388 (-530)))) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) (|has| |#1| (-768)) (((#0=(-851 |#1|) #0#) . T) (($ $) . T) ((#1=(-388 (-530)) #1#) . T)) ((((-388 |#2|)) . T)) (|has| |#1| (-793)) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) (((|#1| |#1|) . T) ((#0=(-388 (-530)) #0#) . T) ((#1=(-530) #1#) . T) (($ $) . T)) ((((-851 |#1|)) . T) (($) . T) (((-388 (-530))) . T)) (((|#2|) |has| |#2| (-984)) (((-530)) -12 (|has| |#2| (-593 (-530))) (|has| |#2| (-984)))) @@ -2266,25 +2266,25 @@ (|has| |#1| (-138)) (((|#2|) . T)) ((((-804)) . T)) -(-1450 (|has| |#1| (-138)) (|has| |#1| (-349))) -(-1450 (|has| |#1| (-138)) (|has| |#1| (-349))) -(-1450 (|has| |#1| (-138)) (|has| |#1| (-349))) -((((-2 (|:| -2913 (-1099)) (|:| -1782 (-51)))) . T)) -(((#0=(-51)) . T) (((-2 (|:| -2913 (-1099)) (|:| -1782 #0#))) . T)) +(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) +(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) +(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) +((((-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))) . T)) +(((#0=(-51)) . T) (((-2 (|:| -2940 (-1099)) (|:| -1806 #0#))) . T)) (|has| |#1| (-330)) ((((-530)) . T)) ((((-804)) . T)) (((#0=(-1167 |#1| |#2| |#3| |#4|) $) |has| #0# (-268 #0# #0#))) (|has| |#1| (-344)) (((#0=(-1012) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-330))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-330))) (((#0=(-388 (-530)) #0#) . T) ((#1=(-647) #1#) . T) (($ $) . T)) ((((-297 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-388 (-530))) |has| |#1| (-344))) (|has| |#1| (-1027)) (((|#1|) . T)) -(((|#1|) -1450 (|has| |#2| (-348 |#1|)) (|has| |#2| (-398 |#1|)))) -(((|#1|) -1450 (|has| |#2| (-348 |#1|)) (|has| |#2| (-398 |#1|)))) +(((|#1|) -1476 (|has| |#2| (-348 |#1|)) (|has| |#2| (-398 |#1|)))) +(((|#1|) -1476 (|has| |#2| (-348 |#1|)) (|has| |#2| (-398 |#1|)))) (((|#2|) . T)) ((((-388 (-530))) . T) (((-647)) . T) (($) . T)) (((|#3| |#3|) . T)) @@ -2303,7 +2303,7 @@ (((|#2|) . T)) (((|#1|) . T)) ((((-530)) . T)) -(-1450 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) +(-1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) (((|#2|) . T) (((-530)) |has| |#2| (-593 (-530)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2340,7 +2340,7 @@ (|has| |#2| (-960)) ((($) . T)) (|has| |#1| (-850)) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2348,24 +2348,24 @@ ((($) . T)) (|has| |#1| (-344)) ((((-851 |#1|)) . T)) -((($) -1450 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) +((($) -1476 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) ((($ $) . T) ((#0=(-388 (-530)) #0#) . T)) -(-1450 (|has| |#1| (-349)) (|has| |#1| (-795))) +(-1476 (|has| |#1| (-349)) (|has| |#1| (-795))) (((|#1|) . T)) ((((-804)) . T)) ((((-1099)) -12 (|has| |#1| (-15 * (|#1| (-388 (-530)) |#1|))) (|has| |#1| (-841 (-1099))))) ((((-388 |#2|) |#3|) . T)) ((($) . T) (((-388 (-530))) . T)) ((((-719) |#1|) . T)) -(((|#2| (-223 (-2144 |#1|) (-719))) . T)) +(((|#2| (-223 (-2167 |#1|) (-719))) . T)) (((|#1| (-502 |#3|)) . T)) ((((-388 (-530))) . T)) -(-1450 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) +(-1476 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((((-804)) . T)) -(((#0=(-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) #0#) |has| (-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) (-291 (-2 (|:| -2913 (-1099)) (|:| -1782 (-51)))))) +(((#0=(-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) #0#) |has| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (-291 (-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))))) (|has| |#1| (-850)) (|has| |#2| (-344)) -(-1450 (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1476 (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) ((((-159 (-360))) . T) (((-208)) . T) (((-360)) . T)) ((((-804)) . T)) (((|#1|) . T)) @@ -2382,11 +2382,11 @@ (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-37 (-388 (-530)))) -(-1450 (|has| |#1| (-289)) (|has| |#1| (-344)) (|has| |#1| (-330))) +(-1476 (|has| |#1| (-289)) (|has| |#1| (-344)) (|has| |#1| (-330))) (|has| |#1| (-37 (-388 (-530)))) (-12 (|has| |#1| (-515)) (|has| |#1| (-776))) ((((-804)) . T)) -((((-1099)) -1450 (-12 (|has| |#1| (-15 * (|#1| (-530) |#1|))) (|has| |#1| (-841 (-1099)))) (-12 (|has| |#1| (-344)) (|has| |#2| (-841 (-1099)))))) +((((-1099)) -1476 (-12 (|has| |#1| (-15 * (|#1| (-530) |#1|))) (|has| |#1| (-841 (-1099)))) (-12 (|has| |#1| (-344)) (|has| |#2| (-841 (-1099)))))) (|has| |#1| (-344)) ((((-1099)) -12 (|has| |#1| (-15 * (|#1| (-388 (-530)) |#1|))) (|has| |#1| (-841 (-1099))))) (|has| |#1| (-344)) @@ -2396,7 +2396,7 @@ (((|#1|) . T)) (((|#2|) |has| |#1| (-344))) (((|#2|) |has| |#1| (-344))) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-162))) (((|#1|) . T)) @@ -2421,30 +2421,30 @@ ((((-360)) -12 (|has| |#1| (-344)) (|has| |#2| (-827 (-360)))) (((-530)) -12 (|has| |#1| (-344)) (|has| |#2| (-827 (-530))))) (|has| |#1| (-344)) (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) (|has| |#1| (-344)) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) (|has| |#1| (-344)) (|has| |#1| (-522)) (((|#4| |#4|) -12 (|has| |#4| (-291 |#4|)) (|has| |#4| (-1027)))) (((|#3|) . T)) (((|#1|) . T)) -(-1450 (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1476 (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) (((|#2|) . T)) (((|#2|) . T)) -(-1450 (|has| |#2| (-162)) (|has| |#2| (-675)) (|has| |#2| (-793)) (|has| |#2| (-984))) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) -((((-2 (|:| -2913 (-1082)) (|:| -1782 |#1|))) . T)) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +(-1476 (|has| |#2| (-162)) (|has| |#2| (-675)) (|has| |#2| (-793)) (|has| |#2| (-984))) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) (|has| |#1| (-37 (-388 (-530)))) (((|#1| |#2|) . T)) (|has| |#1| (-37 (-388 (-530)))) -(-1450 (|has| |#1| (-138)) (|has| |#1| (-349))) +(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) (|has| |#1| (-140)) ((((-1082) |#1|) . T)) -(-1450 (|has| |#1| (-138)) (|has| |#1| (-349))) +(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) (|has| |#1| (-140)) -(-1450 (|has| |#1| (-138)) (|has| |#1| (-349))) +(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) (|has| |#1| (-140)) ((((-543 |#1|)) . T)) ((($) . T)) @@ -2452,7 +2452,7 @@ (|has| |#1| (-522)) (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-37 (-388 (-530)))) -(-1450 (|has| |#1| (-138)) (|has| |#1| (-330))) +(-1476 (|has| |#1| (-138)) (|has| |#1| (-330))) (|has| |#1| (-140)) ((((-804)) . T)) ((($) . T)) @@ -2477,7 +2477,7 @@ (|has| |#1| (-739)) (|has| |#1| (-739)) ((((-506)) |has| |#1| (-572 (-506)))) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) ((((-112)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2498,7 +2498,7 @@ ((((-530)) . T)) ((((-804)) . T)) ((((-530)) . T)) -(-1450 (|has| |#2| (-741)) (|has| |#2| (-793))) +(-1476 (|has| |#2| (-741)) (|has| |#2| (-793))) ((((-159 (-360))) . T) (((-208)) . T) (((-360)) . T)) ((((-804)) . T)) ((((-804)) . T)) @@ -2510,9 +2510,9 @@ (((|#1|) . T) (($) . T) (((-388 (-530))) . T)) (|has| |#1| (-344)) (|has| |#1| (-344)) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) -(-1450 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-453)) (|has| |#1| (-675)) (|has| |#1| (-841 (-1099))) (|has| |#1| (-984)) (|has| |#1| (-1039)) (|has| |#1| (-1027))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +(-1476 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-453)) (|has| |#1| (-675)) (|has| |#1| (-841 (-1099))) (|has| |#1| (-984)) (|has| |#1| (-1039)) (|has| |#1| (-1027))) (|has| |#1| (-1075)) ((((-530) |#1|) . T)) (((|#1|) . T)) @@ -2530,8 +2530,8 @@ (((|#1|) . T)) (|has| |#1| (-522)) ((((-388 |#2|)) . T) (((-388 (-530))) . T) (($) . T)) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-522))) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) ((((-360)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2540,7 +2540,7 @@ (|has| |#1| (-522)) (|has| |#1| (-1027)) ((((-728 |#1| (-806 |#2|))) |has| (-728 |#1| (-806 |#2|)) (-291 (-728 |#1| (-806 |#2|))))) -(-1450 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) +(-1476 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) (((|#1|) . T)) (((|#2| |#3|) . T)) (|has| |#2| (-850)) @@ -2550,12 +2550,12 @@ (|has| |#1| (-216)) (((|#1| (-502 (-1017 (-1099)))) . T)) (|has| |#2| (-344)) -((((-2 (|:| -2913 (-1082)) (|:| -1782 (-51)))) . T)) +((((-2 (|:| -2940 (-1082)) (|:| -1806 (-51)))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) ((((-804)) . T)) ((((-804)) . T)) -(-1450 (|has| |#3| (-741)) (|has| |#3| (-793))) +(-1476 (|has| |#3| (-741)) (|has| |#3| (-793))) ((((-804)) . T)) ((((-1046)) . T) (((-804)) . T)) ((((-804)) . T)) @@ -2565,8 +2565,8 @@ ((((-530)) . T)) (((|#3|) . T)) ((((-804)) . T)) -(-1450 (|has| |#1| (-289)) (|has| |#1| (-344)) (|has| |#1| (-330))) -(-1450 (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-522)) (|has| |#1| (-984))) +(-1476 (|has| |#1| (-289)) (|has| |#1| (-344)) (|has| |#1| (-330))) +(-1476 (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-522)) (|has| |#1| (-984))) (((#0=(-543 |#1|) #0#) . T) (($ $) . T) ((#1=(-388 (-530)) #1#) . T)) ((($ $) . T) ((#0=(-388 (-530)) #0#) . T)) (((|#1|) |has| |#1| (-162))) @@ -2579,7 +2579,7 @@ (((|#1|) . T)) ((((-804)) |has| |#1| (-571 (-804)))) ((((-276 |#3|)) . T)) -(((#0=(-388 (-530)) #0#) |has| |#2| (-37 (-388 (-530)))) ((|#2| |#2|) . T) (($ $) -1450 (|has| |#2| (-162)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850)))) +(((#0=(-388 (-530)) #0#) |has| |#2| (-37 (-388 (-530)))) ((|#2| |#2|) . T) (($ $) -1476 (|has| |#2| (-162)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-388 (-530))) |has| |#2| (-37 (-388 (-530)))) ((|#2|) . T)) @@ -2587,20 +2587,20 @@ (((|#1|) . T) (((-388 (-530))) . T) (($) . T)) (((|#1|) . T) (((-388 (-530))) . T) (($) . T)) (((|#1|) . T) (((-388 (-530))) . T) (($) . T)) -((($ $) -1450 (|has| |#1| (-162)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1| |#1|) . T) ((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530))))) -((($ $) -1450 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1| |#1|) . T) ((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530))))) +((($ $) -1476 (|has| |#1| (-162)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1| |#1|) . T) ((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530))))) +((($ $) -1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1| |#1|) . T) ((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530))))) (((|#2|) . T)) -((((-388 (-530))) |has| |#2| (-37 (-388 (-530)))) ((|#2|) . T) (($) -1450 (|has| |#2| (-162)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850)))) +((((-388 (-530))) |has| |#2| (-37 (-388 (-530)))) ((|#2|) . T) (($) -1476 (|has| |#2| (-162)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850)))) (((|#2|) . T) ((|#6|) . T)) -((($ $) -1450 (|has| |#1| (-162)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1| |#1|) . T) ((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530))))) +((($ $) -1476 (|has| |#1| (-162)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1| |#1|) . T) ((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530))))) ((((-804)) . T)) -((($) -1450 (|has| |#1| (-162)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) -((($) -1450 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) +((($) -1476 (|has| |#1| (-162)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) +((($) -1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) (|has| |#2| (-850)) (|has| |#1| (-850)) -((($) -1450 (|has| |#1| (-162)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) +((($) -1476 (|has| |#1| (-162)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) (((|#1|) . T)) -((((-2 (|:| -2913 (-1082)) (|:| -1782 |#1|))) . T)) +((((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) . T)) @@ -2614,10 +2614,10 @@ (((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) (((#0=(-388 (-530)) #0#) . T)) ((((-388 (-530))) . T)) -(-1450 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1476 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) (((|#1|) . T)) (((|#1|) . T)) -(-1450 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1476 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-793)) (|has| |#2| (-984))) ((((-506)) . T)) ((((-804)) . T)) ((((-1099)) |has| |#2| (-841 (-1099))) (((-1012)) . T)) @@ -2632,12 +2632,12 @@ ((($ $) . T) ((#0=(-388 (-530)) #0#) . T)) ((((-1099)) |has| |#1| (-841 (-1099)))) ((((-851 |#1|)) . T) (((-388 (-530))) . T) (($) . T)) -((($) . T) (((-388 (-530))) -1450 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) ((|#1|) . T)) -(((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530)))) ((|#1| |#1|) . T) (($ $) -1450 (|has| |#1| (-162)) (|has| |#1| (-522)))) +((($) . T) (((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) ((|#1|) . T)) +(((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530)))) ((|#1| |#1|) . T) (($ $) -1476 (|has| |#1| (-162)) (|has| |#1| (-522)))) ((($) . T) (((-388 (-530))) . T)) (((|#1|) . T) (((-388 (-530))) . T) (((-530)) . T) (($) . T)) (((|#2|) |has| |#2| (-984)) (((-530)) -12 (|has| |#2| (-593 (-530))) (|has| |#2| (-984)))) -((((-388 (-530))) |has| |#1| (-37 (-388 (-530)))) ((|#1|) . T) (($) -1450 (|has| |#1| (-162)) (|has| |#1| (-522)))) +((((-388 (-530))) |has| |#1| (-37 (-388 (-530)))) ((|#1|) . T) (($) -1476 (|has| |#1| (-162)) (|has| |#1| (-522)))) (|has| |#1| (-522)) (((|#1|) |has| |#1| (-344))) ((((-530)) . T)) @@ -2656,8 +2656,8 @@ ((((-804)) . T)) (|has| |#2| (-768)) (|has| |#2| (-768)) -((((-388 (-530))) -1450 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) ((|#2|) |has| |#1| (-344)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-388 (-530))) -1450 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) . T)) +((((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) ((|#2|) |has| |#1| (-344)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (((|#1|) . T) (((-530)) |has| |#1| (-975 (-530))) (((-388 (-530))) |has| |#1| (-975 (-388 (-530))))) ((((-530)) |has| |#1| (-827 (-530))) (((-360)) |has| |#1| (-827 (-360)))) @@ -2683,12 +2683,12 @@ (((|#2| (-719)) . T)) ((((-1099)) . T)) ((((-811 |#1|)) . T)) -(-1450 (|has| |#3| (-25)) (|has| |#3| (-128)) (|has| |#3| (-162)) (|has| |#3| (-344)) (|has| |#3| (-741)) (|has| |#3| (-793)) (|has| |#3| (-984))) -(-1450 (|has| |#3| (-162)) (|has| |#3| (-344)) (|has| |#3| (-793)) (|has| |#3| (-984))) +(-1476 (|has| |#3| (-25)) (|has| |#3| (-128)) (|has| |#3| (-162)) (|has| |#3| (-344)) (|has| |#3| (-741)) (|has| |#3| (-793)) (|has| |#3| (-984))) +(-1476 (|has| |#3| (-162)) (|has| |#3| (-344)) (|has| |#3| (-793)) (|has| |#3| (-984))) ((((-804)) . T)) (((|#1|) . T)) -(-1450 (|has| |#2| (-741)) (|has| |#2| (-793))) -(-1450 (-12 (|has| |#1| (-741)) (|has| |#2| (-741))) (-12 (|has| |#1| (-795)) (|has| |#2| (-795)))) +(-1476 (|has| |#2| (-741)) (|has| |#2| (-793))) +(-1476 (-12 (|has| |#1| (-741)) (|has| |#2| (-741))) (-12 (|has| |#1| (-795)) (|has| |#2| (-795)))) ((((-811 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-349)) @@ -2714,7 +2714,7 @@ (((|#1|) . T)) ((((-804)) . T)) (|has| |#2| (-850)) -((((-2 (|:| -2913 (-1099)) (|:| -1782 (-51)))) . T)) +((((-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))) . T)) ((((-506)) |has| |#2| (-572 (-506))) (((-833 (-360))) |has| |#2| (-572 (-833 (-360)))) (((-833 (-530))) |has| |#2| (-572 (-833 (-530))))) ((((-804)) . T)) ((((-804)) . T)) @@ -2747,12 +2747,12 @@ ((((-388 |#2|) |#3|) . T)) (((|#1|) . T)) (|has| |#1| (-1027)) -(((|#2| (-461 (-2144 |#1|) (-719))) . T)) +(((|#2| (-461 (-2167 |#1|) (-719))) . T)) ((((-530) |#1|) . T)) ((((-1082)) . T) (((-804)) . T)) (((|#2| |#2|) . T)) (((|#1| (-502 (-1099))) . T)) -(-1450 (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1476 (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) ((((-530)) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -2762,9 +2762,9 @@ ((($) . T) (((-388 (-530))) . T)) ((($) . T)) ((($) . T)) -(-1450 (|has| |#1| (-795)) (|has| |#1| (-1027))) +(-1476 (|has| |#1| (-795)) (|has| |#1| (-1027))) (((|#1|) . T)) -((($) -1450 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) +((($) -1476 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) ((((-804)) . T)) ((((-137)) . T)) (((|#1|) . T) (((-388 (-530))) . T)) @@ -2804,27 +2804,27 @@ (|has| |#1| (-216)) (((|#1| (-502 |#3|)) . T)) (|has| |#1| (-349)) -(((|#2| (-223 (-2144 |#1|) (-719))) . T)) +(((|#2| (-223 (-2167 |#1|) (-719))) . T)) (|has| |#1| (-349)) (|has| |#1| (-349)) (((|#1|) . T) (($) . T)) (((|#1| (-502 |#2|)) . 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T) (((-388 (-530))) . T) (($) . T)) ((($ $) . T) ((#0=(-388 (-530)) #0#) . T)) @@ -2837,14 +2837,14 @@ (((|#2|) |has| |#2| (-984)) (((-530)) -12 (|has| |#2| (-593 (-530))) (|has| |#2| (-984)))) (((|#1|) . T)) (|has| |#2| (-344)) -(((#0=(-388 (-530)) #0#) |has| |#2| (-37 (-388 (-530)))) ((|#2| |#2|) . T) (($ $) -1450 (|has| |#2| (-162)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850)))) -((($ $) -1450 (|has| |#1| (-162)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1| |#1|) . T) ((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530))))) +(((#0=(-388 (-530)) #0#) |has| |#2| (-37 (-388 (-530)))) ((|#2| |#2|) . T) (($ $) -1476 (|has| |#2| (-162)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850)))) +((($ $) -1476 (|has| |#1| (-162)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1| |#1|) . T) ((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530))))) (((|#1| |#1|) . T) (($ $) . T) ((#0=(-388 (-530)) #0#) . T)) (((|#1| |#1|) . 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T)) @@ -2863,25 +2863,25 @@ (((|#1|) |has| |#2| (-398 |#1|))) (((|#1|) |has| |#2| (-398 |#1|))) ((((-851 |#1|)) . T) (((-388 (-530))) . T) (($) . T)) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) ((((-506)) |has| |#1| (-572 (-506)))) ((((-804)) . T)) -((((-2 (|:| -2913 (-1099)) (|:| -1782 (-51)))) |has| (-2 (|:| -2913 (-1099)) (|:| -1782 (-51))) (-291 (-2 (|:| -2913 (-1099)) (|:| -1782 (-51)))))) -(-1450 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) +((((-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))) |has| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (-291 (-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))))) +(-1476 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) ((((-530) |#1|) . T)) ((((-530) |#1|) . T)) ((((-530) |#1|) . 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T)) -(-1450 (|has| |#3| (-162)) (|has| |#3| (-675)) (|has| |#3| (-793)) (|has| |#3| (-984))) +(-1476 (|has| |#3| (-162)) (|has| |#3| (-675)) (|has| |#3| (-793)) (|has| |#3| (-984))) (((|#1| |#2|) . T)) (|has| |#1| (-37 (-388 (-530)))) ((((-804)) . T)) @@ -2889,15 +2889,15 @@ (((|#1|) |has| |#1| (-162)) (($) |has| |#1| (-522)) (((-388 (-530))) |has| |#1| (-522))) (((|#2|) . T) (((-530)) |has| |#2| (-593 (-530)))) (|has| |#1| (-344)) -(-1450 (|has| |#1| (-15 * (|#1| (-530) |#1|))) (-12 (|has| |#1| (-344)) (|has| |#2| (-216)))) +(-1476 (|has| |#1| (-15 * (|#1| (-530) |#1|))) (-12 (|has| |#1| (-344)) (|has| |#2| (-216)))) (|has| |#1| (-15 * (|#1| (-388 (-530)) |#1|))) (|has| |#1| (-344)) (((|#1|) . T)) -(((#0=(-388 (-530)) #0#) -1450 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($ $) -1450 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-522))) ((|#1| |#1|) . T)) +(((#0=(-388 (-530)) #0#) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($ $) -1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-522))) ((|#1| |#1|) . T)) ((((-530) |#1|) . T)) ((((-297 |#1|)) . T)) (((#0=(-647) (-1095 #0#)) . T)) -((((-388 (-530))) -1450 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1450 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-522))) ((|#1|) . T)) +((((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-522))) ((|#1|) . T)) (((|#1| |#2| |#3| |#4|) . T)) (|has| |#1| (-793)) ((($ $) . T) ((#0=(-806 |#1|) $) . T) ((#0# |#2|) . T)) @@ -2914,12 +2914,12 @@ (((#0=(-1167 |#1| |#2| |#3| |#4|)) |has| #0# (-291 #0#))) ((($) . T)) (((|#1|) . 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T)) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-330))) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-330))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) ((((-506)) |has| |#1| (-572 (-506)))) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) ((((-506)) |has| |#1| (-572 (-506)))) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) ((((-506)) |has| |#1| (-572 (-506)))) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) (((|#1|) . T)) (((|#2| |#2|) . T) ((#0=(-388 (-530)) #0#) . T) (($ $) . T)) ((((-530)) . T)) @@ -2993,32 +2993,32 @@ ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-344))) ((((-1099)) . T) (((-804)) . T)) (|has| |#1| (-344)) -((((-388 (-530))) |has| |#2| (-37 (-388 (-530)))) ((|#2|) |has| |#2| (-162)) (($) -1450 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850)))) +((((-388 (-530))) |has| |#2| (-37 (-388 (-530)))) ((|#2|) |has| |#2| (-162)) (($) -1476 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-388 (-530))) |has| |#2| (-37 (-388 (-530)))) ((|#2|) . T)) -((($) -1450 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) +((($) -1476 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) ((((-1031)) . T)) ((((-804)) . T)) -((($) -1450 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) +((($) -1476 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) ((($) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530)))) ((|#1|) . T)) ((($) . T)) -((($) -1450 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) +((($) -1476 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) (|has| |#2| (-850)) (|has| |#1| (-850)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-162))) ((((-647)) . T)) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) (((|#1|) |has| |#1| (-162))) (((|#1|) |has| |#1| (-162))) ((((-388 (-530))) . T) (($) . T)) (((|#1| (-530)) . T)) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-330))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-330))) (|has| |#1| (-344)) (|has| |#1| (-344)) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-330))) -(-1450 (|has| |#1| (-162)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-330))) +(-1476 (|has| |#1| (-162)) (|has| |#1| (-522))) (((|#1| (-530)) . T)) (((|#1| (-388 (-530))) . T)) (((|#1| (-719)) . T)) @@ -3033,16 +3033,16 @@ ((((-833 (-360))) . T) (((-833 (-530))) . T) (((-1099)) . T) (((-506)) . T)) (((|#1|) . T)) ((((-804)) . T)) -(-1450 (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) -(-1450 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-128)) (|has| |#2| (-128))) (-12 (|has| |#1| (-741)) (|has| |#2| (-741)))) +(-1476 (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1476 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-128)) (|has| |#2| (-128))) (-12 (|has| |#1| (-741)) (|has| |#2| (-741)))) ((((-530)) . T)) ((((-530)) . T)) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-1450 (|has| |#2| (-162)) (|has| |#2| (-675)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1476 (|has| |#2| (-162)) (|has| |#2| (-675)) (|has| |#2| (-793)) (|has| |#2| (-984))) ((((-1099)) -12 (|has| |#2| (-841 (-1099))) (|has| |#2| (-984)))) -(-1450 (-12 (|has| |#1| (-453)) (|has| |#2| (-453))) (-12 (|has| |#1| (-675)) (|has| |#2| (-675)))) +(-1476 (-12 (|has| |#1| (-453)) (|has| |#2| (-453))) (-12 (|has| |#1| (-675)) (|has| |#2| (-675)))) (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-344)) @@ -3066,7 +3066,7 @@ ((((-1082) (-1099) (-530) (-208) (-804)) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) -(-1450 (|has| |#1| (-330)) (|has| |#1| (-349))) +(-1476 (|has| |#1| (-330)) (|has| |#1| (-349))) (((|#1| |#2|) . T)) ((($) . T) ((|#1|) . T)) ((((-804)) . T)) @@ -3074,7 +3074,7 @@ ((($) . T) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) (((|#2|) |has| |#2| (-1027)) (((-530)) -12 (|has| |#2| (-975 (-530))) (|has| |#2| (-1027))) (((-388 (-530))) -12 (|has| |#2| (-975 (-388 (-530)))) (|has| |#2| (-1027)))) ((((-506)) |has| |#1| (-572 (-506)))) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) ((($) . T) (((-388 (-530))) . T)) (|has| |#1| (-850)) (|has| |#1| (-850)) @@ -3083,14 +3083,14 @@ ((((-804)) . T)) (((|#2| |#2|) . T)) (((|#1| |#1|) |has| |#1| (-162))) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-522))) -(-1450 (|has| |#1| (-21)) (|has| |#1| (-793))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1476 (|has| |#1| (-21)) (|has| |#1| (-793))) (((|#2|) . T)) -(-1450 (|has| |#1| (-21)) (|has| |#1| (-793))) +(-1476 (|has| |#1| (-21)) (|has| |#1| (-793))) (((|#1|) |has| |#1| (-162))) (((|#1|) . T)) (((|#1|) . T)) -((((-804)) -1450 (-12 (|has| |#1| (-571 (-804))) (|has| |#2| (-571 (-804)))) (-12 (|has| |#1| (-1027)) (|has| |#2| (-1027))))) +((((-804)) -1476 (-12 (|has| |#1| (-571 (-804))) (|has| |#2| (-571 (-804)))) (-12 (|has| |#1| (-1027)) (|has| |#2| (-1027))))) ((((-388 |#2|) |#3|) . T)) ((((-388 (-530))) . T) (($) . T)) (|has| |#1| (-37 (-388 (-530)))) @@ -3102,17 +3102,17 @@ (((|#1|) . T) (((-388 (-530))) . T) (((-530)) . T) (($) . T)) (((#0=(-530) #0#) . T)) ((($) . T) (((-388 (-530))) . T)) -(-1450 (|has| |#4| (-162)) (|has| |#4| (-675)) (|has| |#4| (-793)) (|has| |#4| (-984))) -(-1450 (|has| |#3| (-162)) (|has| |#3| (-675)) (|has| |#3| (-793)) (|has| |#3| (-984))) +(-1476 (|has| |#4| (-162)) (|has| |#4| (-675)) (|has| |#4| (-793)) (|has| |#4| (-984))) +(-1476 (|has| |#3| (-162)) (|has| |#3| (-675)) (|has| |#3| (-793)) (|has| |#3| (-984))) (|has| |#4| (-741)) -(-1450 (|has| |#4| (-741)) (|has| |#4| (-793))) +(-1476 (|has| |#4| (-741)) (|has| |#4| (-793))) (|has| |#4| (-793)) (|has| |#3| (-741)) -(-1450 (|has| |#3| (-741)) (|has| |#3| (-793))) +(-1476 (|has| |#3| (-741)) (|has| |#3| (-793))) (|has| |#3| (-793)) ((((-530)) . T)) (((|#2|) . T)) -((((-1099)) -1450 (-12 (|has| (-1097 |#1| |#2| |#3|) (-841 (-1099))) (|has| |#1| (-344))) (-12 (|has| |#1| (-15 * (|#1| (-530) |#1|))) (|has| |#1| (-841 (-1099)))))) +((((-1099)) -1476 (-12 (|has| (-1097 |#1| |#2| |#3|) (-841 (-1099))) (|has| |#1| (-344))) (-12 (|has| |#1| (-15 * (|#1| (-530) |#1|))) (|has| |#1| (-841 (-1099)))))) ((((-1099)) -12 (|has| |#1| (-15 * (|#1| (-388 (-530)) |#1|))) (|has| |#1| (-841 (-1099))))) ((((-1099)) -12 (|has| |#1| (-15 * (|#1| (-719) |#1|))) (|has| |#1| (-841 (-1099))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3127,11 +3127,11 @@ ((((-1097 |#1| |#2| |#3|)) |has| |#1| (-344))) ((((-1064 |#1| |#2|)) . T)) ((((-1097 |#1| |#2| |#3|)) |has| |#1| (-344))) -(((|#2|) . T) (((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) -((((-2 (|:| -2913 (-1099)) (|:| -1782 (-51)))) . T)) +(((|#2|) . T) (((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))) . T)) ((($) . T)) (|has| |#1| (-960)) -(((|#2|) . T) (((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) ((((-804)) . T)) ((((-506)) |has| |#2| (-572 (-506))) (((-833 (-530))) |has| |#2| (-572 (-833 (-530)))) (((-833 (-360))) |has| |#2| (-572 (-833 (-360)))) (((-360)) . #0=(|has| |#2| (-960))) (((-208)) . #0#)) ((((-1099) (-51)) . T)) @@ -3143,15 +3143,15 @@ ((((-1097 |#1| |#2| |#3|)) . T)) ((((-1097 |#1| |#2| |#3|)) . T) (((-1090 |#1| |#2| |#3|)) . T)) ((((-804)) . T)) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) ((((-530) |#1|) . T)) ((((-1097 |#1| |#2| |#3|)) |has| |#1| (-344))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-344)) -(((|#3|) . T) ((|#2|) . T) (($) -1450 (|has| |#4| (-162)) (|has| |#4| (-793)) (|has| |#4| (-984))) ((|#4|) -1450 (|has| |#4| (-162)) (|has| |#4| (-344)) (|has| |#4| (-984)))) -(((|#2|) . T) (($) -1450 (|has| |#3| (-162)) (|has| |#3| (-793)) (|has| |#3| (-984))) ((|#3|) -1450 (|has| |#3| (-162)) (|has| |#3| (-344)) (|has| |#3| (-984)))) +(((|#3|) . T) ((|#2|) . T) (($) -1476 (|has| |#4| (-162)) (|has| |#4| (-793)) (|has| |#4| (-984))) ((|#4|) -1476 (|has| |#4| (-162)) (|has| |#4| (-344)) (|has| |#4| (-984)))) +(((|#2|) . T) (($) -1476 (|has| |#3| (-162)) (|has| |#3| (-793)) (|has| |#3| (-984))) ((|#3|) -1476 (|has| |#3| (-162)) (|has| |#3| (-344)) (|has| |#3| (-984)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-344)) @@ -3163,7 +3163,7 @@ ((((-804)) . T)) ((((-804)) . T)) (((|#1|) . T)) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) ((((-127)) . T) (((-804)) . T)) ((((-530) |#1|) . T)) (((|#1|) . T)) @@ -3171,31 +3171,31 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-344)) (|has| |#2| (-268 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-850))) -(-1450 (|has| |#1| (-795)) (|has| |#1| (-1027))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-850))) +(-1476 (|has| |#1| (-795)) (|has| |#1| (-1027))) ((((-804)) . T)) ((((-804)) . T)) ((((-804)) . T)) (((|#1| (-502 |#2|)) . T)) -((((-2 (|:| -2913 (-1099)) (|:| -1782 (-51)))) . T)) +((((-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))) . T)) (((|#1| (-530)) . T)) (((|#1| (-388 (-530))) . T)) (((|#1| (-719)) . T)) ((((-1104)) . T) (((-804)) . T)) ((((-114 |#1|)) . T) (($) . T) (((-388 (-530))) . T)) -(-1450 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) -(-1450 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) +(-1476 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) +(-1476 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((($) . T)) (((|#2| (-502 (-806 |#1|))) . T)) ((((-530) |#1|) . T)) (((|#2|) . T)) (((|#2| (-719)) . T)) -((((-804)) -1450 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) (((|#1|) . T)) (((|#1| |#2|) . T)) ((((-1082) |#1|) . T)) ((((-388 |#2|)) . T)) -((((-2 (|:| -2913 |#1|) (|:| -1782 |#2|))) . T)) +((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) (|has| |#1| (-522)) (|has| |#1| (-522)) ((($) . T) ((|#2|) . T)) @@ -3203,12 +3203,12 @@ (((|#1| |#2|) . T)) (((|#2| $) |has| |#2| (-268 |#2| |#2|))) (((|#1| (-597 |#1|)) |has| |#1| (-793))) -(-1450 (|has| |#1| (-216)) (|has| |#1| (-330))) -(-1450 (|has| |#1| (-344)) (|has| |#1| (-330))) +(-1476 (|has| |#1| (-216)) (|has| |#1| (-330))) +(-1476 (|has| |#1| (-344)) (|has| |#1| (-330))) (|has| |#1| (-1027)) (((|#1|) . T)) ((((-388 (-530))) . T) (($) . T)) -((((-938 |#1|)) . T) ((|#1|) . T) (((-530)) -1450 (|has| (-938 |#1|) (-975 (-530))) (|has| |#1| (-975 (-530)))) (((-388 (-530))) -1450 (|has| (-938 |#1|) (-975 (-388 (-530)))) (|has| |#1| (-975 (-388 (-530)))))) +((((-938 |#1|)) . T) ((|#1|) . T) (((-530)) -1476 (|has| (-938 |#1|) (-975 (-530))) (|has| |#1| (-975 (-530)))) (((-388 (-530))) -1476 (|has| (-938 |#1|) (-975 (-388 (-530)))) (|has| |#1| (-975 (-388 (-530)))))) (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) @@ -3219,9 +3219,9 @@ (((|#1|) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1064 |#1| |#2|) #0#) |has| (-1064 |#1| |#2|) (-291 (-1064 |#1| |#2|)))) -(((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) ((#0=(-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) #0#) |has| (-2 (|:| -2913 |#1|) (|:| -1782 |#2|)) (-291 (-2 (|:| -2913 |#1|) (|:| -1782 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) ((#0=(-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) #0#) |has| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (-291 (-2 (|:| -2940 |#1|) (|:| -1806 |#2|))))) (((#0=(-114 |#1|)) |has| #0# (-291 #0#))) -(-1450 (|has| |#1| (-795)) (|has| |#1| (-1027))) +(-1476 (|has| |#1| (-795)) (|has| |#1| (-1027))) ((($ $) . T)) ((($ $) . T) ((#0=(-806 |#1|) $) . T) ((#0# |#2|) . T)) ((($ $) . T) ((|#2| $) |has| |#1| (-216)) ((|#2| |#1|) |has| |#1| (-216)) ((|#3| |#1|) . T) ((|#3| $) . T)) diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 06965869..59326d3b 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3429202587) +(30 . 3429209004) (4273 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -461,651 +461,650 @@ |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |fortranCompilerName| |rightNorm| |dAndcExp| - |generalizedInverse| |denominator| |perfectNthPower?| |nary?| - |factor1| |leftRankPolynomial| |normDeriv2| |corrPoly| |mesh?| - |headAst| |typeList| |makeCrit| |changeThreshhold| |pushdown| |droot| - |f07fdf| |symmetricRemainder| |resultant| |dom| |e02adf| |jacobian| - |c06gqf| |minColIndex| |critpOrder| |rootOf| |s13aaf| |set| |graeffe| - |csc2sin| |factorial| |setprevious!| |plus!| |minPoints3D| - |listConjugateBases| |splitConstant| |setMinPoints3D| |/\\| - |fortranLiteral| |stop| |realRoots| |indicialEquation| |mapSolve| - |createPrimitiveNormalPoly| |nextSublist| |maxPoints3D| |\\/| - |univariatePolynomials| |drawCurves| |extensionDegree| |decimal| - |radicalEigenvectors| |decompose| |subNode?| |gramschmidt| - |numberOfComposites| |oblateSpheroidal| |commutator| - |numberOfVariables| |insertionSort!| |binding| |defineProperty| - |chebyshevU| |lieAlgebra?| |UpTriBddDenomInv| |s18acf| |crest| - |f02aff| |title| |mat| |swap| |figureUnits| |intersect| |hspace| - |viewDeltaYDefault| |schwerpunkt| |preprocess| |sincos| - |newSubProgram| |cAsec| |vconcat| |doubleResultant| |sqfrFactor| - |normalized?| |shanksDiscLogAlgorithm| |antiCommutator| |e02bcf| - |removeCoshSq| |rotatez| |lflimitedint| |sort| |stFuncN| |minIndex| - |isPlus| |makeUnit| |Frobenius| |e| |removeRedundantFactors| |isPower| - |minRowIndex| |algebraicCoefficients?| |evaluate| - |monicDecomposeIfCan| |monicDivide| |triangulate| |orbits| |shiftLeft| - |primeFrobenius| |generalizedContinuumHypothesisAssumed| - |characteristic| |linGenPos| |stirling1| |triangularSystems| |failed?| - |semiIndiceSubResultantEuclidean| F |viewport3D| |diagonalMatrix| |mr| - |makeSketch| |drawComplexVectorField| |showSummary| - |patternMatchTimes| |screenResolution| |nextsubResultant2| |show| - |listexp| |queue| |minimize| |maxPoints| |style| |laguerreL| - |summation| |s17ahf| |mapBivariate| |var1StepsDefault| - |noncommutativeJordanAlgebra?| |countRealRoots| |imagj| - |createLowComplexityNormalBasis| |getZechTable| |makeCos| |insertTop!| - |showAttributes| |random| |maxIndex| |characteristicPolynomial| - |trace| |extractPoint| |ratPoly| |setImagSteps| |var1Steps| |testDim| - |d03eef| |qroot| |lift| |stFunc1| |semiSubResultantGcdEuclidean2| - |deepCopy| |numberOfPrimitivePoly| |fixedPoints| |dimensions| - |delete!| |associates?| |variationOfParameters| |reduce| |clipBoolean| - |sizeMultiplication| |stFunc2| |bit?| |OMgetType| |basisOfNucleus| - |virtualDegree| |yCoordinates| |squareMatrix| |iicoth| - |factorsOfDegree| |innerSolve| |f04faf| |ref| |coefficient| - |positiveRemainder| |universe| |readable?| |ode2| - |rightFactorCandidate| |elRow2!| |implies?| |weakBiRank| |splitLinear| - |zoom| |untab| |transform| |pile| |palgextint0| |leaf?| |s18adf| - |divideIfCan| |useNagFunctions| |fractionPart| - |createLowComplexityTable| |colorDef| |squareFreeLexTriangular| |Si| - |noKaratsuba| |getCode| |addPoint2| |mapUp!| |selectFiniteRoutines| - |trim| |PollardSmallFactor| |logGamma| |initiallyReduced?| |OMputBVar| - |trueEqual| |pow| |heapSort| |c02aff| |tablePow| |leadingSupport| - |zeroSquareMatrix| |genericRightTrace| |width| |s01eaf| - |unprotectedRemoveRedundantFactors| |orOperands| NOT - |rightDiscriminant| |getBadValues| |inverseColeman| |maxrank| - |factorsOfCyclicGroupSize| |c06fuf| |problemPoints| GF2FG |fi2df| OR - |f04atf| |ScanFloatIgnoreSpacesIfCan| |squareFreePrim| - |separateDegrees| |duplicates| |OMopenString| |resetAttributeButtons| - |degreeSubResultant| |front| AND |lexico| |stoseInvertibleSetreg| - |plusInfinity| |lhs| |modularGcdPrimitive| |midpoint| |returnType!| - |cyclicEqual?| |elliptic| |fixedDivisor| |simplifyExp| |rowEchelon| - |sign| |minusInfinity| |rhs| |f04arf| |acotIfCan| |f01ref| |s17dgf| - |supDimElseRittWu?| |upperCase?| |e01bhf| |iisqrt3| |iicos| - |OMgetFloat| |invertIfCan| |representationType| |lazyEvaluate| - |numberOfIrreduciblePoly| |zero| |leadingIdeal| |e04ucf| |digits| - |roughSubIdeal?| |OMgetError| |numberOfCycles| |infieldint| - |complexNormalize| |optional| |solveLinearPolynomialEquation| - |collect| |removeIrreducibleRedundantFactors| |wreath| - |lazyPremWithDefault| |makeEq| |constDsolve| |overlabel| - |zeroSetSplitIntoTriangularSystems| |setright!| |And| - |nativeModuleExtension| |cross| |interval| |points| |e04fdf| - |contract| |badNum| |leastMonomial| |node| |Or| |cycles| - |changeWeightLevel| |squareFree| |distdfact| |makingStats?| |c06gcf| - |ptFunc| |iiacsch| |s21bbf| |Not| |paren| |LagrangeInterpolation| - |irreducibleFactors| |setleft!| |square?| |type| |atanIfCan| |sin?| - |objectOf| |OMputEndAtp| |irreducibleRepresentation| |unitNormalize| - |changeMeasure| |mapMatrixIfCan| |repeating?| |rootProduct| |invmod| - |basisOfRightAnnihilator| |testModulus| |uncouplingMatrices| - |contours| |asinhIfCan| * |shade| |binomial| |d01gaf| |maxColIndex| - |palgRDE0| |radicalEigenvector| |setFormula!| |push| |equiv| - |extension| |eyeDistance| |top| |elliptic?| |integralBasisAtInfinity| - |repSq| |variable?| |setPosition| |skewSFunction| |ffactor| |print| - |f02ajf| |setPredicates| |continue| |iiacoth| |pop!| |modulus| - |sts2stst| |datalist| |sizePascalTriangle| |useSingleFactorBound| - |infRittWu?| |close!| |nextLatticePermutation| |e02bef| |ef2edf| - |conjugates| |dimension| |chvar| |GospersMethod| |allRootsOf| - |toScale| |getOperator| |pToDmp| |kmax| |rowEchelonLocal| |tree| - |rationalPower| |cons| |iiasin| |numberOfOperations| |approxSqrt| - |asimpson| |torsion?| |lex| |sup| |expint| |rightRecip| - |setAdaptive3D| |polarCoordinates| |phiCoord| |normalizedAssociate| - |nthFactor| |palgextint| |imagK| |linears| |polygon?| - |nonSingularModel| |complexEigenvectors| |nor| |solid| |addmod| - |d01gbf| |expenseOfEvaluationIF| |edf2ef| |randnum| |term?| |level| - |zeroDimPrime?| |pol| |equation| |showTypeInOutput| |divideExponents| - |leastPower| |internalDecompose| |OMputEndApp| |light| - |unrankImproperPartitions0| |lowerCase!| |f2df| |asechIfCan| |d01asf| - |withPredicates| |palgRDE| |univariatePolynomial| |supersub| - |vectorise| |unaryFunction| |solve1| |mainSquareFreePart| - |findBinding| |enqueue!| |returns| |besselY| |intcompBasis| - |algebraic?| |radicalEigenvalues| |bipolar| |ignore?| |divergence| - |source| |combineFeatureCompatibility| |s20acf| |dec| |extractClosed| - |sumOfDivisors| |nextColeman| |extendedIntegrate| |lazyPquo| |push!| - |aromberg| |rightQuotient| |createNormalPoly| F2FG |associatedSystem| - |f01rdf| |traceMatrix| |scalarTypeOf| |showAll?| |e02ajf| |janko2| - |shrinkable| |certainlySubVariety?| |s17aff| |infinityNorm| |fill!| - |find| |duplicates?| |commonDenominator| |lookup| |symbolIfCan| - |exponents| |makeGraphImage| |OMputError| |rroot| |s19abf| |getOrder| - |flexibleArray| |term| |bright| |drawToScale| |createGenericMatrix| - |readIfCan!| |target| |lfintegrate| |chiSquare1| |mainContent| - |minPol| |reverse!| |numberOfHues| |laurentIfCan| |addMatchRestricted| - |curryRight| |root| |degreePartition| |charpol| - |univariatePolynomialsGcds| |specialTrigs| |cRationalPower| - |inconsistent?| |solve| |hitherPlane| |palgintegrate| |OMcloseConn| - |meshPar2Var| |intermediateResultsIF| |genericPosition| - |removeSuperfluousQuasiComponents| |max| |exprToGenUPS| - |useEisensteinCriterion| |property| |position!| |setMaxPoints3D| - |patternMatch| |splitSquarefree| |OMgetObject| |empty?| |precision| - |graphImage| |perfectNthRoot| |getButtonValue| - |stiffnessAndStabilityOfODEIF| |trunc| |computeCycleLength| |comp| - |binaryFunction| |adjoint| |selectsecond| |insertBottom!| |hconcat| - |delete| |totalfract| |basisOfLeftNucloid| |invmultisect| - |alphanumeric?| |bernoulli| |seed| |result| |units| - |coerceListOfPairs| |headRemainder| |rectangularMatrix| - |setProperties!| |collectQuasiMonic| |upperCase!| - |semiLastSubResultantEuclidean| |closed?| |polynomialZeros| |f02axf| - |fortranReal| |semiDegreeSubResultantEuclidean| |monicRightDivide| - |radicalRoots| |semiResultantEuclidean1| |root?| |controlPanel| - |critM| |transcendent?| |entry| |SturmHabicht| |closeComponent| UTS2UP - |OMputEndBVar| |OMUnknownSymbol?| |listOfMonoms| |low| |printingInfo?| - |infieldIntegrate| |changeNameToObjf| |quotedOperators| |factorList| - |conjugate| |li| |uniform01| |pushup| |airyBi| |thetaCoord| - |tracePowMod| |createRandomElement| |code| |clearCache| |setRealSteps| - |quasiMonic?| |fibonacci| |elt| |charClass| |reduction| - |getIdentifier| |polyPart| |iiexp| |viewPosDefault| - |rightCharacteristicPolynomial| |createNormalPrimitivePoly| |d01bbf| - |raisePolynomial| |dimensionOfIrreducibleRepresentation| - |multiplyExponents| |showTheRoutinesTable| |basisOfLeftAnnihilator| - |c06eaf| |inR?| |OMReadError?| |numer| |mvar| |leftFactor| |minPoly| - |B1solve| |tab1| |makeViewport2D| |rootNormalize| |charthRoot| |denom| - |writeLine!| |point?| |block| |OMmakeConn| |semiDiscriminantEuclidean| - |algebraicOf| |subst| |s14aaf| |OMgetVariable| |calcRanges| |rule| - |printHeader| |getMeasure| |currentScope| |doubleRank| - |zeroDimPrimary?| |log10| |unparse| |invertible?| - |purelyTranscendental?| |pi| |any| |operation| |rischDE| - |powerAssociative?| |lowerCase| |weights| |ratpart| |bitand| |heap| - |infinity| |magnitude| |quasiRegular?| |besselK| |makeTerm| - |compound?| |rk4a| |sub| |extendedResultant| |complexNumericIfCan| - |fintegrate| |df2mf| |lepol| |nthCoef| |generator| |sequences| - |stoseInvertible?| |yCoord| |completeEval| |decomposeFunc| - |gcdcofactprim| |cSin| |leftScalarTimes!| |df2fi| |particularSolution| - |index| |kernel| |hessian| |pushucoef| |latex| |hypergeometric0F1| - |ideal| |isTimes| |factorAndSplit| |diophantineSystem| |s14baf| |draw| - |sec2cos| |symmetricProduct| |tube| |hexDigit| |option| - |areEquivalent?| |comment| |atrapezoidal| |restorePrecision| - |clearTheIFTable| |quoted?| |subNodeOf?| |iiacos| |algSplitSimple| - |complexForm| |factorSquareFreePolynomial| |repeating| - |rationalApproximation| |endOfFile?| |pair| - |lastSubResultantEuclidean| BY |edf2fi| |leftMinimalPolynomial| - |position| |iroot| |univcase| |ricDsolve| |leftOne| - |stoseSquareFreePart| |weighted| |lowerCase?| |prolateSpheroidal| - |equality| |palglimint0| |recip| |leftTraceMatrix| |cAsin| - |makeObject| |d01amf| |presuper| |stoseLastSubResultant| |function| - |select!| |s15aef| |RittWuCompare| |genericLeftDiscriminant| - |cotIfCan| |Hausdorff| |c06fpf| |presub| |extractTop!| |fracPart| |lo| - |setClosed| |minimumDegree| |bat1| |ranges| |positiveSolve| |e02aef| - |coef| |scopes| |OMreceive| |sinIfCan| |incr| |OMgetEndError| |scale| - |orthonormalBasis| |socf2socdf| |s17adf| |condition| |splitNodeOf!| - |leftLcm| |primitivePart!| |hi| |leftRecip| |relativeApprox| |iomode| - |zero?| |tubeRadiusDefault| |Lazard2| |normalizeAtInfinity| |e01sbf| - |screenResolution3D| |resetVariableOrder| |clearTheFTable| - |nextNormalPrimitivePoly| |lazyResidueClass| |singularitiesOf| - |aQuartic| |dmpToP| |stronglyReduced?| |nothing| |totalGroebner| - |cycleSplit!| |e02baf| |subTriSet?| |exponential1| |rischNormalize| - |selectfirst| |bindings| |groebSolve| |intensity| |elementary| |log2| - |iiatanh| |jacobiIdentity?| |halfExtendedResultant1| |redPo| - |structuralConstants| |delta| |changeBase| |argument| - |pointSizeDefault| |sample| |cLog| |slex| |multiEuclideanTree| - |fixedPointExquo| |tail| |asecIfCan| |exprex| |badValues| |callForm?| - |eisensteinIrreducible?| |commutative?| |critB| - |standardBasisOfCyclicSubmodule| |pattern| |tableau| |cyclicGroup| - |acoshIfCan| |s21baf| |leftNorm| |f04jgf| |exprHasLogarithmicWeights| - |relerror| |rightRegularRepresentation| |cycleRagits| |column| |goto| - |safetyMargin| RF2UTS |stirling2| |internalSubPolSet?| |taylorRep| - |physicalLength| |clearTheSymbolTable| |log| |cond| |lcm| - |minimalPolynomial| |erf| |cPower| |wholeRadix| |compBound| |zag| - |OMlistCDs| |maxint| |real?| |useSingleFactorBound?| |HenselLift| - |stopTable!| |userOrdered?| |message| |sqfree| |idealSimplify| - |output| |quote| |createThreeSpace| |append| |generalSqFr| |deref| - |lazyGintegrate| |unravel| |power| |lambda| |outputList| |f04qaf| - |status| |f01bsf| |unitVector| |localReal?| |gcd| |dilog| |reseed| - |generate| |superscript| |rational| |diagonal?| |properties| - |nextItem| |fixPredicate| |composites| |false| |iitan| |sin| - |partialNumerators| |weierstrass| |bitLength| |getDatabase| - |translate| |outputAsScript| |padecf| |nthRootIfCan| |double?| - |compile| |incrementBy| |cos| |meshPar1Var| |drawStyle| - |euclideanNormalForm| |usingTable?| |partialQuotients| - |upDateBranches| |maxRowIndex| |branchIfCan| - |tryFunctionalDecomposition| |d03edf| |s18def| |tan| |realEigenvalues| - |expand| |OMputEndBind| = |setAdaptive| |exprHasWeightCosWXorSinWX| - |deepestInitial| |Ci| |cot| |check| |c02agf| |filterWhile| |inspect| - |curveColor| |basisOfRightNucleus| |unary?| |matrix| - |numberOfImproperPartitions| |iisinh| |d02raf| |#| |quatern| |sec| - |filterUntil| < |ReduceOrder| |prepareDecompose| |norm| - |primaryDecomp| |denomRicDE| |Aleph| |complexEigenvalues| |select| - |csc| |nextPrime| > |double| |poisson| |augment| |morphism| |generic?| - |antisymmetricTensors| |modTree| |iiabs| |asin| |in?| <= - |permutationGroup| |cosh2sech| |normInvertible?| - |solveLinearPolynomialEquationByFractions| |besselJ| |rank| |innerint| - |identification| |acos| |finiteBasis| >= |doubleDisc| - |getVariableOrder| |fortranTypeOf| |middle| |multisect| |atan| - |eulerE| |equiv?| |incrementKthElement| |att2Result| |nil?| |cycleElt| - |d01aqf| |infLex?| |rightOne| |acot| |brillhartIrreducible?| - |setPrologue!| |leftUnits| |coth2trigh| |factorSquareFreeByRecursion| - |alphabetic| |moebiusMu| |binaryTree| |polCase| |asec| |f02adf| - |viewDefaults| |dot| + |optional?| |setchildren!| |symmetricTensors| - |times!| |makeRecord| |acsc| |numFunEvals3D| |e01bgf| |besselI| - |cubic| - ~= |numberOfMonomials| |rationalFunction| |rquo| |setRow!| - |close| |viewPhiDefault| |sinh| |rCoord| |definingPolynomial| - |declare!| / |coerce| |npcoef| |functionIsOscillatory| |logical?| - |lists| |lSpaceBasis| |cosh| |distFact| |recur| |euclideanSize| - |errorKind| |construct| |mergeFactors| |increasePrecision| - |constantRight| |remove| |initial| |binomThmExpt| |factorSFBRlcUnit| - |tanh| |row| |display| |curveColorPalette| |less?| |expt| |csch2sinh| - |split!| |checkPrecision| |character?| |coth| |basisOfCentroid| - |stiffnessAndStabilityFactor| |space| |integral?| |genericLeftTrace| - |swapColumns!| |last| |numerator| |sech| |changeName| |getProperty| - |cosIfCan| |expandLog| |pair?| |makeFR| |vspace| |assoc| - |rationalPoint?| |csch| |makeResult| |sinhcosh| |d01akf| |triangular?| - |super| |OMsetEncoding| |diagonal| |completeHermite| |asinh| |e02akf| - |e02daf| |Ei| |lazyPseudoDivide| |fillPascalTriangle| - |basisOfRightNucloid| |imagk| |idealiser| |acosh| |twist| - |purelyAlgebraicLeadingMonomial?| |direction| |consnewpol| |setOrder| - |quasiMonicPolynomials| |lazyIrreducibleFactors| |curve| |puiseux| - |atanh| |collectUnder| |printTypes| |binaryTournament| |setProperty| - |solid?| |SFunction| |lazyPseudoQuotient| |wordsForStrongGenerators| - |acoth| |tower| |drawComplex| |pointPlot| |lazyVariations| |measure| - |region| |iisqrt2| |rightAlternative?| |inv| |null?| |asech| - |euclideanGroebner| |SturmHabichtCoefficients| |explicitEntries?| - |ground?| |computeBasis| |factorOfDegree| |enterPointData| - |ScanArabic| |generalInfiniteProduct| |LyndonBasis| |measure2Result| - |setStatus!| |irreducible?| |deepExpand| |tValues| |ground| |multiple| - |rightTraceMatrix| |interReduce| |declare| |quasiAlgebraicSet| |even?| - |tab| |applyQuote| |taylorQuoByVar| |lprop| |mapExpon| - |leadingMonomial| |tableForDiscreteLogarithm| |singleFactorBound| ~ - |segment| |f07adf| |integerIfCan| |argumentList!| |constructorName| - |iisech| |transpose| |scaleRoots| |leadingCoefficient| - |complexNumeric| |number?| |LyndonWordsList| |logIfCan| |say| - |internalIntegrate| |primintegrate| |OMgetEndApp| |primitiveMonomials| - |extractProperty| |graphStates| |open| |setelt| |d02gbf| |moduleSum| - |minimumExponent| |kernels| |constantIfCan| |rombergo| |OMbindTCP| - |reductum| |ruleset| |exptMod| |stosePrepareSubResAlgo| |rootSimp| - |obj| |expressIdealMember| |BumInSepFFE| |iilog| - |invertibleElseSplit?| |roughBasicSet| |numericalIntegration| - |diagonalProduct| |univariate| |copy| |cache| |zeroSetSplit| - |leftQuotient| |bumprow| |retract| |iiasech| |reducedSystem| - |exponential| |saturate| |innerEigenvectors| |jacobi| |any?| |cCoth| - |e02dcf| |alternative?| |getRef| |components| |suchThat| |mdeg| - |basicSet| |subset?| |wordInGenerators| |extractIfCan| |Nul| - |subtractIfCan| |algintegrate| |d01alf| |polyred| |determinant| - |factor| |autoCoerce| |makeSeries| |linearAssociatedLog| |monomRDEsys| - |entry?| |exteriorDifferential| |shellSort| |rationalIfCan| |reset| - |polygon| |ratDsolve| |hash| |sqrt| |setScreenResolution| - |cardinality| |karatsubaDivide| |f01maf| |alphanumeric| |setnext!| - |showScalarValues| |count| |cAcosh| |getGoodPrime| |real| - |stoseInvertible?sqfreg| |biRank| |rightMult| |s21bcf| |Vectorise| - |errorInfo| |write| |generalLambert| |rotate!| |prefixRagits| |imag| - |fortranInteger| |halfExtendedSubResultantGcd2| |getCurve| |rk4qc| - |cartesian| |save| |s13acf| |setTex!| |axes| |directProduct| - |leftUnit| |primintfldpoly| |totalDifferential| |s17dcf| - |nextPartition| |factorSquareFree| |branchPointAtInfinity?| - |enterInCache| |constantOpIfCan| |rightLcm| |pdf2df| - |explicitlyFinite?| |reduced?| |solveRetract| |predicate| - |createMultiplicationTable| |localIntegralBasis| |f01brf| |remove!| - |destruct| |mathieu23| |froot| |extendIfCan| |product| - |bezoutDiscriminant| |extendedint| |topFortranOutputStack| - |showIntensityFunctions| |fullDisplay| |permutations| - |wordInStrongGenerators| |irreducibleFactor| |setEmpty!| - |resultantnaif| |e02bdf| |basisOfMiddleNucleus| |roughEqualIdeals?| - |movedPoints| |possiblyNewVariety?| |coHeight| |simpsono| - |lineColorDefault| |constant| |arguments| |compiledFunction| |inverse| - |subMatrix| |composite| |nextsousResultant2| |coefficients| |eq?| - |ddFact| |internal?| |s17agf| |bezoutMatrix| |modifyPointData| - |distribute| |s17ajf| |monomial| |argscript| |fortranDouble| - |realEigenvectors| |primPartElseUnitCanonical!| |cylindrical| - |outputFixed| |unitNormal| |subresultantSequence| |rowEchLocal| - |clikeUniv| |pushdterm| |multivariate| |meatAxe| |var2Steps| |e04jaf| - |setFieldInfo| |conditionsForIdempotents| |increment| |buildSyntax| - |algint| |nullary| |variables| |lllip| |mkAnswer| |f04asf| - |evenlambert| |cCot| |algebraicDecompose| |f04axf| |setStatus| - |notelem| |htrigs| |antiCommutative?| |algDsolve| FG2F |An| - |removeRoughlyRedundantFactorsInPols| |parameters| |search| - |initTable!| |numberOfNormalPoly| |mainForm| |elRow1!| - |resultantEuclideannaif| |setAttributeButtonStep| |nonLinearPart| |eq| - |initials| |OMlistSymbols| |quasiComponent| |hMonic| |c05pbf| - |toroidal| |ScanRoman| |qinterval| |symbolTableOf| |iter| |limitPlus| - |rightExactQuotient| |viewDeltaXDefault| |OMgetEndObject| - |strongGenerators| |rst| |lazyPrem| |iitanh| - |functionIsContinuousAtEndPoints| |approximants| |coleman| - |constantOperator| |accuracyIF| |dn| |sumOfKthPowerDivisors| |taylor| - |leftDivide| |rarrow| |removeConstantTerm| |Is| |ListOfTerms| - |sortConstraints| |or| |laurent| |selectOptimizationRoutines| |or?| - |float?| |OMputEndObject| |expandPower| |d01ajf| |f02bjf| - |validExponential| |deleteRoutine!| |prepareSubResAlgo| |setlast!| - |padicFraction| |factorFraction| |recoverAfterFail| |finiteBound| - |lifting| |trapezoidalo| |quadratic?| |vedf2vef| |curry| |tubeRadius| - |fmecg| |order| |exprToXXP| |perfectSquare?| |exp1| - |solveLinearPolynomialEquationByRecursion| |predicates| - |setsubMatrix!| |tubePointsDefault| |pdct| |limitedint| - |separateFactors| |ode1| |represents| |cSec| |s21bdf| |quoByVar| - |PDESolve| |exp| |trailingCoefficient| |subscriptedVariables| - |cos2sec| |hasSolution?| |computePowers| |dark| |polygamma| - |BasicMethod| |s17def| |over| |totolex| |rightTrim| |backOldPos| - |harmonic| |s20adf| |listOfLists| |complexIntegrate| |rightGcd| - |stoseInternalLastSubResultant| |permutation| |fractionFreeGauss!| - |myDegree| |leftTrim| |removeSinhSq| |OMsupportsCD?| |viewport2D| - |idealiserMatrix| |zCoord| |symmetricSquare| ^ |cyclic| |lfextlimint| - |e04ycf| |fortranCarriageReturn| |explimitedint| |elColumn2!| |zeroOf| - |tanAn| |showFortranOutputStack| |rdregime| |tanIfCan| |swapRows!| - |length| |OMputEndAttr| |stoseInvertible?reg| |leftFactorIfCan| - |central?| |multiset| |lfinfieldint| |coerceImages| - |linearlyDependentOverZ?| |moduloP| |digit| |iipow| |randomLC| - |s17acf| |scripts| |wholePart| |conditions| |makeMulti| - |startPolynomial| |s19aaf| |key?| |linearDependence| |e01baf| - |subHeight| |showTheIFTable| |iFTable| |OMwrite| |match| |d02ejf| - |ptree| |minordet| |hermite| |omError| |curryLeft| |solveLinear| - |listRepresentation| |selectAndPolynomials| |unit?| - 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|stopTableInvSet!| |content| |deepestTail| |apply| |genus| |minGbasis| - |octon| |graphCurves| |normalDenom| |isMult| |factorByRecursion| - |oddInfiniteProduct| |fortranLogical| |d02cjf| |varselect| |suffix?| - |youngGroup| |unvectorise| |setCondition!| |boundOfCauchy| - |autoReduced?| |float| |coerceP| |palglimint| |void| - |evenInfiniteProduct| |bivariatePolynomials| |subQuasiComponent?| - |size| |genericRightTraceForm| |genericRightMinimalPolynomial| |diff| - |odd?| |iidprod| |goodPoint| |singular?| |factorGroebnerBasis| - |submod| |getMultiplicationTable| |physicalLength!| |prefix?| - |routines| |shuffle| |pr2dmp| |spherical| |symmetricGroup| |finite?| - |nthr| |subspace| |primitive?| |lexTriangular| |eigenvectors| - |integralRepresents| |imagI| |multiEuclidean| |geometric| - |halfExtendedSubResultantGcd1| |countRealRootsMultiple| - |outputFloating| |mindeg| |first| |reopen!| |cup| |ocf2ocdf| - |axesColorDefault| |prod| |numberOfFactors| |complexExpand| - |resultantReduit| |OMgetApp| |divide| |rest| |coth2tanh| |iiperm| - |iiGamma| |null| |randomR| |implies| |sech2cosh| - |SturmHabichtSequence| |showClipRegion| |pointData| |getGraph| - |f02awf| |acosIfCan| |substitute| |selectPDERoutines| |pdf2ef| - |OMputInteger| |equivOperands| |case| |integralDerivationMatrix| - |knownInfBasis| |isOp| |e02zaf| |setValue!| |removeDuplicates| |key| - |nodes| |binarySearchTree| |gradient| |Zero| |companionBlocks| - |insertMatch| |d03faf| |xor| |has?| |OMsend| |overbar| |subscript| - |pomopo!| |nsqfree| |external?| |linearlyDependent?| |infix?| |One| - |LyndonCoordinates| |henselFact| GE |tubePlot| |highCommonTerms| - |const| |horizConcat| |filename| |outputArgs| |createZechTable| |mask| - |mkPrim| |semiResultantReduitEuclidean| |choosemon| - |multiplyCoefficients| GT |rightUnit| |sechIfCan| |baseRDE| - |updateStatus!| |not?| |leadingBasisTerm| |f07aef| - |transcendenceDegree| |selectMultiDimensionalRoutines| |mathieu22| LE - |regularRepresentation| |upperCase| |laplacian| |subresultantVector| - |parse| |derivationCoordinates| |OMencodingXML| |lyndon?| LODO2FUN - |sayLength| |addiag| |tanNa| LT |applyRules| |kroneckerDelta| - |conditionP| |unexpand| |zeroMatrix| |makeYoungTableau| |torsionIfCan| - |dmp2rfi| |primitivePart| |explogs2trigs| |recolor| |rotate| - |normalDeriv| |contractSolve| |rightRemainder| |symbolTable| |label| - |retractIfCan| |someBasis| |e04naf| |externalList| |diagonals| - |oddintegers| |iifact| |ravel| |alternating| |kovacic| |lazy?| |byte| - |createMultiplicationMatrix| |leftTrace| |singRicDE| |dim| - |sumOfSquares| |pushFortranOutputStack| |selectNonFiniteRoutines| - |reshape| |rightFactorIfCan| |adaptive| |rightPower| |nthFlag| - |headReduce| |viewpoint| |se2rfi| |weight| |symmetricDifference| - |setErrorBound| |basisOfCenter| |option?| |popFortranOutputStack| - |initializeGroupForWordProblem| |OMgetAtp| |member?| |atanhIfCan| - |string| |FormatRoman| |dflist| |possiblyInfinite?| |newLine| |f01rcf| - |ldf2lst| |printStats!| |iExquo| |empty| |moreAlgebraic?| - |outputAsFortran| |rightRankPolynomial| |digamma| |polyRicDE| |isExpt| - 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|OMgetEndAtp| |ridHack1| |exprToUPS| |rewriteIdealWithHeadRemainder| - |groebgen| |selectPolynomials| |f04adf| |indiceSubResultant| - |flagFactor| |reduceByQuasiMonic| |viewSizeDefault| |hyperelliptic| - |chebyshevT| |groebner?| |bat| |trigs| |unmakeSUP| |second| |ceiling| - |iteratedInitials| |createPrimitiveElement| |numberOfComputedEntries| - |f02abf| |generalPosition| |wronskianMatrix| |outputSpacing| - |mapUnivariate| |infix| |third| |oddlambert| |pquo| |constant?| - |f02akf| |normalizedDivide| |definingEquations| |complexRoots| - |OMputSymbol| |convert| |inrootof| |zerosOf| |inRadical?| - |decreasePrecision| |bringDown| |sturmSequence| |script| |plotPolar| - |computeInt| |eigenMatrix| |typeLists| |monicCompleteDecompose| - |imaginary| |cExp| |cyclePartition| |internalSubQuasiComponent?| - |compactFraction| |normalForm| |rootSplit| |mkIntegral| - |mainCharacterization| |forLoop| |linear?| |interpret| |vector| - |iiacosh| |coord| |removeZeroes| |keys| - |removeRedundantFactorsInContents| |radicalSolve| |radix| - |parabolicCylindrical| |dioSolve| |one?| |removeSuperfluousCases| - |pointLists| |differentiate| |noLinearFactor?| |expintfldpoly| - |vertConcat| |cAcot| |definingInequation| |list?| |tex| |subPolSet?| - |bag| |mapExponents| |reciprocalPolynomial| |f02fjf| |tubePoints| - |tRange| |makeSin| |pack!| |nlde| |monicLeftDivide| |optAttributes| - |d01apf| |RemainderList| |useEisensteinCriterion?| - |rewriteSetByReducingWithParticularGenerators| |dfRange| |sizeLess?| - |integralAtInfinity?| |resetBadValues| |nodeOf?| |tan2cot| |integer?| - |multinomial| |OMputString| |quadraticNorm| |f02aaf| |iisec| |c05adf| - |eigenvector| |OMopenFile| |gethi| |cycleEntry| |identitySquareMatrix| - |discreteLog| |evaluateInverse| |deleteProperty!| |aspFilename| - |getlo| |copyInto!| |mainVariables| |extractIndex| |OMencodingBinary| - |loopPoints| |leadingTerm| |semicolonSeparate| |coerceS| - |pseudoQuotient| |cot2trig| |debug| |rightMinimalPolynomial| - |pseudoDivide| |quickSort| |innerSolve1| |getSyntaxFormsFromFile| - UP2UTS |associatedEquations| |leviCivitaSymbol| - |createIrreduciblePoly| |leftExactQuotient| |scripted?| D - |doubleComplex?| |tensorProduct| |fprindINFO| |dequeue!| - |subResultantChain| |OMgetInteger| |newReduc| |nextIrreduciblePoly| - |simplifyLog| |reducedForm| |llprop| |ratDenom| |monomialIntegrate| - |setButtonValue| |groebner| |sylvesterMatrix| |tanQ| |c06ecf| - |palgLODE| |complexElementary| |leftDiscriminant| |csubst| |extract!| - |bernoulliB| |leadingCoefficientRicDE| |pToHdmp| |iCompose| |int| - |symFunc| |makeVariable| |taylorIfCan| |eigenvalues| - |clearFortranOutputStack| |optpair| |generalizedEigenvector| - |medialSet| |rootBound| |cycleLength| |signAround| |nthExpon| |true| - |indicialEquations| |leftZero| |module| |sparsityIF| |merge!| |yellow| - |insertRoot!| |gcdprim| |normFactors| |lazyPseudoRemainder| - |indiceSubResultantEuclidean| |mightHaveRoots| |and| |brace| |sn| - |e02agf| |split| |cAsinh| |univariate?| |separant| |cTan| |cscIfCan| - |roman| |largest| |create3Space| |leaves| |impliesOperands| - |nextPrimitivePoly| |flexible?| |e01bef| |distance| - |reducedContinuedFraction| |lp| |sin2csc| |graphState| |binary| - |surface| |plot| |bfKeys| |musserTrials| |intChoose| - |generalTwoFactor| |acschIfCan| |integralMatrix| |removeSinSq| - |c05nbf| |closedCurve| |leftCharacteristicPolynomial| |nthExponent| - |complex?| |generalizedContinuumHypothesisAssumed?| |collectUpper| - |lagrange| |andOperands| |negative?| |hcrf| |coordinate| |value| - |extend| |numberOfDivisors| |lllp| |mergeDifference| |e01daf| - |currentSubProgram| |gbasis| |cAcoth| |nullity| |closedCurve?| |sum| - |cfirst| |anfactor| |internalZeroSetSplit| |oneDimensionalArray| - |bandedHessian| |bsolve| |leadingIndex| |bandedJacobian| |countable?| - |color| |setfirst!| |monomials| |tanSum| |antiAssociative?| |e02dff| - |basis| |characteristicSerie| |qelt| |connect| |OMputAttr| - |isAbsolutelyIrreducible?| |sorted?| |gcdPrimitive| - |lastSubResultantElseSplit| |semiResultantEuclidean2| |graphs| - |numberOfFractionalTerms| |totalLex| |permanent| - |transcendentalDecompose| |ipow| |getConstant| - |subResultantGcdEuclidean| |clipWithRanges| - |leftRegularRepresentation| |LiePoly| |cAcsc| |anticoord| - |rangeIsFinite| |lighting| |xRange| |addBadValue| |d01anf| - |halfExtendedResultant2| |OMputAtp| |rightTrace| |c06gbf| |s19acf| - |constantCoefficientRicDE| |exprHasAlgebraicWeight| |yRange| |rspace| - |SturmHabichtMultiple| |setProperties| |associatorDependence| - |argumentListOf| |normal?| |completeSmith| - |rewriteIdealWithQuasiMonicGenerators| |addPointLast| - |computeCycleEntry| |OMputObject| |zRange| |minset| |perfectSqrt| - |nullSpace| |rootRadius| |hex| |HermiteIntegrate| |pushNewContour| - |child| |concat| |map!| |extractSplittingLeaf| |e02bbf| |printInfo!| - |matrixDimensions| |slash| |iflist2Result| |e04gcf| |univariateSolve| - |checkRur| |subCase?| |qsetelt!| |ramified?| |genericLeftNorm| - |adaptive3D?| |balancedFactorisation| |mainValue| |convergents| - |iisin| |c06ebf| |postfix| |delay| |btwFact| |gcdPolynomial| - |mainMonomial| |quotient| |startTableInvSet!| |powmod| |s18aef| - |OMgetBind| |mapDown!| |lfunc| |cSech| |hdmpToP| |id| |realZeros| - |genericLeftTraceForm| |getStream| |homogeneous?| |OMsupportsSymbol?| - |numericalOptimization| |blue| |linearAssociatedOrder| |s14abf| - |members| |selectODEIVPRoutines| |whatInfinity| |smith| |iiasec| - |setScreenResolution3D| |cAcos| |factors| |copies| |minPoints| - |leftMult| |table| |associative?| |resultantEuclidean| - |pointColorDefault| |pole?| |modifyPoint| |node?| |scan| - |characteristicSet| |acsch| |new| |exactQuotient| |mapmult| - |stopMusserTrials| |pseudoRemainder| |iicosh| |mainVariable| - |difference| |bitTruth| |rightDivide| |critT| |e02ahf| - |unrankImproperPartitions1| |rischDEsys| |bits| |exquo| - |reduceBasisAtInfinity| |algebraicSort| |nullary?| |s17akf| - |currentEnv| |palgint0| |coshIfCan| |internalAugment| |matrixGcd| - |extractBottom!| |div| |linearMatrix| - |setLegalFortranSourceExtensions| |rightExtendedGcd| - |integralLastSubResultant| |numFunEvals| |generalizedEigenvectors| - |unit| |semiResultantEuclideannaif| |solveInField| |OMencodingSGML| - |quo| |normalize| |dominantTerm| |expPot| |elements| |categoryFrame| - |ODESolve| |mainMonomials| |nand| |pushuconst| |s15adf| |rename!| - |toseSquareFreePart| |open?| |removeZero| |qfactor| |tanintegrate| - |safeFloor| |s17dhf| |setEpilogue!| |rem| |viewWriteDefault| |qqq| - |basisOfLeftNucleus| |setMinPoints| |shiftRight| |roughBase?| |read!| - |e01sff| |multiple?| |groebnerIdeal| |trivialIdeal?| |aLinear| - |OMclose| |element?| |f01qdf| |OMputEndError| - |removeRedundantFactorsInPols| |makeprod| |toseInvertibleSet| - |radPoly| |f02aef| |regime| |clip| |monic?| |mindegTerm| - |jordanAdmissible?| |iidsum| |separate| |rootsOf| |branchPoint?| - |constantToUnaryFunction| |conjug| |refine| |chineseRemainder| |cCos| - |escape| |fortran| |mesh| |fractRagits| |alphabetic?| |imagE| |schema| - |left| |resetNew| |addMatch| |rational?| |replaceKthElement| - |bubbleSort!| |readLine!| |outputGeneral| |setVariableOrder| |vark| - |right| |outputForm| |bfEntry| |part?| |stopTableGcd!| - |infiniteProduct| |lyndonIfCan| |satisfy?| - |removeRoughlyRedundantFactorsInPol| |acothIfCan| |cap| |f02agf| - |localAbs| |endSubProgram| |e04mbf| |partialFraction| |meshFun2Var| - |moebius| |complete| |assign| |init| |genericRightNorm| |abs| - |resultantReduitEuclidean| |OMputApp| |mathieu12| |parts| - |topPredicate| |completeEchelonBasis| |appendPoint| |replace| - |UnVectorise| |firstSubsetGray| |nthFractionalTerm| |hasoln| - |functionIsFracPolynomial?| |toseInvertible?| - |extendedSubResultantGcd| |multMonom| |ParCond| |xn| |not| - |getMultiplicationMatrix| |s18dcf| |wholeRagits| |ellipticCylindrical| - |showTheSymbolTable| |solveLinearlyOverQ| |iprint| |clearTable!| - |identity| |toseLastSubResultant| |localUnquote| |repeatUntilLoop| - |primitiveElement| |create| |mkcomm| |cot2tan| |cAsech| |iiacot| - |complement| |redPol| |fortranDoubleComplex| |bitCoef| |cCsch| - |f04maf| |reverseLex| |varList| |shufflein| |rules| |bumptab1| - |center| |integralCoordinates| |integralMatrixAtInfinity| |swap!| - |reindex| |bivariate?| |lifting1| |LazardQuotient| |stronglyReduce| - |revert| |monicRightFactorIfCan| |integrate| |pascalTriangle| - |primPartElseUnitCanonical| |principal?| |explicitlyEmpty?| - |frobenius| |bumptab| |bracket| |quasiRegular| |OMParseError?| - |c06gsf| |zeroDim?| |seriesToOutputForm| |cyclotomicFactorization| - |f07fef| |critMonD1| |removeRoughlyRedundantFactorsInContents| - |firstDenom| |is?| |cyclicSubmodule| |factorPolynomial| |bottom!| - |OMgetEndBVar| |range| |changeVar| |enumerate| |deriv| |twoFactor| - |symbol| |expandTrigProducts| |birth| |exponent| |OMgetBVar| - |dmpToHdmp| |match?| |jordanAlgebra?| |integers| |shallowExpand| - |f01qcf| |palgint| |readLineIfCan!| |s17dlf| |simpleBounds?| |setPoly| - |po| |extendedEuclidean| |fortranComplex| |hostPlatform| |shiftRoots| - |inverseLaplace| |legendre| |integer| |bitior| |continuedFraction| - |overset?| ** |setColumn!| |newTypeLists| |e01sef| |simplify| |prime| - |aCubic| |addPoint| |nthRoot| |genericRightDiscriminant| |Lazard| - |safeCeiling| |sturmVariationsOf| |doublyTransitive?| |hexDigit?| - |setClipValue| |f2st| |superHeight| |qPot| |cSinh| |purelyAlgebraic?| - |limitedIntegrate| |generators| |psolve| |getProperties| |reorder| - |ksec| |headReduced?| |startTable!| EQ |exQuo| |quadraticForm| - |trigs2explogs| |back| |genericLeftMinimalPolynomial| |factorset| - |setleaves!| |lazyIntegrate| |bezoutResultant| |lfextendedint| - |gderiv| |wrregime| |objects| |symmetricPower| |operators| |inc| - |mainVariable?| |clearDenominator| |setrest!| |write!| |retractable?| - |updatD| |host| |pade| |numericIfCan| |base| |makeFloatFunction| - |subResultantsChain| |edf2efi| |setvalue!| |belong?| |conical| - |listYoungTableaus| |laplace| |mainDefiningPolynomial| |sumSquares| - |e01bff| |clipParametric| |eulerPhi| |OMgetEndAttr| |adaptive?| - |integerBound| |clipPointsDefault| |plus| SEGMENT |cyclicEntries| - |perspective| |dimensionsOf| |normal01| |rootOfIrreduciblePoly| - |prefix| |rur| |red| |fortranLiteralLine| |setProperty!| - |bivariateSLPEBR| |linearAssociatedExp| |updatF| |cAcsch| - |abelianGroup| |rotatey| |radicalSimplify| |supRittWu?| - |numberOfChildren| |test| |divisor| |prindINFO| |elem?| |mapGen| - |inHallBasis?| |removeSquaresIfCan| |mapCoef| |floor| |checkForZero| - |mainCoefficients| |cothIfCan| |zeroVector| |expIfCan| |build| - |leftPower| |component| |karatsuba| |scanOneDimSubspaces| - |createPrimitivePoly| |fullPartialFraction| |stack| |setref| - |colorFunction| |LyndonWordsList1| |discriminant| |opeval| |times| - |rdHack1| |e02def| |OMreadStr| |critMTonD1| |pureLex| |systemSizeIF| - |OMconnOutDevice| |basisOfCommutingElements| |patternVariable| - |rangePascalTriangle| |curve?| |FormatArabic| |powern| |name| - |divisors| |degreeSubResultantEuclidean| |interpolate| |prime?| - |error| |rootPower| |redmat| |copy!| |OMserve| |rename| |messagePrint| - |body| |mathieu24| |permutationRepresentation| |dictionary| - |beauzamyBound| |assert| |domainOf| |sh| |pointColorPalette| |iiatan| - |partitions| |monomRDE| |optimize| |arity| |primlimitedint| - |squareFreePolynomial| |midpoints| |mulmod| |stoseInvertibleSetsqfreg| - |OMgetAttr| |monom| |inGroundField?| |stoseInvertibleSet| - |splitDenominator| |ran| |ode| |setOfMinN| |removeCosSq| - |goodnessOfFit| |ord| |integral| |palgLODE0| |OMencodingUnknown| - |parametersOf| |lquo| |previous| |OMgetSymbol| - |cyclotomicDecomposition| |powerSum| |initiallyReduce| |concat!| - |unitsColorDefault| |round| |prem| |lexGroebner| |chainSubResultants| - |associator| |expr| |laurentRep| |denominators| |cTanh| |arg1| |size?| - |generateIrredPoly| |common| |complexSolve| - |tryFunctionalDecomposition?| |currentCategoryFrame| - |internalLastSubResultant| |showTheFTable| |expenseOfEvaluation| - |lieAdmissible?| |arg2| |box| |insert!| |d02kef| |imagi| - |fortranCharacter| |string?| |dihedralGroup| |removeDuplicates!| - |totalDegree| |expintegrate| |reduceLODE| |polyRDE| - |rewriteSetWithReduction| |cosSinInfo| |primlimintfrac| - |linearDependenceOverZ| |subSet| |cyclicCopy| |df2st| |epilogue| - |plenaryPower| |e04dgf| |increase| |rightZero| |approxNthRoot| - |simplifyPower| |cycle| |derivative| |reducedQPowers| |rubiksGroup| - |variable| |monomial?| |c06fqf| |semiSubResultantGcdEuclidean1| - |exists?| |internalIntegrate0| |primextendedint| |OMreadFile| - |cyclic?| |coordinates| |rightRank| |antisymmetric?| |karatsubaOnce| - |triangSolve| |primeFactor| |hclf| |getPickedPoints| |iiacsc| - |putGraph| |radicalOfLeftTraceForm| |nextPrimitiveNormalPoly| - |decrease| |linear| |nextSubsetGray| |compdegd| |insert| |failed| - |degree| |rowEch| |orbit| |hasPredicate?| |parametric?| |redpps| - |green| |lowerPolynomial| |isobaric?| |realSolve| |formula| - |pmintegrate| |tanhIfCan| |lyndon| |integralBasis| |t| |shallowCopy| - |selectIntegrationRoutines| |polynomial| |isList| |bombieriNorm| - |entries| |numerators| |next| |LowTriBddDenomInv| |mpsode| - |makeViewport3D| |viewWriteAvailable| |rotatex| |reify| |outputAsTex| - |more?| |digit?| |stoseIntegralLastSubResultant| |getExplanations| - |returnTypeOf| |rootKerSimp| |high| |cyclicParents| |flatten| |minus!| - |alternatingGroup| |startTableGcd!| |divisorCascade| |cn| |merge| - |nextNormalPoly| |xCoord| |indices| |hasHi| |overlap| |s19adf| - |fglmIfCan| |d02bhf| |laguerre| |nrows| |head| |roughUnitIdeal?| - |findCycle| |tanh2coth| |bipolarCylindrical| |sdf2lst| |point| - |scalarMatrix| |internalInfRittWu?| |hdmpToDmp| |reducedDiscriminant| - |complexZeros| |ncols| |reflect| |directory| |linSolve| |trapezoidal| - |firstNumer| |discriminantEuclidean| |eval| |nilFactor| |port| - |isQuotient| |listLoops| |nil| |s17aef| |reverse| |outlineRender| - |UP2ifCan| |d01fcf| |linearPolynomials| |truncate| |f02xef| |secIfCan| - |startStats!| |compose| |processTemplate| |generic| |tanh2trigh| - |getOperands| |viewZoomDefault| |iicsc| |series| |sncndn| |index?| - |frst| |lambert| Y |numberOfComponents| |pmComplexintegrate| |limit| - |move| |identityMatrix| |maximumExponent| |linkToFortran| |traverse| - |OMputFloat| |simpson| |denomLODE| |approximate| |arrayStack| |e02gaf| - |var2StepsDefault| |printInfo| |OMputBind| |cycleTail| |op| |leftGcd| - |balancedBinaryTree| |complex| |doubleFloatFormat| |showRegion| - |systemCommand| |realElementary| |OMUnknownCD?| |iicot| - |indicialEquationAtInfinity| |exponentialOrder| |inf| |height| - |absolutelyIrreducible?| |normalizeIfCan| |sPol| |edf2df| |imagJ| - |brillhartTrials| |printStatement| |invertibleSet| |min| |cAtan| - |f01qef| |firstUncouplingMatrix| |s13adf| |debug3D| |dequeue| - |fractRadix| |minrank| |hue| |putColorInfo| |outerProduct| |positive?| - |listBranches| |acscIfCan| |freeOf?| |child?| |normal| |quotientByP| - |Gamma| |top!| |hermiteH| |monomialIntPoly| |rationalPoints| |primes| - |partition| |printCode| |subResultantGcd| |trace2PowMod| |normalise| - |selectOrPolynomials| |pointColor| |sort!| |cAtanh| |chiSquare| - |e01saf| |f01mcf| |iiasinh| |OMconnInDevice| |union| |KrullNumber| - |prinb| |shift| |probablyZeroDim?| |uniform| |completeHensel| - |partialDenominators| |maxrow| |factorials| |leadingExponent| - |getMatch| |clipSurface| |numeric| |coercePreimagesImages| - |viewThetaDefault| |depth| |mix| |diag| |ParCondList| |df2ef| - |stripCommentsAndBlanks| |radical| |cCsc| |lastSubResultant| |input| - |sinh2csch| |notOperand| |mapdiv| |setTopPredicate| |baseRDEsys| - |constantKernel| |OMread| |inverseIntegralMatrix| |setMaxPoints| - |options| |polar| |e02ddf| |library| |constantLeft| |hasTopPredicate?| - |tan2trig| |makeop| |LiePolyIfCan| |modularFactor| |directSum| |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| |divisor| |choosemon| |precision| |tensorProduct| + |numberOfHues| |nextSublist| |var2StepsDefault| |ellipticCylindrical| + |nextSubsetGray| |useNagFunctions| |transform| + |permutationRepresentation| |blue| |overset?| |tubePointsDefault| + |prolateSpheroidal| |firstSubsetGray| |s17dcf| |setStatus!| + |rationalPoints| |pack!| |completeEchelonBasis| |green| |ParCond| + |tubeRadiusDefault| |dom| |oblateSpheroidal| |clipPointsDefault| + |s17def| |setCondition!| |nonSingularModel| |complexLimit| + |createRandomElement| |set| |yellow| |redmat| |dimension| |bipolar| + |drawToScale| |s17dgf| |setValue!| |algSplitSimple| |limit| + |cyclicSubmodule| |/\\| |red| |bipolarCylindrical| |stop| |adaptive| + |s17dhf| |empty?| |iifact| |hyperelliptic| |linearlyDependent?| + |standardBasisOfCyclicSubmodule| |\\/| |hasTopPredicate?| + |divideExponents| |toroidal| |figureUnits| |s17dlf| |splitNodeOf!| + |iibinom| |elliptic| |linearDependence| |areEquivalent?| + |topPredicate| |unmakeSUP| |conical| |putColorInfo| |s18acf| |remove!| + |iiperm| |integralDerivationMatrix| |solveLinear| + |isAbsolutelyIrreducible?| |setTopPredicate| |makeSUP| |modTree| + |title| |appendPoint| |s18adf| |subNodeOf?| |deleteProperty!| |iipow| + |integralRepresents| |reducedSystem| |meatAxe| |patternVariable| + |vectorise| |multiEuclideanTree| |component| |s18aef| |nodeOf?| |has?| + |iidsum| |integralCoordinates| |duplicates?| |scanOneDimSubspaces| + |withPredicates| |extend| |complexZeros| |ranges| |s18aff| + |updateStatus!| |sort| |iidprod| |yCoordinates| |mapGen| |expt| + |setPredicates| |truncate| |e| |divisorCascade| |pointLists| |s18dcf| + |extractSplittingLeaf| |ipow| |inverseIntegralMatrixAtInfinity| + |mapExpon| |showArrayValues| |predicates| |order| |graeffe| + |makeGraphImage| |s18def| |squareMatrix| |factorial| + |integralMatrixAtInfinity| |commutativeEquality| |showScalarValues| + |hasPredicate?| |terms| F |pleskenSplit| |graphImage| |mr| |s19aaf| + |transpose| |any| |multinomial| |showSummary| |inverseIntegralMatrix| + |leftMult| |solveRetract| |show| |optional?| |squareFreePart| + |reciprocalPolynomial| |groebSolve| |s19abf| |trim| |permutation| + |integralMatrix| |rightMult| |mainVariable| |multiple?| |BumInSepFFE| + |rootRadius| |testDim| |s19acf| |split| |stirling1| + |reduceBasisAtInfinity| |random| |showAttributes| |makeUnit| + |uniform01| |trace| |generic?| |multiplyExponents| |schwerpunkt| + |genericPosition| |s19adf| |upperCase!| |stirling2| + |normalizeAtInfinity| |reverse!| |normal01| |quoted?| |laurentIfCan| + |setErrorBound| |lfunc| |s20acf| |upperCase| |summation| + |complementaryBasis| |makeMulti| |exponential1| |inR?| |laurentRep| + |brillhartIrreducible?| |startPolynomial| |inHallBasis?| |s20adf| + |lowerCase!| |factorials| |integral?| |makeTerm| |chiSquare1| |isList| + |rationalPower| |brillhartTrials| |cycleElt| |reorder| |s21baf| + |lowerCase| |mkcomm| |integralAtInfinity?| |listOfMonoms| + |exponential| |isOp| |dominantTerm| |computeCycleLength| |headAst| + |s21bbf| |KrullNumber| |polarCoordinates| |integralBasisAtInfinity| + |symmetricSquare| |chiSquare| |satisfy?| |limitPlus| + |computeCycleEntry| |heap| |s21bcf| |numberOfVariables| |eq?| + |imaginary| |ramified?| |factor1| |factorFraction| |addBadValue| + |split!| |coerceP| |gcdprim| |s21bdf| |algebraicDecompose| |solid| + |ramifiedAtInfinity?| |symmetricProduct| |uniform| |badValues| + |setlast!| |powerSum| |gcdcofact| |fortranCompilerName| + |transcendentalDecompose| |solid?| |width| |singular?| + |symmetricPower| |binomial| NOT |retractable?| |setrest!| |elementary| + |gcdcofactprim| |fortranLinkerArgs| |internalDecompose| |denominators| + |singularAtInfinity?| |directSum| |poisson| OR |ListOfTerms| + |setfirst!| |alternating| |lintgcd| |aspFilename| |decompose| + |numerators| |branchPoint?| |solveLinearPolynomialEquationByFractions| + |geometric| AND |PDESolve| |cycleSplit!| |plusInfinity| |lhs| |cyclic| + |hex| |dimensionsOf| |upDateBranches| |convergents| + |branchPointAtInfinity?| |hasSolution?| |ridHack1| |leftFactor| + |concat!| |minusInfinity| |rhs| |dihedral| |every?| |restorePrecision| + |preprocess| |approximants| |rationalPoint?| |linSolve| |interpolate| + |rightFactorCandidate| |cycleTail| |cap| |any?| |antiCommutator| + |internalZeroSetSplit| |reducedForm| |absolutelyIrreducible?| |zero| + |LyndonWordsList| |nullSpace| |measure| |cycleLength| |cup| |host| + |commutator| |internalAugment| |optional| |genus| |LyndonWordsList1| + |nullity| |coerceImages| |cycleEntry| |delta| |wreath| |trueEqual| + |associator| |possiblyInfinite?| |getZechTable| |And| |lyndonIfCan| + |rowEchelon| |fixedPoints| |invmultisect| |SFunction| |factorList| + |complexEigenvalues| |explicitlyFinite?| |node| |createZechTable| |Or| + |lyndon| |column| |odd?| |multisect| |skewSFunction| + |listConjugateBases| |complexEigenvectors| |nextItem| + |createMultiplicationTable| |Not| |lyndon?| |row| |even?| |revert| + |type| |cyclotomicDecomposition| |matrixGcd| |normalizedAssociate| + |infiniteProduct| |createMultiplicationMatrix| + |numberOfComputedEntries| |maxColIndex| |numberOfCycles| + |generalLambert| |cyclotomicFactorization| |divideIfCan!| |normalize| + |evenInfiniteProduct| |createLowComplexityTable| |rst| |minColIndex| * + |cyclePartition| |evenlambert| |rangeIsFinite| |leastPower| + |outputArgs| |oddInfiniteProduct| |createLowComplexityNormalBasis| + |frst| |maxRowIndex| |coerceListOfPairs| |oddlambert| |top| + |functionIsContinuousAtEndPoints| |idealiser| |normInvertible?| + |generalInfiniteProduct| |representationType| |lazyEvaluate| |print| + |minRowIndex| |coercePreimagesImages| |lambert| |continue| + |functionIsOscillatory| |idealiserMatrix| |normFactors| |showAll?| + |createPrimitiveElement| |lazy?| |antisymmetric?| |listRepresentation| + |lagrange| |changeName| |moduleSum| |npcoef| |showAllElements| + |tableForDiscreteLogarithm| |explicitlyEmpty?| |symmetric?| + |permanent| |univariatePolynomial| |exprHasWeightCosWXorSinWX| + |mapUnivariate| |listexp| |tree| |delay| |cons| |hexDigit?| + |factorsOfCyclicGroupSize| |explicitEntries?| |diagonal?| |cycles| + |integrate| |exprHasAlgebraicWeight| |mapUnivariateIfCan| + |characteristicPolynomial| |findCycle| |escape| |sizeMultiplication| + |matrixDimensions| |square?| |cycle| |multiplyCoefficients| + |exprHasLogarithmicWeights| |mapMatrixIfCan| |realEigenvalues| + |repeating?| |ord| |getMultiplicationMatrix| |matrixConcat3D| + |rectangularMatrix| |initializeGroupForWordProblem| |quoByVar| + |combineFeatureCompatibility| |mapBivariate| |level| + |realEigenvectors| |repeating| |equation| |mkIntegral| + |getMultiplicationTable| |setelt!| |characteristic| |movedPoints| + |coefficients| |sparsityIF| |fullDisplay| |halfExtendedResultant2| + |recip| |primitive?| |identityMatrix| |round| |wordInGenerators| + |stFunc1| |relationsIdeal| |halfExtendedResultant1| |integers| + |numberOfIrreduciblePoly| |zeroMatrix| |fractionPart| + |wordInStrongGenerators| |stFunc2| |saturate| |extendedResultant| + |oddintegers| |source| |numberOfPrimitivePoly| |dec| |nullary| + |wholePart| |orbits| |stFuncN| |groebner?| |subResultantsChain| |int| + |numberOfNormalPoly| |fixedPoint| |floor| |orbit| |fixedPointExquo| + |groebnerIdeal| |lazyPseudoQuotient| |mapmult| |recur| |ceiling| + |permutationGroup| |ode1| |ideal| |lazyPseudoRemainder| |deriv| + |edf2efi| |const| |norm| |wordsForStrongGenerators| |ode2| + |leadingIdeal| |bernoulliB| |gderiv| |dfRange| |curry| + |mightHaveRoots| |strongGenerators| |ode| |bright| |backOldPos| + |eulerE| |compose| |target| |dflist| |diag| |refine| |generators| + |mpsode| |numericIfCan| |addiag| |df2mf| |curryRight| |middle| + |bivariateSLPEBR| UP2UTS |rangePascalTriangle| |complexNumericIfCan| + |lazyIntegrate| |ldf2vmf| |curryLeft| |roman| + |solveLinearPolynomialEquationByRecursion| UTS2UP |sizePascalTriangle| + |FormatArabic| |nlde| |edf2ef| |max| |constantRight| |property| + |recoverAfterFail| |factorByRecursion| LODO2FUN |fillPascalTriangle| + |ScanArabic| |powern| |vedf2vef| |factorSquareFreeByRecursion| RF2UTS + |safeCeiling| |FormatRoman| |mapdiv| |df2st| |comp| |cCos| |imagK| + |randomR| |magnitude| |delete| |safeFloor| |ScanRoman| + |lazyGintegrate| |f2st| |cSin| |imagJ| |result| |units| + |factorSFBRlcUnit| |cross| |safetyMargin| |ScanFloatIgnoreSpaces| + |power| |ldf2lst| |cLog| |imagI| |charthRoot| |dot| |sumSquares| + |sdf2lst| |cExp| |conjugate| |conditionP| |scan| |euclideanNormalForm| + |f01bsf| |smith| |entry| |getlo| |cRationalPower| |queue| + |solveLinearPolynomialEquation| |graphCurves| |euclideanGroebner| + |f01maf| |completeSmith| |gethi| |cPower| |nthRoot| + |factorSquareFreePolynomial| |drawCurves| |factorGroebnerBasis| |li| + |f01mcf| |diophantineSystem| |outputMeasure| |seriesToOutputForm| + |fractRadix| |code| |clearCache| |groebnerFactorize| |f01qcf| |csubst| + |elt| |measure2Result| |iCompose| |wholeRadix| |overlabel| |basicSet| + |credPol| |f01qdf| |particularSolution| |att2Result| |taylorQuoByVar| + |cycleRagits| |overbar| |infRittWu?| |redPol| |f01qef| |numer| + |mapSolve| |iflist2Result| |iExquo| |prefixRagits| |prime| |getCurve| + |gbasis| |f01rcf| |denom| |quadratic| |pdf2ef| |getStream| + |fractRagits| |quote| |listLoops| |critT| |f01rdf| |rule| |cubic| + |pdf2df| |getRef| |wholeRagits| |supersub| |closed?| |log10| |critM| + |f01ref| |quartic| |pi| |df2ef| |makeSeries| |radix| |presuper| + |open?| |bitand| |critB| |f02aaf| |infinity| |aLinear| |fi2df| GF2FG + |randnum| |presub| |setClosed| |critBonD| |f02abf| |aQuadratic| |mat| + FG2F |generator| |reseed| |super| |tube| |critMTonD1| |f02adf| + |aCubic| |neglist| F2FG |seed| |sub| |unitVector| |index| |critMonD1| + |kernel| |f02aef| |aQuartic| |multiEuclidean| |explogs2trigs| + |rational| |rarrow| |cosSinInfo| |draw| |redPo| |f02aff| + |radicalSolve| |option| |extendedEuclidean| |comment| |trigs2explogs| + |rational?| |assign| |loopPoints| |hMonic| |f02agf| |radicalRoots| + |euclideanSize| |swap!| |rationalIfCan| |slash| |generalTwoFactor| + |pair| |updatF| BY |f02ajf| |contractSolve| |position| |sizeLess?| + |fill!| |setvalue!| |over| |generalSqFr| |sPol| |f02akf| + |decomposeFunc| |simplifyPower| |minIndex| |setchildren!| |zag| + |twoFactor| |makeObject| |updatD| |f02awf| |unvectorise| |function| + |predicate| |number?| |maxIndex| |node?| |postfix| |setOrder| + |minGbasis| |f02axf| |bubbleSort!| |seriesSolve| |entry?| |child?| + |lo| |infix| |getOrder| |lepol| |f02bbf| |insertionSort!| |coef| + |constantToUnaryFunction| |indices| |distance| |incr| |vconcat| + |less?| |prinshINFO| |f02bjf| |check| |condition| |tubePlot| |index?| + |nodes| |hi| |hconcat| |userOrdered?| |prindINFO| |f02fjf| |lprop| + |exponentialOrder| |entries| |rename| |rspace| |largest| |fprindINFO| + |f02wef| |llprop| |completeEval| |key?| |nothing| |rename!| |vspace| + |more?| |prinpolINFO| |f02xef| |lllp| |lowerPolynomial| |symbolIfCan| + |mainValue| |hspace| |setVariableOrder| |prinb| |f04adf| |lllip| + |raisePolynomial| |argument| |mainDefiningPolynomial| |superHeight| + |getVariableOrder| |critpOrder| |f04arf| |mesh?| |parameters| + |normalDeriv| |constantKernel| |mainForm| |subHeight| + |resetVariableOrder| |tail| |makeCrit| |f04asf| |mesh| |ran| + |constantIfCan| |messagePrint| |rischDE| |pattern| |prime?| + |virtualDegree| |f04atf| |polygon?| |highCommonTerms| |kovacic| + |rischDEsys| |padecf| |rationalFunction| |alphanumeric| + |conditionsForIdempotents| |f04axf| |polygon| |mapCoef| |laplace| + |monomRDE| |pade| |taylorIfCan| |genericRightDiscriminant| |f04faf| + |closedCurve?| |log| |cond| |lcm| |nthCoef| |erf| + |trailingCoefficient| |baseRDE| |root| |removeZeroes| |alphabetic| + |genericRightTraceForm| |f04jgf| |closedCurve| |digit| |binomThmExpt| + |normalizeIfCan| |message| |polyRDE| |quotientByP| |taylorRep| + |hexDigit| |genericLeftDiscriminant| |output| |f04maf| |curve?| + |charClass| |append| |pomopo!| |polCase| |monomRDEsys| |moduloP| + |factorSquareFree| |outputList| |genericLeftTraceForm| |status| + |f04mbf| |curve| |mapExponents| |gcd| |distFact| |dilog| |baseRDEsys| + |generate| |modulus| |henselFact| |properties| |genericRightNorm| + |f04mcf| |point?| |false| |linearAssociatedLog| |sin| |identification| + |weighted| |digits| |hasHi| |translate| |genericRightTrace| |f04qaf| + |enterPointData| |linearAssociatedOrder| |compile| |incrementBy| |cos| + |LyndonCoordinates| |rdHack1| |continuedFraction| |fmecg| |upperCase?| + |genericRightMinimalPolynomial| |f07adf| |composites| + |linearAssociatedExp| |LyndonBasis| |tan| |light| |midpoint| |expand| + = |commonDenominator| |rightRankPolynomial| |f07aef| |components| + |createNormalElement| |zeroDimensional?| |cot| |midpoints| + |filterWhile| |pastel| |clearDenominator| |genericLeftNorm| |f07fdf| + |matrix| |numberOfComposites| |setLabelValue| |fglmIfCan| |realZeros| + |#| |filterUntil| |sec| |dark| |length| < |splitDenominator| + |genericLeftTrace| |f07fef| |numberOfComponents| |getCode| |groebner| + |mainCharacterization| |select| |csc| > |getSyntaxFormsFromFile| + |scripts| |double| |monicRightFactorIfCan| + |genericLeftMinimalPolynomial| |s01eaf| |create3Space| |printCode| + |lexTriangular| |asin| |algebraicOf| |surface| <= |rightFactorIfCan| + |leftRankPolynomial| |s13aaf| |outputAsScript| |printStatement| + |squareFreeLexTriangular| |acos| |ReduceOrder| >= |coordinate| + |leftFactorIfCan| |generic| |s13acf| |outputAsTex| |block| |atan| + |belong?| |setref| |partitions| |monicDecomposeIfCan| |rightUnits| + |s13adf| |abs| |returns| |acot| |operator| |deref| |conjugates| + |monicCompleteDecompose| |leftUnits| |s14aaf| |Beta| |goto| |Ci| + |asec| |ref| |shuffle| |divideIfCan| + |compBound| |s14abf| |digamma| + |repeatUntilLoop| |Si| |makeRecord| |acsc| |radicalEigenvectors| + |shufflein| |noKaratsuba| - ~= |tablePow| |s14baf| |polygamma| |Ei| + |radicalEigenvector| |close| |sinh| |sequences| |declare!| + |karatsubaOnce| / |coerce| |solveid| |s15adf| |Gamma| |iiacosh| |cosh| + |linGenPos| |radicalEigenvalues| |permutations| |karatsuba| + |construct| |testModulus| |s15aef| |besselJ| |remove| |initial| + |iiatanh| |groebgen| |tanh| |eigenMatrix| |display| |atoms| |separate| + |HenselLift| |s17acf| |besselY| |checkPrecision| |iiacoth| + |rootKerSimp| |coth| |totolex| |normalise| |makeResult| |pseudoDivide| + |s17adf| |besselI| |last| |iiasech| |leftRank| |sech| |minPol| + |gramschmidt| |is?| |pseudoQuotient| |complement| |s17aef| |besselK| + |assoc| |iiacsch| |rightRank| |csch| |computeBasis| |orthonormalBasis| + |Is| |composite| |cardinality| |s17aff| |airyAi| |specialTrigs| + |doubleRank| |asinh| |coord| |antisymmetricTensors| + |addMatchRestricted| |subResultantGcd| |internalIntegrate0| + |noLinearFactor?| |s17agf| |airyBi| |localReal?| |acosh| |insertMatch| + |resultant| |makeCos| |insertRoot!| |s17ahf| |subNode?| + |rischNormalize| |mkPrim| |changeBase| |puiseux| |atanh| |addMatch| + |discriminant| |makeSin| |s17ajf| |infLex?| |alphanumeric?| + |realElementary| |intPatternMatch| |companionBlocks| |acoth| |tower| + |getMatch| |pseudoRemainder| |iiGamma| |s17akf| |setEmpty!| + |lowerCase?| |validExponential| |primintegrate| |inv| |xCoord| |asech| + |failed?| |shiftLeft| |iiabs| |rootNormalize| |ground?| |expintegrate| + |yCoord| |optpair| |shiftRight| |bringDown| |d01anf| |algebraicSort| + |tanQ| |ground| |tanintegrate| |zCoord| |multiple| |getBadValues| + |karatsubaDivide| |newReduc| |declare| |d01apf| |moreAlgebraic?| + |callForm?| |applyQuote| |primextendedint| |leadingMonomial| |rCoord| + ~ |resetBadValues| |segment| |monicDivide| |doublyTransitive?| + |logical?| |d01aqf| |subTriSet?| |constructorName| |getIdentifier| + |expextendedint| |thetaCoord| |leadingCoefficient| |complexNumeric| + |knownInfBasis| |character?| |d01asf| |subPolSet?| |say| |getConstant| + |primlimitedint| |primitiveMonomials| |phiCoord| |OMUnknownCD?| + |complexNormalize| |open| |setelt| |rootSplit| |doubleComplex?| + |d01bbf| |internalSubPolSet?| |select!| |kernels| |explimitedint| + |color| |reductum| |ruleset| |OMParseError?| |complexElementary| + |ratDenom| |obj| |complex?| |d01fcf| |internalInfRittWu?| |delete!| + |primextintfrac| |hue| |OMwrite| |trigs| |univariate| |ratPoly| |copy| + |double?| |cache| |d01gaf| |internalSubQuasiComponent?| |retract| |sn| + |primlimintfrac| |shade| |po| |real?| |rootPower| |ffactor| |d01gbf| + |subQuasiComponent?| |parts| |isTimes| |dn| |primintfldpoly| + |nthRootIfCan| |suchThat| |OMread| |complexForm| |qfactor| |d02bbf| + |removeSuperfluousQuasiComponents| |isExpt| |sncndn| |expintfldpoly| + |expIfCan| |OMreadFile| |UpTriBddDenomInv| |factor| |autoCoerce| + |rootProduct| |UP2ifCan| |d02bhf| |subCase?| |isPower| |categoryFrame| + |monomialIntegrate| |logIfCan| |reset| |OMreadStr| |hash| + |LowTriBddDenomInv| |sqrt| |rootSimp| |anfactor| |d02cjf| + |removeSuperfluousCases| |rroot| |setProperties!| |count| + |monomialIntPoly| |sinIfCan| |OMlistCDs| |simplify| |real| + |fortranCharacter| |d02ejf| |prepareDecompose| |qroot| |getProperties| + |inverseLaplace| |write| |cosIfCan| |OMlistSymbols| |htrigs| |imag| + |fortranDoubleComplex| |d02gaf| |branchIfCan| |froot| |directProduct| + |setProperty!| |save| |iprint| |tanIfCan| |OMsupportsCD?| + |simplifyExp| |fortranComplex| |d02gbf| |startTableGcd!| |nthr| + |getProperty| |elem?| |cotIfCan| |OMsupportsSymbol?| |simplifyLog| + |fortranLogical| |d02kef| |stopTableGcd!| |port| |scopes| |notelem| + |destruct| |secIfCan| |OMunhandledSymbol| |expandPower| + |fortranInteger| |d02raf| |startTableInvSet!| |firstUncouplingMatrix| + |eigenvalues| |logpart| |cscIfCan| |OMreceive| |expandLog| + |fortranDouble| |d03edf| |stopTableInvSet!| |integral| |eigenvector| + |ratpart| |asinIfCan| |OMsend| |cos2sec| |fortranReal| |d03eef| + |stosePrepareSubResAlgo| |constant| |primitiveElement| + |generalizedEigenvector| |mkAnswer| |acosIfCan| |OMserve| |cosh2sech| + |external?| |d03faf| |stoseInternalLastSubResultant| |nextPrime| + |generalizedEigenvectors| |perfectNthPower?| |monomial| |atanIfCan| + |makeop| |cot2trig| |scalarTypeOf| |e01baf| + |stoseIntegralLastSubResultant| |arguments| |prevPrime| |eigenvectors| + |perfectNthRoot| |multivariate| |acotIfCan| |opeval| |coth2trigh| + |fortranCarriageReturn| |e01bef| |stoseLastSubResultant| |primes| + |factorAndSplit| |approxNthRoot| |variables| |asecIfCan| + |evaluateInverse| |csc2sin| |fortranLiteral| |e01bff| + |stoseInvertible?sqfreg| |selectsecond| |rightOne| |perfectSquare?| + |acscIfCan| |evaluate| |csch2sinh| |alphabetic?| |fortranLiteralLine| + |e01bgf| |stoseInvertibleSetsqfreg| |selectfirst| |search| + |basisOfRightAnnihilator| |leftOne| |perfectSqrt| |sinhIfCan| |conjug| + |sec2cos| |processTemplate| |e01bhf| |eq| |stoseInvertible?reg| + |makeprod| |basisOfLeftNucleus| |rightZero| |approxSqrt| |coshIfCan| + |adjoint| |sech2cosh| |makeFR| |iter| |e01daf| |stoseInvertibleSetreg| + |equivOperands| |leftZero| |generateIrredPoly| |tanhIfCan| + |getDatabase| |sin2csc| |musserTrials| |e01saf| |stoseInvertible?| + |equiv?| |swap| |complexExpand| |taylor| |cothIfCan| + |numericalOptimization| |sinh2csch| |stopMusserTrials| |e01sbf| + |stoseInvertibleSet| |impliesOperands| |or| |minPoly| + |complexIntegrate| |laurent| |sechIfCan| |goodnessOfFit| |tan2trig| + |numberOfFactors| |e01sef| |stoseSquareFreePart| |implies?| |freeOf?| + |dimensionOfIrreducibleRepresentation| |cschIfCan| |whatInfinity| + |tanh2trigh| |modularFactor| |e01sff| |coleman| |orOperands| + |operators| |irreducibleRepresentation| |asinhIfCan| |infinite?| + |tan2cot| |useSingleFactorBound?| |e02adf| |inverseColeman| |or?| + |mainKernel| |checkRur| |acoshIfCan| |finite?| |tanh2coth| + |useSingleFactorBound| |e02aef| |listYoungTableaus| |exp| + |andOperands| |distribute| |cAcsch| |atanhIfCan| |pureLex| |cot2tan| + |unravel| |useEisensteinCriterion?| |e02agf| |makeYoungTableau| |and?| + |rightTrim| |functionIsFracPolynomial?| |cAsech| |acothIfCan| + |totalLex| |coth2tanh| |leviCivitaSymbol| |useEisensteinCriterion| + |e02ahf| |nextColeman| |notOperand| |leftTrim| |problemPoints| + |cAcoth| |asechIfCan| |reverseLex| |removeCosSq| + |eisensteinIrreducible?| ^ |e02ajf| |nextLatticePermutation| + |variable?| |basisOfRightNucleus| |zerosOf| |cAtanh| |acschIfCan| + |leftLcm| |removeSinSq| |tryFunctionalDecomposition?| |e02akf| + |nextPartition| |term| |basisOfMiddleNucleus| |singularitiesOf| + |cAcosh| |pushdown| |rightExtendedGcd| |removeCoshSq| + |tryFunctionalDecomposition| |e02baf| |numberOfImproperPartitions| + |term?| |polynomialZeros| |cAsinh| |pushup| |rightGcd| |removeSinhSq| + |conditions| |btwFact| |e02bbf| |subSet| |equiv| |f2df| |cCsch| + |reducedDiscriminant| |rightExactQuotient| |expandTrigProducts| + |match| |beauzamyBound| |ptree| |e02bcf| |unrankImproperPartitions0| + |merge!| |ef2edf| |cSech| |idealSimplify| |rightRemainder| + |fintegrate| |call| |bombieriNorm| |e02bdf| + |unrankImproperPartitions1| |resultantEuclidean| |ocf2ocdf| |cCoth| + |definingInequation| |rightQuotient| |coefficient| |list| |rootBound| + |e02bef| |subresultantSequence| |qelt| |semiResultantEuclidean2| + |basisOfCommutingElements| |leader| |socf2socdf| |cTanh| + |definingEquations| |rightLcm| |coHeight| |kroneckerDelta| |car| + |singleFactorBound| |e02daf| |SturmHabichtSequence| + |semiResultantEuclidean1| |basisOfLeftAnnihilator| |df2fi| |cCosh| + |setStatus| |leftExtendedGcd| |extendIfCan| |reindex| |cdr| + |quadraticNorm| |e02dcf| |SturmHabichtCoefficients| |xRange| + |indiceSubResultant| |edf2fi| |loadNativeModule| |cSinh| + |quasiAlgebraicSet| |leftGcd| |algebraicVariables| |setDifference| + |infinityNorm| |e02ddf| |SturmHabicht| |yRange| + |indiceSubResultantEuclidean| |char| |edf2df| |cAcsc| + |radicalSimplify| |leftExactQuotient| + |zeroSetSplitIntoTriangularSystems| |lambda| |setIntersection| + |scaleRoots| |e02def| |countRealRoots| |zRange| + |semiIndiceSubResultantEuclidean| |expenseOfEvaluation| |cAsec| + |denominator| |leftRemainder| |zeroSetSplit| |setUnion| |shiftRoots| + |map!| |e02dff| |SturmHabichtMultiple| |substring?| + |degreeSubResultant| |numberOfOperations| |cAcot| |numerator| + |leftQuotient| |reduceByQuasiMonic| |apply| |qsetelt!| + |degreePartition| |e02gaf| |countRealRootsMultiple| + |degreeSubResultantEuclidean| |cAtan| |quadraticForm| + |monicLeftDivide| |collectQuasiMonic| |factorOfDegree| |e02zaf| + |suffix?| |pop!| |semiDegreeSubResultantEuclidean| |setImagSteps| + |float| |cAcos| |void| |back| |monicRightDivide| |removeZero| |size| + |factorsOfDegree| |e04dgf| |push!| |lastSubResultantEuclidean| + |setClipValue| |cAsin| |front| |leftDivide| |initiallyReduce| + |pascalTriangle| |e04fdf| |prefix?| |minordet| + |semiLastSubResultantEuclidean| |option?| |cCsc| |rotate!| + |rightDivide| |headReduce| |e04gcf| |determinant| + |subResultantGcdEuclidean| |range| |cSec| |dequeue!| |hermiteH| + |stronglyReduce| |first| |exp1| |e04jaf| |acsch| |diagonalProduct| + |semiSubResultantGcdEuclidean2| |colorFunction| |cCot| |enqueue!| + |laguerreL| |rewriteSetWithReduction| |rest| |log2| |null| |e04mbf| + |diagonal| |semiSubResultantGcdEuclidean1| |curveColor| |implies| + |cTan| |quatern| |legendreP| |autoReduced?| |substitute| + |rationalApproximation| |e04naf| |diagonalMatrix| |case| + |discriminantEuclidean| |pointColor| |blankSeparate| + |initiallyReduced?| |removeDuplicates| |key| |relerror| |e04ucf| + |Zero| |scalarMatrix| |semiDiscriminantEuclidean| |clip| |xor| + |bitTruth| |resultantnaif| |semicolonSeparate| |headReduced?| + |complexSolve| |e04ycf| |infix?| |One| |hermite| |chainSubResultants| + |clipBoolean| GE |contains?| |resultantEuclideannaif| |commaSeparate| + |stronglyReduced?| |filename| |complexRoots| |mask| |f01brf| + |completeHermite| |generalizedContinuumHypothesisAssumed| |schema| + |style| GT |inf| |semiResultantEuclideannaif| |pile| |reduced?| |not?| + |realRoots| |setColumn!| |generalizedContinuumHypothesisAssumed?| + |resultantReduit| |toScale| LE |qinterval| |pdct| |paren| + |normalized?| |parse| |leadingTerm| |computePowers| |positive?| + |setRow!| |resultantReduitEuclidean| |pointColorPalette| LT |interval| + |powers| |bracket| |quasiComponent| |writable?| |pow| |negative?| + |oneDimensionalArray| |semiResultantReduitEuclidean| + |curveColorPalette| |unit?| |prod| |partition| |label| |symbolTable| + |initials| |retractIfCan| |readable?| |An| |zero?| |associatedSystem| + |divide| |ravel| |var1Steps| |associates?| |complete| |exists?| + |UnVectorise| |dim| |augment| |uncouplingMatrices| |var2Steps| + |Lazard| |pushFortranOutputStack| |reshape| |unitCanonical| |pole?| + |OMconnInDevice| |getOperator| |extension| |Vectorise| + |lastSubResultant| |associatedEquations| |space| |Lazard2| + |popFortranOutputStack| |unitNormal| |OMconnOutDevice| |listBranches| + |string| |nil?| |shallowExpand| |setPoly| |lastSubResultantElseSplit| + |arrayStack| |nextsousResultant2| |tubePoints| |lfextendedint| + |OMconnectTCP| |triangular?| |buildSyntax| |outputAsFortran| + |deepExpand| |exponent| |invertibleSet| |setButtonValue| |tubeRadius| + |lflimitedint| |rewriteIdealWithRemainder| |OMbindTCP| |solve| + |setAttributeButtonStep| |clearFortranOutputStack| |exQuo| + |invertible?| |regime| |crest| |weight| |replace| |lfinfieldint| + |rewriteIdealWithHeadRemainder| |OMopenFile| |triangularSystems| + |resetAttributeButtons| |showFortranOutputStack| |moebius| + |invertibleElseSplit?| |sqfree| |cfirst| |makeVariable| |update| + |lfintegrate| |remainder| |OMopenString| |rootDirectory| + |getButtonValue| |topFortranOutputStack| |rightRecip| + |purelyAlgebraicLeadingMonomial?| |inconsistent?| |sts2stst| + |finiteBound| |lfextlimint| |headRemainder| |OMclose| |hostPlatform| + |mantissa| |decrease| |setFormula!| |leftRecip| + |algebraicCoefficients?| |numFunEvals| |clikeUniv| |sortConstraints| + |BasicMethod| |roughUnitIdeal?| |OMsetEncoding| + |nativeModuleExtension| |map| |increase| |linkToFortran| |leftPower| + |purelyTranscendental?| |setAdaptive| |weierstrass| |sumOfSquares| + |PollardSmallFactor| |roughEqualIdeals?| |OMputApp| |bumprow| + |morphism| |setLegalFortranSourceExtensions| |rightPower| + |purelyAlgebraic?| |adaptive?| |qqq| |splitLinear| |showTheFTable| + |roughSubIdeal?| |OMputAtp| |bumptab| |balancedFactorisation| + |fracPart| |derivationCoordinates| |prepareSubResAlgo| + |setScreenResolution| |integralBasis| |simpleBounds?| |clearTheFTable| + |roughBase?| |OMputAttr| |bumptab1| |mapDown!| |polyPart| |one?| + |internalLastSubResultant| |second| |screenResolution| + |localIntegralBasis| |subst| |linearMatrix| |fTable| |trivialIdeal?| + |OMputBind| |untab| |mapUp!| |fullPartialFraction| |splitSquarefree| + |integralLastSubResultant| |third| |setMaxPoints| |changeWeightLevel| + |linearPart| |palgint0| |collectUpper| |OMputBVar| |bat1| |convert| + |setleaves!| |primeFrobenius| |normalDenom| |toseLastSubResultant| + |maxPoints| |script| |characteristicSerie| |nonLinearPart| + |palgextint0| |collect| |OMputError| |bat| |balancedBinaryTree| + |discreteLog| |totalfract| |toseInvertible?| |setMinPoints| + |characteristicSet| |quadratic?| |interpret| |palglimint0| + |OMputObject| |collectUnder| |tab1| |vector| |sylvesterMatrix| + |decreasePrecision| |pushdterm| |keys| |toseInvertibleSet| |minPoints| + |medialSet| |changeNameToObjf| |palgRDE0| |OMputEndApp| + |mainVariable?| |tab| |differentiate| |bezoutMatrix| |nullary?| + |increasePrecision| |pushucoef| |toseSquareFreePart| |parametric?| + |tex| |Hausdorff| |optAttributes| |palgLODE0| |mainVariables| + |OMputEndAtp| |lex| |bezoutResultant| |arity| |bits| |pushuconst| + |quotedOperators| |plotPolar| |Frobenius| |Nul| |chineseRemainder| + |removeSquaresIfCan| |OMputEndAttr| |slex| |bezoutDiscriminant| + |unitNormalize| |numberOfMonomials| |rur| |debug3D| + |transcendenceDegree| |objects| |exponents| |divisors| + |unprotectedRemoveRedundantFactors| |OMputEndBind| |inverse| + |setright!| |bfEntry| |unit| |members| |create| |numFunEvals3D| + |extensionDegree| |base| |iisqrt2| |eulerPhi| |removeRedundantFactors| + |OMputEndBVar| |maxrow| |setleft!| |bfKeys| |flagFactor| |multiset| + |enterInCache| |setAdaptive3D| |inGroundField?| |iisqrt3| |fibonacci| + |OMputEndError| |certainlySubVariety?| |tableau| |debug| |inspect| + |sqfrFactor| |mergeDifference| |currentCategoryFrame| |adaptive3D?| + |transcendent?| |iiexp| |harmonic| |OMputEndObject| + |possiblyNewVariety?| |listOfLists| D |extract!| |primeFactor| + |squareFreePrim| |currentScope| |setScreenResolution3D| |algebraic?| + |iilog| |jacobi| |probablyZeroDim?| |OMputInteger| |tanSum| |bag| + |nthFlag| |compdegd| |pushNewContour| |screenResolution3D| |sh| + |iisin| |moebiusMu| |selectPolynomials| |OMputFloat| |tanAn| |nand| + |binding| |nthExponent| |univcase| |findBinding| |setMaxPoints3D| + |mirror| |iicos| |numberOfDivisors| |selectOrPolynomials| + |OMputVariable| |tanNa| |binaryTournament| |position!| + |irreducibleFactor| |consnewpol| |contours| |maxPoints3D| |monomial?| + |true| |iitan| |sumOfDivisors| |selectAndPolynomials| |OMputString| + |initTable!| |setProperties| |nilFactor| |nsqfree| + |structuralConstants| |setMinPoints3D| |rquo| |and| |brace| |iicot| + |sumOfKthPowerDivisors| |quasiMonicPolynomials| |OMputSymbol| + |printInfo!| |setProperty| |regularRepresentation| |intChoose| + |minPoints3D| |coordinates| |lquo| |leaves| |iisec| |HermiteIntegrate| + |univariate?| |OMgetApp| |startStats!| |traceMatrix| |lp| |coefChoose| + |high| |tValues| |mindegTerm| |iicsc| |palgint| + |univariatePolynomials| |OMgetAtp| |printStats!| |randomLC| |myDegree| + |low| |tRange| |product| |iiasin| |palgextint| |linear?| |OMgetAttr| + |clearTable!| |binaryTree| |minimize| |normDeriv2| |subset?| |plot| + |LiePolyIfCan| |previous| |value| |iiacos| |palglimint| + |linearPolynomials| |OMgetBind| |usingTable?| |byte| |module| + |plenaryPower| |symmetricDifference| |pointPlot| |trunc| |iiatan| + |sum| |palgRDE| |bivariate?| |OMgetBVar| |printingInfo?| + |rightRegularRepresentation| |c02aff| |difference| |calcRanges| + |degree| |basisOfNucleus| |iiacot| |palgLODE| |bivariatePolynomials| + |OMgetError| |makingStats?| |leftRegularRepresentation| |c02agf| + |intersect| |fixPredicate| |quasiRegular| |countable?| |basisOfCenter| + |iiasec| |splitConstant| |removeRoughlyRedundantFactorsInPols| + |OMgetObject| |extractIfCan| |rightTraceMatrix| |c05adf| |part?| + |patternMatch| |quasiRegular?| |basisOfLeftNucloid| |Aleph| + |binarySearchTree| |iiacsc| |pmComplexintegrate| + |removeRoughlyRedundantFactorsInPol| |OMgetEndApp| |insert!| + |leftTraceMatrix| |c05nbf| |latex| |patternMatchTimes| |constant?| + |basisOfRightNucloid| |nor| |iisinh| |pmintegrate| |interReduce| + |OMgetEndAtp| |interpretString| |rightDiscriminant| |c05pbf| |member?| + |bernoulli| |mindeg| |basisOfCentroid| |iicosh| |infieldint| + |roughBasicSet| |OMgetEndAttr| |stripCommentsAndBlanks| + |leftDiscriminant| |c06eaf| |enumerate| |chebyshevT| |maxdeg| + |radicalOfLeftTraceForm| |iitanh| |extendedint| |linear| |crushedSet| + |OMgetEndBind| |setPrologue!| |concat| |represents| |c06ebf| + |setOfMinN| |chebyshevU| |RemainderList| |showTypeInOutput| |iicoth| + |limitedint| |rewriteSetByReducingWithParticularGenerators| + |OMgetEndBVar| |setTex!| |formula| |mergeFactors| |c06ecf| |elements| + |cyclotomic| |unexpand| |iisech| |integerIfCan| |polynomial| + |rewriteIdealWithQuasiMonicGenerators| |OMgetEndError| |setEpilogue!| + |isMult| |c06ekf| |replaceKthElement| |euler| |triangSolve| |iicsch| + |internalIntegrate| |squareFreeFactors| |OMgetEndObject| |prologue| + |exprToXXP| |id| |c06fpf| |incrementKthElement| |fixedDivisor| + |univariateSolve| |iiasinh| |infieldIntegrate| + |univariatePolynomialsGcds| |OMgetInteger| |epilogue| |exprToUPS| + |c06fqf| |float?| |laguerre| |realSolve| |limitedIntegrate| + |removeRoughlyRedundantFactorsInContents| |OMgetFloat| |endOfFile?| + |derivative| |nrows| |exprToGenUPS| |c06frf| |table| |integer?| + |legendre| |positiveSolve| |stiffnessAndStabilityFactor| + |extendedIntegrate| |removeRedundantFactorsInContents| |OMgetVariable| + |readIfCan!| |constantOperator| |ncols| |localAbs| |c06fuf| |new| + |symbol?| |dmpToHdmp| |squareFree| |stiffnessAndStabilityOfODEIF| + |varselect| |removeRedundantFactorsInPols| |OMgetString| + |readLineIfCan!| |universe| |c06gbf| |string?| |hdmpToDmp| + |linearlyDependentOverZ?| |systemSizeIF| |exquo| |kmax| + |irreducibleFactors| |OMgetSymbol| |readLine!| |comparison| + |currentEnv| |c06gcf| |list?| |pToHdmp| |linearDependenceOverZ| + |expenseOfEvaluationIF| |objectOf| |div| |ksec| + |lazyIrreducibleFactors| |OMgetType| |writeLine!| |equality| + |createIrreduciblePoly| |c06gqf| |pair?| |hdmpToP| + |solveLinearlyOverQ| |accuracyIF| |domainOf| |quo| |vark| + |removeIrreducibleRedundantFactors| |OMencodingBinary| |sign| + |createPrimitivePoly| |c06gsf| |atom?| |dmpToP| + |intermediateResultsIF| |removeConstantTerm| |normalForm| + |OMencodingSGML| |nonQsign| |createNormalPoly| |d01ajf| |null?| + |pToDmp| |subscriptedVariables| |rem| |OMencodingXML| |direction| + |createNormalPrimitivePoly| |d01akf| |startTable!| |sylvesterSequence| + |central?| |generalPosition| |OMencodingUnknown| |createThreeSpace| + |subtractIfCan| |createPrimitiveNormalPoly| |d01alf| |stopTable!| + |sturmSequence| |elliptic?| |quotient| |omError| |cyclicParents| + |setPosition| |nextIrreduciblePoly| |d01amf| |supDimElseRittWu?| + |boundOfCauchy| |doubleResultant| |constantOpIfCan| |zeroDim?| + |errorInfo| |cyclicEqual?| |nextPrimitivePoly| |sturmVariationsOf| + |distdfact| |integerBound| |inRadical?| |errorKind| |fortran| + |cyclicEntries| |nextNormalPoly| |constantLeft| |showTheRoutinesTable| + |left| |lazyVariations| |separateDegrees| |in?| |OMReadError?| + |cyclicCopy| |nextNormalPrimitivePoly| |twist| |deleteRoutine!| + |right| |content| |trace2PowMod| |element?| |numeric| + |OMUnknownSymbol?| |cyclic?| |nextPrimitiveNormalPoly| |setsubMatrix!| + |getExplanations| |totalDegree| |tracePowMod| |zeroDimPrime?| + |radical| |leastAffineMultiple| |subMatrix| |getMeasure| + |minimumDegree| |irreducible?| |zeroDimPrimary?| |init| + |ScanFloatIgnoreSpacesIfCan| |sincos| |reducedQPowers| |swapColumns!| + |changeMeasure| |monomials| |decimal| |primaryDecomp| + |numericalIntegration| |sinhcosh| |rootOfIrreduciblePoly| |swapRows!| + |changeThreshhold| |isPlus| |innerint| |contract| |not| |rk4| + |subresultantVector| |write!| |vertConcat| + |selectMultiDimensionalRoutines| |exteriorDifferential| + |leadingSupport| |rk4a| |primitivePart| |read!| |horizConcat| + |selectNonFiniteRoutines| |factorPolynomial| |scale| + |totalDifferential| |shrinkable| |rk4qc| |pointData| |iomode| + |squareTop| |squareFreePolynomial| |selectSumOfSquaresRoutines| + |varList| |connect| |rules| |homogeneous?| |center| |physicalLength!| + |rk4f| |parent| |close!| |elRow1!| |selectFiniteRoutines| + |gcdPolynomial| |region| |leadingBasisTerm| |physicalLength| + |aromberg| |extractProperty| |reopen!| |elRow2!| + |selectODEIVPRoutines| |torsion?| |points| |ignore?| |flexibleArray| + |asimpson| |extractClosed| |rightUnit| |elColumn2!| + |selectPDERoutines| |torsionIfCan| |getGraph| |computeInt| |operation| + |generalizedInverse| |atrapezoidal| |extractIndex| |leftUnit| + |fractionFreeGauss!| |getGoodPrime| |selectOptimizationRoutines| + |putGraph| |symbol| |checkForZero| |setFieldInfo| |romberg| + |extractPoint| |match?| |rightMinimalPolynomial| |invertIfCan| + |selectIntegrationRoutines| |badNum| |graphs| |doubleFloatFormat| + |pol| |simpson| |traverse| |leftMinimalPolynomial| |copy!| |mix| + |routines| |graphStates| |integer| |bitior| |logGamma| |xn| ** + |trapezoidal| |defineProperty| |associatorDependence| |plus!| + |mainSquareFreePart| |doubleDisc| |graphState| |hypergeometric0F1| + |dAndcExp| |rombergo| |closeComponent| |lieAlgebra?| |minus!| + |mainPrimitivePart| |polyred| |makeViewport2D| |rotatez| |repSq| + |simpsono| |modifyPoint| |jordanAlgebra?| |leftScalarTimes!| + |mainContent| EQ |padicFraction| |viewport2D| |rotatey| |expPot| + |trapezoidalo| |addPointLast| |noncommutativeJordanAlgebra?| + |rightScalarTimes!| |primitivePart!| |padicallyExpand| + |getPickedPoints| |rotatex| |qPot| |inc| |sup| |addPoint2| + |applyRules| |jordanAdmissible?| |times!| |nextsubResultant2| + |numberOfFractionalTerms| |colorDef| |identity| |lookup| |imagE| + |addPoint| |localUnquote| |lieAdmissible?| |power!| |LazardQuotient2| + |nthFractionalTerm| |intensity| |dictionary| |normal?| |imagk| |merge| + |jacobiIdentity?| |lift| |plus| SEGMENT |gradient| |LazardQuotient| + |firstNumer| |lighting| |dioSolve| |prefix| |basis| |imagj| |deepCopy| + |reduce| |powerAssociative?| |divergence| |subResultantChain| + |firstDenom| |clipSurface| |newLine| |normalElement| |imagi| + |shallowCopy| |test| |alternative?| |laplacian| + |halfExtendedSubResultantGcd2| |compactFraction| |showClipRegion| + |copies| |minimalPolynomial| |octon| |numberOfChildren| |flexible?| + |hessian| |halfExtendedSubResultantGcd1| |partialFraction| + |showRegion| |sayLength| |increment| |stack| |ODESolve| |children| + |rightAlternative?| |bandedHessian| |times| |extendedSubResultantGcd| + |gcdPrimitive| |hitherPlane| |setnext!| |charpol| |constDsolve| + |child| |leftAlternative?| |jacobian| |exactQuotient!| + |symmetricGroup| |eyeDistance| |name| |setprevious!| |solve1| + |showTheIFTable| |birth| |error| |antiAssociative?| |bandedJacobian| + |exactQuotient| |alternatingGroup| |perspective| |body| + |shanksDiscLogAlgorithm| |innerEigenvectors| |clearTheIFTable| + |internal?| |assert| |associative?| |duplicates| + |primPartElseUnitCanonical!| |abelianGroup| |zoom| |optimize| + |reflect| |unparse| |iFTable| |root?| |antiCommutative?| + |removeDuplicates!| |primPartElseUnitCanonical| |monom| |cyclicGroup| + |rotate| |reify| |binary| |showIntensityFunctions| |leaf?| + |commutative?| |linears| |lazyResidueClass| |dihedralGroup| + |drawStyle| |separant| |packageCall| |expint| |outputForm| + |rightCharacteristicPolynomial| |ddFact| |monicModulo| |mathieu11| + |outlineRender| |isobaric?| |innerSolve1| |expr| |diff| |sample| + |arg1| |common| |leftCharacteristicPolynomial| |separateFactors| + |lazyPseudoDivide| |mathieu12| |diagonals| |weights| |innerSolve| + |algDsolve| |argscript| |arg2| |rightNorm| |exptMod| + |lazyPremWithDefault| |mathieu22| |axes| |differentialVariables| + |makeEq| |denomLODE| |superscript| |leftNorm| |meshPar2Var| |lazyPquo| + |mathieu23| |controlPanel| |extractBottom!| |modularGcdPrimitive| + |indicialEquations| |subscript| |rightTrace| |meshFun2Var| |lazyPrem| + |mathieu24| |viewpoint| |extractTop!| |modularGcd| |variable| + |indicialEquation| |scripted?| |leftTrace| |box| |meshPar1Var| |pquo| + |janko2| |dimensions| |insertBottom!| |reduction| |denomRicDE| + |resetNew| |someBasis| |ptFunc| |prem| |rubiksGroup| |resize| + |insertTop!| |signAround| |leadingCoefficientRicDE| |symFunc| |insert| + |sort!| |failed| |minimumExponent| |supRittWu?| |youngGroup| |move| + |bottom!| |invmod| |constantCoefficientRicDE| |symbolTableOf| + |copyInto!| |maximumExponent| |RittWuCompare| |lexGroebner| |t| + |modifyPointData| |top!| |powmod| |changeVar| |argumentListOf| |next| + |sorted?| |rowEch| |mainMonomials| |totalGroebner| |subspace| + |dequeue| |mulmod| |ratDsolve| |returnTypeOf| |digit?| |LiePoly| + |rowEchLocal| |mainCoefficients| |expressIdealMember| |makeViewport3D| + |recolor| |flatten| |submod| |indicialEquationAtInfinity| + |printHeader| |datalist| |cn| |quickSort| |rowEchelonLocal| + |leastMonomial| |principalIdeal| |viewport3D| |drawComplex| |addmod| + |reduceLODE| |returnType!| |heapSort| |normalizedDivide| + |mainMonomial| |LagrangeInterpolation| |viewDeltaYDefault| + |drawComplexVectorField| |symmetricRemainder| |singRicDE| + |argumentList!| |shellSort| |directory| |maxint| |quasiMonic?| + |psolve| |viewDeltaXDefault| |eval| |setRealSteps| |positiveRemainder| + |nil| |isQuotient| |polyRicDE| |endSubProgram| |iroot| |outputSpacing| + |reverse| |binaryFunction| |monic?| |wrregime| |viewZoomDefault| + |bit?| |ricDsolve| |currentSubProgram| |zeroOf| |size?| + |outputGeneral| |makeFloatFunction| |deepestInitial| |rdregime| + |viewPhiDefault| |partialQuotients| |point| |algint| |triangulate| + |newSubProgram| |rank| Y |rootsOf| |outputFixed| |unaryFunction| + |iteratedInitials| |bsolve| |viewThetaDefault| |partialDenominators| + |algintegrate| |solveInField| |clearTheSymbolTable| |approximate| + |makeSketch| |weakBiRank| |outputFloating| |compiledFunction| + |deepestTail| |printInfo| |dmp2rfi| |pointColorDefault| + |partialNumerators| |op| |complex| |palgintegrate| |wronskianMatrix| + |showTheSymbolTable| |systemCommand| |inrootof| |biRank| |corrPoly| + |head| |se2rfi| |lineColorDefault| |reducedContinuedFraction| |series| + |palginfieldint| |height| |variationOfParameters| |printTypes| |nary?| + |whileLoop| |droot| |lifting| |mdeg| |pr2dmp| |axesColorDefault| + |push| |bitLength| |factors| |newTypeLists| |unary?| |forLoop| + |lifting1| |mvar| |hasoln| |unitsColorDefault| |bindings| |bitCoef| + |outerProduct| |nthFactor| |typeLists| |sin?| |normal| |radPoly| + |exprex| |relativeApprox| |ParCondList| |pointSizeDefault| |cartesian| + |nthExpon| |externalList| |lists| |zeroVector| |rootPoly| |coerceL| + |rootOf| |redpps| |viewPosDefault| |polar| |completeHensel| |min| + |overlap| |typeList| |zeroSquareMatrix| |goodPoint| |coerceS| + |allRootsOf| |B1solve| |viewSizeDefault| |cylindrical| |union| + |multMonom| |shift| |hcrf| |parametersOf| |identitySquareMatrix| + |chvar| |frobenius| |definingPolynomial| |factorset| |viewDefaults| + |spherical| |build| |hclf| |fortranTypeOf| |depth| |lSpaceBasis| + |find| |maxrank| |viewWriteDefault| |parabolic| |leadingIndex| + |lexico| |empty| |input| |finiteBasis| |anticoord| + |createGenericMatrix| |clipParametric| |minrank| |viewWriteAvailable| + |parabolicCylindrical| |leadingExponent| |OMmakeConn| |compound?| + |options| |principal?| |intcompBasis| |library| |symmetricTensors| + |clipWithRanges| |minset| |var1StepsDefault| |paraboloidal| + |GospersMethod| |OMcloseConn| |getOperands| |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) ((-23) . T) ((-25) . T) ((-37 #0=(-388 (-530))) -1476 (|has| |#1| (-330)) (|has| |#1| (-344))) ((-37 |#1|) . T) ((-37 $) -1476 (|has| |#1| (-522)) (|has| |#1| (-330)) (|has| |#1| (-344)) (|has| |#1| (-289))) ((-34) |has| |#1| (-1121)) ((-93) |has| |#1| (-1121)) ((-99) . T) ((-109 #0# #0#) -1476 (|has| |#1| (-330)) (|has| |#1| (-344))) ((-109 |#1| |#1|) . T) ((-109 $ $) . T) ((-128) . T) ((-138) -1476 (|has| |#1| (-330)) (|has| |#1| (-138))) ((-140) |has| |#1| (-140)) ((-571 (-804)) . T) ((-162) . T) ((-572 (-159 (-208))) |has| |#1| (-960)) ((-572 (-159 (-360))) |has| |#1| (-960)) ((-572 (-506)) |has| |#1| (-572 (-506))) ((-572 (-833 (-360))) |has| |#1| (-572 (-833 (-360)))) ((-572 (-833 (-530))) |has| |#1| (-572 (-833 (-530)))) ((-572 #1=(-1095 |#1|)) . T) ((-214 |#1|) . 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T) ((-358 |#1|) . T) ((-392 |#1|) . T) ((-432) -1450 (|has| |#1| (-850)) (|has| |#1| (-432))) ((-491 |#2| |#1|) |has| |#1| (-216)) ((-491 |#2| $) |has| |#1| (-216)) ((-491 |#3| |#1|) . T) ((-491 |#3| $) . T) ((-491 $ $) . T) ((-522) -1450 (|has| |#1| (-850)) (|has| |#1| (-522)) (|has| |#1| (-432))) ((-599 #0#) |has| |#1| (-37 (-388 (-530)))) ((-599 |#1|) . T) ((-599 $) . T) ((-593 (-530)) |has| |#1| (-593 (-530))) ((-593 |#1|) . T) ((-666 #0#) |has| |#1| (-37 (-388 (-530)))) ((-666 |#1|) |has| |#1| (-162)) ((-666 $) -1450 (|has| |#1| (-850)) (|has| |#1| (-522)) (|has| |#1| (-432))) ((-675) . T) ((-795) |has| |#1| (-795)) ((-841 (-1099)) |has| |#1| (-841 (-1099))) ((-841 |#3|) . T) ((-827 (-360)) -12 (|has| |#1| (-827 (-360))) (|has| |#3| (-827 (-360)))) ((-827 (-530)) -12 (|has| |#1| (-827 (-530))) (|has| |#3| (-827 (-530)))) ((-890 |#1| |#4| |#3|) . 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T) ((-23) . T) ((-46 |#1| |#4|) . T) ((-25) . T) ((-37 #0=(-388 (-530))) |has| |#1| (-37 (-388 (-530)))) ((-37 |#1|) |has| |#1| (-162)) ((-37 $) -1476 (|has| |#1| (-850)) (|has| |#1| (-522)) (|has| |#1| (-432))) ((-99) . T) ((-109 #0# #0#) |has| |#1| (-37 (-388 (-530)))) ((-109 |#1| |#1|) . T) ((-109 $ $) -1476 (|has| |#1| (-850)) (|has| |#1| (-522)) (|has| |#1| (-432)) (|has| |#1| (-162))) ((-128) . T) ((-138) |has| |#1| (-138)) ((-140) |has| |#1| (-140)) ((-571 (-804)) . T) ((-162) -1476 (|has| |#1| (-850)) (|has| |#1| (-522)) (|has| |#1| (-432)) (|has| |#1| (-162))) ((-572 (-506)) -12 (|has| |#1| (-572 (-506))) (|has| |#3| (-572 (-506)))) ((-572 (-833 (-360))) -12 (|has| |#1| (-572 (-833 (-360)))) (|has| |#3| (-572 (-833 (-360))))) ((-572 (-833 (-530))) -12 (|has| |#1| (-572 (-833 (-530)))) (|has| |#3| (-572 (-833 (-530))))) ((-214 |#1|) . T) ((-216) |has| |#1| (-216)) ((-272) -1476 (|has| |#1| (-850)) (|has| |#1| (-522)) (|has| |#1| (-432))) ((-291 $) . T) ((-307 |#1| |#4|) . T) ((-358 |#1|) . T) ((-392 |#1|) . T) ((-432) -1476 (|has| |#1| (-850)) (|has| |#1| (-432))) ((-491 |#2| |#1|) |has| |#1| (-216)) ((-491 |#2| $) |has| |#1| (-216)) ((-491 |#3| |#1|) . T) ((-491 |#3| $) . T) ((-491 $ $) . T) ((-522) -1476 (|has| |#1| (-850)) (|has| |#1| (-522)) (|has| |#1| (-432))) ((-599 #0#) |has| |#1| (-37 (-388 (-530)))) ((-599 |#1|) . T) ((-599 $) . T) ((-593 (-530)) |has| |#1| (-593 (-530))) ((-593 |#1|) . T) ((-666 #0#) |has| |#1| (-37 (-388 (-530)))) ((-666 |#1|) |has| |#1| (-162)) ((-666 $) -1476 (|has| |#1| (-850)) (|has| |#1| (-522)) (|has| |#1| (-432))) ((-675) . T) ((-795) |has| |#1| (-795)) ((-841 (-1099)) |has| |#1| (-841 (-1099))) ((-841 |#3|) . T) ((-827 (-360)) -12 (|has| |#1| (-827 (-360))) (|has| |#3| (-827 (-360)))) ((-827 (-530)) -12 (|has| |#1| (-827 (-530))) (|has| |#3| (-827 (-530)))) ((-890 |#1| |#4| |#3|) . 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NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1189 3100585 3101012 3101474 "WEIER" 3102253 NIL WEIER (NIL T) -7 NIL NIL) (-1188 3099734 3100158 3100200 "VSPACE" 3100336 NIL VSPACE (NIL T) -9 NIL 3100410) (-1187 3099572 3099599 3099690 "VSPACE-" 3099695 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1186 3099318 3099361 3099432 "VOID" 3099523 T VOID (NIL) -8 NIL NIL) (-1185 3097454 3097813 3098219 "VIEW" 3098934 T VIEW (NIL) -7 NIL NIL) (-1184 3093879 3094517 3095254 "VIEWDEF" 3096739 T VIEWDEF (NIL) -7 NIL NIL) (-1183 3083217 3085427 3087600 "VIEW3D" 3091728 T VIEW3D (NIL) -8 NIL NIL) (-1182 3075499 3077128 3078707 "VIEW2D" 3081660 T VIEW2D (NIL) -8 NIL NIL) (-1181 3070908 3075269 3075361 "VECTOR" 3075442 NIL VECTOR (NIL T) -8 NIL NIL) (-1180 3069485 3069744 3070062 "VECTOR2" 3070638 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1179 3063025 3067277 3067320 "VECTCAT" 3068308 NIL VECTCAT (NIL T) -9 NIL 3068892) (-1178 3062039 3062293 3062683 "VECTCAT-" 3062688 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1177 3061520 3061690 3061810 "VARIABLE" 3061954 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1176 3061453 3061458 3061488 "UTYPE" 3061493 T UTYPE (NIL) -9 NIL NIL) (-1175 3060288 3060442 3060703 "UTSODETL" 3061279 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1174 3057728 3058188 3058712 "UTSODE" 3059829 NIL UTSODE (NIL T T) -7 NIL NIL) (-1173 3049572 3055368 3055856 "UTS" 3057297 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1172 3040917 3046282 3046324 "UTSCAT" 3047425 NIL UTSCAT (NIL T) -9 NIL 3048182) (-1171 3038272 3038988 3039976 "UTSCAT-" 3039981 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1170 3037903 3037946 3038077 "UTS2" 3038223 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1169 3032179 3034744 3034787 "URAGG" 3036857 NIL URAGG (NIL T) -9 NIL 3037579) (-1168 3029118 3029981 3031104 "URAGG-" 3031109 NIL URAGG- (NIL T T) -8 NIL NIL) (-1167 3024804 3027735 3028206 "UPXSSING" 3028782 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1166 3016695 3023925 3024205 "UPXS" 3024581 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1165 3009724 3016600 3016671 "UPXSCONS" 3016676 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1164 3000013 3006843 3006904 "UPXSCCA" 3007553 NIL UPXSCCA (NIL T T) -9 NIL 3007794) (-1163 2999652 2999737 2999910 "UPXSCCA-" 2999915 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1162 2989863 2996466 2996508 "UPXSCAT" 2997151 NIL UPXSCAT (NIL T) -9 NIL 2997759) (-1161 2989297 2989376 2989553 "UPXS2" 2989778 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1160 2987951 2988204 2988555 "UPSQFREE" 2989040 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1159 2981842 2984897 2984951 "UPSCAT" 2986100 NIL UPSCAT (NIL T T) -9 NIL 2986874) (-1158 2981047 2981254 2981580 "UPSCAT-" 2981585 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1157 2967133 2975170 2975212 "UPOLYC" 2977290 NIL UPOLYC (NIL T) -9 NIL 2978511) (-1156 2958463 2960888 2964034 "UPOLYC-" 2964039 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1155 2958094 2958137 2958268 "UPOLYC2" 2958414 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1154 2949513 2957663 2957800 "UP" 2958004 NIL UP (NIL NIL T) -8 NIL NIL) (-1153 2948856 2948963 2949126 "UPMP" 2949402 NIL UPMP (NIL T T) -7 NIL NIL) (-1152 2948409 2948490 2948629 "UPDIVP" 2948769 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1151 2946977 2947226 2947542 "UPDECOMP" 2948158 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1150 2946212 2946324 2946509 "UPCDEN" 2946861 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1149 2945735 2945804 2945951 "UP2" 2946137 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1148 2944252 2944939 2945216 "UNISEG" 2945493 NIL UNISEG (NIL T) -8 NIL NIL) (-1147 2943467 2943594 2943799 "UNISEG2" 2944095 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1146 2942527 2942707 2942933 "UNIFACT" 2943283 NIL UNIFACT (NIL T) -7 NIL NIL) (-1145 2926423 2941708 2941958 "ULS" 2942334 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1144 2914388 2926328 2926399 "ULSCONS" 2926404 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1143 2897138 2909151 2909212 "ULSCCAT" 2909924 NIL ULSCCAT (NIL T T) -9 NIL 2910220) (-1142 2896189 2896434 2896821 "ULSCCAT-" 2896826 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1141 2886179 2892696 2892738 "ULSCAT" 2893594 NIL ULSCAT (NIL T) -9 NIL 2894324) (-1140 2885613 2885692 2885869 "ULS2" 2886094 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1139 2884011 2884978 2885008 "UFD" 2885220 T UFD (NIL) -9 NIL 2885334) (-1138 2883805 2883851 2883946 "UFD-" 2883951 NIL UFD- (NIL T) -8 NIL NIL) (-1137 2882887 2883070 2883286 "UDVO" 2883611 T UDVO (NIL) -7 NIL NIL) (-1136 2880703 2881112 2881583 "UDPO" 2882451 NIL UDPO (NIL T) -7 NIL NIL) (-1135 2880636 2880641 2880671 "TYPE" 2880676 T TYPE (NIL) -9 NIL NIL) (-1134 2879607 2879809 2880049 "TWOFACT" 2880430 NIL TWOFACT (NIL T) -7 NIL NIL) (-1133 2878545 2878882 2879145 "TUPLE" 2879379 NIL TUPLE (NIL T) -8 NIL NIL) (-1132 2876236 2876755 2877294 "TUBETOOL" 2878028 T TUBETOOL (NIL) -7 NIL NIL) (-1131 2875085 2875290 2875531 "TUBE" 2876029 NIL TUBE (NIL T) -8 NIL NIL) (-1130 2869809 2874063 2874345 "TS" 2874837 NIL TS (NIL T) -8 NIL NIL) (-1129 2858513 2862605 2862701 "TSETCAT" 2867935 NIL TSETCAT (NIL T T T T) -9 NIL 2869466) (-1128 2853248 2854846 2856736 "TSETCAT-" 2856741 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1127 2847511 2848357 2849299 "TRMANIP" 2852384 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1126 2846952 2847015 2847178 "TRIMAT" 2847443 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1125 2844758 2844995 2845358 "TRIGMNIP" 2846701 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1124 2844278 2844391 2844421 "TRIGCAT" 2844634 T TRIGCAT (NIL) -9 NIL NIL) (-1123 2843947 2844026 2844167 "TRIGCAT-" 2844172 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1122 2840846 2842807 2843087 "TREE" 2843702 NIL TREE (NIL T) -8 NIL NIL) (-1121 2840120 2840648 2840678 "TRANFUN" 2840713 T TRANFUN (NIL) -9 NIL 2840779) (-1120 2839399 2839590 2839870 "TRANFUN-" 2839875 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1119 2839203 2839235 2839296 "TOPSP" 2839360 T TOPSP (NIL) -7 NIL NIL) (-1118 2838555 2838670 2838823 "TOOLSIGN" 2839084 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1117 2837216 2837732 2837971 "TEXTFILE" 2838338 T TEXTFILE (NIL) -8 NIL NIL) (-1116 2835081 2835595 2836033 "TEX" 2836800 T TEX (NIL) -8 NIL NIL) (-1115 2834862 2834893 2834965 "TEX1" 2835044 NIL TEX1 (NIL T) -7 NIL NIL) (-1114 2834510 2834573 2834663 "TEMUTL" 2834794 T TEMUTL (NIL) -7 NIL NIL) (-1113 2832664 2832944 2833269 "TBCMPPK" 2834233 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1112 2824553 2830825 2830881 "TBAGG" 2831281 NIL TBAGG (NIL T T) -9 NIL 2831492) (-1111 2819623 2821111 2822865 "TBAGG-" 2822870 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1110 2819007 2819114 2819259 "TANEXP" 2819512 NIL TANEXP (NIL T) -7 NIL NIL) (-1109 2812508 2818864 2818957 "TABLE" 2818962 NIL TABLE (NIL T T) -8 NIL NIL) (-1108 2811920 2812019 2812157 "TABLEAU" 2812405 NIL TABLEAU (NIL T) -8 NIL NIL) (-1107 2806528 2807748 2808996 "TABLBUMP" 2810706 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1106 2805956 2806056 2806184 "SYSTEM" 2806422 T SYSTEM (NIL) -7 NIL NIL) (-1105 2802419 2803114 2803897 "SYSSOLP" 2805207 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1104 2798710 2799418 2800152 "SYNTAX" 2801707 T SYNTAX (NIL) -8 NIL NIL) (-1103 2795844 2796452 2797090 "SYMTAB" 2798094 T SYMTAB (NIL) -8 NIL NIL) (-1102 2791093 2791995 2792978 "SYMS" 2794883 T SYMS (NIL) -8 NIL NIL) (-1101 2788326 2790553 2790782 "SYMPOLY" 2790898 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1100 2787846 2787921 2788043 "SYMFUNC" 2788238 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1099 2783823 2785083 2785905 "SYMBOL" 2787046 T SYMBOL (NIL) -8 NIL NIL) (-1098 2777362 2779051 2780771 "SWITCH" 2782125 T SWITCH (NIL) -8 NIL NIL) (-1097 2770592 2776189 2776491 "SUTS" 2777117 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1096 2762482 2769713 2769993 "SUPXS" 2770369 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1095 2753974 2762103 2762228 "SUP" 2762391 NIL SUP (NIL T) -8 NIL NIL) (-1094 2753133 2753260 2753477 "SUPFRACF" 2753842 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1093 2752758 2752817 2752928 "SUP2" 2753068 NIL SUP2 (NIL T T) -7 NIL NIL) (-1092 2751176 2751450 2751812 "SUMRF" 2752457 NIL SUMRF (NIL T) -7 NIL NIL) (-1091 2750493 2750559 2750757 "SUMFS" 2751097 NIL SUMFS (NIL T T) -7 NIL NIL) (-1090 2734429 2749674 2749924 "SULS" 2750300 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1089 2733751 2733954 2734094 "SUCH" 2734337 NIL SUCH (NIL T T) -8 NIL NIL) (-1088 2727678 2728690 2729648 "SUBSPACE" 2732839 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1087 2727108 2727198 2727362 "SUBRESP" 2727566 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1086 2720477 2721773 2723084 "STTF" 2725844 NIL STTF (NIL T) -7 NIL NIL) (-1085 2714650 2715770 2716917 "STTFNC" 2719377 NIL STTFNC (NIL T) -7 NIL NIL) (-1084 2706001 2707868 2709661 "STTAYLOR" 2712891 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1083 2699245 2705865 2705948 "STRTBL" 2705953 NIL STRTBL (NIL T) -8 NIL NIL) (-1082 2694636 2699200 2699231 "STRING" 2699236 T STRING (NIL) -8 NIL NIL) (-1081 2689525 2694010 2694040 "STRICAT" 2694099 T STRICAT (NIL) -9 NIL 2694161) (-1080 2682239 2687048 2687668 "STREAM" 2688940 NIL STREAM (NIL T) -8 NIL NIL) (-1079 2681749 2681826 2681970 "STREAM3" 2682156 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1078 2680731 2680914 2681149 "STREAM2" 2681562 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1077 2680419 2680471 2680564 "STREAM1" 2680673 NIL STREAM1 (NIL T) -7 NIL NIL) (-1076 2679435 2679616 2679847 "STINPROD" 2680235 NIL STINPROD (NIL T) -7 NIL NIL) (-1075 2679014 2679198 2679228 "STEP" 2679308 T STEP (NIL) -9 NIL 2679386) (-1074 2672557 2678913 2678990 "STBL" 2678995 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1073 2667733 2671780 2671823 "STAGG" 2671976 NIL STAGG (NIL T) -9 NIL 2672065) (-1072 2665435 2666037 2666909 "STAGG-" 2666914 NIL STAGG- (NIL T T) -8 NIL NIL) (-1071 2663630 2665205 2665297 "STACK" 2665378 NIL STACK (NIL T) -8 NIL NIL) (-1070 2656361 2661777 2662232 "SREGSET" 2663260 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1069 2648801 2650169 2651681 "SRDCMPK" 2654967 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1068 2641769 2646242 2646272 "SRAGG" 2647575 T SRAGG (NIL) -9 NIL 2648183) (-1067 2640786 2641041 2641420 "SRAGG-" 2641425 NIL SRAGG- (NIL T) -8 NIL NIL) (-1066 2635235 2639705 2640132 "SQMATRIX" 2640405 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1065 2628987 2631955 2632681 "SPLTREE" 2634581 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1064 2624977 2625643 2626289 "SPLNODE" 2628413 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1063 2624024 2624257 2624287 "SPFCAT" 2624731 T SPFCAT (NIL) -9 NIL NIL) (-1062 2622761 2622971 2623235 "SPECOUT" 2623782 T SPECOUT (NIL) -7 NIL NIL) (-1061 2622522 2622562 2622631 "SPADPRSR" 2622714 T SPADPRSR (NIL) -7 NIL NIL) (-1060 2614545 2616292 2616334 "SPACEC" 2620657 NIL SPACEC (NIL T) -9 NIL 2622473) (-1059 2612717 2614478 2614526 "SPACE3" 2614531 NIL SPACE3 (NIL T) -8 NIL NIL) (-1058 2611469 2611640 2611931 "SORTPAK" 2612522 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1057 2609525 2609828 2610246 "SOLVETRA" 2611133 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1056 2608536 2608758 2609032 "SOLVESER" 2609298 NIL SOLVESER (NIL T) -7 NIL NIL) (-1055 2603756 2604637 2605639 "SOLVERAD" 2607588 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1054 2599571 2600180 2600909 "SOLVEFOR" 2603123 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1053 2593870 2598922 2599018 "SNTSCAT" 2599023 NIL SNTSCAT (NIL T T T T) -9 NIL 2599093) (-1052 2587974 2592201 2592591 "SMTS" 2593560 NIL SMTS (NIL T T T) -8 NIL NIL) (-1051 2582384 2587863 2587939 "SMP" 2587944 NIL SMP (NIL T T) -8 NIL NIL) (-1050 2580543 2580844 2581242 "SMITH" 2582081 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1049 2573508 2577704 2577806 "SMATCAT" 2579146 NIL SMATCAT (NIL NIL T T T) -9 NIL 2579695) (-1048 2570449 2571272 2572449 "SMATCAT-" 2572454 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1047 2568163 2569686 2569729 "SKAGG" 2569990 NIL SKAGG (NIL T) -9 NIL 2570125) (-1046 2564221 2567267 2567545 "SINT" 2567907 T SINT (NIL) -8 NIL NIL) (-1045 2563993 2564031 2564097 "SIMPAN" 2564177 T SIMPAN (NIL) -7 NIL NIL) (-1044 2563509 2563695 2563794 "SIG" 2563916 T SIG (NIL) -8 NIL NIL) (-1043 2562347 2562568 2562843 "SIGNRF" 2563268 NIL SIGNRF (NIL T) -7 NIL NIL) (-1042 2561156 2561307 2561597 "SIGNEF" 2562176 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1041 2558846 2559300 2559806 "SHP" 2560697 NIL SHP (NIL T NIL) -7 NIL NIL) (-1040 2552699 2558747 2558823 "SHDP" 2558828 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1039 2552189 2552381 2552411 "SGROUP" 2552563 T SGROUP (NIL) -9 NIL 2552650) (-1038 2551959 2552011 2552115 "SGROUP-" 2552120 NIL SGROUP- (NIL T) -8 NIL NIL) (-1037 2548795 2549492 2550215 "SGCF" 2551258 T SGCF (NIL) -7 NIL NIL) (-1036 2543192 2548244 2548340 "SFRTCAT" 2548345 NIL SFRTCAT (NIL T T T T) -9 NIL 2548384) (-1035 2536634 2537649 2538784 "SFRGCD" 2542175 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1034 2529781 2530852 2532037 "SFQCMPK" 2535567 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1033 2529403 2529492 2529602 "SFORT" 2529722 NIL SFORT (NIL T T) -8 NIL NIL) (-1032 2528548 2529243 2529364 "SEXOF" 2529369 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1031 2527682 2528429 2528497 "SEX" 2528502 T SEX (NIL) -8 NIL NIL) (-1030 2522459 2523148 2523243 "SEXCAT" 2527014 NIL SEXCAT (NIL T T T T T) -9 NIL 2527633) (-1029 2519639 2522393 2522441 "SET" 2522446 NIL SET (NIL T) -8 NIL NIL) (-1028 2517890 2518352 2518657 "SETMN" 2519380 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1027 2517498 2517624 2517654 "SETCAT" 2517771 T SETCAT (NIL) -9 NIL 2517855) (-1026 2517278 2517330 2517429 "SETCAT-" 2517434 NIL SETCAT- (NIL T) -8 NIL NIL) (-1025 2513666 2515740 2515783 "SETAGG" 2516653 NIL SETAGG (NIL T) -9 NIL 2516993) (-1024 2513124 2513240 2513477 "SETAGG-" 2513482 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1023 2512328 2512621 2512682 "SEGXCAT" 2512968 NIL SEGXCAT (NIL T T) -9 NIL 2513088) (-1022 2511384 2511994 2512176 "SEG" 2512181 NIL SEG (NIL T) -8 NIL NIL) (-1021 2510291 2510504 2510547 "SEGCAT" 2511129 NIL SEGCAT (NIL T) -9 NIL 2511367) (-1020 2509340 2509670 2509870 "SEGBIND" 2510126 NIL SEGBIND (NIL T) -8 NIL NIL) (-1019 2508961 2509020 2509133 "SEGBIND2" 2509275 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1018 2508180 2508306 2508510 "SEG2" 2508805 NIL SEG2 (NIL T T) -7 NIL NIL) (-1017 2507617 2508115 2508162 "SDVAR" 2508167 NIL SDVAR (NIL T) -8 NIL NIL) (-1016 2499869 2507390 2507518 "SDPOL" 2507523 NIL SDPOL (NIL T) -8 NIL NIL) (-1015 2498462 2498728 2499047 "SCPKG" 2499584 NIL SCPKG (NIL T) -7 NIL NIL) (-1014 2497598 2497778 2497978 "SCOPE" 2498284 T SCOPE (NIL) -8 NIL NIL) (-1013 2496819 2496952 2497131 "SCACHE" 2497453 NIL SCACHE (NIL T) -7 NIL NIL) (-1012 2496258 2496579 2496664 "SAOS" 2496756 T SAOS (NIL) -8 NIL NIL) (-1011 2495823 2495858 2496031 "SAERFFC" 2496217 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1010 2489717 2495720 2495800 "SAE" 2495805 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1009 2489310 2489345 2489504 "SAEFACT" 2489676 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1008 2487631 2487945 2488346 "RURPK" 2488976 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1007 2486271 2486550 2486861 "RULESET" 2487465 NIL RULESET (NIL T T T) -8 NIL NIL) (-1006 2483469 2483972 2484435 "RULE" 2485953 NIL RULE (NIL T T T) -8 NIL NIL) (-1005 2483108 2483263 2483346 "RULECOLD" 2483421 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1004 2477971 2478765 2479684 "RSETGCD" 2482307 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1003 2467257 2472309 2472405 "RSETCAT" 2476497 NIL RSETCAT (NIL T T T T) -9 NIL 2477594) (-1002 2465185 2465724 2466547 "RSETCAT-" 2466552 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1001 2457586 2458961 2460480 "RSDCMPK" 2463784 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1000 2455592 2456033 2456107 "RRCC" 2457193 NIL RRCC (NIL T T) -9 NIL 2457537) (-999 2454945 2455119 2455396 "RRCC-" 2455401 NIL RRCC- (NIL T T T) -8 NIL NIL) (-998 2429312 2438937 2439001 "RPOLCAT" 2449503 NIL RPOLCAT (NIL T T T) -9 NIL 2452661) (-997 2420816 2423154 2426272 "RPOLCAT-" 2426277 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-996 2411882 2419046 2419526 "ROUTINE" 2420356 T ROUTINE (NIL) -8 NIL NIL) (-995 2408587 2411438 2411585 "ROMAN" 2411755 T ROMAN (NIL) -8 NIL NIL) (-994 2406871 2407456 2407714 "ROIRC" 2408392 NIL ROIRC (NIL T T) -8 NIL NIL) (-993 2403276 2405580 2405608 "RNS" 2405904 T RNS (NIL) -9 NIL 2406174) (-992 2401790 2402173 2402704 "RNS-" 2402777 NIL RNS- (NIL T) -8 NIL NIL) (-991 2401216 2401624 2401652 "RNG" 2401657 T RNG (NIL) -9 NIL 2401678) (-990 2400614 2400976 2401016 "RMODULE" 2401076 NIL RMODULE (NIL T) -9 NIL 2401118) (-989 2399466 2399560 2399890 "RMCAT2" 2400515 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-988 2396180 2398649 2398970 "RMATRIX" 2399201 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-987 2389177 2391411 2391523 "RMATCAT" 2394832 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2395814) (-986 2388556 2388703 2389006 "RMATCAT-" 2389011 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-985 2388126 2388201 2388327 "RINTERP" 2388475 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-984 2387177 2387741 2387769 "RING" 2387879 T RING (NIL) -9 NIL 2387973) (-983 2386972 2387016 2387110 "RING-" 2387115 NIL RING- (NIL T) -8 NIL NIL) (-982 2385820 2386057 2386313 "RIDIST" 2386736 T RIDIST (NIL) -7 NIL NIL) (-981 2377140 2385292 2385496 "RGCHAIN" 2385668 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-980 2374145 2374759 2375427 "RF" 2376504 NIL RF (NIL T) -7 NIL NIL) (-979 2373794 2373857 2373958 "RFFACTOR" 2374076 NIL RFFACTOR (NIL T) -7 NIL NIL) (-978 2373522 2373557 2373652 "RFFACT" 2373753 NIL RFFACT (NIL T) -7 NIL NIL) (-977 2371652 2372016 2372396 "RFDIST" 2373162 T RFDIST (NIL) -7 NIL NIL) (-976 2371110 2371202 2371362 "RETSOL" 2371554 NIL RETSOL (NIL T T) -7 NIL NIL) (-975 2370703 2370783 2370824 "RETRACT" 2371014 NIL RETRACT (NIL T) -9 NIL NIL) (-974 2370555 2370580 2370664 "RETRACT-" 2370669 NIL RETRACT- (NIL T T) -8 NIL NIL) (-973 2363413 2370212 2370337 "RESULT" 2370450 T RESULT (NIL) -8 NIL NIL) (-972 2361998 2362687 2362884 "RESRING" 2363316 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-971 2361638 2361687 2361783 "RESLATC" 2361935 NIL RESLATC (NIL T) -7 NIL NIL) (-970 2361347 2361381 2361486 "REPSQ" 2361597 NIL REPSQ (NIL T) -7 NIL NIL) (-969 2358778 2359358 2359958 "REP" 2360767 T REP (NIL) -7 NIL NIL) (-968 2358479 2358513 2358622 "REPDB" 2358737 NIL REPDB (NIL T) -7 NIL NIL) (-967 2352424 2353803 2355023 "REP2" 2357291 NIL REP2 (NIL T) -7 NIL NIL) (-966 2348830 2349511 2350316 "REP1" 2351651 NIL REP1 (NIL T) -7 NIL NIL) (-965 2341574 2346989 2347442 "REGSET" 2348460 NIL REGSET (NIL T T T T) -8 NIL NIL) (-964 2340395 2340730 2340978 "REF" 2341359 NIL REF (NIL T) -8 NIL NIL) (-963 2339776 2339879 2340044 "REDORDER" 2340279 NIL REDORDER (NIL T T) -7 NIL NIL) (-962 2335745 2339010 2339231 "RECLOS" 2339607 NIL RECLOS (NIL T) -8 NIL NIL) (-961 2334802 2334983 2335196 "REALSOLV" 2335552 T REALSOLV (NIL) -7 NIL NIL) (-960 2334650 2334691 2334719 "REAL" 2334724 T REAL (NIL) -9 NIL 2334759) (-959 2331141 2331943 2332825 "REAL0Q" 2333815 NIL REAL0Q (NIL T) -7 NIL NIL) (-958 2326752 2327740 2328799 "REAL0" 2330122 NIL REAL0 (NIL T) -7 NIL NIL) (-957 2326160 2326232 2326437 "RDIV" 2326674 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-956 2325233 2325407 2325618 "RDIST" 2325982 NIL RDIST (NIL T) -7 NIL NIL) (-955 2323837 2324124 2324493 "RDETRS" 2324941 NIL RDETRS (NIL T T) -7 NIL NIL) (-954 2321658 2322112 2322647 "RDETR" 2323379 NIL RDETR (NIL T T) -7 NIL NIL) (-953 2320274 2320552 2320953 "RDEEFS" 2321374 NIL RDEEFS (NIL T T) -7 NIL NIL) (-952 2318774 2319080 2319509 "RDEEF" 2319962 NIL RDEEF (NIL T T) -7 NIL NIL) (-951 2313059 2315991 2316019 "RCFIELD" 2317296 T RCFIELD (NIL) -9 NIL 2318026) (-950 2311128 2311632 2312325 "RCFIELD-" 2312398 NIL RCFIELD- (NIL T) -8 NIL NIL) (-949 2307460 2309245 2309286 "RCAGG" 2310357 NIL RCAGG (NIL T) -9 NIL 2310822) (-948 2307091 2307185 2307345 "RCAGG-" 2307350 NIL RCAGG- (NIL T T) -8 NIL NIL) (-947 2306435 2306547 2306709 "RATRET" 2306975 NIL RATRET (NIL T) -7 NIL NIL) (-946 2305992 2306059 2306178 "RATFACT" 2306363 NIL RATFACT (NIL T) -7 NIL NIL) (-945 2305307 2305427 2305577 "RANDSRC" 2305862 T RANDSRC (NIL) -7 NIL NIL) (-944 2305044 2305088 2305159 "RADUTIL" 2305256 T RADUTIL (NIL) -7 NIL NIL) (-943 2298051 2303787 2304104 "RADIX" 2304759 NIL RADIX (NIL NIL) -8 NIL NIL) (-942 2289620 2297895 2298023 "RADFF" 2298028 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-941 2289272 2289347 2289375 "RADCAT" 2289532 T RADCAT (NIL) -9 NIL NIL) (-940 2289057 2289105 2289202 "RADCAT-" 2289207 NIL RADCAT- (NIL T) -8 NIL NIL) (-939 2287208 2288832 2288921 "QUEUE" 2289001 NIL QUEUE (NIL T) -8 NIL NIL) (-938 2283705 2287145 2287190 "QUAT" 2287195 NIL QUAT (NIL T) -8 NIL NIL) (-937 2283343 2283386 2283513 "QUATCT2" 2283656 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-936 2277137 2280517 2280557 "QUATCAT" 2281336 NIL QUATCAT (NIL T) -9 NIL 2282101) (-935 2273281 2274318 2275705 "QUATCAT-" 2275799 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-934 2270802 2272366 2272407 "QUAGG" 2272782 NIL QUAGG (NIL T) -9 NIL 2272957) (-933 2269727 2270200 2270372 "QFORM" 2270674 NIL QFORM (NIL NIL T) -8 NIL NIL) (-932 2261024 2266282 2266322 "QFCAT" 2266980 NIL QFCAT (NIL T) -9 NIL 2267973) (-931 2256596 2257797 2259388 "QFCAT-" 2259482 NIL QFCAT- (NIL T T) -8 NIL NIL) (-930 2256234 2256277 2256404 "QFCAT2" 2256547 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-929 2255694 2255804 2255934 "QEQUAT" 2256124 T QEQUAT (NIL) -8 NIL NIL) (-928 2248861 2249932 2251115 "QCMPACK" 2254627 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-927 2246437 2246858 2247286 "QALGSET" 2248516 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-926 2245682 2245856 2246088 "QALGSET2" 2246257 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-925 2244373 2244596 2244913 "PWFFINTB" 2245455 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-924 2242561 2242729 2243082 "PUSHVAR" 2244187 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-923 2238479 2239533 2239574 "PTRANFN" 2241458 NIL PTRANFN (NIL T) -9 NIL NIL) (-922 2236891 2237182 2237503 "PTPACK" 2238190 NIL PTPACK (NIL T) -7 NIL NIL) (-921 2236527 2236584 2236691 "PTFUNC2" 2236828 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-920 2231004 2235345 2235385 "PTCAT" 2235753 NIL PTCAT (NIL T) -9 NIL 2235915) (-919 2230662 2230697 2230821 "PSQFR" 2230963 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-918 2229257 2229555 2229889 "PSEUDLIN" 2230360 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-917 2216064 2218429 2220752 "PSETPK" 2227017 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-916 2209151 2211865 2211959 "PSETCAT" 2214940 NIL PSETCAT (NIL T T T T) -9 NIL 2215754) (-915 2206989 2207623 2208442 "PSETCAT-" 2208447 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-914 2206338 2206503 2206531 "PSCURVE" 2206799 T PSCURVE (NIL) -9 NIL 2206966) (-913 2202790 2204316 2204380 "PSCAT" 2205216 NIL PSCAT (NIL T T T) -9 NIL 2205456) (-912 2201854 2202070 2202469 "PSCAT-" 2202474 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-911 2200506 2201139 2201353 "PRTITION" 2201660 T PRTITION (NIL) -8 NIL NIL) (-910 2189604 2191810 2193998 "PRS" 2198368 NIL PRS (NIL T T) -7 NIL NIL) (-909 2187463 2188955 2188995 "PRQAGG" 2189178 NIL PRQAGG (NIL T) -9 NIL 2189280) (-908 2187034 2187136 2187164 "PROPLOG" 2187349 T PROPLOG (NIL) -9 NIL NIL) (-907 2184157 2184722 2185249 "PROPFRML" 2186539 NIL PROPFRML (NIL T) -8 NIL NIL) (-906 2183617 2183727 2183857 "PROPERTY" 2184047 T PROPERTY (NIL) -8 NIL NIL) (-905 2177391 2181783 2182603 "PRODUCT" 2182843 NIL PRODUCT (NIL T T) -8 NIL NIL) (-904 2174667 2176851 2177084 "PR" 2177202 NIL PR (NIL T T) -8 NIL NIL) (-903 2174463 2174495 2174554 "PRINT" 2174628 T PRINT (NIL) -7 NIL NIL) (-902 2173803 2173920 2174072 "PRIMES" 2174343 NIL PRIMES (NIL T) -7 NIL NIL) (-901 2171868 2172269 2172735 "PRIMELT" 2173382 NIL PRIMELT (NIL T) -7 NIL NIL) (-900 2171597 2171646 2171674 "PRIMCAT" 2171798 T PRIMCAT (NIL) -9 NIL NIL) (-899 2167758 2171535 2171580 "PRIMARR" 2171585 NIL PRIMARR (NIL T) -8 NIL NIL) (-898 2166765 2166943 2167171 "PRIMARR2" 2167576 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-897 2166408 2166464 2166575 "PREASSOC" 2166703 NIL PREASSOC (NIL T T) -7 NIL NIL) (-896 2165883 2166016 2166044 "PPCURVE" 2166249 T PPCURVE (NIL) -9 NIL 2166385) (-895 2165505 2165678 2165761 "PORTNUM" 2165820 T PORTNUM (NIL) -8 NIL NIL) (-894 2162864 2163263 2163855 "POLYROOT" 2165086 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-893 2156770 2162470 2162629 "POLY" 2162737 NIL POLY (NIL T) -8 NIL NIL) (-892 2156155 2156213 2156446 "POLYLIFT" 2156706 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-891 2152440 2152889 2153517 "POLYCATQ" 2155700 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-890 2139481 2144878 2144942 "POLYCAT" 2148427 NIL POLYCAT (NIL T T T) -9 NIL 2150354) (-889 2132932 2134793 2137176 "POLYCAT-" 2137181 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-888 2132521 2132589 2132708 "POLY2UP" 2132858 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-887 2132157 2132214 2132321 "POLY2" 2132458 NIL POLY2 (NIL T T) -7 NIL NIL) (-886 2130842 2131081 2131357 "POLUTIL" 2131931 NIL POLUTIL (NIL T T) -7 NIL NIL) (-885 2129204 2129481 2129811 "POLTOPOL" 2130564 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-884 2124727 2129141 2129186 "POINT" 2129191 NIL POINT (NIL T) -8 NIL NIL) (-883 2122914 2123271 2123646 "PNTHEORY" 2124372 T PNTHEORY (NIL) -7 NIL NIL) (-882 2121342 2121639 2122048 "PMTOOLS" 2122612 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-881 2120935 2121013 2121130 "PMSYM" 2121258 NIL PMSYM (NIL T) -7 NIL NIL) (-880 2120445 2120514 2120688 "PMQFCAT" 2120860 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-879 2119800 2119910 2120066 "PMPRED" 2120322 NIL PMPRED (NIL T) -7 NIL NIL) (-878 2119196 2119282 2119443 "PMPREDFS" 2119701 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-877 2117842 2118050 2118434 "PMPLCAT" 2118958 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-876 2117374 2117453 2117605 "PMLSAGG" 2117757 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-875 2116851 2116927 2117107 "PMKERNEL" 2117292 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-874 2116468 2116543 2116656 "PMINS" 2116770 NIL PMINS (NIL T) -7 NIL NIL) (-873 2115898 2115967 2116182 "PMFS" 2116393 NIL PMFS (NIL T T T) -7 NIL NIL) (-872 2115129 2115247 2115451 "PMDOWN" 2115775 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-871 2114292 2114451 2114633 "PMASS" 2114967 T PMASS (NIL) -7 NIL NIL) (-870 2113566 2113677 2113840 "PMASSFS" 2114178 NIL PMASSFS (NIL T T) -7 NIL NIL) (-869 2113221 2113289 2113383 "PLOTTOOL" 2113492 T PLOTTOOL (NIL) -7 NIL NIL) (-868 2107843 2109032 2110180 "PLOT" 2112093 T PLOT (NIL) -8 NIL NIL) (-867 2103657 2104691 2105612 "PLOT3D" 2106942 T PLOT3D (NIL) -8 NIL NIL) (-866 2102569 2102746 2102981 "PLOT1" 2103461 NIL PLOT1 (NIL T) -7 NIL NIL) (-865 2077963 2082635 2087486 "PLEQN" 2097835 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-864 2077281 2077403 2077583 "PINTERP" 2077828 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-863 2076974 2077021 2077124 "PINTERPA" 2077228 NIL PINTERPA (NIL T T) -7 NIL NIL) (-862 2076213 2076780 2076867 "PI" 2076907 T PI (NIL) -8 NIL NIL) (-861 2074605 2075590 2075618 "PID" 2075800 T PID (NIL) -9 NIL 2075934) (-860 2074330 2074367 2074455 "PICOERCE" 2074562 NIL PICOERCE (NIL T) -7 NIL NIL) (-859 2073650 2073789 2073965 "PGROEB" 2074186 NIL PGROEB (NIL T) -7 NIL NIL) (-858 2069237 2070051 2070956 "PGE" 2072765 T PGE (NIL) -7 NIL NIL) (-857 2067361 2067607 2067973 "PGCD" 2068954 NIL PGCD (NIL T T T T) -7 NIL NIL) (-856 2066699 2066802 2066963 "PFRPAC" 2067245 NIL PFRPAC (NIL T) -7 NIL NIL) (-855 2063314 2065247 2065600 "PFR" 2066378 NIL PFR (NIL T) -8 NIL NIL) (-854 2061703 2061947 2062272 "PFOTOOLS" 2063061 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-853 2060236 2060475 2060826 "PFOQ" 2061460 NIL PFOQ (NIL T T T) -7 NIL NIL) (-852 2058713 2058925 2059287 "PFO" 2060020 NIL PFO (NIL T T T T T) -7 NIL NIL) (-851 2055236 2058602 2058671 "PF" 2058676 NIL PF (NIL NIL) -8 NIL NIL) (-850 2052665 2053946 2053974 "PFECAT" 2054559 T PFECAT (NIL) -9 NIL 2054943) (-849 2052110 2052264 2052478 "PFECAT-" 2052483 NIL PFECAT- (NIL T) -8 NIL NIL) (-848 2050714 2050965 2051266 "PFBRU" 2051859 NIL PFBRU (NIL T T) -7 NIL NIL) (-847 2048581 2048932 2049364 "PFBR" 2050365 NIL PFBR (NIL T T T T) -7 NIL NIL) (-846 2044432 2045957 2046633 "PERM" 2047938 NIL PERM (NIL T) -8 NIL NIL) (-845 2039698 2040639 2041509 "PERMGRP" 2043595 NIL PERMGRP (NIL T) -8 NIL NIL) (-844 2037769 2038762 2038803 "PERMCAT" 2039249 NIL PERMCAT (NIL T) -9 NIL 2039554) (-843 2037424 2037465 2037588 "PERMAN" 2037722 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-842 2034864 2036993 2037124 "PENDTREE" 2037326 NIL PENDTREE (NIL T) -8 NIL NIL) (-841 2032937 2033715 2033756 "PDRING" 2034413 NIL PDRING (NIL T) -9 NIL 2034698) (-840 2032040 2032258 2032620 "PDRING-" 2032625 NIL PDRING- (NIL T T) -8 NIL NIL) (-839 2029181 2029932 2030623 "PDEPROB" 2031369 T PDEPROB (NIL) -8 NIL NIL) (-838 2026752 2027248 2027797 "PDEPACK" 2028652 T PDEPACK (NIL) -7 NIL NIL) (-837 2025664 2025854 2026105 "PDECOMP" 2026551 NIL PDECOMP (NIL T T) -7 NIL NIL) (-836 2023276 2024091 2024119 "PDECAT" 2024904 T PDECAT (NIL) -9 NIL 2025615) (-835 2023029 2023062 2023151 "PCOMP" 2023237 NIL PCOMP (NIL T T) -7 NIL NIL) (-834 2021236 2021832 2022128 "PBWLB" 2022759 NIL PBWLB (NIL T) -8 NIL NIL) (-833 2013744 2015313 2016649 "PATTERN" 2019921 NIL PATTERN (NIL T) -8 NIL NIL) (-832 2013376 2013433 2013542 "PATTERN2" 2013681 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-831 2011133 2011521 2011978 "PATTERN1" 2012965 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-830 2008528 2009082 2009563 "PATRES" 2010698 NIL PATRES (NIL T T) -8 NIL NIL) (-829 2008092 2008159 2008291 "PATRES2" 2008455 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-828 2005989 2006389 2006794 "PATMATCH" 2007761 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-827 2005526 2005709 2005750 "PATMAB" 2005857 NIL PATMAB (NIL T) -9 NIL 2005940) (-826 2004071 2004380 2004638 "PATLRES" 2005331 NIL PATLRES (NIL T T T) -8 NIL NIL) (-825 2003617 2003740 2003781 "PATAB" 2003786 NIL PATAB (NIL T) -9 NIL 2003958) (-824 2001098 2001630 2002203 "PARTPERM" 2003064 T PARTPERM (NIL) -7 NIL NIL) (-823 2000719 2000782 2000884 "PARSURF" 2001029 NIL PARSURF (NIL T) -8 NIL NIL) (-822 2000351 2000408 2000517 "PARSU2" 2000656 NIL PARSU2 (NIL T T) -7 NIL NIL) (-821 2000115 2000155 2000222 "PARSER" 2000304 T PARSER (NIL) -7 NIL NIL) (-820 1999736 1999799 1999901 "PARSCURV" 2000046 NIL PARSCURV (NIL T) -8 NIL NIL) (-819 1999368 1999425 1999534 "PARSC2" 1999673 NIL PARSC2 (NIL T T) -7 NIL NIL) (-818 1999007 1999065 1999162 "PARPCURV" 1999304 NIL PARPCURV (NIL T) -8 NIL NIL) (-817 1998639 1998696 1998805 "PARPC2" 1998944 NIL PARPC2 (NIL T T) -7 NIL NIL) (-816 1998159 1998245 1998364 "PAN2EXPR" 1998540 T PAN2EXPR (NIL) -7 NIL NIL) (-815 1996965 1997280 1997508 "PALETTE" 1997951 T PALETTE (NIL) -8 NIL NIL) (-814 1995433 1995970 1996330 "PAIR" 1996651 NIL PAIR (NIL T T) -8 NIL NIL) (-813 1989283 1994692 1994886 "PADICRC" 1995288 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-812 1982491 1988629 1988813 "PADICRAT" 1989131 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-811 1980795 1982428 1982473 "PADIC" 1982478 NIL PADIC (NIL NIL) -8 NIL NIL) (-810 1978000 1979574 1979614 "PADICCT" 1980195 NIL PADICCT (NIL NIL) -9 NIL 1980477) (-809 1976957 1977157 1977425 "PADEPAC" 1977787 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-808 1976169 1976302 1976508 "PADE" 1976819 NIL PADE (NIL T T T) -7 NIL NIL) (-807 1974180 1975012 1975327 "OWP" 1975937 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-806 1973289 1973785 1973957 "OVAR" 1974048 NIL OVAR (NIL NIL) -8 NIL NIL) (-805 1972553 1972674 1972835 "OUT" 1973148 T OUT (NIL) -7 NIL NIL) (-804 1961607 1963778 1965948 "OUTFORM" 1970403 T OUTFORM (NIL) -8 NIL NIL) (-803 1961015 1961336 1961425 "OSI" 1961538 T OSI (NIL) -8 NIL NIL) (-802 1960546 1960884 1960912 "OSGROUP" 1960917 T OSGROUP (NIL) -9 NIL 1960939) (-801 1959291 1959518 1959803 "ORTHPOL" 1960293 NIL ORTHPOL (NIL T) -7 NIL NIL) (-800 1956662 1958952 1959090 "OREUP" 1959234 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-799 1954058 1956355 1956481 "ORESUP" 1956604 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-798 1951593 1952093 1952653 "OREPCTO" 1953547 NIL OREPCTO (NIL T T) -7 NIL NIL) (-797 1945503 1947709 1947749 "OREPCAT" 1950070 NIL OREPCAT (NIL T) -9 NIL 1951173) (-796 1942651 1943433 1944490 "OREPCAT-" 1944495 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-795 1941829 1942101 1942129 "ORDSET" 1942438 T ORDSET (NIL) -9 NIL 1942602) (-794 1941348 1941470 1941663 "ORDSET-" 1941668 NIL ORDSET- (NIL T) -8 NIL NIL) (-793 1939962 1940763 1940791 "ORDRING" 1940993 T ORDRING (NIL) -9 NIL 1941117) (-792 1939607 1939701 1939845 "ORDRING-" 1939850 NIL ORDRING- (NIL T) -8 NIL NIL) (-791 1938970 1939451 1939479 "ORDMON" 1939484 T ORDMON (NIL) -9 NIL 1939505) (-790 1938132 1938279 1938474 "ORDFUNS" 1938819 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-789 1937644 1938003 1938031 "ORDFIN" 1938036 T ORDFIN (NIL) -9 NIL 1938057) (-788 1934156 1936230 1936639 "ORDCOMP" 1937268 NIL ORDCOMP (NIL T) -8 NIL NIL) (-787 1933422 1933549 1933735 "ORDCOMP2" 1934016 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-786 1929929 1930812 1931649 "OPTPROB" 1932605 T OPTPROB (NIL) -8 NIL NIL) (-785 1926771 1927400 1928094 "OPTPACK" 1929255 T OPTPACK (NIL) -7 NIL NIL) (-784 1924497 1925233 1925261 "OPTCAT" 1926076 T OPTCAT (NIL) -9 NIL 1926722) (-783 1924265 1924304 1924370 "OPQUERY" 1924451 T OPQUERY (NIL) -7 NIL NIL) (-782 1921401 1922592 1923092 "OP" 1923797 NIL OP (NIL T) -8 NIL NIL) (-781 1918166 1920198 1920567 "ONECOMP" 1921065 NIL ONECOMP (NIL T) -8 NIL NIL) (-780 1917471 1917586 1917760 "ONECOMP2" 1918038 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-779 1916890 1916996 1917126 "OMSERVER" 1917361 T OMSERVER (NIL) -7 NIL NIL) (-778 1913779 1916331 1916371 "OMSAGG" 1916432 NIL OMSAGG (NIL T) -9 NIL 1916496) (-777 1912402 1912665 1912947 "OMPKG" 1913517 T OMPKG (NIL) -7 NIL NIL) (-776 1911832 1911935 1911963 "OM" 1912262 T OM (NIL) -9 NIL NIL) (-775 1910371 1911384 1911552 "OMLO" 1911713 NIL OMLO (NIL T T) -8 NIL NIL) (-774 1909301 1909448 1909674 "OMEXPR" 1910197 NIL OMEXPR (NIL T) -7 NIL NIL) (-773 1908619 1908847 1908983 "OMERR" 1909185 T OMERR (NIL) -8 NIL NIL) (-772 1907797 1908040 1908200 "OMERRK" 1908479 T OMERRK (NIL) -8 NIL NIL) (-771 1907275 1907474 1907582 "OMENC" 1907709 T OMENC (NIL) -8 NIL NIL) (-770 1901170 1902355 1903526 "OMDEV" 1906124 T OMDEV (NIL) -8 NIL NIL) (-769 1900239 1900410 1900604 "OMCONN" 1900996 T OMCONN (NIL) -8 NIL NIL) (-768 1898855 1899841 1899869 "OINTDOM" 1899874 T OINTDOM (NIL) -9 NIL 1899895) (-767 1894617 1895847 1896562 "OFMONOID" 1898172 NIL OFMONOID (NIL T) -8 NIL NIL) (-766 1894055 1894554 1894599 "ODVAR" 1894604 NIL ODVAR (NIL T) -8 NIL NIL) (-765 1891180 1893552 1893737 "ODR" 1893930 NIL ODR (NIL T T NIL) -8 NIL NIL) (-764 1883486 1890959 1891083 "ODPOL" 1891088 NIL ODPOL (NIL T) -8 NIL NIL) (-763 1877309 1883358 1883463 "ODP" 1883468 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-762 1876075 1876290 1876565 "ODETOOLS" 1877083 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-761 1873044 1873700 1874416 "ODESYS" 1875408 NIL ODESYS (NIL T T) -7 NIL NIL) (-760 1867948 1868856 1869879 "ODERTRIC" 1872119 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-759 1867374 1867456 1867650 "ODERED" 1867860 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-758 1864276 1864824 1865499 "ODERAT" 1866797 NIL ODERAT (NIL T T) -7 NIL NIL) (-757 1861244 1861708 1862304 "ODEPRRIC" 1863805 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-756 1859113 1859682 1860191 "ODEPROB" 1860755 T ODEPROB (NIL) -8 NIL NIL) (-755 1855645 1856128 1856774 "ODEPRIM" 1858592 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-754 1854898 1855000 1855258 "ODEPAL" 1855537 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-753 1851100 1851881 1852735 "ODEPACK" 1854064 T ODEPACK (NIL) -7 NIL NIL) (-752 1850137 1850244 1850472 "ODEINT" 1850989 NIL ODEINT (NIL T T) -7 NIL NIL) (-751 1844238 1845663 1847110 "ODEIFTBL" 1848710 T ODEIFTBL (NIL) -8 NIL NIL) (-750 1839582 1840368 1841326 "ODEEF" 1843397 NIL ODEEF (NIL T T) -7 NIL NIL) (-749 1838919 1839008 1839237 "ODECONST" 1839487 NIL ODECONST (NIL T T T) -7 NIL NIL) (-748 1837077 1837710 1837738 "ODECAT" 1838341 T ODECAT (NIL) -9 NIL 1838870) (-747 1833949 1836789 1836908 "OCT" 1836990 NIL OCT (NIL T) -8 NIL NIL) (-746 1833587 1833630 1833757 "OCTCT2" 1833900 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-745 1828421 1830859 1830899 "OC" 1831995 NIL OC (NIL T) -9 NIL 1832852) (-744 1825648 1826396 1827386 "OC-" 1827480 NIL OC- (NIL T T) -8 NIL NIL) (-743 1825027 1825469 1825497 "OCAMON" 1825502 T OCAMON (NIL) -9 NIL 1825523) (-742 1824585 1824900 1824928 "OASGP" 1824933 T OASGP (NIL) -9 NIL 1824953) (-741 1823873 1824336 1824364 "OAMONS" 1824404 T OAMONS (NIL) -9 NIL 1824447) (-740 1823314 1823721 1823749 "OAMON" 1823754 T OAMON (NIL) -9 NIL 1823774) (-739 1822619 1823111 1823139 "OAGROUP" 1823144 T OAGROUP (NIL) -9 NIL 1823164) (-738 1822309 1822359 1822447 "NUMTUBE" 1822563 NIL NUMTUBE (NIL T) -7 NIL NIL) (-737 1815882 1817400 1818936 "NUMQUAD" 1820793 T NUMQUAD (NIL) -7 NIL NIL) (-736 1811638 1812626 1813651 "NUMODE" 1814877 T NUMODE (NIL) -7 NIL NIL) (-735 1809042 1809888 1809916 "NUMINT" 1810833 T NUMINT (NIL) -9 NIL 1811589) (-734 1807990 1808187 1808405 "NUMFMT" 1808844 T NUMFMT (NIL) -7 NIL NIL) (-733 1794369 1797306 1799836 "NUMERIC" 1805499 NIL NUMERIC (NIL T) -7 NIL NIL) (-732 1788768 1793820 1793914 "NTSCAT" 1793919 NIL NTSCAT (NIL T T T T) -9 NIL 1793958) (-731 1787962 1788127 1788320 "NTPOLFN" 1788607 NIL NTPOLFN (NIL T) -7 NIL NIL) (-730 1775778 1784804 1785614 "NSUP" 1787184 NIL NSUP (NIL T) -8 NIL NIL) (-729 1775414 1775471 1775578 "NSUP2" 1775715 NIL NSUP2 (NIL T T) -7 NIL NIL) (-728 1765376 1775193 1775323 "NSMP" 1775328 NIL NSMP (NIL T T) -8 NIL NIL) (-727 1763808 1764109 1764466 "NREP" 1765064 NIL NREP (NIL T) -7 NIL NIL) (-726 1762399 1762651 1763009 "NPCOEF" 1763551 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-725 1761465 1761580 1761796 "NORMRETR" 1762280 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-724 1759512 1759802 1760210 "NORMPK" 1761173 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-723 1759197 1759225 1759349 "NORMMA" 1759478 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-722 1759024 1759154 1759183 "NONE" 1759188 T NONE (NIL) -8 NIL NIL) (-721 1758813 1758842 1758911 "NONE1" 1758988 NIL NONE1 (NIL T) -7 NIL NIL) (-720 1758298 1758360 1758545 "NODE1" 1758745 NIL NODE1 (NIL T T) -7 NIL NIL) (-719 1756592 1757461 1757716 "NNI" 1758063 T NNI (NIL) -8 NIL NIL) (-718 1755012 1755325 1755689 "NLINSOL" 1756260 NIL NLINSOL (NIL T) -7 NIL NIL) (-717 1751179 1752147 1753069 "NIPROB" 1754110 T NIPROB (NIL) -8 NIL NIL) (-716 1749936 1750170 1750472 "NFINTBAS" 1750941 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-715 1748644 1748875 1749156 "NCODIV" 1749704 NIL NCODIV (NIL T T) -7 NIL NIL) (-714 1748406 1748443 1748518 "NCNTFRAC" 1748601 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-713 1746586 1746950 1747370 "NCEP" 1748031 NIL NCEP (NIL T) -7 NIL NIL) (-712 1745498 1746237 1746265 "NASRING" 1746375 T NASRING (NIL) -9 NIL 1746449) (-711 1745293 1745337 1745431 "NASRING-" 1745436 NIL NASRING- (NIL T) -8 NIL NIL) (-710 1744447 1744946 1744974 "NARNG" 1745091 T NARNG (NIL) -9 NIL 1745182) (-709 1744139 1744206 1744340 "NARNG-" 1744345 NIL NARNG- (NIL T) -8 NIL NIL) (-708 1743018 1743225 1743460 "NAGSP" 1743924 T NAGSP (NIL) -7 NIL NIL) (-707 1734442 1736088 1737723 "NAGS" 1741403 T NAGS (NIL) -7 NIL NIL) (-706 1733006 1733310 1733637 "NAGF07" 1734135 T NAGF07 (NIL) -7 NIL NIL) (-705 1727588 1728868 1730164 "NAGF04" 1731730 T NAGF04 (NIL) -7 NIL NIL) (-704 1720620 1722218 1723835 "NAGF02" 1725991 T NAGF02 (NIL) -7 NIL NIL) (-703 1715884 1716974 1718081 "NAGF01" 1719533 T NAGF01 (NIL) -7 NIL NIL) (-702 1709544 1711102 1712679 "NAGE04" 1714327 T NAGE04 (NIL) -7 NIL NIL) (-701 1700785 1702888 1705000 "NAGE02" 1707452 T NAGE02 (NIL) -7 NIL NIL) (-700 1696778 1697715 1698669 "NAGE01" 1699851 T NAGE01 (NIL) -7 NIL NIL) (-699 1694585 1695116 1695671 "NAGD03" 1696243 T NAGD03 (NIL) -7 NIL NIL) (-698 1686371 1688290 1690235 "NAGD02" 1692660 T NAGD02 (NIL) -7 NIL NIL) (-697 1680230 1681643 1683071 "NAGD01" 1684963 T NAGD01 (NIL) -7 NIL NIL) (-696 1676487 1677297 1678122 "NAGC06" 1679425 T NAGC06 (NIL) -7 NIL NIL) (-695 1674964 1675293 1675646 "NAGC05" 1676154 T NAGC05 (NIL) -7 NIL NIL) (-694 1674348 1674465 1674607 "NAGC02" 1674842 T NAGC02 (NIL) -7 NIL NIL) (-693 1673410 1673967 1674007 "NAALG" 1674086 NIL NAALG (NIL T) -9 NIL 1674147) (-692 1673245 1673274 1673364 "NAALG-" 1673369 NIL NAALG- (NIL T T) -8 NIL NIL) (-691 1667195 1668303 1669490 "MULTSQFR" 1672141 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-690 1666514 1666589 1666773 "MULTFACT" 1667107 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-689 1659708 1663619 1663671 "MTSCAT" 1664731 NIL MTSCAT (NIL T T) -9 NIL 1665245) (-688 1659420 1659474 1659566 "MTHING" 1659648 NIL MTHING (NIL T) -7 NIL NIL) (-687 1659212 1659245 1659305 "MSYSCMD" 1659380 T MSYSCMD (NIL) -7 NIL NIL) (-686 1655324 1657967 1658287 "MSET" 1658925 NIL MSET (NIL T) -8 NIL NIL) (-685 1652420 1654886 1654927 "MSETAGG" 1654932 NIL MSETAGG (NIL T) -9 NIL 1654966) (-684 1648276 1649818 1650559 "MRING" 1651723 NIL MRING (NIL T T) -8 NIL NIL) (-683 1647846 1647913 1648042 "MRF2" 1648203 NIL MRF2 (NIL T T T) -7 NIL NIL) (-682 1647464 1647499 1647643 "MRATFAC" 1647805 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-681 1645076 1645371 1645802 "MPRFF" 1647169 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-680 1639096 1644931 1645027 "MPOLY" 1645032 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-679 1638586 1638621 1638829 "MPCPF" 1639055 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-678 1638102 1638145 1638328 "MPC3" 1638537 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-677 1637303 1637384 1637603 "MPC2" 1638017 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-676 1635604 1635941 1636331 "MONOTOOL" 1636963 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-675 1634729 1635064 1635092 "MONOID" 1635369 T MONOID (NIL) -9 NIL 1635541) (-674 1634107 1634270 1634513 "MONOID-" 1634518 NIL MONOID- (NIL T) -8 NIL NIL) (-673 1625088 1631074 1631133 "MONOGEN" 1631807 NIL MONOGEN (NIL T T) -9 NIL 1632263) (-672 1622306 1623041 1624041 "MONOGEN-" 1624160 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-671 1621166 1621586 1621614 "MONADWU" 1622006 T MONADWU (NIL) -9 NIL 1622244) (-670 1620538 1620697 1620945 "MONADWU-" 1620950 NIL MONADWU- (NIL T) -8 NIL NIL) (-669 1619924 1620142 1620170 "MONAD" 1620377 T MONAD (NIL) -9 NIL 1620489) (-668 1619609 1619687 1619819 "MONAD-" 1619824 NIL MONAD- (NIL T) -8 NIL NIL) (-667 1617860 1618522 1618801 "MOEBIUS" 1619362 NIL MOEBIUS (NIL T) -8 NIL NIL) (-666 1617254 1617632 1617672 "MODULE" 1617677 NIL MODULE (NIL T) -9 NIL 1617703) (-665 1616822 1616918 1617108 "MODULE-" 1617113 NIL MODULE- (NIL T T) -8 NIL NIL) (-664 1614493 1615188 1615514 "MODRING" 1616647 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-663 1611449 1612614 1613131 "MODOP" 1614025 NIL MODOP (NIL T T) -8 NIL NIL) (-662 1609636 1610088 1610429 "MODMONOM" 1611248 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-661 1599315 1607840 1608262 "MODMON" 1609264 NIL MODMON (NIL T T) -8 NIL NIL) (-660 1596441 1598159 1598435 "MODFIELD" 1599190 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-659 1595445 1595722 1595912 "MMLFORM" 1596271 T MMLFORM (NIL) -8 NIL NIL) (-658 1594971 1595014 1595193 "MMAP" 1595396 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-657 1593208 1593985 1594025 "MLO" 1594442 NIL MLO (NIL T) -9 NIL 1594683) (-656 1590575 1591090 1591692 "MLIFT" 1592689 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-655 1589966 1590050 1590204 "MKUCFUNC" 1590486 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-654 1589565 1589635 1589758 "MKRECORD" 1589889 NIL MKRECORD (NIL T T) -7 NIL NIL) (-653 1588613 1588774 1589002 "MKFUNC" 1589376 NIL MKFUNC (NIL T) -7 NIL NIL) (-652 1588001 1588105 1588261 "MKFLCFN" 1588496 NIL MKFLCFN (NIL T) -7 NIL NIL) (-651 1587427 1587794 1587883 "MKCHSET" 1587945 NIL MKCHSET (NIL T) -8 NIL NIL) (-650 1586704 1586806 1586991 "MKBCFUNC" 1587320 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-649 1583388 1586258 1586394 "MINT" 1586588 T MINT (NIL) -8 NIL NIL) (-648 1582200 1582443 1582720 "MHROWRED" 1583143 NIL MHROWRED (NIL T) -7 NIL NIL) (-647 1577471 1580645 1581069 "MFLOAT" 1581796 T MFLOAT (NIL) -8 NIL NIL) (-646 1576828 1576904 1577075 "MFINFACT" 1577383 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-645 1573143 1573991 1574875 "MESH" 1575964 T MESH (NIL) -7 NIL NIL) (-644 1571533 1571845 1572198 "MDDFACT" 1572830 NIL MDDFACT (NIL T) -7 NIL NIL) (-643 1568376 1570693 1570734 "MDAGG" 1570989 NIL MDAGG (NIL T) -9 NIL 1571132) (-642 1558074 1567669 1567876 "MCMPLX" 1568189 T MCMPLX (NIL) -8 NIL NIL) (-641 1557215 1557361 1557561 "MCDEN" 1557923 NIL MCDEN (NIL T T) -7 NIL NIL) (-640 1555105 1555375 1555755 "MCALCFN" 1556945 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-639 1554016 1554189 1554430 "MAYBE" 1554903 NIL MAYBE (NIL T) -8 NIL NIL) (-638 1551638 1552161 1552722 "MATSTOR" 1553487 NIL MATSTOR (NIL T) -7 NIL NIL) (-637 1547647 1551013 1551260 "MATRIX" 1551423 NIL MATRIX (NIL T) -8 NIL NIL) (-636 1543416 1544120 1544856 "MATLIN" 1547004 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-635 1533614 1536752 1536828 "MATCAT" 1541666 NIL MATCAT (NIL T T T) -9 NIL 1543083) (-634 1529979 1530992 1532347 "MATCAT-" 1532352 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-633 1528581 1528734 1529065 "MATCAT2" 1529814 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-632 1526693 1527017 1527401 "MAPPKG3" 1528256 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-631 1525674 1525847 1526069 "MAPPKG2" 1526517 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-630 1524173 1524457 1524784 "MAPPKG1" 1525380 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-629 1523784 1523842 1523965 "MAPHACK3" 1524109 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-628 1523376 1523437 1523551 "MAPHACK2" 1523716 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-627 1522814 1522917 1523059 "MAPHACK1" 1523267 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-626 1520922 1521516 1521819 "MAGMA" 1522543 NIL MAGMA (NIL T) -8 NIL NIL) (-625 1517397 1519166 1519626 "M3D" 1520495 NIL M3D (NIL T) -8 NIL NIL) (-624 1511553 1515768 1515809 "LZSTAGG" 1516591 NIL LZSTAGG (NIL T) -9 NIL 1516886) (-623 1507526 1508684 1510141 "LZSTAGG-" 1510146 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-622 1504642 1505419 1505905 "LWORD" 1507072 NIL LWORD (NIL T) -8 NIL NIL) (-621 1497802 1504413 1504547 "LSQM" 1504552 NIL LSQM (NIL NIL T) -8 NIL NIL) (-620 1497026 1497165 1497393 "LSPP" 1497657 NIL LSPP (NIL T T T T) -7 NIL NIL) (-619 1494838 1495139 1495595 "LSMP" 1496715 NIL LSMP (NIL T T T T) -7 NIL NIL) (-618 1491617 1492291 1493021 "LSMP1" 1494140 NIL LSMP1 (NIL T) -7 NIL NIL) (-617 1485544 1490786 1490827 "LSAGG" 1490889 NIL LSAGG (NIL T) -9 NIL 1490967) (-616 1482239 1483163 1484376 "LSAGG-" 1484381 NIL LSAGG- (NIL T T) -8 NIL NIL) (-615 1479865 1481383 1481632 "LPOLY" 1482034 NIL LPOLY (NIL T T) -8 NIL NIL) (-614 1479447 1479532 1479655 "LPEFRAC" 1479774 NIL LPEFRAC (NIL T) -7 NIL NIL) (-613 1477794 1478541 1478794 "LO" 1479279 NIL LO (NIL T T T) -8 NIL NIL) (-612 1477448 1477560 1477588 "LOGIC" 1477699 T LOGIC (NIL) -9 NIL 1477779) (-611 1477310 1477333 1477404 "LOGIC-" 1477409 NIL LOGIC- (NIL T) -8 NIL NIL) (-610 1476503 1476643 1476836 "LODOOPS" 1477166 NIL LODOOPS (NIL T T) -7 NIL NIL) (-609 1473921 1476420 1476485 "LODO" 1476490 NIL LODO (NIL T NIL) -8 NIL NIL) (-608 1472467 1472702 1473053 "LODOF" 1473668 NIL LODOF (NIL T T) -7 NIL NIL) (-607 1468887 1471323 1471363 "LODOCAT" 1471795 NIL LODOCAT (NIL T) -9 NIL 1472006) (-606 1468621 1468679 1468805 "LODOCAT-" 1468810 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-605 1465935 1468462 1468580 "LODO2" 1468585 NIL LODO2 (NIL T T) -8 NIL NIL) (-604 1463364 1465872 1465917 "LODO1" 1465922 NIL LODO1 (NIL T) -8 NIL NIL) (-603 1462227 1462392 1462703 "LODEEF" 1463187 NIL LODEEF (NIL T T T) -7 NIL NIL) (-602 1457514 1460358 1460399 "LNAGG" 1461346 NIL LNAGG (NIL T) -9 NIL 1461790) (-601 1456661 1456875 1457217 "LNAGG-" 1457222 NIL LNAGG- (NIL T T) -8 NIL NIL) (-600 1452826 1453588 1454226 "LMOPS" 1456077 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-599 1452224 1452586 1452626 "LMODULE" 1452686 NIL LMODULE (NIL T) -9 NIL 1452728) (-598 1449470 1451869 1451992 "LMDICT" 1452134 NIL LMDICT (NIL T) -8 NIL NIL) (-597 1442697 1448416 1448714 "LIST" 1449205 NIL LIST (NIL T) -8 NIL NIL) (-596 1442222 1442296 1442435 "LIST3" 1442617 NIL LIST3 (NIL T T T) -7 NIL NIL) (-595 1441229 1441407 1441635 "LIST2" 1442040 NIL LIST2 (NIL T T) -7 NIL NIL) (-594 1439363 1439675 1440074 "LIST2MAP" 1440876 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-593 1438076 1438756 1438796 "LINEXP" 1439049 NIL LINEXP (NIL T) -9 NIL 1439197) (-592 1436723 1436983 1437280 "LINDEP" 1437828 NIL LINDEP (NIL T T) -7 NIL NIL) (-591 1433490 1434209 1434986 "LIMITRF" 1435978 NIL LIMITRF (NIL T) -7 NIL NIL) (-590 1431770 1432065 1432480 "LIMITPS" 1433185 NIL LIMITPS (NIL T T) -7 NIL NIL) (-589 1426225 1431281 1431509 "LIE" 1431591 NIL LIE (NIL T T) -8 NIL NIL) (-588 1425276 1425719 1425759 "LIECAT" 1425899 NIL LIECAT (NIL T) -9 NIL 1426050) (-587 1425117 1425144 1425232 "LIECAT-" 1425237 NIL LIECAT- (NIL T T) -8 NIL NIL) (-586 1417729 1424566 1424731 "LIB" 1424972 T LIB (NIL) -8 NIL NIL) (-585 1413366 1414247 1415182 "LGROBP" 1416846 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-584 1411232 1411506 1411868 "LF" 1413087 NIL LF (NIL T T) -7 NIL NIL) (-583 1410072 1410764 1410792 "LFCAT" 1410999 T LFCAT (NIL) -9 NIL 1411138) (-582 1406984 1407610 1408296 "LEXTRIPK" 1409438 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-581 1403690 1404554 1405057 "LEXP" 1406564 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-580 1402088 1402401 1402802 "LEADCDET" 1403372 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-579 1401281 1401355 1401583 "LAZM3PK" 1402009 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-578 1396198 1399360 1399897 "LAUPOL" 1400794 NIL LAUPOL (NIL T T) -8 NIL NIL) (-577 1395765 1395809 1395976 "LAPLACE" 1396148 NIL LAPLACE (NIL T T) -7 NIL NIL) (-576 1393693 1394866 1395117 "LA" 1395598 NIL LA (NIL T T T) -8 NIL NIL) (-575 1392756 1393350 1393390 "LALG" 1393451 NIL LALG (NIL T) -9 NIL 1393509) (-574 1392471 1392530 1392665 "LALG-" 1392670 NIL LALG- (NIL T T) -8 NIL NIL) (-573 1391381 1391568 1391865 "KOVACIC" 1392271 NIL KOVACIC (NIL T T) -7 NIL NIL) (-572 1391216 1391240 1391281 "KONVERT" 1391343 NIL KONVERT (NIL T) -9 NIL NIL) (-571 1391051 1391075 1391116 "KOERCE" 1391178 NIL KOERCE (NIL T) -9 NIL NIL) (-570 1388785 1389545 1389938 "KERNEL" 1390690 NIL KERNEL (NIL T) -8 NIL NIL) (-569 1388287 1388368 1388498 "KERNEL2" 1388699 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-568 1382139 1386827 1386881 "KDAGG" 1387258 NIL KDAGG (NIL T T) -9 NIL 1387464) (-567 1381668 1381792 1381997 "KDAGG-" 1382002 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-566 1374843 1381329 1381484 "KAFILE" 1381546 NIL KAFILE (NIL T) -8 NIL NIL) (-565 1369298 1374354 1374582 "JORDAN" 1374664 NIL JORDAN (NIL T T) -8 NIL NIL) (-564 1369027 1369086 1369173 "JAVACODE" 1369231 T JAVACODE (NIL) -8 NIL NIL) (-563 1365327 1367233 1367287 "IXAGG" 1368216 NIL IXAGG (NIL T T) -9 NIL 1368675) (-562 1364246 1364552 1364971 "IXAGG-" 1364976 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-561 1359831 1364168 1364227 "IVECTOR" 1364232 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-560 1358597 1358834 1359100 "ITUPLE" 1359598 NIL ITUPLE (NIL T) -8 NIL NIL) (-559 1357033 1357210 1357516 "ITRIGMNP" 1358419 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-558 1355778 1355982 1356265 "ITFUN3" 1356809 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-557 1355410 1355467 1355576 "ITFUN2" 1355715 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-556 1353212 1354283 1354580 "ITAYLOR" 1355145 NIL ITAYLOR (NIL T) -8 NIL NIL) (-555 1342200 1347398 1348557 "ISUPS" 1352085 NIL ISUPS (NIL T) -8 NIL NIL) (-554 1341304 1341444 1341680 "ISUMP" 1342047 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-553 1336568 1341105 1341184 "ISTRING" 1341257 NIL ISTRING (NIL NIL) -8 NIL NIL) (-552 1335781 1335862 1336077 "IRURPK" 1336482 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-551 1334717 1334918 1335158 "IRSN" 1335561 T IRSN (NIL) -7 NIL NIL) (-550 1332752 1333107 1333542 "IRRF2F" 1334355 NIL IRRF2F (NIL T) -7 NIL NIL) (-549 1332499 1332537 1332613 "IRREDFFX" 1332708 NIL IRREDFFX (NIL T) -7 NIL NIL) (-548 1331114 1331373 1331672 "IROOT" 1332232 NIL IROOT (NIL T) -7 NIL NIL) (-547 1327752 1328803 1329493 "IR" 1330456 NIL IR (NIL T) -8 NIL NIL) (-546 1325365 1325860 1326426 "IR2" 1327230 NIL IR2 (NIL T T) -7 NIL NIL) (-545 1324441 1324554 1324774 "IR2F" 1325248 NIL IR2F (NIL T T) -7 NIL NIL) (-544 1324232 1324266 1324326 "IPRNTPK" 1324401 T IPRNTPK (NIL) -7 NIL NIL) (-543 1320786 1324121 1324190 "IPF" 1324195 NIL IPF (NIL NIL) -8 NIL NIL) (-542 1319103 1320711 1320768 "IPADIC" 1320773 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-541 1318602 1318660 1318849 "INVLAPLA" 1319039 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-540 1308251 1310604 1312990 "INTTR" 1316266 NIL INTTR (NIL T T) -7 NIL NIL) (-539 1304599 1305340 1306203 "INTTOOLS" 1307437 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-538 1304185 1304276 1304393 "INTSLPE" 1304502 T INTSLPE (NIL) -7 NIL NIL) (-537 1302135 1304108 1304167 "INTRVL" 1304172 NIL INTRVL (NIL T) -8 NIL NIL) (-536 1299742 1300254 1300828 "INTRF" 1301620 NIL INTRF (NIL T) -7 NIL NIL) (-535 1299157 1299254 1299395 "INTRET" 1299640 NIL INTRET (NIL T) -7 NIL NIL) (-534 1297159 1297548 1298017 "INTRAT" 1298765 NIL INTRAT (NIL T T) -7 NIL NIL) (-533 1294392 1294975 1295600 "INTPM" 1296644 NIL INTPM (NIL T T) -7 NIL NIL) (-532 1291101 1291700 1292444 "INTPAF" 1293778 NIL INTPAF (NIL T T T) -7 NIL NIL) (-531 1286344 1287290 1288325 "INTPACK" 1290086 T INTPACK (NIL) -7 NIL NIL) (-530 1283198 1286073 1286200 "INT" 1286237 T INT (NIL) -8 NIL NIL) (-529 1282450 1282602 1282810 "INTHERTR" 1283040 NIL INTHERTR (NIL T T) -7 NIL NIL) (-528 1281889 1281969 1282157 "INTHERAL" 1282364 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-527 1279735 1280178 1280635 "INTHEORY" 1281452 T INTHEORY (NIL) -7 NIL NIL) (-526 1271057 1272678 1274456 "INTG0" 1278087 NIL INTG0 (NIL T T T) -7 NIL NIL) (-525 1251630 1256420 1261230 "INTFTBL" 1266267 T INTFTBL (NIL) -8 NIL NIL) (-524 1250879 1251017 1251190 "INTFACT" 1251489 NIL INTFACT (NIL T) -7 NIL NIL) (-523 1248270 1248716 1249279 "INTEF" 1250433 NIL INTEF (NIL T T) -7 NIL NIL) (-522 1246732 1247481 1247509 "INTDOM" 1247810 T INTDOM (NIL) -9 NIL 1248017) (-521 1246101 1246275 1246517 "INTDOM-" 1246522 NIL INTDOM- (NIL T) -8 NIL NIL) (-520 1242594 1244526 1244580 "INTCAT" 1245379 NIL INTCAT (NIL T) -9 NIL 1245698) (-519 1242067 1242169 1242297 "INTBIT" 1242486 T INTBIT (NIL) -7 NIL NIL) (-518 1240742 1240896 1241209 "INTALG" 1241912 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-517 1240199 1240289 1240459 "INTAF" 1240646 NIL INTAF (NIL T T) -7 NIL NIL) (-516 1233653 1240009 1240149 "INTABL" 1240154 NIL INTABL (NIL T T T) -8 NIL NIL) (-515 1228604 1231333 1231361 "INS" 1232329 T INS (NIL) -9 NIL 1233010) (-514 1225844 1226615 1227589 "INS-" 1227662 NIL INS- (NIL T) -8 NIL NIL) (-513 1224623 1224850 1225147 "INPSIGN" 1225597 NIL INPSIGN (NIL T T) -7 NIL NIL) (-512 1223741 1223858 1224055 "INPRODPF" 1224503 NIL INPRODPF (NIL T T) -7 NIL NIL) (-511 1222635 1222752 1222989 "INPRODFF" 1223621 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-510 1221635 1221787 1222047 "INNMFACT" 1222471 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-509 1220832 1220929 1221117 "INMODGCD" 1221534 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-508 1219341 1219585 1219909 "INFSP" 1220577 NIL INFSP (NIL T T T) -7 NIL NIL) (-507 1218525 1218642 1218825 "INFPROD0" 1219221 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-506 1215536 1216694 1217185 "INFORM" 1218042 T INFORM (NIL) -8 NIL NIL) (-505 1215146 1215206 1215304 "INFORM1" 1215471 NIL INFORM1 (NIL T) -7 NIL NIL) (-504 1214669 1214758 1214872 "INFINITY" 1215052 T INFINITY (NIL) -7 NIL NIL) (-503 1213286 1213535 1213856 "INEP" 1214417 NIL INEP (NIL T T T) -7 NIL NIL) (-502 1212562 1213183 1213248 "INDE" 1213253 NIL INDE (NIL T) -8 NIL NIL) (-501 1212126 1212194 1212311 "INCRMAPS" 1212489 NIL INCRMAPS (NIL T) -7 NIL NIL) (-500 1207437 1208362 1209306 "INBFF" 1211214 NIL INBFF (NIL T) -7 NIL NIL) (-499 1203932 1207282 1207385 "IMATRIX" 1207390 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-498 1202644 1202767 1203082 "IMATQF" 1203788 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-497 1200864 1201091 1201428 "IMATLIN" 1202400 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-496 1195490 1200788 1200846 "ILIST" 1200851 NIL ILIST (NIL T NIL) -8 NIL NIL) (-495 1193443 1195350 1195463 "IIARRAY2" 1195468 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-494 1188811 1193354 1193418 "IFF" 1193423 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-493 1183854 1188103 1188291 "IFARRAY" 1188668 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-492 1183061 1183758 1183831 "IFAMON" 1183836 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-491 1182645 1182710 1182764 "IEVALAB" 1182971 NIL IEVALAB (NIL T T) -9 NIL NIL) (-490 1182320 1182388 1182548 "IEVALAB-" 1182553 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-489 1181978 1182234 1182297 "IDPO" 1182302 NIL IDPO (NIL T T) -8 NIL NIL) (-488 1181255 1181867 1181942 "IDPOAMS" 1181947 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-487 1180589 1181144 1181219 "IDPOAM" 1181224 NIL IDPOAM (NIL T T) -8 NIL NIL) (-486 1179675 1179925 1179978 "IDPC" 1180391 NIL IDPC (NIL T T) -9 NIL 1180540) (-485 1179171 1179567 1179640 "IDPAM" 1179645 NIL IDPAM (NIL T T) -8 NIL NIL) (-484 1178574 1179063 1179136 "IDPAG" 1179141 NIL IDPAG (NIL T T) -8 NIL NIL) (-483 1174829 1175677 1176572 "IDECOMP" 1177731 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-482 1167702 1168752 1169799 "IDEAL" 1173865 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-481 1166866 1166978 1167177 "ICDEN" 1167586 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-480 1165965 1166346 1166493 "ICARD" 1166739 T ICARD (NIL) -8 NIL NIL) (-479 1164037 1164350 1164753 "IBPTOOLS" 1165642 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-478 1159671 1163657 1163770 "IBITS" 1163956 NIL IBITS (NIL NIL) -8 NIL NIL) (-477 1156394 1156970 1157665 "IBATOOL" 1159088 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-476 1154174 1154635 1155168 "IBACHIN" 1155929 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-475 1152051 1154020 1154123 "IARRAY2" 1154128 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-474 1148204 1151977 1152034 "IARRAY1" 1152039 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-473 1142142 1146622 1147100 "IAN" 1147746 T IAN (NIL) -8 NIL NIL) (-472 1141653 1141710 1141883 "IALGFACT" 1142079 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-471 1141181 1141294 1141322 "HYPCAT" 1141529 T HYPCAT (NIL) -9 NIL NIL) (-470 1140719 1140836 1141022 "HYPCAT-" 1141027 NIL HYPCAT- (NIL T) -8 NIL NIL) (-469 1140341 1140514 1140597 "HOSTNAME" 1140656 T HOSTNAME (NIL) -8 NIL NIL) (-468 1137021 1138352 1138393 "HOAGG" 1139374 NIL HOAGG (NIL T) -9 NIL 1140053) (-467 1135615 1136014 1136540 "HOAGG-" 1136545 NIL HOAGG- (NIL T T) -8 NIL NIL) (-466 1129445 1135056 1135222 "HEXADEC" 1135469 T HEXADEC (NIL) -8 NIL NIL) (-465 1128193 1128415 1128678 "HEUGCD" 1129222 NIL HEUGCD (NIL T) -7 NIL NIL) (-464 1127296 1128030 1128160 "HELLFDIV" 1128165 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-463 1125524 1127073 1127161 "HEAP" 1127240 NIL HEAP (NIL T) -8 NIL NIL) (-462 1124863 1125103 1125231 "HEADAST" 1125416 T HEADAST (NIL) -8 NIL NIL) (-461 1118730 1124778 1124840 "HDP" 1124845 NIL HDP (NIL NIL T) -8 NIL NIL) (-460 1112442 1118367 1118518 "HDMP" 1118631 NIL HDMP (NIL NIL T) -8 NIL NIL) (-459 1111767 1111906 1112070 "HB" 1112298 T HB (NIL) -7 NIL NIL) (-458 1105264 1111613 1111717 "HASHTBL" 1111722 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-457 1103017 1104892 1105071 "HACKPI" 1105105 T HACKPI (NIL) -8 NIL NIL) (-456 1098713 1102871 1102983 "GTSET" 1102988 NIL GTSET (NIL T T T T) -8 NIL NIL) (-455 1092239 1098591 1098689 "GSTBL" 1098694 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-454 1084472 1091275 1091539 "GSERIES" 1092030 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-453 1083495 1083948 1083976 "GROUP" 1084237 T GROUP (NIL) -9 NIL 1084396) (-452 1082611 1082834 1083178 "GROUP-" 1083183 NIL GROUP- (NIL T) -8 NIL NIL) (-451 1080980 1081299 1081686 "GROEBSOL" 1082288 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-450 1079921 1080183 1080234 "GRMOD" 1080763 NIL GRMOD (NIL T T) -9 NIL 1080931) (-449 1079689 1079725 1079853 "GRMOD-" 1079858 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-448 1075014 1076043 1077043 "GRIMAGE" 1078709 T GRIMAGE (NIL) -8 NIL NIL) (-447 1073481 1073741 1074065 "GRDEF" 1074710 T GRDEF (NIL) -7 NIL NIL) (-446 1072925 1073041 1073182 "GRAY" 1073360 T GRAY (NIL) -7 NIL NIL) (-445 1072159 1072539 1072590 "GRALG" 1072743 NIL GRALG (NIL T T) -9 NIL 1072835) (-444 1071820 1071893 1072056 "GRALG-" 1072061 NIL GRALG- (NIL T T T) -8 NIL NIL) (-443 1068628 1071409 1071585 "GPOLSET" 1071727 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-442 1067984 1068041 1068298 "GOSPER" 1068565 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-441 1063743 1064422 1064948 "GMODPOL" 1067683 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-440 1062748 1062932 1063170 "GHENSEL" 1063555 NIL GHENSEL (NIL T T) -7 NIL NIL) (-439 1056814 1057657 1058683 "GENUPS" 1061832 NIL GENUPS (NIL T T) -7 NIL NIL) (-438 1056511 1056562 1056651 "GENUFACT" 1056757 NIL GENUFACT (NIL T) -7 NIL NIL) (-437 1055923 1056000 1056165 "GENPGCD" 1056429 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-436 1055397 1055432 1055645 "GENMFACT" 1055882 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-435 1053965 1054220 1054527 "GENEEZ" 1055140 NIL GENEEZ (NIL T T) -7 NIL NIL) (-434 1047839 1053578 1053739 "GDMP" 1053888 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-433 1037216 1041610 1042716 "GCNAALG" 1046822 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-432 1035638 1036510 1036538 "GCDDOM" 1036793 T GCDDOM (NIL) -9 NIL 1036950) (-431 1035108 1035235 1035450 "GCDDOM-" 1035455 NIL GCDDOM- (NIL T) -8 NIL NIL) (-430 1033780 1033965 1034269 "GB" 1034887 NIL GB (NIL T T T T) -7 NIL NIL) (-429 1022400 1024726 1027118 "GBINTERN" 1031471 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-428 1020237 1020529 1020950 "GBF" 1022075 NIL GBF (NIL T T T T) -7 NIL NIL) (-427 1019018 1019183 1019450 "GBEUCLID" 1020053 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-426 1018367 1018492 1018641 "GAUSSFAC" 1018889 T GAUSSFAC (NIL) -7 NIL NIL) (-425 1016744 1017046 1017359 "GALUTIL" 1018086 NIL GALUTIL (NIL T) -7 NIL NIL) (-424 1015061 1015335 1015658 "GALPOLYU" 1016471 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-423 1012450 1012740 1013145 "GALFACTU" 1014758 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-422 1004256 1005755 1007363 "GALFACT" 1010882 NIL GALFACT (NIL T) -7 NIL NIL) (-421 1001644 1002302 1002330 "FVFUN" 1003486 T FVFUN (NIL) -9 NIL 1004206) (-420 1000910 1001092 1001120 "FVC" 1001411 T FVC (NIL) -9 NIL 1001594) (-419 1000552 1000707 1000788 "FUNCTION" 1000862 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-418 998222 998773 999262 "FT" 1000083 T FT (NIL) -8 NIL NIL) (-417 997040 997523 997726 "FTEM" 998039 T FTEM (NIL) -8 NIL NIL) (-416 995305 995593 995995 "FSUPFACT" 996732 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-415 993702 993991 994323 "FST" 994993 T FST (NIL) -8 NIL NIL) (-414 992877 992983 993177 "FSRED" 993584 NIL FSRED (NIL T T) -7 NIL NIL) (-413 991556 991811 992165 "FSPRMELT" 992592 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-412 988641 989079 989578 "FSPECF" 991119 NIL FSPECF (NIL T T) -7 NIL NIL) (-411 971015 979572 979612 "FS" 983450 NIL FS (NIL T) -9 NIL 985732) (-410 959665 962655 966711 "FS-" 967008 NIL FS- (NIL T T) -8 NIL NIL) (-409 959181 959235 959411 "FSINT" 959606 NIL FSINT (NIL T T) -7 NIL NIL) (-408 957462 958174 958477 "FSERIES" 958960 NIL FSERIES (NIL T T) -8 NIL NIL) (-407 956480 956596 956826 "FSCINT" 957342 NIL FSCINT (NIL T T) -7 NIL NIL) (-406 952715 955425 955466 "FSAGG" 955836 NIL FSAGG (NIL T) -9 NIL 956095) (-405 950477 951078 951874 "FSAGG-" 951969 NIL FSAGG- (NIL T T) -8 NIL NIL) (-404 949519 949662 949889 "FSAGG2" 950330 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-403 947178 947457 948010 "FS2UPS" 949237 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-402 946764 946807 946960 "FS2" 947129 NIL FS2 (NIL T T T T) -7 NIL NIL) (-401 945624 945795 946103 "FS2EXPXP" 946589 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-400 945050 945165 945317 "FRUTIL" 945504 NIL FRUTIL (NIL T) -7 NIL NIL) (-399 936470 940549 941905 "FR" 943726 NIL FR (NIL T) -8 NIL NIL) (-398 931547 934190 934230 "FRNAALG" 935626 NIL FRNAALG (NIL T) -9 NIL 936233) (-397 927225 928296 929571 "FRNAALG-" 930321 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-396 926863 926906 927033 "FRNAAF2" 927176 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-395 925228 925720 926014 "FRMOD" 926676 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-394 922950 923619 923935 "FRIDEAL" 925019 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-393 922149 922236 922523 "FRIDEAL2" 922857 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-392 921407 921815 921856 "FRETRCT" 921861 NIL FRETRCT (NIL T) -9 NIL 922032) (-391 920519 920750 921101 "FRETRCT-" 921106 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-390 917729 918949 919008 "FRAMALG" 919890 NIL FRAMALG (NIL T T) -9 NIL 920182) (-389 915863 916318 916948 "FRAMALG-" 917171 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-388 909765 915338 915614 "FRAC" 915619 NIL FRAC (NIL T) -8 NIL NIL) (-387 909401 909458 909565 "FRAC2" 909702 NIL FRAC2 (NIL T T) -7 NIL NIL) (-386 909037 909094 909201 "FR2" 909338 NIL FR2 (NIL T T) -7 NIL NIL) (-385 903711 906624 906652 "FPS" 907771 T FPS (NIL) -9 NIL 908327) (-384 903160 903269 903433 "FPS-" 903579 NIL FPS- (NIL T) -8 NIL NIL) (-383 900609 902306 902334 "FPC" 902559 T FPC (NIL) -9 NIL 902701) (-382 900402 900442 900539 "FPC-" 900544 NIL FPC- (NIL T) -8 NIL NIL) (-381 899281 899891 899932 "FPATMAB" 899937 NIL FPATMAB (NIL T) -9 NIL 900089) (-380 896981 897457 897883 "FPARFRAC" 898918 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-379 892374 892873 893555 "FORTRAN" 896413 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-378 890090 890590 891129 "FORT" 891855 T FORT (NIL) -7 NIL NIL) (-377 887766 888328 888356 "FORTFN" 889416 T FORTFN (NIL) -9 NIL 890040) (-376 887530 887580 887608 "FORTCAT" 887667 T FORTCAT (NIL) -9 NIL 887729) (-375 885590 886073 886472 "FORMULA" 887151 T FORMULA (NIL) -8 NIL NIL) (-374 885378 885408 885477 "FORMULA1" 885554 NIL FORMULA1 (NIL T) -7 NIL NIL) (-373 884901 884953 885126 "FORDER" 885320 NIL FORDER (NIL T T T T) -7 NIL NIL) (-372 883997 884161 884354 "FOP" 884728 T FOP (NIL) -7 NIL NIL) (-371 882605 883277 883451 "FNLA" 883879 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-370 881274 881663 881691 "FNCAT" 882263 T FNCAT (NIL) -9 NIL 882556) (-369 880840 881233 881261 "FNAME" 881266 T FNAME (NIL) -8 NIL NIL) (-368 879500 880473 880501 "FMTC" 880506 T FMTC (NIL) -9 NIL 880541) (-367 875818 877025 877653 "FMONOID" 878905 NIL FMONOID (NIL T) -8 NIL NIL) (-366 875038 875561 875709 "FM" 875714 NIL FM (NIL T T) -8 NIL NIL) (-365 872462 873108 873136 "FMFUN" 874280 T FMFUN (NIL) -9 NIL 874988) (-364 871731 871912 871940 "FMC" 872230 T FMC (NIL) -9 NIL 872412) (-363 868961 869795 869848 "FMCAT" 871030 NIL FMCAT (NIL T T) -9 NIL 871524) (-362 867856 868729 868828 "FM1" 868906 NIL FM1 (NIL T T) -8 NIL NIL) (-361 865630 866046 866540 "FLOATRP" 867407 NIL FLOATRP (NIL T) -7 NIL NIL) (-360 859116 863286 863916 "FLOAT" 865020 T FLOAT (NIL) -8 NIL NIL) (-359 856554 857054 857632 "FLOATCP" 858583 NIL FLOATCP (NIL T) -7 NIL NIL) (-358 855343 856191 856231 "FLINEXP" 856236 NIL FLINEXP (NIL T) -9 NIL 856329) (-357 854498 854733 855060 "FLINEXP-" 855065 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-356 853574 853718 853942 "FLASORT" 854350 NIL FLASORT (NIL T T) -7 NIL NIL) (-355 850793 851635 851687 "FLALG" 852914 NIL FLALG (NIL T T) -9 NIL 853381) (-354 844578 848280 848321 "FLAGG" 849583 NIL FLAGG (NIL T) -9 NIL 850235) (-353 843304 843643 844133 "FLAGG-" 844138 NIL FLAGG- (NIL T T) -8 NIL NIL) (-352 842346 842489 842716 "FLAGG2" 843157 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-351 839319 840337 840396 "FINRALG" 841524 NIL FINRALG (NIL T T) -9 NIL 842032) (-350 838479 838708 839047 "FINRALG-" 839052 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-349 837886 838099 838127 "FINITE" 838323 T FINITE (NIL) -9 NIL 838430) (-348 830346 832507 832547 "FINAALG" 836214 NIL FINAALG (NIL T) -9 NIL 837667) (-347 825687 826728 827872 "FINAALG-" 829251 NIL FINAALG- (NIL T T) -8 NIL NIL) (-346 825082 825442 825545 "FILE" 825617 NIL FILE (NIL T) -8 NIL NIL) (-345 823767 824079 824133 "FILECAT" 824817 NIL FILECAT (NIL T T) -9 NIL 825033) (-344 821630 823186 823214 "FIELD" 823254 T FIELD (NIL) -9 NIL 823334) (-343 820250 820635 821146 "FIELD-" 821151 NIL FIELD- (NIL T) -8 NIL NIL) (-342 818065 818887 819233 "FGROUP" 819937 NIL FGROUP (NIL T) -8 NIL NIL) (-341 817155 817319 817539 "FGLMICPK" 817897 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-340 812957 817080 817137 "FFX" 817142 NIL FFX (NIL T NIL) -8 NIL NIL) (-339 812558 812619 812754 "FFSLPE" 812890 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-338 808551 809330 810126 "FFPOLY" 811794 NIL FFPOLY (NIL T) -7 NIL NIL) (-337 808055 808091 808300 "FFPOLY2" 808509 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-336 803876 807974 808037 "FFP" 808042 NIL FFP (NIL T NIL) -8 NIL NIL) (-335 799244 803787 803851 "FF" 803856 NIL FF (NIL NIL NIL) -8 NIL NIL) (-334 794340 798587 798777 "FFNBX" 799098 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-333 789249 793475 793733 "FFNBP" 794194 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-332 783852 788533 788744 "FFNB" 789082 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-331 782684 782882 783197 "FFINTBAS" 783649 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-330 778908 781148 781176 "FFIELDC" 781796 T FFIELDC (NIL) -9 NIL 782172) (-329 777571 777941 778438 "FFIELDC-" 778443 NIL FFIELDC- (NIL T) -8 NIL NIL) (-328 777141 777186 777310 "FFHOM" 777513 NIL FFHOM (NIL T T T) -7 NIL NIL) (-327 774839 775323 775840 "FFF" 776656 NIL FFF (NIL T) -7 NIL NIL) (-326 770427 774581 774682 "FFCGX" 774782 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-325 766029 770159 770266 "FFCGP" 770370 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-324 761182 765756 765864 "FFCG" 765965 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-323 743128 752251 752337 "FFCAT" 757502 NIL FFCAT (NIL T T T) -9 NIL 758989) (-322 738326 739373 740687 "FFCAT-" 741917 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-321 737737 737780 738015 "FFCAT2" 738277 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-320 726937 730727 731944 "FEXPR" 736592 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-319 725937 726372 726413 "FEVALAB" 726497 NIL FEVALAB (NIL T) -9 NIL 726758) (-318 725096 725306 725644 "FEVALAB-" 725649 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-317 723689 724479 724682 "FDIV" 724995 NIL FDIV (NIL T T T T) -8 NIL NIL) (-316 720756 721471 721586 "FDIVCAT" 723154 NIL FDIVCAT (NIL T T T T) -9 NIL 723591) (-315 720518 720545 720715 "FDIVCAT-" 720720 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-314 719738 719825 720102 "FDIV2" 720425 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-313 718424 718683 718972 "FCPAK1" 719469 T FCPAK1 (NIL) -7 NIL NIL) (-312 717552 717924 718065 "FCOMP" 718315 NIL FCOMP (NIL T) -8 NIL NIL) (-311 701187 704601 708162 "FC" 714011 T FC (NIL) -8 NIL NIL) (-310 693783 697829 697869 "FAXF" 699671 NIL FAXF (NIL T) -9 NIL 700362) (-309 691062 691717 692542 "FAXF-" 693007 NIL FAXF- (NIL T T) -8 NIL NIL) (-308 686162 690438 690614 "FARRAY" 690919 NIL FARRAY (NIL T) -8 NIL NIL) (-307 681553 683624 683676 "FAMR" 684688 NIL FAMR (NIL T T) -9 NIL 685148) (-306 680444 680746 681180 "FAMR-" 681185 NIL FAMR- (NIL T T T) -8 NIL NIL) (-305 679640 680366 680419 "FAMONOID" 680424 NIL FAMONOID (NIL T) -8 NIL NIL) (-304 677473 678157 678210 "FAMONC" 679151 NIL FAMONC (NIL T T) -9 NIL 679536) (-303 676165 677227 677364 "FAGROUP" 677369 NIL FAGROUP (NIL T) -8 NIL NIL) (-302 673968 674287 674689 "FACUTIL" 675846 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-301 673067 673252 673474 "FACTFUNC" 673778 NIL FACTFUNC (NIL T) -7 NIL NIL) (-300 665387 672318 672530 "EXPUPXS" 672923 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-299 662870 663410 663996 "EXPRTUBE" 664821 T EXPRTUBE (NIL) -7 NIL NIL) (-298 659064 659656 660393 "EXPRODE" 662209 NIL EXPRODE (NIL T T) -7 NIL NIL) (-297 644223 657723 658149 "EXPR" 658670 NIL EXPR (NIL T) -8 NIL NIL) (-296 638651 639238 640050 "EXPR2UPS" 643521 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-295 638287 638344 638451 "EXPR2" 638588 NIL EXPR2 (NIL T T) -7 NIL NIL) (-294 629641 637424 637719 "EXPEXPAN" 638125 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-293 629468 629598 629627 "EXIT" 629632 T EXIT (NIL) -8 NIL NIL) (-292 629095 629157 629270 "EVALCYC" 629400 NIL EVALCYC (NIL T) -7 NIL NIL) (-291 628636 628754 628795 "EVALAB" 628965 NIL EVALAB (NIL T) -9 NIL 629069) (-290 628117 628239 628460 "EVALAB-" 628465 NIL EVALAB- (NIL T T) -8 NIL NIL) (-289 625580 626892 626920 "EUCDOM" 627475 T EUCDOM (NIL) -9 NIL 627825) (-288 623985 624427 625017 "EUCDOM-" 625022 NIL EUCDOM- (NIL T) -8 NIL NIL) (-287 611563 614311 617051 "ESTOOLS" 621265 T ESTOOLS (NIL) -7 NIL NIL) (-286 611199 611256 611363 "ESTOOLS2" 611500 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-285 610950 610992 611072 "ESTOOLS1" 611151 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-284 604888 606612 606640 "ES" 609404 T ES (NIL) -9 NIL 610810) (-283 599835 601122 602939 "ES-" 603103 NIL ES- (NIL T) -8 NIL NIL) (-282 596210 596970 597750 "ESCONT" 599075 T ESCONT (NIL) -7 NIL NIL) (-281 595955 595987 596069 "ESCONT1" 596172 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-280 595630 595680 595780 "ES2" 595899 NIL ES2 (NIL T T) -7 NIL NIL) (-279 595260 595318 595427 "ES1" 595566 NIL ES1 (NIL T T) -7 NIL NIL) (-278 594476 594605 594781 "ERROR" 595104 T ERROR (NIL) -7 NIL NIL) (-277 587979 594335 594426 "EQTBL" 594431 NIL EQTBL (NIL T T) -8 NIL NIL) (-276 580416 583297 584744 "EQ" 586565 NIL -3784 (NIL T) -8 NIL NIL) (-275 580048 580105 580214 "EQ2" 580353 NIL EQ2 (NIL T T) -7 NIL NIL) (-274 575340 576386 577479 "EP" 578987 NIL EP (NIL T) -7 NIL NIL) (-273 573922 574223 574540 "ENV" 575043 T ENV (NIL) -8 NIL NIL) (-272 573082 573646 573674 "ENTIRER" 573679 T ENTIRER (NIL) -9 NIL 573724) (-271 569538 571037 571407 "EMR" 572881 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-270 568682 568867 568921 "ELTAGG" 569301 NIL ELTAGG (NIL T T) -9 NIL 569512) (-269 568401 568463 568604 "ELTAGG-" 568609 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-268 568190 568219 568273 "ELTAB" 568357 NIL ELTAB (NIL T T) -9 NIL NIL) (-267 567316 567462 567661 "ELFUTS" 568041 NIL ELFUTS (NIL T T) -7 NIL NIL) (-266 567058 567114 567142 "ELEMFUN" 567247 T ELEMFUN (NIL) -9 NIL NIL) (-265 566928 566949 567017 "ELEMFUN-" 567022 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-264 561820 565029 565070 "ELAGG" 566010 NIL ELAGG (NIL T) -9 NIL 566473) (-263 560105 560539 561202 "ELAGG-" 561207 NIL ELAGG- (NIL T T) -8 NIL NIL) (-262 558762 559042 559337 "ELABEXPR" 559830 T ELABEXPR (NIL) -8 NIL NIL) (-261 551628 553429 554256 "EFUPXS" 558038 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-260 545078 546879 547689 "EFULS" 550904 NIL EFULS (NIL T T T) -8 NIL NIL) (-259 542509 542867 543345 "EFSTRUC" 544710 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-258 531581 533146 534706 "EF" 541024 NIL EF (NIL T T) -7 NIL NIL) (-257 530682 531066 531215 "EAB" 531452 T EAB (NIL) -8 NIL NIL) (-256 529895 530641 530669 "E04UCFA" 530674 T E04UCFA (NIL) -8 NIL NIL) (-255 529108 529854 529882 "E04NAFA" 529887 T E04NAFA (NIL) -8 NIL NIL) (-254 528321 529067 529095 "E04MBFA" 529100 T E04MBFA (NIL) -8 NIL NIL) (-253 527534 528280 528308 "E04JAFA" 528313 T E04JAFA (NIL) -8 NIL NIL) (-252 526749 527493 527521 "E04GCFA" 527526 T E04GCFA (NIL) -8 NIL NIL) (-251 525964 526708 526736 "E04FDFA" 526741 T E04FDFA (NIL) -8 NIL NIL) (-250 525177 525923 525951 "E04DGFA" 525956 T E04DGFA (NIL) -8 NIL NIL) (-249 519362 520707 522069 "E04AGNT" 523835 T E04AGNT (NIL) -7 NIL NIL) (-248 518089 518569 518609 "DVARCAT" 519084 NIL DVARCAT (NIL T) -9 NIL 519282) (-247 517293 517505 517819 "DVARCAT-" 517824 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-246 510155 517095 517222 "DSMP" 517227 NIL DSMP (NIL T T T) -8 NIL NIL) (-245 504965 506100 507168 "DROPT" 509107 T DROPT (NIL) -8 NIL NIL) (-244 504630 504689 504787 "DROPT1" 504900 NIL DROPT1 (NIL T) -7 NIL NIL) (-243 499745 500871 502008 "DROPT0" 503513 T DROPT0 (NIL) -7 NIL NIL) (-242 498090 498415 498801 "DRAWPT" 499379 T DRAWPT (NIL) -7 NIL NIL) (-241 492677 493600 494679 "DRAW" 497064 NIL DRAW (NIL T) -7 NIL NIL) (-240 492310 492363 492481 "DRAWHACK" 492618 NIL DRAWHACK (NIL T) -7 NIL NIL) (-239 491041 491310 491601 "DRAWCX" 492039 T DRAWCX (NIL) -7 NIL NIL) (-238 490559 490627 490777 "DRAWCURV" 490967 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-237 481030 482989 485104 "DRAWCFUN" 488464 T DRAWCFUN (NIL) -7 NIL NIL) (-236 477844 479726 479767 "DQAGG" 480396 NIL DQAGG (NIL T) -9 NIL 480669) (-235 466351 473089 473171 "DPOLCAT" 475009 NIL DPOLCAT (NIL T T T T) -9 NIL 475553) (-234 461191 462537 464494 "DPOLCAT-" 464499 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-233 453987 461053 461150 "DPMO" 461155 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-232 446686 453768 453934 "DPMM" 453939 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-231 446106 446309 446423 "DOMAIN" 446592 T DOMAIN (NIL) -8 NIL NIL) (-230 439818 445743 445894 "DMP" 446007 NIL DMP (NIL NIL T) -8 NIL NIL) (-229 439418 439474 439618 "DLP" 439756 NIL DLP (NIL T) -7 NIL NIL) (-228 433062 438519 438746 "DLIST" 439223 NIL DLIST (NIL T) -8 NIL NIL) (-227 429909 431918 431959 "DLAGG" 432509 NIL DLAGG (NIL T) -9 NIL 432738) (-226 428619 429311 429339 "DIVRING" 429489 T DIVRING (NIL) -9 NIL 429597) (-225 427607 427860 428253 "DIVRING-" 428258 NIL DIVRING- (NIL T) -8 NIL NIL) (-224 425709 426066 426472 "DISPLAY" 427221 T DISPLAY (NIL) -7 NIL NIL) (-223 419598 425623 425686 "DIRPROD" 425691 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-222 418446 418649 418914 "DIRPROD2" 419391 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-221 407965 413970 414023 "DIRPCAT" 414431 NIL DIRPCAT (NIL NIL T) -9 NIL 415270) (-220 405291 405933 406814 "DIRPCAT-" 407151 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-219 404578 404738 404924 "DIOSP" 405125 T DIOSP (NIL) -7 NIL NIL) (-218 401281 403491 403532 "DIOPS" 403966 NIL DIOPS (NIL T) -9 NIL 404195) (-217 400830 400944 401135 "DIOPS-" 401140 NIL DIOPS- (NIL T T) -8 NIL NIL) (-216 399702 400340 400368 "DIFRING" 400555 T DIFRING (NIL) -9 NIL 400664) (-215 399348 399425 399577 "DIFRING-" 399582 NIL DIFRING- (NIL T) -8 NIL NIL) (-214 397138 398420 398460 "DIFEXT" 398819 NIL DIFEXT (NIL T) -9 NIL 399112) (-213 395424 395852 396517 "DIFEXT-" 396522 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-212 392747 394957 394998 "DIAGG" 395003 NIL DIAGG (NIL T) -9 NIL 395023) (-211 392131 392288 392540 "DIAGG-" 392545 NIL DIAGG- (NIL T T) -8 NIL NIL) (-210 387596 391090 391367 "DHMATRIX" 391900 NIL DHMATRIX (NIL T) -8 NIL NIL) (-209 383208 384117 385127 "DFSFUN" 386606 T DFSFUN (NIL) -7 NIL NIL) (-208 377994 381922 382287 "DFLOAT" 382863 T DFLOAT (NIL) -8 NIL NIL) (-207 376227 376508 376903 "DFINTTLS" 377702 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-206 373260 374262 374660 "DERHAM" 375894 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-205 371109 373035 373124 "DEQUEUE" 373204 NIL DEQUEUE (NIL T) -8 NIL NIL) (-204 370327 370460 370655 "DEGRED" 370971 NIL DEGRED (NIL T T) -7 NIL NIL) (-203 366727 367472 368324 "DEFINTRF" 369555 NIL DEFINTRF (NIL T) -7 NIL NIL) (-202 364258 364727 365325 "DEFINTEF" 366246 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-201 358088 363699 363865 "DECIMAL" 364112 T DECIMAL (NIL) -8 NIL NIL) (-200 355600 356058 356564 "DDFACT" 357632 NIL DDFACT (NIL T T) -7 NIL NIL) (-199 355196 355239 355390 "DBLRESP" 355551 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-198 352906 353240 353609 "DBASE" 354954 NIL DBASE (NIL T) -8 NIL NIL) (-197 352175 352386 352532 "DATABUF" 352805 NIL DATABUF (NIL NIL T) -8 NIL NIL) (-196 351310 352134 352162 "D03FAFA" 352167 T D03FAFA (NIL) -8 NIL NIL) (-195 350446 351269 351297 "D03EEFA" 351302 T D03EEFA (NIL) -8 NIL NIL) (-194 348396 348862 349351 "D03AGNT" 349977 T D03AGNT (NIL) -7 NIL NIL) (-193 347714 348355 348383 "D02EJFA" 348388 T D02EJFA (NIL) -8 NIL NIL) (-192 347032 347673 347701 "D02CJFA" 347706 T D02CJFA (NIL) -8 NIL NIL) (-191 346350 346991 347019 "D02BHFA" 347024 T D02BHFA (NIL) -8 NIL NIL) (-190 345668 346309 346337 "D02BBFA" 346342 T D02BBFA (NIL) -8 NIL NIL) (-189 338866 340454 342060 "D02AGNT" 344082 T D02AGNT (NIL) -7 NIL NIL) (-188 336635 337157 337703 "D01WGTS" 338340 T D01WGTS (NIL) -7 NIL NIL) (-187 335738 336594 336622 "D01TRNS" 336627 T D01TRNS (NIL) -8 NIL NIL) (-186 334841 335697 335725 "D01GBFA" 335730 T D01GBFA (NIL) -8 NIL NIL) (-185 333944 334800 334828 "D01FCFA" 334833 T D01FCFA (NIL) -8 NIL NIL) (-184 333047 333903 333931 "D01ASFA" 333936 T D01ASFA (NIL) -8 NIL NIL) (-183 332150 333006 333034 "D01AQFA" 333039 T D01AQFA (NIL) -8 NIL NIL) (-182 331253 332109 332137 "D01APFA" 332142 T D01APFA (NIL) -8 NIL NIL) (-181 330356 331212 331240 "D01ANFA" 331245 T D01ANFA (NIL) -8 NIL NIL) (-180 329459 330315 330343 "D01AMFA" 330348 T D01AMFA (NIL) -8 NIL NIL) (-179 328562 329418 329446 "D01ALFA" 329451 T D01ALFA (NIL) -8 NIL NIL) (-178 327665 328521 328549 "D01AKFA" 328554 T D01AKFA (NIL) -8 NIL NIL) (-177 326768 327624 327652 "D01AJFA" 327657 T D01AJFA (NIL) -8 NIL NIL) (-176 320072 321621 323180 "D01AGNT" 325229 T D01AGNT (NIL) -7 NIL NIL) (-175 319409 319537 319689 "CYCLOTOM" 319940 T CYCLOTOM (NIL) -7 NIL NIL) (-174 316144 316857 317584 "CYCLES" 318702 T CYCLES (NIL) -7 NIL NIL) (-173 315456 315590 315761 "CVMP" 316005 NIL CVMP (NIL T) -7 NIL NIL) (-172 313237 313495 313870 "CTRIGMNP" 315184 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-171 312748 312937 313036 "CTORCALL" 313158 T CTORCALL (NIL) -8 NIL NIL) (-170 312122 312221 312374 "CSTTOOLS" 312645 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-169 307921 308578 309336 "CRFP" 311434 NIL CRFP (NIL T T) -7 NIL NIL) (-168 306968 307153 307381 "CRAPACK" 307725 NIL CRAPACK (NIL T) -7 NIL NIL) (-167 306352 306453 306657 "CPMATCH" 306844 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-166 306077 306105 306211 "CPIMA" 306318 NIL CPIMA (NIL T T T) -7 NIL NIL) (-165 302441 303113 303831 "COORDSYS" 305412 NIL COORDSYS (NIL T) -7 NIL NIL) (-164 301825 301954 302104 "CONTOUR" 302311 T CONTOUR (NIL) -8 NIL NIL) (-163 297686 299828 300320 "CONTFRAC" 301365 NIL CONTFRAC (NIL T) -8 NIL NIL) (-162 296840 297404 297432 "COMRING" 297437 T COMRING (NIL) -9 NIL 297488) (-161 295921 296198 296382 "COMPPROP" 296676 T COMPPROP (NIL) -8 NIL NIL) (-160 295582 295617 295745 "COMPLPAT" 295880 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-159 285563 295391 295500 "COMPLEX" 295505 NIL COMPLEX (NIL T) -8 NIL NIL) (-158 285199 285256 285363 "COMPLEX2" 285500 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-157 284917 284952 285050 "COMPFACT" 285158 NIL COMPFACT (NIL T T) -7 NIL NIL) (-156 269252 279546 279586 "COMPCAT" 280588 NIL COMPCAT (NIL T) -9 NIL 281981) (-155 258767 261691 265318 "COMPCAT-" 265674 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-154 258498 258526 258628 "COMMUPC" 258733 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-153 258293 258326 258385 "COMMONOP" 258459 T COMMONOP (NIL) -7 NIL NIL) (-152 257876 258044 258131 "COMM" 258226 T COMM (NIL) -8 NIL NIL) (-151 257125 257319 257347 "COMBOPC" 257685 T COMBOPC (NIL) -9 NIL 257860) (-150 256021 256231 256473 "COMBINAT" 256915 NIL COMBINAT (NIL T) -7 NIL NIL) (-149 252219 252792 253432 "COMBF" 255443 NIL COMBF (NIL T T) -7 NIL NIL) (-148 251005 251335 251570 "COLOR" 252004 T COLOR (NIL) -8 NIL NIL) (-147 250645 250692 250817 "CMPLXRT" 250952 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-146 246147 247175 248255 "CLIP" 249585 T CLIP (NIL) -7 NIL NIL) (-145 244485 245255 245493 "CLIF" 245975 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-144 240708 242632 242673 "CLAGG" 243602 NIL CLAGG (NIL T) -9 NIL 244138) (-143 239130 239587 240170 "CLAGG-" 240175 NIL CLAGG- (NIL T T) -8 NIL NIL) (-142 238674 238759 238899 "CINTSLPE" 239039 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-141 236175 236646 237194 "CHVAR" 238202 NIL CHVAR (NIL T T T) -7 NIL NIL) (-140 235398 235962 235990 "CHARZ" 235995 T CHARZ (NIL) -9 NIL 236009) (-139 235152 235192 235270 "CHARPOL" 235352 NIL CHARPOL (NIL T) -7 NIL NIL) (-138 234259 234856 234884 "CHARNZ" 234931 T CHARNZ (NIL) -9 NIL 234986) (-137 232284 232949 233284 "CHAR" 233944 T CHAR (NIL) -8 NIL NIL) (-136 232010 232071 232099 "CFCAT" 232210 T CFCAT (NIL) -9 NIL NIL) (-135 231255 231366 231548 "CDEN" 231894 NIL CDEN (NIL T T T) -7 NIL NIL) (-134 227247 230408 230688 "CCLASS" 230995 T CCLASS (NIL) -8 NIL NIL) (-133 227166 227192 227227 "CATEGORY" 227232 T -10 (NIL) -8 NIL NIL) (-132 222218 223195 223948 "CARTEN" 226469 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-131 221326 221474 221695 "CARTEN2" 222065 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-130 219624 220478 220734 "CARD" 221090 T CARD (NIL) -8 NIL NIL) (-129 218997 219325 219353 "CACHSET" 219485 T CACHSET (NIL) -9 NIL 219562) (-128 218494 218790 218818 "CABMON" 218868 T CABMON (NIL) -9 NIL 218924) (-127 217662 218041 218184 "BYTE" 218371 T BYTE (NIL) -8 NIL NIL) (-126 213610 217609 217643 "BYTEARY" 217648 T BYTEARY (NIL) -8 NIL NIL) (-125 211167 213302 213409 "BTREE" 213536 NIL BTREE (NIL T) -8 NIL NIL) (-124 208665 210815 210937 "BTOURN" 211077 NIL BTOURN (NIL T) -8 NIL NIL) (-123 206084 208137 208178 "BTCAT" 208246 NIL BTCAT (NIL T) -9 NIL 208323) (-122 205751 205831 205980 "BTCAT-" 205985 NIL BTCAT- (NIL T T) -8 NIL NIL) (-121 201044 204895 204923 "BTAGG" 205145 T BTAGG (NIL) -9 NIL 205306) (-120 200534 200659 200865 "BTAGG-" 200870 NIL BTAGG- (NIL T) -8 NIL NIL) (-119 197578 199812 200027 "BSTREE" 200351 NIL BSTREE (NIL T) -8 NIL NIL) (-118 196716 196842 197026 "BRILL" 197434 NIL BRILL (NIL T) -7 NIL NIL) (-117 193418 195445 195486 "BRAGG" 196135 NIL BRAGG (NIL T) -9 NIL 196392) (-116 191947 192353 192908 "BRAGG-" 192913 NIL BRAGG- (NIL T T) -8 NIL NIL) (-115 185155 191293 191477 "BPADICRT" 191795 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-114 183459 185092 185137 "BPADIC" 185142 NIL BPADIC (NIL NIL) -8 NIL NIL) (-113 183159 183189 183302 "BOUNDZRO" 183423 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-112 178674 179765 180632 "BOP" 182312 T BOP (NIL) -8 NIL NIL) (-111 176295 176739 177259 "BOP1" 178187 NIL BOP1 (NIL T) -7 NIL NIL) (-110 175019 175705 175905 "BOOLEAN" 176115 T BOOLEAN (NIL) -8 NIL NIL) (-109 174386 174764 174816 "BMODULE" 174821 NIL BMODULE (NIL T T) -9 NIL 174885) (-108 170216 174184 174257 "BITS" 174333 T BITS (NIL) -8 NIL NIL) (-107 169313 169748 169900 "BINFILE" 170084 T BINFILE (NIL) -8 NIL NIL) (-106 168725 168847 168989 "BINDING" 169191 T BINDING (NIL) -8 NIL NIL) (-105 162559 168169 168334 "BINARY" 168580 T BINARY (NIL) -8 NIL NIL) (-104 160387 161815 161856 "BGAGG" 162116 NIL BGAGG (NIL T) -9 NIL 162253) (-103 160218 160250 160341 "BGAGG-" 160346 NIL BGAGG- (NIL T T) -8 NIL NIL) (-102 159316 159602 159807 "BFUNCT" 160033 T BFUNCT (NIL) -8 NIL NIL) (-101 158011 158189 158476 "BEZOUT" 159140 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-100 154528 156863 157193 "BBTREE" 157714 NIL BBTREE (NIL T) -8 NIL NIL) (-99 154266 154319 154345 "BASTYPE" 154462 T BASTYPE (NIL) -9 NIL NIL) (-98 154121 154150 154220 "BASTYPE-" 154225 NIL BASTYPE- (NIL T) -8 NIL NIL) (-97 153559 153635 153785 "BALFACT" 154032 NIL BALFACT (NIL T T) -7 NIL NIL) (-96 152381 152978 153163 "AUTOMOR" 153404 NIL AUTOMOR (NIL T) -8 NIL NIL) (-95 152107 152112 152138 "ATTREG" 152143 T ATTREG (NIL) -9 NIL NIL) (-94 150386 150804 151156 "ATTRBUT" 151773 T ATTRBUT (NIL) -8 NIL NIL) (-93 149922 150035 150061 "ATRIG" 150262 T ATRIG (NIL) -9 NIL NIL) (-92 149731 149772 149859 "ATRIG-" 149864 NIL ATRIG- (NIL T) -8 NIL NIL) (-91 149457 149600 149626 "ASTCAT" 149631 T ASTCAT (NIL) -9 NIL 149661) (-90 149254 149297 149389 "ASTCAT-" 149394 NIL ASTCAT- (NIL T) -8 NIL NIL) (-89 147451 149030 149118 "ASTACK" 149197 NIL ASTACK (NIL T) -8 NIL NIL) (-88 145956 146253 146618 "ASSOCEQ" 147133 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 144988 145615 145739 "ASP9" 145863 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 144752 144936 144975 "ASP8" 144980 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 143621 144357 144499 "ASP80" 144641 NIL ASP80 (NIL NIL) -8 NIL NIL) (-84 142520 143256 143388 "ASP7" 143520 NIL ASP7 (NIL NIL) -8 NIL NIL) (-83 141474 142197 142315 "ASP78" 142433 NIL ASP78 (NIL NIL) -8 NIL NIL) (-82 140443 141154 141271 "ASP77" 141388 NIL ASP77 (NIL NIL) -8 NIL NIL) (-81 139355 140081 140212 "ASP74" 140343 NIL ASP74 (NIL NIL) -8 NIL NIL) (-80 138255 138990 139122 "ASP73" 139254 NIL ASP73 (NIL NIL) -8 NIL NIL) (-79 137210 137932 138050 "ASP6" 138168 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 136158 136887 137005 "ASP55" 137123 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 135108 135832 135951 "ASP50" 136070 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 134196 134809 134919 "ASP4" 135029 NIL ASP4 (NIL NIL) -8 NIL NIL) (-75 133284 133897 134007 "ASP49" 134117 NIL ASP49 (NIL NIL) -8 NIL NIL) (-74 132069 132823 132991 "ASP42" 133173 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130846 131602 131772 "ASP41" 131956 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-72 129796 130523 130641 "ASP35" 130759 NIL ASP35 (NIL NIL) -8 NIL NIL) (-71 129561 129744 129783 "ASP34" 129788 NIL ASP34 (NIL NIL) -8 NIL NIL) (-70 129298 129365 129441 "ASP33" 129516 NIL ASP33 (NIL NIL) -8 NIL NIL) (-69 128193 128933 129065 "ASP31" 129197 NIL ASP31 (NIL NIL) -8 NIL NIL) (-68 127958 128141 128180 "ASP30" 128185 NIL ASP30 (NIL NIL) -8 NIL NIL) (-67 127693 127762 127838 "ASP29" 127913 NIL ASP29 (NIL NIL) -8 NIL NIL) (-66 127458 127641 127680 "ASP28" 127685 NIL ASP28 (NIL NIL) -8 NIL NIL) (-65 127223 127406 127445 "ASP27" 127450 NIL ASP27 (NIL NIL) -8 NIL NIL) (-64 126307 126921 127032 "ASP24" 127143 NIL ASP24 (NIL NIL) -8 NIL NIL) (-63 125223 125948 126078 "ASP20" 126208 NIL ASP20 (NIL NIL) -8 NIL NIL) (-62 124311 124924 125034 "ASP1" 125144 NIL ASP1 (NIL NIL) -8 NIL NIL) (-61 123255 123985 124104 "ASP19" 124223 NIL ASP19 (NIL NIL) -8 NIL NIL) (-60 122992 123059 123135 "ASP12" 123210 NIL ASP12 (NIL NIL) -8 NIL NIL) (-59 121844 122591 122735 "ASP10" 122879 NIL ASP10 (NIL NIL) -8 NIL NIL) (-58 119743 121688 121779 "ARRAY2" 121784 NIL ARRAY2 (NIL T) -8 NIL NIL) (-57 115559 119391 119505 "ARRAY1" 119660 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 114591 114764 114985 "ARRAY12" 115382 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-55 108951 110822 110897 "ARR2CAT" 113527 NIL ARR2CAT (NIL T T T) -9 NIL 114285) (-54 106385 107129 108083 "ARR2CAT-" 108088 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-53 105137 105289 105594 "APPRULE" 106221 NIL APPRULE (NIL T T T) -7 NIL NIL) (-52 104790 104838 104956 "APPLYORE" 105083 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-51 103764 104055 104250 "ANY" 104613 T ANY (NIL) -8 NIL NIL) (-50 103042 103165 103322 "ANY1" 103638 NIL ANY1 (NIL T) -7 NIL NIL) (-49 100574 101492 101817 "ANTISYM" 102767 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-48 100089 100278 100375 "ANON" 100495 T ANON (NIL) -8 NIL NIL) (-47 94166 98634 99085 "AN" 99656 T AN (NIL) -8 NIL NIL) (-46 90520 91918 91968 "AMR" 92707 NIL AMR (NIL T T) -9 NIL 93306) (-45 89633 89854 90216 "AMR-" 90221 NIL AMR- (NIL T T T) -8 NIL NIL) (-44 74183 89550 89611 "ALIST" 89616 NIL ALIST (NIL T T) -8 NIL NIL) (-43 71020 73777 73946 "ALGSC" 74101 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-42 67576 68130 68737 "ALGPKG" 70460 NIL ALGPKG (NIL T T) -7 NIL NIL) (-41 66853 66954 67138 "ALGMFACT" 67462 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-40 62602 63283 63937 "ALGMANIP" 66377 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-39 53921 62228 62378 "ALGFF" 62535 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-38 53117 53248 53427 "ALGFACT" 53779 NIL ALGFACT (NIL T) -7 NIL NIL) (-37 52108 52718 52756 "ALGEBRA" 52816 NIL ALGEBRA (NIL T) -9 NIL 52874) (-36 51826 51885 52017 "ALGEBRA-" 52022 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-35 34087 49830 49882 "ALAGG" 50018 NIL ALAGG (NIL T T) -9 NIL 50179) (-34 33623 33736 33762 "AHYP" 33963 T AHYP (NIL) -9 NIL NIL) (-33 32554 32802 32828 "AGG" 33327 T AGG (NIL) -9 NIL 33606) (-32 31988 32150 32364 "AGG-" 32369 NIL AGG- (NIL T) -8 NIL NIL) (-31 29675 30093 30510 "AF" 31631 NIL AF (NIL T T) -7 NIL NIL) (-30 28944 29202 29358 "ACPLOT" 29537 T ACPLOT (NIL) -8 NIL NIL) (-29 18411 26357 26408 "ACFS" 27119 NIL ACFS (NIL T) -9 NIL 27358) (-28 16425 16915 17690 "ACFS-" 17695 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12693 14649 14675 "ACF" 15554 T ACF (NIL) -9 NIL 15966) (-26 11397 11731 12224 "ACF-" 12229 NIL ACF- (NIL T) -8 NIL NIL) (-25 10996 11165 11191 "ABELSG" 11283 T ABELSG (NIL) -9 NIL 11348) (-24 10863 10888 10954 "ABELSG-" 10959 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10233 10494 10520 "ABELMON" 10690 T ABELMON (NIL) -9 NIL 10802) (-22 9897 9981 10119 "ABELMON-" 10124 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9232 9578 9604 "ABELGRP" 9729 T ABELGRP (NIL) -9 NIL 9811) (-20 8695 8824 9040 "ABELGRP-" 9045 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL))
\ No newline at end of file +((-3 3152487 3152492 3152497 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-2 3152472 3152477 3152482 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1 3152457 3152462 3152467 NIL NIL NIL NIL (NIL) -8 NIL NIL) (0 3152442 3152447 3152452 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1207 3151572 3152317 3152394 "ZMOD" 3152399 NIL ZMOD (NIL NIL) -8 NIL NIL) (-1206 3150682 3150846 3151055 "ZLINDEP" 3151404 NIL ZLINDEP (NIL T) -7 NIL NIL) (-1205 3140086 3141831 3143783 "ZDSOLVE" 3148831 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL) (-1204 3139332 3139473 3139662 "YSTREAM" 3139932 NIL YSTREAM (NIL T) -7 NIL NIL) (-1203 3137101 3138637 3138840 "XRPOLY" 3139175 NIL XRPOLY (NIL T T) -8 NIL NIL) (-1202 3133563 3134892 3135474 "XPR" 3136565 NIL XPR (NIL T T) -8 NIL NIL) (-1201 3131277 3132898 3133101 "XPOLY" 3133394 NIL XPOLY (NIL T) -8 NIL NIL) (-1200 3129091 3130469 3130523 "XPOLYC" 3130808 NIL XPOLYC (NIL T T) -9 NIL 3130921) (-1199 3125463 3127608 3127996 "XPBWPOLY" 3128749 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1198 3121391 3123704 3123746 "XF" 3124367 NIL XF (NIL T) -9 NIL 3124766) (-1197 3121012 3121100 3121269 "XF-" 3121274 NIL XF- (NIL T T) -8 NIL NIL) (-1196 3116392 3117691 3117745 "XFALG" 3119893 NIL XFALG (NIL T T) -9 NIL 3120680) (-1195 3115529 3115633 3115837 "XEXPPKG" 3116284 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1194 3113628 3115380 3115475 "XDPOLY" 3115480 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1193 3112507 3113117 3113159 "XALG" 3113221 NIL XALG (NIL T) -9 NIL 3113340) (-1192 3105983 3110491 3110984 "WUTSET" 3112099 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1191 3103795 3104602 3104953 "WP" 3105765 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1190 3102681 3102879 3103174 "WFFINTBS" 3103592 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1189 3100585 3101012 3101474 "WEIER" 3102253 NIL WEIER (NIL T) -7 NIL NIL) (-1188 3099734 3100158 3100200 "VSPACE" 3100336 NIL VSPACE (NIL T) -9 NIL 3100410) (-1187 3099572 3099599 3099690 "VSPACE-" 3099695 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1186 3099318 3099361 3099432 "VOID" 3099523 T VOID (NIL) -8 NIL NIL) (-1185 3097454 3097813 3098219 "VIEW" 3098934 T VIEW (NIL) -7 NIL NIL) (-1184 3093879 3094517 3095254 "VIEWDEF" 3096739 T VIEWDEF (NIL) -7 NIL NIL) (-1183 3083217 3085427 3087600 "VIEW3D" 3091728 T VIEW3D (NIL) -8 NIL NIL) (-1182 3075499 3077128 3078707 "VIEW2D" 3081660 T VIEW2D (NIL) -8 NIL NIL) (-1181 3070908 3075269 3075361 "VECTOR" 3075442 NIL VECTOR (NIL T) -8 NIL NIL) (-1180 3069485 3069744 3070062 "VECTOR2" 3070638 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1179 3063025 3067277 3067320 "VECTCAT" 3068308 NIL VECTCAT (NIL T) -9 NIL 3068892) (-1178 3062039 3062293 3062683 "VECTCAT-" 3062688 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1177 3061520 3061690 3061810 "VARIABLE" 3061954 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1176 3061453 3061458 3061488 "UTYPE" 3061493 T UTYPE (NIL) -9 NIL NIL) (-1175 3060288 3060442 3060703 "UTSODETL" 3061279 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1174 3057728 3058188 3058712 "UTSODE" 3059829 NIL UTSODE (NIL T T) -7 NIL NIL) (-1173 3049572 3055368 3055856 "UTS" 3057297 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1172 3040917 3046282 3046324 "UTSCAT" 3047425 NIL UTSCAT (NIL T) -9 NIL 3048182) (-1171 3038272 3038988 3039976 "UTSCAT-" 3039981 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1170 3037903 3037946 3038077 "UTS2" 3038223 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1169 3032179 3034744 3034787 "URAGG" 3036857 NIL URAGG (NIL T) -9 NIL 3037579) (-1168 3029118 3029981 3031104 "URAGG-" 3031109 NIL URAGG- (NIL T T) -8 NIL NIL) (-1167 3024804 3027735 3028206 "UPXSSING" 3028782 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1166 3016695 3023925 3024205 "UPXS" 3024581 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1165 3009724 3016600 3016671 "UPXSCONS" 3016676 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1164 3000013 3006843 3006904 "UPXSCCA" 3007553 NIL UPXSCCA (NIL T T) -9 NIL 3007794) (-1163 2999652 2999737 2999910 "UPXSCCA-" 2999915 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1162 2989863 2996466 2996508 "UPXSCAT" 2997151 NIL UPXSCAT (NIL T) -9 NIL 2997759) (-1161 2989297 2989376 2989553 "UPXS2" 2989778 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1160 2987951 2988204 2988555 "UPSQFREE" 2989040 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1159 2981842 2984897 2984951 "UPSCAT" 2986100 NIL UPSCAT (NIL T T) -9 NIL 2986874) (-1158 2981047 2981254 2981580 "UPSCAT-" 2981585 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1157 2967133 2975170 2975212 "UPOLYC" 2977290 NIL UPOLYC (NIL T) -9 NIL 2978511) (-1156 2958463 2960888 2964034 "UPOLYC-" 2964039 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1155 2958094 2958137 2958268 "UPOLYC2" 2958414 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1154 2949513 2957663 2957800 "UP" 2958004 NIL UP (NIL NIL T) -8 NIL NIL) (-1153 2948856 2948963 2949126 "UPMP" 2949402 NIL UPMP (NIL T T) -7 NIL NIL) (-1152 2948409 2948490 2948629 "UPDIVP" 2948769 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1151 2946977 2947226 2947542 "UPDECOMP" 2948158 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1150 2946212 2946324 2946509 "UPCDEN" 2946861 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1149 2945735 2945804 2945951 "UP2" 2946137 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1148 2944252 2944939 2945216 "UNISEG" 2945493 NIL UNISEG (NIL T) -8 NIL NIL) (-1147 2943467 2943594 2943799 "UNISEG2" 2944095 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1146 2942527 2942707 2942933 "UNIFACT" 2943283 NIL UNIFACT (NIL T) -7 NIL NIL) (-1145 2926423 2941708 2941958 "ULS" 2942334 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1144 2914388 2926328 2926399 "ULSCONS" 2926404 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1143 2897138 2909151 2909212 "ULSCCAT" 2909924 NIL ULSCCAT (NIL T T) -9 NIL 2910220) (-1142 2896189 2896434 2896821 "ULSCCAT-" 2896826 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1141 2886179 2892696 2892738 "ULSCAT" 2893594 NIL ULSCAT (NIL T) -9 NIL 2894324) (-1140 2885613 2885692 2885869 "ULS2" 2886094 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1139 2884011 2884978 2885008 "UFD" 2885220 T UFD (NIL) -9 NIL 2885334) (-1138 2883805 2883851 2883946 "UFD-" 2883951 NIL UFD- (NIL T) -8 NIL NIL) (-1137 2882887 2883070 2883286 "UDVO" 2883611 T UDVO (NIL) -7 NIL NIL) (-1136 2880703 2881112 2881583 "UDPO" 2882451 NIL UDPO (NIL T) -7 NIL NIL) (-1135 2880636 2880641 2880671 "TYPE" 2880676 T TYPE (NIL) -9 NIL NIL) (-1134 2879607 2879809 2880049 "TWOFACT" 2880430 NIL TWOFACT (NIL T) -7 NIL NIL) (-1133 2878545 2878882 2879145 "TUPLE" 2879379 NIL TUPLE (NIL T) -8 NIL NIL) (-1132 2876236 2876755 2877294 "TUBETOOL" 2878028 T TUBETOOL (NIL) -7 NIL NIL) (-1131 2875085 2875290 2875531 "TUBE" 2876029 NIL TUBE (NIL T) -8 NIL NIL) (-1130 2869809 2874063 2874345 "TS" 2874837 NIL TS (NIL T) -8 NIL NIL) (-1129 2858513 2862605 2862701 "TSETCAT" 2867935 NIL TSETCAT (NIL T T T T) -9 NIL 2869466) (-1128 2853248 2854846 2856736 "TSETCAT-" 2856741 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1127 2847511 2848357 2849299 "TRMANIP" 2852384 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1126 2846952 2847015 2847178 "TRIMAT" 2847443 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1125 2844758 2844995 2845358 "TRIGMNIP" 2846701 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1124 2844278 2844391 2844421 "TRIGCAT" 2844634 T TRIGCAT (NIL) -9 NIL NIL) (-1123 2843947 2844026 2844167 "TRIGCAT-" 2844172 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1122 2840846 2842807 2843087 "TREE" 2843702 NIL TREE (NIL T) -8 NIL NIL) (-1121 2840120 2840648 2840678 "TRANFUN" 2840713 T TRANFUN (NIL) -9 NIL 2840779) (-1120 2839399 2839590 2839870 "TRANFUN-" 2839875 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1119 2839203 2839235 2839296 "TOPSP" 2839360 T TOPSP (NIL) -7 NIL NIL) (-1118 2838555 2838670 2838823 "TOOLSIGN" 2839084 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1117 2837216 2837732 2837971 "TEXTFILE" 2838338 T TEXTFILE (NIL) -8 NIL NIL) (-1116 2835081 2835595 2836033 "TEX" 2836800 T TEX (NIL) -8 NIL NIL) (-1115 2834862 2834893 2834965 "TEX1" 2835044 NIL TEX1 (NIL T) -7 NIL NIL) (-1114 2834510 2834573 2834663 "TEMUTL" 2834794 T TEMUTL (NIL) -7 NIL NIL) (-1113 2832664 2832944 2833269 "TBCMPPK" 2834233 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1112 2824553 2830825 2830881 "TBAGG" 2831281 NIL TBAGG (NIL T T) -9 NIL 2831492) (-1111 2819623 2821111 2822865 "TBAGG-" 2822870 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1110 2819007 2819114 2819259 "TANEXP" 2819512 NIL TANEXP (NIL T) -7 NIL NIL) (-1109 2812508 2818864 2818957 "TABLE" 2818962 NIL TABLE (NIL T T) -8 NIL NIL) (-1108 2811920 2812019 2812157 "TABLEAU" 2812405 NIL TABLEAU (NIL T) -8 NIL NIL) (-1107 2806528 2807748 2808996 "TABLBUMP" 2810706 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1106 2805956 2806056 2806184 "SYSTEM" 2806422 T SYSTEM (NIL) -7 NIL NIL) (-1105 2802419 2803114 2803897 "SYSSOLP" 2805207 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1104 2798710 2799418 2800152 "SYNTAX" 2801707 T SYNTAX (NIL) -8 NIL NIL) (-1103 2795844 2796452 2797090 "SYMTAB" 2798094 T SYMTAB (NIL) -8 NIL NIL) (-1102 2791093 2791995 2792978 "SYMS" 2794883 T SYMS (NIL) -8 NIL NIL) (-1101 2788326 2790553 2790782 "SYMPOLY" 2790898 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1100 2787846 2787921 2788043 "SYMFUNC" 2788238 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1099 2783823 2785083 2785905 "SYMBOL" 2787046 T SYMBOL (NIL) -8 NIL NIL) (-1098 2777362 2779051 2780771 "SWITCH" 2782125 T SWITCH (NIL) -8 NIL NIL) (-1097 2770592 2776189 2776491 "SUTS" 2777117 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1096 2762482 2769713 2769993 "SUPXS" 2770369 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1095 2753974 2762103 2762228 "SUP" 2762391 NIL SUP (NIL T) -8 NIL NIL) (-1094 2753133 2753260 2753477 "SUPFRACF" 2753842 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1093 2752758 2752817 2752928 "SUP2" 2753068 NIL SUP2 (NIL T T) -7 NIL NIL) (-1092 2751176 2751450 2751812 "SUMRF" 2752457 NIL SUMRF (NIL T) -7 NIL NIL) (-1091 2750493 2750559 2750757 "SUMFS" 2751097 NIL SUMFS (NIL T T) -7 NIL NIL) (-1090 2734429 2749674 2749924 "SULS" 2750300 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1089 2733751 2733954 2734094 "SUCH" 2734337 NIL SUCH (NIL T T) -8 NIL NIL) (-1088 2727678 2728690 2729648 "SUBSPACE" 2732839 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1087 2727108 2727198 2727362 "SUBRESP" 2727566 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1086 2720477 2721773 2723084 "STTF" 2725844 NIL STTF (NIL T) -7 NIL NIL) (-1085 2714650 2715770 2716917 "STTFNC" 2719377 NIL STTFNC (NIL T) -7 NIL NIL) (-1084 2706001 2707868 2709661 "STTAYLOR" 2712891 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1083 2699245 2705865 2705948 "STRTBL" 2705953 NIL STRTBL (NIL T) -8 NIL NIL) (-1082 2694636 2699200 2699231 "STRING" 2699236 T STRING (NIL) -8 NIL NIL) (-1081 2689525 2694010 2694040 "STRICAT" 2694099 T STRICAT (NIL) -9 NIL 2694161) (-1080 2682239 2687048 2687668 "STREAM" 2688940 NIL STREAM (NIL T) -8 NIL NIL) (-1079 2681749 2681826 2681970 "STREAM3" 2682156 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1078 2680731 2680914 2681149 "STREAM2" 2681562 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1077 2680419 2680471 2680564 "STREAM1" 2680673 NIL STREAM1 (NIL T) -7 NIL NIL) (-1076 2679435 2679616 2679847 "STINPROD" 2680235 NIL STINPROD (NIL T) -7 NIL NIL) (-1075 2679014 2679198 2679228 "STEP" 2679308 T STEP (NIL) -9 NIL 2679386) (-1074 2672557 2678913 2678990 "STBL" 2678995 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1073 2667733 2671780 2671823 "STAGG" 2671976 NIL STAGG (NIL T) -9 NIL 2672065) (-1072 2665435 2666037 2666909 "STAGG-" 2666914 NIL STAGG- (NIL T T) -8 NIL NIL) (-1071 2663630 2665205 2665297 "STACK" 2665378 NIL STACK (NIL T) -8 NIL NIL) (-1070 2656361 2661777 2662232 "SREGSET" 2663260 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1069 2648801 2650169 2651681 "SRDCMPK" 2654967 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1068 2641769 2646242 2646272 "SRAGG" 2647575 T SRAGG (NIL) -9 NIL 2648183) (-1067 2640786 2641041 2641420 "SRAGG-" 2641425 NIL SRAGG- (NIL T) -8 NIL NIL) (-1066 2635235 2639705 2640132 "SQMATRIX" 2640405 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1065 2628987 2631955 2632681 "SPLTREE" 2634581 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1064 2624977 2625643 2626289 "SPLNODE" 2628413 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1063 2624024 2624257 2624287 "SPFCAT" 2624731 T SPFCAT (NIL) -9 NIL NIL) (-1062 2622761 2622971 2623235 "SPECOUT" 2623782 T SPECOUT (NIL) -7 NIL NIL) (-1061 2622522 2622562 2622631 "SPADPRSR" 2622714 T SPADPRSR (NIL) -7 NIL NIL) (-1060 2614545 2616292 2616334 "SPACEC" 2620657 NIL SPACEC (NIL T) -9 NIL 2622473) (-1059 2612717 2614478 2614526 "SPACE3" 2614531 NIL SPACE3 (NIL T) -8 NIL NIL) (-1058 2611469 2611640 2611931 "SORTPAK" 2612522 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1057 2609525 2609828 2610246 "SOLVETRA" 2611133 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1056 2608536 2608758 2609032 "SOLVESER" 2609298 NIL SOLVESER (NIL T) -7 NIL NIL) (-1055 2603756 2604637 2605639 "SOLVERAD" 2607588 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1054 2599571 2600180 2600909 "SOLVEFOR" 2603123 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1053 2593870 2598922 2599018 "SNTSCAT" 2599023 NIL SNTSCAT (NIL T T T T) -9 NIL 2599093) (-1052 2587974 2592201 2592591 "SMTS" 2593560 NIL SMTS (NIL T T T) -8 NIL NIL) (-1051 2582384 2587863 2587939 "SMP" 2587944 NIL SMP (NIL T T) -8 NIL NIL) (-1050 2580543 2580844 2581242 "SMITH" 2582081 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1049 2573508 2577704 2577806 "SMATCAT" 2579146 NIL SMATCAT (NIL NIL T T T) -9 NIL 2579695) (-1048 2570449 2571272 2572449 "SMATCAT-" 2572454 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1047 2568163 2569686 2569729 "SKAGG" 2569990 NIL SKAGG (NIL T) -9 NIL 2570125) (-1046 2564221 2567267 2567545 "SINT" 2567907 T SINT (NIL) -8 NIL NIL) (-1045 2563993 2564031 2564097 "SIMPAN" 2564177 T SIMPAN (NIL) -7 NIL NIL) (-1044 2563509 2563695 2563794 "SIG" 2563916 T SIG (NIL) -8 NIL NIL) (-1043 2562347 2562568 2562843 "SIGNRF" 2563268 NIL SIGNRF (NIL T) -7 NIL NIL) (-1042 2561156 2561307 2561597 "SIGNEF" 2562176 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1041 2558846 2559300 2559806 "SHP" 2560697 NIL SHP (NIL T NIL) -7 NIL NIL) (-1040 2552699 2558747 2558823 "SHDP" 2558828 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1039 2552189 2552381 2552411 "SGROUP" 2552563 T SGROUP (NIL) -9 NIL 2552650) (-1038 2551959 2552011 2552115 "SGROUP-" 2552120 NIL SGROUP- (NIL T) -8 NIL NIL) (-1037 2548795 2549492 2550215 "SGCF" 2551258 T SGCF (NIL) -7 NIL NIL) (-1036 2543192 2548244 2548340 "SFRTCAT" 2548345 NIL SFRTCAT (NIL T T T T) -9 NIL 2548384) (-1035 2536634 2537649 2538784 "SFRGCD" 2542175 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1034 2529781 2530852 2532037 "SFQCMPK" 2535567 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1033 2529403 2529492 2529602 "SFORT" 2529722 NIL SFORT (NIL T T) -8 NIL NIL) (-1032 2528548 2529243 2529364 "SEXOF" 2529369 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1031 2527682 2528429 2528497 "SEX" 2528502 T SEX (NIL) -8 NIL NIL) (-1030 2522459 2523148 2523243 "SEXCAT" 2527014 NIL SEXCAT (NIL T T T T T) -9 NIL 2527633) (-1029 2519639 2522393 2522441 "SET" 2522446 NIL SET (NIL T) -8 NIL NIL) (-1028 2517890 2518352 2518657 "SETMN" 2519380 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1027 2517498 2517624 2517654 "SETCAT" 2517771 T SETCAT (NIL) -9 NIL 2517855) (-1026 2517278 2517330 2517429 "SETCAT-" 2517434 NIL SETCAT- (NIL T) -8 NIL NIL) (-1025 2513666 2515740 2515783 "SETAGG" 2516653 NIL SETAGG (NIL T) -9 NIL 2516993) (-1024 2513124 2513240 2513477 "SETAGG-" 2513482 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1023 2512328 2512621 2512682 "SEGXCAT" 2512968 NIL SEGXCAT (NIL T T) -9 NIL 2513088) (-1022 2511384 2511994 2512176 "SEG" 2512181 NIL SEG (NIL T) -8 NIL NIL) (-1021 2510291 2510504 2510547 "SEGCAT" 2511129 NIL SEGCAT (NIL T) -9 NIL 2511367) (-1020 2509340 2509670 2509870 "SEGBIND" 2510126 NIL SEGBIND (NIL T) -8 NIL NIL) (-1019 2508961 2509020 2509133 "SEGBIND2" 2509275 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1018 2508180 2508306 2508510 "SEG2" 2508805 NIL SEG2 (NIL T T) -7 NIL NIL) (-1017 2507617 2508115 2508162 "SDVAR" 2508167 NIL SDVAR (NIL T) -8 NIL NIL) (-1016 2499869 2507390 2507518 "SDPOL" 2507523 NIL SDPOL (NIL T) -8 NIL NIL) (-1015 2498462 2498728 2499047 "SCPKG" 2499584 NIL SCPKG (NIL T) -7 NIL NIL) (-1014 2497598 2497778 2497978 "SCOPE" 2498284 T SCOPE (NIL) -8 NIL NIL) (-1013 2496819 2496952 2497131 "SCACHE" 2497453 NIL SCACHE (NIL T) -7 NIL NIL) (-1012 2496258 2496579 2496664 "SAOS" 2496756 T SAOS (NIL) -8 NIL NIL) (-1011 2495823 2495858 2496031 "SAERFFC" 2496217 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1010 2489717 2495720 2495800 "SAE" 2495805 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1009 2489310 2489345 2489504 "SAEFACT" 2489676 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1008 2487631 2487945 2488346 "RURPK" 2488976 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1007 2486271 2486550 2486861 "RULESET" 2487465 NIL RULESET (NIL T T T) -8 NIL NIL) (-1006 2483469 2483972 2484435 "RULE" 2485953 NIL RULE (NIL T T T) -8 NIL NIL) (-1005 2483108 2483263 2483346 "RULECOLD" 2483421 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1004 2477971 2478765 2479684 "RSETGCD" 2482307 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1003 2467257 2472309 2472405 "RSETCAT" 2476497 NIL RSETCAT (NIL T T T T) -9 NIL 2477594) (-1002 2465185 2465724 2466547 "RSETCAT-" 2466552 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1001 2457586 2458961 2460480 "RSDCMPK" 2463784 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1000 2455592 2456033 2456107 "RRCC" 2457193 NIL RRCC (NIL T T) -9 NIL 2457537) (-999 2454945 2455119 2455396 "RRCC-" 2455401 NIL RRCC- (NIL T T T) -8 NIL NIL) (-998 2429312 2438937 2439001 "RPOLCAT" 2449503 NIL RPOLCAT (NIL T T T) -9 NIL 2452661) (-997 2420816 2423154 2426272 "RPOLCAT-" 2426277 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-996 2411882 2419046 2419526 "ROUTINE" 2420356 T ROUTINE (NIL) -8 NIL NIL) (-995 2408587 2411438 2411585 "ROMAN" 2411755 T ROMAN (NIL) -8 NIL NIL) (-994 2406871 2407456 2407714 "ROIRC" 2408392 NIL ROIRC (NIL T T) -8 NIL NIL) (-993 2403276 2405580 2405608 "RNS" 2405904 T RNS (NIL) -9 NIL 2406174) (-992 2401790 2402173 2402704 "RNS-" 2402777 NIL RNS- (NIL T) -8 NIL NIL) (-991 2401216 2401624 2401652 "RNG" 2401657 T RNG (NIL) -9 NIL 2401678) (-990 2400614 2400976 2401016 "RMODULE" 2401076 NIL RMODULE (NIL T) -9 NIL 2401118) (-989 2399466 2399560 2399890 "RMCAT2" 2400515 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-988 2396180 2398649 2398970 "RMATRIX" 2399201 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-987 2389177 2391411 2391523 "RMATCAT" 2394832 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2395814) (-986 2388556 2388703 2389006 "RMATCAT-" 2389011 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-985 2388126 2388201 2388327 "RINTERP" 2388475 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-984 2387177 2387741 2387769 "RING" 2387879 T RING (NIL) -9 NIL 2387973) (-983 2386972 2387016 2387110 "RING-" 2387115 NIL RING- (NIL T) -8 NIL NIL) (-982 2385820 2386057 2386313 "RIDIST" 2386736 T RIDIST (NIL) -7 NIL NIL) (-981 2377140 2385292 2385496 "RGCHAIN" 2385668 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-980 2374145 2374759 2375427 "RF" 2376504 NIL RF (NIL T) -7 NIL NIL) (-979 2373794 2373857 2373958 "RFFACTOR" 2374076 NIL RFFACTOR (NIL T) -7 NIL NIL) (-978 2373522 2373557 2373652 "RFFACT" 2373753 NIL RFFACT (NIL T) -7 NIL NIL) (-977 2371652 2372016 2372396 "RFDIST" 2373162 T RFDIST (NIL) -7 NIL NIL) (-976 2371110 2371202 2371362 "RETSOL" 2371554 NIL RETSOL (NIL T T) -7 NIL NIL) (-975 2370703 2370783 2370824 "RETRACT" 2371014 NIL RETRACT (NIL T) -9 NIL NIL) (-974 2370555 2370580 2370664 "RETRACT-" 2370669 NIL RETRACT- (NIL T T) -8 NIL NIL) (-973 2363413 2370212 2370337 "RESULT" 2370450 T RESULT (NIL) -8 NIL NIL) (-972 2361998 2362687 2362884 "RESRING" 2363316 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-971 2361638 2361687 2361783 "RESLATC" 2361935 NIL RESLATC (NIL T) -7 NIL NIL) (-970 2361347 2361381 2361486 "REPSQ" 2361597 NIL REPSQ (NIL T) -7 NIL NIL) (-969 2358778 2359358 2359958 "REP" 2360767 T REP (NIL) -7 NIL NIL) (-968 2358479 2358513 2358622 "REPDB" 2358737 NIL REPDB (NIL T) -7 NIL NIL) (-967 2352424 2353803 2355023 "REP2" 2357291 NIL REP2 (NIL T) -7 NIL NIL) (-966 2348830 2349511 2350316 "REP1" 2351651 NIL REP1 (NIL T) -7 NIL NIL) (-965 2341574 2346989 2347442 "REGSET" 2348460 NIL REGSET (NIL T T T T) -8 NIL NIL) (-964 2340395 2340730 2340978 "REF" 2341359 NIL REF (NIL T) -8 NIL NIL) (-963 2339776 2339879 2340044 "REDORDER" 2340279 NIL REDORDER (NIL T T) -7 NIL NIL) (-962 2335745 2339010 2339231 "RECLOS" 2339607 NIL RECLOS (NIL T) -8 NIL NIL) (-961 2334802 2334983 2335196 "REALSOLV" 2335552 T REALSOLV (NIL) -7 NIL NIL) (-960 2334650 2334691 2334719 "REAL" 2334724 T REAL (NIL) -9 NIL 2334759) (-959 2331141 2331943 2332825 "REAL0Q" 2333815 NIL REAL0Q (NIL T) -7 NIL NIL) (-958 2326752 2327740 2328799 "REAL0" 2330122 NIL REAL0 (NIL T) -7 NIL NIL) (-957 2326160 2326232 2326437 "RDIV" 2326674 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-956 2325233 2325407 2325618 "RDIST" 2325982 NIL RDIST (NIL T) -7 NIL NIL) (-955 2323837 2324124 2324493 "RDETRS" 2324941 NIL RDETRS (NIL T T) -7 NIL NIL) (-954 2321658 2322112 2322647 "RDETR" 2323379 NIL RDETR (NIL T T) -7 NIL NIL) (-953 2320274 2320552 2320953 "RDEEFS" 2321374 NIL RDEEFS (NIL T T) -7 NIL NIL) (-952 2318774 2319080 2319509 "RDEEF" 2319962 NIL RDEEF (NIL T T) -7 NIL NIL) (-951 2313059 2315991 2316019 "RCFIELD" 2317296 T RCFIELD (NIL) -9 NIL 2318026) (-950 2311128 2311632 2312325 "RCFIELD-" 2312398 NIL RCFIELD- (NIL T) -8 NIL NIL) (-949 2307460 2309245 2309286 "RCAGG" 2310357 NIL RCAGG (NIL T) -9 NIL 2310822) (-948 2307091 2307185 2307345 "RCAGG-" 2307350 NIL RCAGG- (NIL T T) -8 NIL NIL) (-947 2306435 2306547 2306709 "RATRET" 2306975 NIL RATRET (NIL T) -7 NIL NIL) (-946 2305992 2306059 2306178 "RATFACT" 2306363 NIL RATFACT (NIL T) -7 NIL NIL) (-945 2305307 2305427 2305577 "RANDSRC" 2305862 T RANDSRC (NIL) -7 NIL NIL) (-944 2305044 2305088 2305159 "RADUTIL" 2305256 T RADUTIL (NIL) -7 NIL NIL) (-943 2298051 2303787 2304104 "RADIX" 2304759 NIL RADIX (NIL NIL) -8 NIL NIL) (-942 2289620 2297895 2298023 "RADFF" 2298028 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-941 2289272 2289347 2289375 "RADCAT" 2289532 T RADCAT (NIL) -9 NIL NIL) (-940 2289057 2289105 2289202 "RADCAT-" 2289207 NIL RADCAT- (NIL T) -8 NIL NIL) (-939 2287208 2288832 2288921 "QUEUE" 2289001 NIL QUEUE (NIL T) -8 NIL NIL) (-938 2283705 2287145 2287190 "QUAT" 2287195 NIL QUAT (NIL T) -8 NIL NIL) (-937 2283343 2283386 2283513 "QUATCT2" 2283656 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-936 2277137 2280517 2280557 "QUATCAT" 2281336 NIL QUATCAT (NIL T) -9 NIL 2282101) (-935 2273281 2274318 2275705 "QUATCAT-" 2275799 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-934 2270802 2272366 2272407 "QUAGG" 2272782 NIL QUAGG (NIL T) -9 NIL 2272957) (-933 2269727 2270200 2270372 "QFORM" 2270674 NIL QFORM (NIL NIL T) -8 NIL NIL) (-932 2261024 2266282 2266322 "QFCAT" 2266980 NIL QFCAT (NIL T) -9 NIL 2267973) (-931 2256596 2257797 2259388 "QFCAT-" 2259482 NIL QFCAT- (NIL T T) -8 NIL NIL) (-930 2256234 2256277 2256404 "QFCAT2" 2256547 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-929 2255694 2255804 2255934 "QEQUAT" 2256124 T QEQUAT (NIL) -8 NIL NIL) (-928 2248861 2249932 2251115 "QCMPACK" 2254627 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-927 2246437 2246858 2247286 "QALGSET" 2248516 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-926 2245682 2245856 2246088 "QALGSET2" 2246257 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-925 2244373 2244596 2244913 "PWFFINTB" 2245455 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-924 2242561 2242729 2243082 "PUSHVAR" 2244187 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-923 2238479 2239533 2239574 "PTRANFN" 2241458 NIL PTRANFN (NIL T) -9 NIL NIL) (-922 2236891 2237182 2237503 "PTPACK" 2238190 NIL PTPACK (NIL T) -7 NIL NIL) (-921 2236527 2236584 2236691 "PTFUNC2" 2236828 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-920 2231004 2235345 2235385 "PTCAT" 2235753 NIL PTCAT (NIL T) -9 NIL 2235915) (-919 2230662 2230697 2230821 "PSQFR" 2230963 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-918 2229257 2229555 2229889 "PSEUDLIN" 2230360 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-917 2216064 2218429 2220752 "PSETPK" 2227017 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-916 2209151 2211865 2211959 "PSETCAT" 2214940 NIL PSETCAT (NIL T T T T) -9 NIL 2215754) (-915 2206989 2207623 2208442 "PSETCAT-" 2208447 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-914 2206338 2206503 2206531 "PSCURVE" 2206799 T PSCURVE (NIL) -9 NIL 2206966) (-913 2202790 2204316 2204380 "PSCAT" 2205216 NIL PSCAT (NIL T T T) -9 NIL 2205456) (-912 2201854 2202070 2202469 "PSCAT-" 2202474 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-911 2200506 2201139 2201353 "PRTITION" 2201660 T PRTITION (NIL) -8 NIL NIL) (-910 2189604 2191810 2193998 "PRS" 2198368 NIL PRS (NIL T T) -7 NIL NIL) (-909 2187463 2188955 2188995 "PRQAGG" 2189178 NIL PRQAGG (NIL T) -9 NIL 2189280) (-908 2187034 2187136 2187164 "PROPLOG" 2187349 T PROPLOG (NIL) -9 NIL NIL) (-907 2184157 2184722 2185249 "PROPFRML" 2186539 NIL PROPFRML (NIL T) -8 NIL NIL) (-906 2183617 2183727 2183857 "PROPERTY" 2184047 T PROPERTY (NIL) -8 NIL NIL) (-905 2177391 2181783 2182603 "PRODUCT" 2182843 NIL PRODUCT (NIL T T) -8 NIL NIL) (-904 2174667 2176851 2177084 "PR" 2177202 NIL PR (NIL T T) -8 NIL NIL) (-903 2174463 2174495 2174554 "PRINT" 2174628 T PRINT (NIL) -7 NIL NIL) (-902 2173803 2173920 2174072 "PRIMES" 2174343 NIL PRIMES (NIL T) -7 NIL NIL) (-901 2171868 2172269 2172735 "PRIMELT" 2173382 NIL PRIMELT (NIL T) -7 NIL NIL) (-900 2171597 2171646 2171674 "PRIMCAT" 2171798 T PRIMCAT (NIL) -9 NIL NIL) (-899 2167758 2171535 2171580 "PRIMARR" 2171585 NIL PRIMARR (NIL T) -8 NIL NIL) (-898 2166765 2166943 2167171 "PRIMARR2" 2167576 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-897 2166408 2166464 2166575 "PREASSOC" 2166703 NIL PREASSOC (NIL T T) -7 NIL NIL) (-896 2165883 2166016 2166044 "PPCURVE" 2166249 T PPCURVE (NIL) -9 NIL 2166385) (-895 2165505 2165678 2165761 "PORTNUM" 2165820 T PORTNUM (NIL) -8 NIL NIL) (-894 2162864 2163263 2163855 "POLYROOT" 2165086 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-893 2156770 2162470 2162629 "POLY" 2162737 NIL POLY (NIL T) -8 NIL NIL) (-892 2156155 2156213 2156446 "POLYLIFT" 2156706 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-891 2152440 2152889 2153517 "POLYCATQ" 2155700 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-890 2139481 2144878 2144942 "POLYCAT" 2148427 NIL POLYCAT (NIL T T T) -9 NIL 2150354) (-889 2132932 2134793 2137176 "POLYCAT-" 2137181 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-888 2132521 2132589 2132708 "POLY2UP" 2132858 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-887 2132157 2132214 2132321 "POLY2" 2132458 NIL POLY2 (NIL T T) -7 NIL NIL) (-886 2130842 2131081 2131357 "POLUTIL" 2131931 NIL POLUTIL (NIL T T) -7 NIL NIL) (-885 2129204 2129481 2129811 "POLTOPOL" 2130564 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-884 2124727 2129141 2129186 "POINT" 2129191 NIL POINT (NIL T) -8 NIL NIL) (-883 2122914 2123271 2123646 "PNTHEORY" 2124372 T PNTHEORY (NIL) -7 NIL NIL) (-882 2121342 2121639 2122048 "PMTOOLS" 2122612 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-881 2120935 2121013 2121130 "PMSYM" 2121258 NIL PMSYM (NIL T) -7 NIL NIL) (-880 2120445 2120514 2120688 "PMQFCAT" 2120860 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-879 2119800 2119910 2120066 "PMPRED" 2120322 NIL PMPRED (NIL T) -7 NIL NIL) (-878 2119196 2119282 2119443 "PMPREDFS" 2119701 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-877 2117842 2118050 2118434 "PMPLCAT" 2118958 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-876 2117374 2117453 2117605 "PMLSAGG" 2117757 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-875 2116851 2116927 2117107 "PMKERNEL" 2117292 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-874 2116468 2116543 2116656 "PMINS" 2116770 NIL PMINS (NIL T) -7 NIL NIL) (-873 2115898 2115967 2116182 "PMFS" 2116393 NIL PMFS (NIL T T T) -7 NIL NIL) (-872 2115129 2115247 2115451 "PMDOWN" 2115775 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-871 2114292 2114451 2114633 "PMASS" 2114967 T PMASS (NIL) -7 NIL NIL) (-870 2113566 2113677 2113840 "PMASSFS" 2114178 NIL PMASSFS (NIL T T) -7 NIL NIL) (-869 2113221 2113289 2113383 "PLOTTOOL" 2113492 T PLOTTOOL (NIL) -7 NIL NIL) (-868 2107843 2109032 2110180 "PLOT" 2112093 T PLOT (NIL) -8 NIL NIL) (-867 2103657 2104691 2105612 "PLOT3D" 2106942 T PLOT3D (NIL) -8 NIL NIL) (-866 2102569 2102746 2102981 "PLOT1" 2103461 NIL PLOT1 (NIL T) -7 NIL NIL) (-865 2077963 2082635 2087486 "PLEQN" 2097835 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-864 2077281 2077403 2077583 "PINTERP" 2077828 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-863 2076974 2077021 2077124 "PINTERPA" 2077228 NIL PINTERPA (NIL T T) -7 NIL NIL) (-862 2076213 2076780 2076867 "PI" 2076907 T PI (NIL) -8 NIL NIL) (-861 2074605 2075590 2075618 "PID" 2075800 T PID (NIL) -9 NIL 2075934) (-860 2074330 2074367 2074455 "PICOERCE" 2074562 NIL PICOERCE (NIL T) -7 NIL NIL) (-859 2073650 2073789 2073965 "PGROEB" 2074186 NIL PGROEB (NIL T) -7 NIL NIL) (-858 2069237 2070051 2070956 "PGE" 2072765 T PGE (NIL) -7 NIL NIL) (-857 2067361 2067607 2067973 "PGCD" 2068954 NIL PGCD (NIL T T T T) -7 NIL NIL) (-856 2066699 2066802 2066963 "PFRPAC" 2067245 NIL PFRPAC (NIL T) -7 NIL NIL) (-855 2063314 2065247 2065600 "PFR" 2066378 NIL PFR (NIL T) -8 NIL NIL) (-854 2061703 2061947 2062272 "PFOTOOLS" 2063061 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-853 2060236 2060475 2060826 "PFOQ" 2061460 NIL PFOQ (NIL T T T) -7 NIL NIL) (-852 2058713 2058925 2059287 "PFO" 2060020 NIL PFO (NIL T T T T T) -7 NIL NIL) (-851 2055236 2058602 2058671 "PF" 2058676 NIL PF (NIL NIL) -8 NIL NIL) (-850 2052665 2053946 2053974 "PFECAT" 2054559 T PFECAT (NIL) -9 NIL 2054943) (-849 2052110 2052264 2052478 "PFECAT-" 2052483 NIL PFECAT- (NIL T) -8 NIL NIL) (-848 2050714 2050965 2051266 "PFBRU" 2051859 NIL PFBRU (NIL T T) -7 NIL NIL) (-847 2048581 2048932 2049364 "PFBR" 2050365 NIL PFBR (NIL T T T T) -7 NIL NIL) (-846 2044432 2045957 2046633 "PERM" 2047938 NIL PERM (NIL T) -8 NIL NIL) (-845 2039698 2040639 2041509 "PERMGRP" 2043595 NIL PERMGRP (NIL T) -8 NIL NIL) (-844 2037769 2038762 2038803 "PERMCAT" 2039249 NIL PERMCAT (NIL T) -9 NIL 2039554) (-843 2037424 2037465 2037588 "PERMAN" 2037722 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-842 2034864 2036993 2037124 "PENDTREE" 2037326 NIL PENDTREE (NIL T) -8 NIL NIL) (-841 2032937 2033715 2033756 "PDRING" 2034413 NIL PDRING (NIL T) -9 NIL 2034698) (-840 2032040 2032258 2032620 "PDRING-" 2032625 NIL PDRING- (NIL T T) -8 NIL NIL) (-839 2029181 2029932 2030623 "PDEPROB" 2031369 T PDEPROB (NIL) -8 NIL NIL) (-838 2026752 2027248 2027797 "PDEPACK" 2028652 T PDEPACK (NIL) -7 NIL NIL) (-837 2025664 2025854 2026105 "PDECOMP" 2026551 NIL PDECOMP (NIL T T) -7 NIL NIL) (-836 2023276 2024091 2024119 "PDECAT" 2024904 T PDECAT (NIL) -9 NIL 2025615) (-835 2023029 2023062 2023151 "PCOMP" 2023237 NIL PCOMP (NIL T T) -7 NIL NIL) (-834 2021236 2021832 2022128 "PBWLB" 2022759 NIL PBWLB (NIL T) -8 NIL NIL) (-833 2013744 2015313 2016649 "PATTERN" 2019921 NIL PATTERN (NIL T) -8 NIL NIL) (-832 2013376 2013433 2013542 "PATTERN2" 2013681 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-831 2011133 2011521 2011978 "PATTERN1" 2012965 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-830 2008528 2009082 2009563 "PATRES" 2010698 NIL PATRES (NIL T T) -8 NIL NIL) (-829 2008092 2008159 2008291 "PATRES2" 2008455 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-828 2005989 2006389 2006794 "PATMATCH" 2007761 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-827 2005526 2005709 2005750 "PATMAB" 2005857 NIL PATMAB (NIL T) -9 NIL 2005940) (-826 2004071 2004380 2004638 "PATLRES" 2005331 NIL PATLRES (NIL T T T) -8 NIL NIL) (-825 2003617 2003740 2003781 "PATAB" 2003786 NIL PATAB (NIL T) -9 NIL 2003958) (-824 2001098 2001630 2002203 "PARTPERM" 2003064 T PARTPERM (NIL) -7 NIL NIL) (-823 2000719 2000782 2000884 "PARSURF" 2001029 NIL PARSURF (NIL T) -8 NIL NIL) (-822 2000351 2000408 2000517 "PARSU2" 2000656 NIL PARSU2 (NIL T T) -7 NIL NIL) (-821 2000115 2000155 2000222 "PARSER" 2000304 T PARSER (NIL) -7 NIL NIL) (-820 1999736 1999799 1999901 "PARSCURV" 2000046 NIL PARSCURV (NIL T) -8 NIL NIL) (-819 1999368 1999425 1999534 "PARSC2" 1999673 NIL PARSC2 (NIL T T) -7 NIL NIL) (-818 1999007 1999065 1999162 "PARPCURV" 1999304 NIL PARPCURV (NIL T) -8 NIL NIL) (-817 1998639 1998696 1998805 "PARPC2" 1998944 NIL PARPC2 (NIL T T) -7 NIL NIL) (-816 1998159 1998245 1998364 "PAN2EXPR" 1998540 T PAN2EXPR (NIL) -7 NIL NIL) (-815 1996965 1997280 1997508 "PALETTE" 1997951 T PALETTE (NIL) -8 NIL NIL) (-814 1995433 1995970 1996330 "PAIR" 1996651 NIL PAIR (NIL T T) -8 NIL NIL) (-813 1989283 1994692 1994886 "PADICRC" 1995288 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-812 1982491 1988629 1988813 "PADICRAT" 1989131 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-811 1980795 1982428 1982473 "PADIC" 1982478 NIL PADIC (NIL NIL) -8 NIL NIL) (-810 1978000 1979574 1979614 "PADICCT" 1980195 NIL PADICCT (NIL NIL) -9 NIL 1980477) (-809 1976957 1977157 1977425 "PADEPAC" 1977787 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-808 1976169 1976302 1976508 "PADE" 1976819 NIL PADE (NIL T T T) -7 NIL NIL) (-807 1974180 1975012 1975327 "OWP" 1975937 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-806 1973289 1973785 1973957 "OVAR" 1974048 NIL OVAR (NIL NIL) -8 NIL NIL) (-805 1972553 1972674 1972835 "OUT" 1973148 T OUT (NIL) -7 NIL NIL) (-804 1961607 1963778 1965948 "OUTFORM" 1970403 T OUTFORM (NIL) -8 NIL NIL) (-803 1961015 1961336 1961425 "OSI" 1961538 T OSI (NIL) -8 NIL NIL) (-802 1960546 1960884 1960912 "OSGROUP" 1960917 T OSGROUP (NIL) -9 NIL 1960939) (-801 1959291 1959518 1959803 "ORTHPOL" 1960293 NIL ORTHPOL (NIL T) -7 NIL NIL) (-800 1956662 1958952 1959090 "OREUP" 1959234 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-799 1954058 1956355 1956481 "ORESUP" 1956604 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-798 1951593 1952093 1952653 "OREPCTO" 1953547 NIL OREPCTO (NIL T T) -7 NIL NIL) (-797 1945503 1947709 1947749 "OREPCAT" 1950070 NIL OREPCAT (NIL T) -9 NIL 1951173) (-796 1942651 1943433 1944490 "OREPCAT-" 1944495 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-795 1941829 1942101 1942129 "ORDSET" 1942438 T ORDSET (NIL) -9 NIL 1942602) (-794 1941348 1941470 1941663 "ORDSET-" 1941668 NIL ORDSET- (NIL T) -8 NIL NIL) (-793 1939962 1940763 1940791 "ORDRING" 1940993 T ORDRING (NIL) -9 NIL 1941117) (-792 1939607 1939701 1939845 "ORDRING-" 1939850 NIL ORDRING- (NIL T) -8 NIL NIL) (-791 1938970 1939451 1939479 "ORDMON" 1939484 T ORDMON (NIL) -9 NIL 1939505) (-790 1938132 1938279 1938474 "ORDFUNS" 1938819 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-789 1937644 1938003 1938031 "ORDFIN" 1938036 T ORDFIN (NIL) -9 NIL 1938057) (-788 1934156 1936230 1936639 "ORDCOMP" 1937268 NIL ORDCOMP (NIL T) -8 NIL NIL) (-787 1933422 1933549 1933735 "ORDCOMP2" 1934016 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-786 1929929 1930812 1931649 "OPTPROB" 1932605 T OPTPROB (NIL) -8 NIL NIL) (-785 1926771 1927400 1928094 "OPTPACK" 1929255 T OPTPACK (NIL) -7 NIL NIL) (-784 1924497 1925233 1925261 "OPTCAT" 1926076 T OPTCAT (NIL) -9 NIL 1926722) (-783 1924265 1924304 1924370 "OPQUERY" 1924451 T OPQUERY (NIL) -7 NIL NIL) (-782 1921401 1922592 1923092 "OP" 1923797 NIL OP (NIL T) -8 NIL NIL) (-781 1918166 1920198 1920567 "ONECOMP" 1921065 NIL ONECOMP (NIL T) -8 NIL NIL) (-780 1917471 1917586 1917760 "ONECOMP2" 1918038 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-779 1916890 1916996 1917126 "OMSERVER" 1917361 T OMSERVER (NIL) -7 NIL NIL) (-778 1913779 1916331 1916371 "OMSAGG" 1916432 NIL OMSAGG (NIL T) -9 NIL 1916496) (-777 1912402 1912665 1912947 "OMPKG" 1913517 T OMPKG (NIL) -7 NIL NIL) (-776 1911832 1911935 1911963 "OM" 1912262 T OM (NIL) -9 NIL NIL) (-775 1910371 1911384 1911552 "OMLO" 1911713 NIL OMLO (NIL T T) -8 NIL NIL) (-774 1909301 1909448 1909674 "OMEXPR" 1910197 NIL OMEXPR (NIL T) -7 NIL NIL) (-773 1908619 1908847 1908983 "OMERR" 1909185 T OMERR (NIL) -8 NIL NIL) (-772 1907797 1908040 1908200 "OMERRK" 1908479 T OMERRK (NIL) -8 NIL NIL) (-771 1907275 1907474 1907582 "OMENC" 1907709 T OMENC (NIL) -8 NIL NIL) (-770 1901170 1902355 1903526 "OMDEV" 1906124 T OMDEV (NIL) -8 NIL NIL) (-769 1900239 1900410 1900604 "OMCONN" 1900996 T OMCONN (NIL) -8 NIL NIL) (-768 1898855 1899841 1899869 "OINTDOM" 1899874 T OINTDOM (NIL) -9 NIL 1899895) (-767 1894617 1895847 1896562 "OFMONOID" 1898172 NIL OFMONOID (NIL T) -8 NIL NIL) (-766 1894055 1894554 1894599 "ODVAR" 1894604 NIL ODVAR (NIL T) -8 NIL NIL) (-765 1891180 1893552 1893737 "ODR" 1893930 NIL ODR (NIL T T NIL) -8 NIL NIL) (-764 1883486 1890959 1891083 "ODPOL" 1891088 NIL ODPOL (NIL T) -8 NIL NIL) (-763 1877309 1883358 1883463 "ODP" 1883468 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-762 1876075 1876290 1876565 "ODETOOLS" 1877083 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-761 1873044 1873700 1874416 "ODESYS" 1875408 NIL ODESYS (NIL T T) -7 NIL NIL) (-760 1867948 1868856 1869879 "ODERTRIC" 1872119 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-759 1867374 1867456 1867650 "ODERED" 1867860 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-758 1864276 1864824 1865499 "ODERAT" 1866797 NIL ODERAT (NIL T T) -7 NIL NIL) (-757 1861244 1861708 1862304 "ODEPRRIC" 1863805 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-756 1859113 1859682 1860191 "ODEPROB" 1860755 T ODEPROB (NIL) -8 NIL NIL) (-755 1855645 1856128 1856774 "ODEPRIM" 1858592 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-754 1854898 1855000 1855258 "ODEPAL" 1855537 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-753 1851100 1851881 1852735 "ODEPACK" 1854064 T ODEPACK (NIL) -7 NIL NIL) (-752 1850137 1850244 1850472 "ODEINT" 1850989 NIL ODEINT (NIL T T) -7 NIL NIL) (-751 1844238 1845663 1847110 "ODEIFTBL" 1848710 T ODEIFTBL (NIL) -8 NIL NIL) (-750 1839582 1840368 1841326 "ODEEF" 1843397 NIL ODEEF (NIL T T) -7 NIL NIL) (-749 1838919 1839008 1839237 "ODECONST" 1839487 NIL ODECONST (NIL T T T) -7 NIL NIL) (-748 1837077 1837710 1837738 "ODECAT" 1838341 T ODECAT (NIL) -9 NIL 1838870) (-747 1833949 1836789 1836908 "OCT" 1836990 NIL OCT (NIL T) -8 NIL NIL) (-746 1833587 1833630 1833757 "OCTCT2" 1833900 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-745 1828421 1830859 1830899 "OC" 1831995 NIL OC (NIL T) -9 NIL 1832852) (-744 1825648 1826396 1827386 "OC-" 1827480 NIL OC- (NIL T T) -8 NIL NIL) (-743 1825027 1825469 1825497 "OCAMON" 1825502 T OCAMON (NIL) -9 NIL 1825523) (-742 1824585 1824900 1824928 "OASGP" 1824933 T OASGP (NIL) -9 NIL 1824953) (-741 1823873 1824336 1824364 "OAMONS" 1824404 T OAMONS (NIL) -9 NIL 1824447) (-740 1823314 1823721 1823749 "OAMON" 1823754 T OAMON (NIL) -9 NIL 1823774) (-739 1822619 1823111 1823139 "OAGROUP" 1823144 T OAGROUP (NIL) -9 NIL 1823164) (-738 1822309 1822359 1822447 "NUMTUBE" 1822563 NIL NUMTUBE (NIL T) -7 NIL NIL) (-737 1815882 1817400 1818936 "NUMQUAD" 1820793 T NUMQUAD (NIL) -7 NIL NIL) (-736 1811638 1812626 1813651 "NUMODE" 1814877 T NUMODE (NIL) -7 NIL NIL) (-735 1809042 1809888 1809916 "NUMINT" 1810833 T NUMINT (NIL) -9 NIL 1811589) (-734 1807990 1808187 1808405 "NUMFMT" 1808844 T NUMFMT (NIL) -7 NIL NIL) (-733 1794369 1797306 1799836 "NUMERIC" 1805499 NIL NUMERIC (NIL T) -7 NIL NIL) (-732 1788768 1793820 1793914 "NTSCAT" 1793919 NIL NTSCAT (NIL T T T T) -9 NIL 1793958) (-731 1787962 1788127 1788320 "NTPOLFN" 1788607 NIL NTPOLFN (NIL T) -7 NIL NIL) (-730 1775778 1784804 1785614 "NSUP" 1787184 NIL NSUP (NIL T) -8 NIL NIL) (-729 1775414 1775471 1775578 "NSUP2" 1775715 NIL NSUP2 (NIL T T) -7 NIL NIL) (-728 1765376 1775193 1775323 "NSMP" 1775328 NIL NSMP (NIL T T) -8 NIL NIL) (-727 1763808 1764109 1764466 "NREP" 1765064 NIL NREP (NIL T) -7 NIL NIL) (-726 1762399 1762651 1763009 "NPCOEF" 1763551 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-725 1761465 1761580 1761796 "NORMRETR" 1762280 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-724 1759512 1759802 1760210 "NORMPK" 1761173 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-723 1759197 1759225 1759349 "NORMMA" 1759478 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-722 1759024 1759154 1759183 "NONE" 1759188 T NONE (NIL) -8 NIL NIL) (-721 1758813 1758842 1758911 "NONE1" 1758988 NIL NONE1 (NIL T) -7 NIL NIL) (-720 1758298 1758360 1758545 "NODE1" 1758745 NIL NODE1 (NIL T T) -7 NIL NIL) (-719 1756592 1757461 1757716 "NNI" 1758063 T NNI (NIL) -8 NIL NIL) (-718 1755012 1755325 1755689 "NLINSOL" 1756260 NIL NLINSOL (NIL T) -7 NIL NIL) (-717 1751179 1752147 1753069 "NIPROB" 1754110 T NIPROB (NIL) -8 NIL NIL) (-716 1749936 1750170 1750472 "NFINTBAS" 1750941 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-715 1748644 1748875 1749156 "NCODIV" 1749704 NIL NCODIV (NIL T T) -7 NIL NIL) (-714 1748406 1748443 1748518 "NCNTFRAC" 1748601 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-713 1746586 1746950 1747370 "NCEP" 1748031 NIL NCEP (NIL T) -7 NIL NIL) (-712 1745498 1746237 1746265 "NASRING" 1746375 T NASRING (NIL) -9 NIL 1746449) (-711 1745293 1745337 1745431 "NASRING-" 1745436 NIL NASRING- (NIL T) -8 NIL NIL) (-710 1744447 1744946 1744974 "NARNG" 1745091 T NARNG (NIL) -9 NIL 1745182) (-709 1744139 1744206 1744340 "NARNG-" 1744345 NIL NARNG- (NIL T) -8 NIL NIL) (-708 1743018 1743225 1743460 "NAGSP" 1743924 T NAGSP (NIL) -7 NIL NIL) (-707 1734442 1736088 1737723 "NAGS" 1741403 T NAGS (NIL) -7 NIL NIL) (-706 1733006 1733310 1733637 "NAGF07" 1734135 T NAGF07 (NIL) -7 NIL NIL) (-705 1727588 1728868 1730164 "NAGF04" 1731730 T NAGF04 (NIL) -7 NIL NIL) (-704 1720620 1722218 1723835 "NAGF02" 1725991 T NAGF02 (NIL) -7 NIL NIL) (-703 1715884 1716974 1718081 "NAGF01" 1719533 T NAGF01 (NIL) -7 NIL NIL) (-702 1709544 1711102 1712679 "NAGE04" 1714327 T NAGE04 (NIL) -7 NIL NIL) (-701 1700785 1702888 1705000 "NAGE02" 1707452 T NAGE02 (NIL) -7 NIL NIL) (-700 1696778 1697715 1698669 "NAGE01" 1699851 T NAGE01 (NIL) -7 NIL NIL) (-699 1694585 1695116 1695671 "NAGD03" 1696243 T NAGD03 (NIL) -7 NIL NIL) (-698 1686371 1688290 1690235 "NAGD02" 1692660 T NAGD02 (NIL) -7 NIL NIL) (-697 1680230 1681643 1683071 "NAGD01" 1684963 T NAGD01 (NIL) -7 NIL NIL) (-696 1676487 1677297 1678122 "NAGC06" 1679425 T NAGC06 (NIL) -7 NIL NIL) (-695 1674964 1675293 1675646 "NAGC05" 1676154 T NAGC05 (NIL) -7 NIL NIL) (-694 1674348 1674465 1674607 "NAGC02" 1674842 T NAGC02 (NIL) -7 NIL NIL) (-693 1673410 1673967 1674007 "NAALG" 1674086 NIL NAALG (NIL T) -9 NIL 1674147) (-692 1673245 1673274 1673364 "NAALG-" 1673369 NIL NAALG- (NIL T T) -8 NIL NIL) (-691 1667195 1668303 1669490 "MULTSQFR" 1672141 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-690 1666514 1666589 1666773 "MULTFACT" 1667107 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-689 1659708 1663619 1663671 "MTSCAT" 1664731 NIL MTSCAT (NIL T T) -9 NIL 1665245) (-688 1659420 1659474 1659566 "MTHING" 1659648 NIL MTHING (NIL T) -7 NIL NIL) (-687 1659212 1659245 1659305 "MSYSCMD" 1659380 T MSYSCMD (NIL) -7 NIL NIL) (-686 1655324 1657967 1658287 "MSET" 1658925 NIL MSET (NIL T) -8 NIL NIL) (-685 1652420 1654886 1654927 "MSETAGG" 1654932 NIL MSETAGG (NIL T) -9 NIL 1654966) (-684 1648276 1649818 1650559 "MRING" 1651723 NIL MRING (NIL T T) -8 NIL NIL) (-683 1647846 1647913 1648042 "MRF2" 1648203 NIL MRF2 (NIL T T T) -7 NIL NIL) (-682 1647464 1647499 1647643 "MRATFAC" 1647805 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-681 1645076 1645371 1645802 "MPRFF" 1647169 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-680 1639096 1644931 1645027 "MPOLY" 1645032 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-679 1638586 1638621 1638829 "MPCPF" 1639055 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-678 1638102 1638145 1638328 "MPC3" 1638537 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-677 1637303 1637384 1637603 "MPC2" 1638017 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-676 1635604 1635941 1636331 "MONOTOOL" 1636963 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-675 1634729 1635064 1635092 "MONOID" 1635369 T MONOID (NIL) -9 NIL 1635541) (-674 1634107 1634270 1634513 "MONOID-" 1634518 NIL MONOID- (NIL T) -8 NIL NIL) (-673 1625088 1631074 1631133 "MONOGEN" 1631807 NIL MONOGEN (NIL T T) -9 NIL 1632263) (-672 1622306 1623041 1624041 "MONOGEN-" 1624160 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-671 1621166 1621586 1621614 "MONADWU" 1622006 T MONADWU (NIL) -9 NIL 1622244) (-670 1620538 1620697 1620945 "MONADWU-" 1620950 NIL MONADWU- (NIL T) -8 NIL NIL) (-669 1619924 1620142 1620170 "MONAD" 1620377 T MONAD (NIL) -9 NIL 1620489) (-668 1619609 1619687 1619819 "MONAD-" 1619824 NIL MONAD- (NIL T) -8 NIL NIL) (-667 1617860 1618522 1618801 "MOEBIUS" 1619362 NIL MOEBIUS (NIL T) -8 NIL NIL) (-666 1617254 1617632 1617672 "MODULE" 1617677 NIL MODULE (NIL T) -9 NIL 1617703) (-665 1616822 1616918 1617108 "MODULE-" 1617113 NIL MODULE- (NIL T T) -8 NIL NIL) (-664 1614493 1615188 1615514 "MODRING" 1616647 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-663 1611449 1612614 1613131 "MODOP" 1614025 NIL MODOP (NIL T T) -8 NIL NIL) (-662 1609636 1610088 1610429 "MODMONOM" 1611248 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-661 1599315 1607840 1608262 "MODMON" 1609264 NIL MODMON (NIL T T) -8 NIL NIL) (-660 1596441 1598159 1598435 "MODFIELD" 1599190 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-659 1595445 1595722 1595912 "MMLFORM" 1596271 T MMLFORM (NIL) -8 NIL NIL) (-658 1594971 1595014 1595193 "MMAP" 1595396 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-657 1593208 1593985 1594025 "MLO" 1594442 NIL MLO (NIL T) -9 NIL 1594683) (-656 1590575 1591090 1591692 "MLIFT" 1592689 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-655 1589966 1590050 1590204 "MKUCFUNC" 1590486 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-654 1589565 1589635 1589758 "MKRECORD" 1589889 NIL MKRECORD (NIL T T) -7 NIL NIL) (-653 1588613 1588774 1589002 "MKFUNC" 1589376 NIL MKFUNC (NIL T) -7 NIL NIL) (-652 1588001 1588105 1588261 "MKFLCFN" 1588496 NIL MKFLCFN (NIL T) -7 NIL NIL) (-651 1587427 1587794 1587883 "MKCHSET" 1587945 NIL MKCHSET (NIL T) -8 NIL NIL) (-650 1586704 1586806 1586991 "MKBCFUNC" 1587320 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-649 1583388 1586258 1586394 "MINT" 1586588 T MINT (NIL) -8 NIL NIL) (-648 1582200 1582443 1582720 "MHROWRED" 1583143 NIL MHROWRED (NIL T) -7 NIL NIL) (-647 1577471 1580645 1581069 "MFLOAT" 1581796 T MFLOAT (NIL) -8 NIL NIL) (-646 1576828 1576904 1577075 "MFINFACT" 1577383 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-645 1573143 1573991 1574875 "MESH" 1575964 T MESH (NIL) -7 NIL NIL) (-644 1571533 1571845 1572198 "MDDFACT" 1572830 NIL MDDFACT (NIL T) -7 NIL NIL) (-643 1568376 1570693 1570734 "MDAGG" 1570989 NIL MDAGG (NIL T) -9 NIL 1571132) (-642 1558074 1567669 1567876 "MCMPLX" 1568189 T MCMPLX (NIL) -8 NIL NIL) (-641 1557215 1557361 1557561 "MCDEN" 1557923 NIL MCDEN (NIL T T) -7 NIL NIL) (-640 1555105 1555375 1555755 "MCALCFN" 1556945 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-639 1554016 1554189 1554430 "MAYBE" 1554903 NIL MAYBE (NIL T) -8 NIL NIL) (-638 1551638 1552161 1552722 "MATSTOR" 1553487 NIL MATSTOR (NIL T) -7 NIL NIL) (-637 1547647 1551013 1551260 "MATRIX" 1551423 NIL MATRIX (NIL T) -8 NIL NIL) (-636 1543416 1544120 1544856 "MATLIN" 1547004 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-635 1533614 1536752 1536828 "MATCAT" 1541666 NIL MATCAT (NIL T T T) -9 NIL 1543083) (-634 1529979 1530992 1532347 "MATCAT-" 1532352 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-633 1528581 1528734 1529065 "MATCAT2" 1529814 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-632 1526693 1527017 1527401 "MAPPKG3" 1528256 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-631 1525674 1525847 1526069 "MAPPKG2" 1526517 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-630 1524173 1524457 1524784 "MAPPKG1" 1525380 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-629 1523784 1523842 1523965 "MAPHACK3" 1524109 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-628 1523376 1523437 1523551 "MAPHACK2" 1523716 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-627 1522814 1522917 1523059 "MAPHACK1" 1523267 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-626 1520922 1521516 1521819 "MAGMA" 1522543 NIL MAGMA (NIL T) -8 NIL NIL) (-625 1517397 1519166 1519626 "M3D" 1520495 NIL M3D (NIL T) -8 NIL NIL) (-624 1511553 1515768 1515809 "LZSTAGG" 1516591 NIL LZSTAGG (NIL T) -9 NIL 1516886) (-623 1507526 1508684 1510141 "LZSTAGG-" 1510146 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-622 1504642 1505419 1505905 "LWORD" 1507072 NIL LWORD (NIL T) -8 NIL NIL) (-621 1497802 1504413 1504547 "LSQM" 1504552 NIL LSQM (NIL NIL T) -8 NIL NIL) (-620 1497026 1497165 1497393 "LSPP" 1497657 NIL LSPP (NIL T T T T) -7 NIL NIL) (-619 1494838 1495139 1495595 "LSMP" 1496715 NIL LSMP (NIL T T T T) -7 NIL NIL) (-618 1491617 1492291 1493021 "LSMP1" 1494140 NIL LSMP1 (NIL T) -7 NIL NIL) (-617 1485544 1490786 1490827 "LSAGG" 1490889 NIL LSAGG (NIL T) -9 NIL 1490967) (-616 1482239 1483163 1484376 "LSAGG-" 1484381 NIL LSAGG- (NIL T T) -8 NIL NIL) (-615 1479865 1481383 1481632 "LPOLY" 1482034 NIL LPOLY (NIL T T) -8 NIL NIL) (-614 1479447 1479532 1479655 "LPEFRAC" 1479774 NIL LPEFRAC (NIL T) -7 NIL NIL) (-613 1477794 1478541 1478794 "LO" 1479279 NIL LO (NIL T T T) -8 NIL NIL) (-612 1477448 1477560 1477588 "LOGIC" 1477699 T LOGIC (NIL) -9 NIL 1477779) (-611 1477310 1477333 1477404 "LOGIC-" 1477409 NIL LOGIC- (NIL T) -8 NIL NIL) (-610 1476503 1476643 1476836 "LODOOPS" 1477166 NIL LODOOPS (NIL T T) -7 NIL NIL) (-609 1473921 1476420 1476485 "LODO" 1476490 NIL LODO (NIL T NIL) -8 NIL NIL) (-608 1472467 1472702 1473053 "LODOF" 1473668 NIL LODOF (NIL T T) -7 NIL NIL) (-607 1468887 1471323 1471363 "LODOCAT" 1471795 NIL LODOCAT (NIL T) -9 NIL 1472006) (-606 1468621 1468679 1468805 "LODOCAT-" 1468810 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-605 1465935 1468462 1468580 "LODO2" 1468585 NIL LODO2 (NIL T T) -8 NIL NIL) (-604 1463364 1465872 1465917 "LODO1" 1465922 NIL LODO1 (NIL T) -8 NIL NIL) (-603 1462227 1462392 1462703 "LODEEF" 1463187 NIL LODEEF (NIL T T T) -7 NIL NIL) (-602 1457514 1460358 1460399 "LNAGG" 1461346 NIL LNAGG (NIL T) -9 NIL 1461790) (-601 1456661 1456875 1457217 "LNAGG-" 1457222 NIL LNAGG- (NIL T T) -8 NIL NIL) (-600 1452826 1453588 1454226 "LMOPS" 1456077 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-599 1452224 1452586 1452626 "LMODULE" 1452686 NIL LMODULE (NIL T) -9 NIL 1452728) (-598 1449470 1451869 1451992 "LMDICT" 1452134 NIL LMDICT (NIL T) -8 NIL NIL) (-597 1442697 1448416 1448714 "LIST" 1449205 NIL LIST (NIL T) -8 NIL NIL) (-596 1442222 1442296 1442435 "LIST3" 1442617 NIL LIST3 (NIL T T T) -7 NIL NIL) (-595 1441229 1441407 1441635 "LIST2" 1442040 NIL LIST2 (NIL T T) -7 NIL NIL) (-594 1439363 1439675 1440074 "LIST2MAP" 1440876 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-593 1438076 1438756 1438796 "LINEXP" 1439049 NIL LINEXP (NIL T) -9 NIL 1439197) (-592 1436723 1436983 1437280 "LINDEP" 1437828 NIL LINDEP (NIL T T) -7 NIL NIL) (-591 1433490 1434209 1434986 "LIMITRF" 1435978 NIL LIMITRF (NIL T) -7 NIL NIL) (-590 1431770 1432065 1432480 "LIMITPS" 1433185 NIL LIMITPS (NIL T T) -7 NIL NIL) (-589 1426225 1431281 1431509 "LIE" 1431591 NIL LIE (NIL T T) -8 NIL NIL) (-588 1425276 1425719 1425759 "LIECAT" 1425899 NIL LIECAT (NIL T) -9 NIL 1426050) (-587 1425117 1425144 1425232 "LIECAT-" 1425237 NIL LIECAT- (NIL T T) -8 NIL NIL) (-586 1417729 1424566 1424731 "LIB" 1424972 T LIB (NIL) -8 NIL NIL) (-585 1413366 1414247 1415182 "LGROBP" 1416846 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-584 1411232 1411506 1411868 "LF" 1413087 NIL LF (NIL T T) -7 NIL NIL) (-583 1410072 1410764 1410792 "LFCAT" 1410999 T LFCAT (NIL) -9 NIL 1411138) (-582 1406984 1407610 1408296 "LEXTRIPK" 1409438 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-581 1403690 1404554 1405057 "LEXP" 1406564 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-580 1402088 1402401 1402802 "LEADCDET" 1403372 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-579 1401281 1401355 1401583 "LAZM3PK" 1402009 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-578 1396198 1399360 1399897 "LAUPOL" 1400794 NIL LAUPOL (NIL T T) -8 NIL NIL) (-577 1395765 1395809 1395976 "LAPLACE" 1396148 NIL LAPLACE (NIL T T) -7 NIL NIL) (-576 1393693 1394866 1395117 "LA" 1395598 NIL LA (NIL T T T) -8 NIL NIL) (-575 1392756 1393350 1393390 "LALG" 1393451 NIL LALG (NIL T) -9 NIL 1393509) (-574 1392471 1392530 1392665 "LALG-" 1392670 NIL LALG- (NIL T T) -8 NIL NIL) (-573 1391381 1391568 1391865 "KOVACIC" 1392271 NIL KOVACIC (NIL T T) -7 NIL NIL) (-572 1391216 1391240 1391281 "KONVERT" 1391343 NIL KONVERT (NIL T) -9 NIL NIL) (-571 1391051 1391075 1391116 "KOERCE" 1391178 NIL KOERCE (NIL T) -9 NIL NIL) (-570 1388785 1389545 1389938 "KERNEL" 1390690 NIL KERNEL (NIL T) -8 NIL NIL) (-569 1388287 1388368 1388498 "KERNEL2" 1388699 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-568 1382139 1386827 1386881 "KDAGG" 1387258 NIL KDAGG (NIL T T) -9 NIL 1387464) (-567 1381668 1381792 1381997 "KDAGG-" 1382002 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-566 1374843 1381329 1381484 "KAFILE" 1381546 NIL KAFILE (NIL T) -8 NIL NIL) (-565 1369298 1374354 1374582 "JORDAN" 1374664 NIL JORDAN (NIL T T) -8 NIL NIL) (-564 1369027 1369086 1369173 "JAVACODE" 1369231 T JAVACODE (NIL) -8 NIL NIL) (-563 1365327 1367233 1367287 "IXAGG" 1368216 NIL IXAGG (NIL T T) -9 NIL 1368675) (-562 1364246 1364552 1364971 "IXAGG-" 1364976 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-561 1359831 1364168 1364227 "IVECTOR" 1364232 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-560 1358597 1358834 1359100 "ITUPLE" 1359598 NIL ITUPLE (NIL T) -8 NIL NIL) (-559 1357033 1357210 1357516 "ITRIGMNP" 1358419 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-558 1355778 1355982 1356265 "ITFUN3" 1356809 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-557 1355410 1355467 1355576 "ITFUN2" 1355715 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-556 1353212 1354283 1354580 "ITAYLOR" 1355145 NIL ITAYLOR (NIL T) -8 NIL NIL) (-555 1342200 1347398 1348557 "ISUPS" 1352085 NIL ISUPS (NIL T) -8 NIL NIL) (-554 1341304 1341444 1341680 "ISUMP" 1342047 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-553 1336568 1341105 1341184 "ISTRING" 1341257 NIL ISTRING (NIL NIL) -8 NIL NIL) (-552 1335781 1335862 1336077 "IRURPK" 1336482 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-551 1334717 1334918 1335158 "IRSN" 1335561 T IRSN (NIL) -7 NIL NIL) (-550 1332752 1333107 1333542 "IRRF2F" 1334355 NIL IRRF2F (NIL T) -7 NIL NIL) (-549 1332499 1332537 1332613 "IRREDFFX" 1332708 NIL IRREDFFX (NIL T) -7 NIL NIL) (-548 1331114 1331373 1331672 "IROOT" 1332232 NIL IROOT (NIL T) -7 NIL NIL) (-547 1327752 1328803 1329493 "IR" 1330456 NIL IR (NIL T) -8 NIL NIL) (-546 1325365 1325860 1326426 "IR2" 1327230 NIL IR2 (NIL T T) -7 NIL NIL) (-545 1324441 1324554 1324774 "IR2F" 1325248 NIL IR2F (NIL T T) -7 NIL NIL) (-544 1324232 1324266 1324326 "IPRNTPK" 1324401 T IPRNTPK (NIL) -7 NIL NIL) (-543 1320786 1324121 1324190 "IPF" 1324195 NIL IPF (NIL NIL) -8 NIL NIL) (-542 1319103 1320711 1320768 "IPADIC" 1320773 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-541 1318602 1318660 1318849 "INVLAPLA" 1319039 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-540 1308251 1310604 1312990 "INTTR" 1316266 NIL INTTR (NIL T T) -7 NIL NIL) (-539 1304599 1305340 1306203 "INTTOOLS" 1307437 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-538 1304185 1304276 1304393 "INTSLPE" 1304502 T INTSLPE (NIL) -7 NIL NIL) (-537 1302135 1304108 1304167 "INTRVL" 1304172 NIL INTRVL (NIL T) -8 NIL NIL) (-536 1299742 1300254 1300828 "INTRF" 1301620 NIL INTRF (NIL T) -7 NIL NIL) (-535 1299157 1299254 1299395 "INTRET" 1299640 NIL INTRET (NIL T) -7 NIL NIL) (-534 1297159 1297548 1298017 "INTRAT" 1298765 NIL INTRAT (NIL T T) -7 NIL NIL) (-533 1294392 1294975 1295600 "INTPM" 1296644 NIL INTPM (NIL T T) -7 NIL NIL) (-532 1291101 1291700 1292444 "INTPAF" 1293778 NIL INTPAF (NIL T T T) -7 NIL NIL) (-531 1286344 1287290 1288325 "INTPACK" 1290086 T INTPACK (NIL) -7 NIL NIL) (-530 1283198 1286073 1286200 "INT" 1286237 T INT (NIL) -8 NIL NIL) (-529 1282450 1282602 1282810 "INTHERTR" 1283040 NIL INTHERTR (NIL T T) -7 NIL NIL) (-528 1281889 1281969 1282157 "INTHERAL" 1282364 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-527 1279735 1280178 1280635 "INTHEORY" 1281452 T INTHEORY (NIL) -7 NIL NIL) (-526 1271057 1272678 1274456 "INTG0" 1278087 NIL INTG0 (NIL T T T) -7 NIL NIL) (-525 1251630 1256420 1261230 "INTFTBL" 1266267 T INTFTBL (NIL) -8 NIL NIL) (-524 1250879 1251017 1251190 "INTFACT" 1251489 NIL INTFACT (NIL T) -7 NIL NIL) (-523 1248270 1248716 1249279 "INTEF" 1250433 NIL INTEF (NIL T T) -7 NIL NIL) (-522 1246732 1247481 1247509 "INTDOM" 1247810 T INTDOM (NIL) -9 NIL 1248017) (-521 1246101 1246275 1246517 "INTDOM-" 1246522 NIL INTDOM- (NIL T) -8 NIL NIL) (-520 1242594 1244526 1244580 "INTCAT" 1245379 NIL INTCAT (NIL T) -9 NIL 1245698) (-519 1242067 1242169 1242297 "INTBIT" 1242486 T INTBIT (NIL) -7 NIL NIL) (-518 1240742 1240896 1241209 "INTALG" 1241912 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-517 1240199 1240289 1240459 "INTAF" 1240646 NIL INTAF (NIL T T) -7 NIL NIL) (-516 1233653 1240009 1240149 "INTABL" 1240154 NIL INTABL (NIL T T T) -8 NIL NIL) (-515 1228604 1231333 1231361 "INS" 1232329 T INS (NIL) -9 NIL 1233010) (-514 1225844 1226615 1227589 "INS-" 1227662 NIL INS- (NIL T) -8 NIL NIL) (-513 1224623 1224850 1225147 "INPSIGN" 1225597 NIL INPSIGN (NIL T T) -7 NIL NIL) (-512 1223741 1223858 1224055 "INPRODPF" 1224503 NIL INPRODPF (NIL T T) -7 NIL NIL) (-511 1222635 1222752 1222989 "INPRODFF" 1223621 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-510 1221635 1221787 1222047 "INNMFACT" 1222471 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-509 1220832 1220929 1221117 "INMODGCD" 1221534 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-508 1219341 1219585 1219909 "INFSP" 1220577 NIL INFSP (NIL T T T) -7 NIL NIL) (-507 1218525 1218642 1218825 "INFPROD0" 1219221 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-506 1215536 1216694 1217185 "INFORM" 1218042 T INFORM (NIL) -8 NIL NIL) (-505 1215146 1215206 1215304 "INFORM1" 1215471 NIL INFORM1 (NIL T) -7 NIL NIL) (-504 1214669 1214758 1214872 "INFINITY" 1215052 T INFINITY (NIL) -7 NIL NIL) (-503 1213286 1213535 1213856 "INEP" 1214417 NIL INEP (NIL T T T) -7 NIL NIL) (-502 1212562 1213183 1213248 "INDE" 1213253 NIL INDE (NIL T) -8 NIL NIL) (-501 1212126 1212194 1212311 "INCRMAPS" 1212489 NIL INCRMAPS (NIL T) -7 NIL NIL) (-500 1207437 1208362 1209306 "INBFF" 1211214 NIL INBFF (NIL T) -7 NIL NIL) (-499 1203932 1207282 1207385 "IMATRIX" 1207390 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-498 1202644 1202767 1203082 "IMATQF" 1203788 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-497 1200864 1201091 1201428 "IMATLIN" 1202400 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-496 1195490 1200788 1200846 "ILIST" 1200851 NIL ILIST (NIL T NIL) -8 NIL NIL) (-495 1193443 1195350 1195463 "IIARRAY2" 1195468 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-494 1188811 1193354 1193418 "IFF" 1193423 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-493 1183854 1188103 1188291 "IFARRAY" 1188668 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-492 1183061 1183758 1183831 "IFAMON" 1183836 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-491 1182645 1182710 1182764 "IEVALAB" 1182971 NIL IEVALAB (NIL T T) -9 NIL NIL) (-490 1182320 1182388 1182548 "IEVALAB-" 1182553 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-489 1181978 1182234 1182297 "IDPO" 1182302 NIL IDPO (NIL T T) -8 NIL NIL) (-488 1181255 1181867 1181942 "IDPOAMS" 1181947 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-487 1180589 1181144 1181219 "IDPOAM" 1181224 NIL IDPOAM (NIL T T) -8 NIL NIL) (-486 1179675 1179925 1179978 "IDPC" 1180391 NIL IDPC (NIL T T) -9 NIL 1180540) (-485 1179171 1179567 1179640 "IDPAM" 1179645 NIL IDPAM (NIL T T) -8 NIL NIL) (-484 1178574 1179063 1179136 "IDPAG" 1179141 NIL IDPAG (NIL T T) -8 NIL NIL) (-483 1174829 1175677 1176572 "IDECOMP" 1177731 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-482 1167702 1168752 1169799 "IDEAL" 1173865 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-481 1166866 1166978 1167177 "ICDEN" 1167586 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-480 1165965 1166346 1166493 "ICARD" 1166739 T ICARD (NIL) -8 NIL NIL) (-479 1164037 1164350 1164753 "IBPTOOLS" 1165642 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-478 1159671 1163657 1163770 "IBITS" 1163956 NIL IBITS (NIL NIL) -8 NIL NIL) (-477 1156394 1156970 1157665 "IBATOOL" 1159088 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-476 1154174 1154635 1155168 "IBACHIN" 1155929 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-475 1152051 1154020 1154123 "IARRAY2" 1154128 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-474 1148204 1151977 1152034 "IARRAY1" 1152039 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-473 1142142 1146622 1147100 "IAN" 1147746 T IAN (NIL) -8 NIL NIL) (-472 1141653 1141710 1141883 "IALGFACT" 1142079 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-471 1141181 1141294 1141322 "HYPCAT" 1141529 T HYPCAT (NIL) -9 NIL NIL) (-470 1140719 1140836 1141022 "HYPCAT-" 1141027 NIL HYPCAT- (NIL T) -8 NIL NIL) (-469 1140341 1140514 1140597 "HOSTNAME" 1140656 T HOSTNAME (NIL) -8 NIL NIL) (-468 1137021 1138352 1138393 "HOAGG" 1139374 NIL HOAGG (NIL T) -9 NIL 1140053) (-467 1135615 1136014 1136540 "HOAGG-" 1136545 NIL HOAGG- (NIL T T) -8 NIL NIL) (-466 1129445 1135056 1135222 "HEXADEC" 1135469 T HEXADEC (NIL) -8 NIL NIL) (-465 1128193 1128415 1128678 "HEUGCD" 1129222 NIL HEUGCD (NIL T) -7 NIL NIL) (-464 1127296 1128030 1128160 "HELLFDIV" 1128165 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-463 1125524 1127073 1127161 "HEAP" 1127240 NIL HEAP (NIL T) -8 NIL NIL) (-462 1124863 1125103 1125231 "HEADAST" 1125416 T HEADAST (NIL) -8 NIL NIL) (-461 1118730 1124778 1124840 "HDP" 1124845 NIL HDP (NIL NIL T) -8 NIL NIL) (-460 1112442 1118367 1118518 "HDMP" 1118631 NIL HDMP (NIL NIL T) -8 NIL NIL) (-459 1111767 1111906 1112070 "HB" 1112298 T HB (NIL) -7 NIL NIL) (-458 1105264 1111613 1111717 "HASHTBL" 1111722 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-457 1103017 1104892 1105071 "HACKPI" 1105105 T HACKPI (NIL) -8 NIL NIL) (-456 1098713 1102871 1102983 "GTSET" 1102988 NIL GTSET (NIL T T T T) -8 NIL NIL) (-455 1092239 1098591 1098689 "GSTBL" 1098694 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-454 1084472 1091275 1091539 "GSERIES" 1092030 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-453 1083495 1083948 1083976 "GROUP" 1084237 T GROUP (NIL) -9 NIL 1084396) (-452 1082611 1082834 1083178 "GROUP-" 1083183 NIL GROUP- (NIL T) -8 NIL NIL) (-451 1080980 1081299 1081686 "GROEBSOL" 1082288 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-450 1079921 1080183 1080234 "GRMOD" 1080763 NIL GRMOD (NIL T T) -9 NIL 1080931) (-449 1079689 1079725 1079853 "GRMOD-" 1079858 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-448 1075014 1076043 1077043 "GRIMAGE" 1078709 T GRIMAGE (NIL) -8 NIL NIL) (-447 1073481 1073741 1074065 "GRDEF" 1074710 T GRDEF (NIL) -7 NIL NIL) (-446 1072925 1073041 1073182 "GRAY" 1073360 T GRAY (NIL) -7 NIL NIL) (-445 1072159 1072539 1072590 "GRALG" 1072743 NIL GRALG (NIL T T) -9 NIL 1072835) (-444 1071820 1071893 1072056 "GRALG-" 1072061 NIL GRALG- (NIL T T T) -8 NIL NIL) (-443 1068628 1071409 1071585 "GPOLSET" 1071727 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-442 1067984 1068041 1068298 "GOSPER" 1068565 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-441 1063743 1064422 1064948 "GMODPOL" 1067683 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-440 1062748 1062932 1063170 "GHENSEL" 1063555 NIL GHENSEL (NIL T T) -7 NIL NIL) (-439 1056814 1057657 1058683 "GENUPS" 1061832 NIL GENUPS (NIL T T) -7 NIL NIL) (-438 1056511 1056562 1056651 "GENUFACT" 1056757 NIL GENUFACT (NIL T) -7 NIL NIL) (-437 1055923 1056000 1056165 "GENPGCD" 1056429 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-436 1055397 1055432 1055645 "GENMFACT" 1055882 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-435 1053965 1054220 1054527 "GENEEZ" 1055140 NIL GENEEZ (NIL T T) -7 NIL NIL) (-434 1047839 1053578 1053739 "GDMP" 1053888 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-433 1037216 1041610 1042716 "GCNAALG" 1046822 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-432 1035638 1036510 1036538 "GCDDOM" 1036793 T GCDDOM (NIL) -9 NIL 1036950) (-431 1035108 1035235 1035450 "GCDDOM-" 1035455 NIL GCDDOM- (NIL T) -8 NIL NIL) (-430 1033780 1033965 1034269 "GB" 1034887 NIL GB (NIL T T T T) -7 NIL NIL) (-429 1022400 1024726 1027118 "GBINTERN" 1031471 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-428 1020237 1020529 1020950 "GBF" 1022075 NIL GBF (NIL T T T T) -7 NIL NIL) (-427 1019018 1019183 1019450 "GBEUCLID" 1020053 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-426 1018367 1018492 1018641 "GAUSSFAC" 1018889 T GAUSSFAC (NIL) -7 NIL NIL) (-425 1016744 1017046 1017359 "GALUTIL" 1018086 NIL GALUTIL (NIL T) -7 NIL NIL) (-424 1015061 1015335 1015658 "GALPOLYU" 1016471 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-423 1012450 1012740 1013145 "GALFACTU" 1014758 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-422 1004256 1005755 1007363 "GALFACT" 1010882 NIL GALFACT (NIL T) -7 NIL NIL) (-421 1001644 1002302 1002330 "FVFUN" 1003486 T FVFUN (NIL) -9 NIL 1004206) (-420 1000910 1001092 1001120 "FVC" 1001411 T FVC (NIL) -9 NIL 1001594) (-419 1000552 1000707 1000788 "FUNCTION" 1000862 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-418 998222 998773 999262 "FT" 1000083 T FT (NIL) -8 NIL NIL) (-417 997040 997523 997726 "FTEM" 998039 T FTEM (NIL) -8 NIL NIL) (-416 995305 995593 995995 "FSUPFACT" 996732 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-415 993702 993991 994323 "FST" 994993 T FST (NIL) -8 NIL NIL) (-414 992877 992983 993177 "FSRED" 993584 NIL FSRED (NIL T T) -7 NIL NIL) (-413 991556 991811 992165 "FSPRMELT" 992592 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-412 988641 989079 989578 "FSPECF" 991119 NIL FSPECF (NIL T T) -7 NIL NIL) (-411 971015 979572 979612 "FS" 983450 NIL FS (NIL T) -9 NIL 985732) (-410 959665 962655 966711 "FS-" 967008 NIL FS- (NIL T T) -8 NIL NIL) (-409 959181 959235 959411 "FSINT" 959606 NIL FSINT (NIL T T) -7 NIL NIL) (-408 957462 958174 958477 "FSERIES" 958960 NIL FSERIES (NIL T T) -8 NIL NIL) (-407 956480 956596 956826 "FSCINT" 957342 NIL FSCINT (NIL T T) -7 NIL NIL) (-406 952715 955425 955466 "FSAGG" 955836 NIL FSAGG (NIL T) -9 NIL 956095) (-405 950477 951078 951874 "FSAGG-" 951969 NIL FSAGG- (NIL T T) -8 NIL NIL) (-404 949519 949662 949889 "FSAGG2" 950330 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-403 947178 947457 948010 "FS2UPS" 949237 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-402 946764 946807 946960 "FS2" 947129 NIL FS2 (NIL T T T T) -7 NIL NIL) (-401 945624 945795 946103 "FS2EXPXP" 946589 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-400 945050 945165 945317 "FRUTIL" 945504 NIL FRUTIL (NIL T) -7 NIL NIL) (-399 936470 940549 941905 "FR" 943726 NIL FR (NIL T) -8 NIL NIL) (-398 931547 934190 934230 "FRNAALG" 935626 NIL FRNAALG (NIL T) -9 NIL 936233) (-397 927225 928296 929571 "FRNAALG-" 930321 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-396 926863 926906 927033 "FRNAAF2" 927176 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-395 925228 925720 926014 "FRMOD" 926676 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-394 922950 923619 923935 "FRIDEAL" 925019 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-393 922149 922236 922523 "FRIDEAL2" 922857 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-392 921407 921815 921856 "FRETRCT" 921861 NIL FRETRCT (NIL T) -9 NIL 922032) (-391 920519 920750 921101 "FRETRCT-" 921106 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-390 917729 918949 919008 "FRAMALG" 919890 NIL FRAMALG (NIL T T) -9 NIL 920182) (-389 915863 916318 916948 "FRAMALG-" 917171 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-388 909765 915338 915614 "FRAC" 915619 NIL FRAC (NIL T) -8 NIL NIL) (-387 909401 909458 909565 "FRAC2" 909702 NIL FRAC2 (NIL T T) -7 NIL NIL) (-386 909037 909094 909201 "FR2" 909338 NIL FR2 (NIL T T) -7 NIL NIL) (-385 903711 906624 906652 "FPS" 907771 T FPS (NIL) -9 NIL 908327) (-384 903160 903269 903433 "FPS-" 903579 NIL FPS- (NIL T) -8 NIL NIL) (-383 900609 902306 902334 "FPC" 902559 T FPC (NIL) -9 NIL 902701) (-382 900402 900442 900539 "FPC-" 900544 NIL FPC- (NIL T) -8 NIL NIL) (-381 899281 899891 899932 "FPATMAB" 899937 NIL FPATMAB (NIL T) -9 NIL 900089) (-380 896981 897457 897883 "FPARFRAC" 898918 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-379 892374 892873 893555 "FORTRAN" 896413 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-378 890090 890590 891129 "FORT" 891855 T FORT (NIL) -7 NIL NIL) (-377 887766 888328 888356 "FORTFN" 889416 T FORTFN (NIL) -9 NIL 890040) (-376 887530 887580 887608 "FORTCAT" 887667 T FORTCAT (NIL) -9 NIL 887729) (-375 885590 886073 886472 "FORMULA" 887151 T FORMULA (NIL) -8 NIL NIL) (-374 885378 885408 885477 "FORMULA1" 885554 NIL FORMULA1 (NIL T) -7 NIL NIL) (-373 884901 884953 885126 "FORDER" 885320 NIL FORDER (NIL T T T T) -7 NIL NIL) (-372 883997 884161 884354 "FOP" 884728 T FOP (NIL) -7 NIL NIL) (-371 882605 883277 883451 "FNLA" 883879 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-370 881274 881663 881691 "FNCAT" 882263 T FNCAT (NIL) -9 NIL 882556) (-369 880840 881233 881261 "FNAME" 881266 T FNAME (NIL) -8 NIL NIL) (-368 879500 880473 880501 "FMTC" 880506 T FMTC (NIL) -9 NIL 880541) (-367 875818 877025 877653 "FMONOID" 878905 NIL FMONOID (NIL T) -8 NIL NIL) (-366 875038 875561 875709 "FM" 875714 NIL FM (NIL T T) -8 NIL NIL) (-365 872462 873108 873136 "FMFUN" 874280 T FMFUN (NIL) -9 NIL 874988) (-364 871731 871912 871940 "FMC" 872230 T FMC (NIL) -9 NIL 872412) (-363 868961 869795 869848 "FMCAT" 871030 NIL FMCAT (NIL T T) -9 NIL 871524) (-362 867856 868729 868828 "FM1" 868906 NIL FM1 (NIL T T) -8 NIL NIL) (-361 865630 866046 866540 "FLOATRP" 867407 NIL FLOATRP (NIL T) -7 NIL NIL) (-360 859116 863286 863916 "FLOAT" 865020 T FLOAT (NIL) -8 NIL NIL) (-359 856554 857054 857632 "FLOATCP" 858583 NIL FLOATCP (NIL T) -7 NIL NIL) (-358 855343 856191 856231 "FLINEXP" 856236 NIL FLINEXP (NIL T) -9 NIL 856329) (-357 854498 854733 855060 "FLINEXP-" 855065 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-356 853574 853718 853942 "FLASORT" 854350 NIL FLASORT (NIL T T) -7 NIL NIL) (-355 850793 851635 851687 "FLALG" 852914 NIL FLALG (NIL T T) -9 NIL 853381) (-354 844578 848280 848321 "FLAGG" 849583 NIL FLAGG (NIL T) -9 NIL 850235) (-353 843304 843643 844133 "FLAGG-" 844138 NIL FLAGG- (NIL T T) -8 NIL NIL) (-352 842346 842489 842716 "FLAGG2" 843157 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-351 839319 840337 840396 "FINRALG" 841524 NIL FINRALG (NIL T T) -9 NIL 842032) (-350 838479 838708 839047 "FINRALG-" 839052 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-349 837886 838099 838127 "FINITE" 838323 T FINITE (NIL) -9 NIL 838430) (-348 830346 832507 832547 "FINAALG" 836214 NIL FINAALG (NIL T) -9 NIL 837667) (-347 825687 826728 827872 "FINAALG-" 829251 NIL FINAALG- (NIL T T) -8 NIL NIL) (-346 825082 825442 825545 "FILE" 825617 NIL FILE (NIL T) -8 NIL NIL) (-345 823767 824079 824133 "FILECAT" 824817 NIL FILECAT (NIL T T) -9 NIL 825033) (-344 821630 823186 823214 "FIELD" 823254 T FIELD (NIL) -9 NIL 823334) (-343 820250 820635 821146 "FIELD-" 821151 NIL FIELD- (NIL T) -8 NIL NIL) (-342 818065 818887 819233 "FGROUP" 819937 NIL FGROUP (NIL T) -8 NIL NIL) (-341 817155 817319 817539 "FGLMICPK" 817897 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-340 812957 817080 817137 "FFX" 817142 NIL FFX (NIL T NIL) -8 NIL NIL) (-339 812558 812619 812754 "FFSLPE" 812890 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-338 808551 809330 810126 "FFPOLY" 811794 NIL FFPOLY (NIL T) -7 NIL NIL) (-337 808055 808091 808300 "FFPOLY2" 808509 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-336 803876 807974 808037 "FFP" 808042 NIL FFP (NIL T NIL) -8 NIL NIL) (-335 799244 803787 803851 "FF" 803856 NIL FF (NIL NIL NIL) -8 NIL NIL) (-334 794340 798587 798777 "FFNBX" 799098 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-333 789249 793475 793733 "FFNBP" 794194 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-332 783852 788533 788744 "FFNB" 789082 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-331 782684 782882 783197 "FFINTBAS" 783649 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-330 778908 781148 781176 "FFIELDC" 781796 T FFIELDC (NIL) -9 NIL 782172) (-329 777571 777941 778438 "FFIELDC-" 778443 NIL FFIELDC- (NIL T) -8 NIL NIL) (-328 777141 777186 777310 "FFHOM" 777513 NIL FFHOM (NIL T T T) -7 NIL NIL) (-327 774839 775323 775840 "FFF" 776656 NIL FFF (NIL T) -7 NIL NIL) (-326 770427 774581 774682 "FFCGX" 774782 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-325 766029 770159 770266 "FFCGP" 770370 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-324 761182 765756 765864 "FFCG" 765965 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-323 743128 752251 752337 "FFCAT" 757502 NIL FFCAT (NIL T T T) -9 NIL 758989) (-322 738326 739373 740687 "FFCAT-" 741917 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-321 737737 737780 738015 "FFCAT2" 738277 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-320 726937 730727 731944 "FEXPR" 736592 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-319 725937 726372 726413 "FEVALAB" 726497 NIL FEVALAB (NIL T) -9 NIL 726758) (-318 725096 725306 725644 "FEVALAB-" 725649 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-317 723689 724479 724682 "FDIV" 724995 NIL FDIV (NIL T T T T) -8 NIL NIL) (-316 720756 721471 721586 "FDIVCAT" 723154 NIL FDIVCAT (NIL T T T T) -9 NIL 723591) (-315 720518 720545 720715 "FDIVCAT-" 720720 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-314 719738 719825 720102 "FDIV2" 720425 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-313 718424 718683 718972 "FCPAK1" 719469 T FCPAK1 (NIL) -7 NIL NIL) (-312 717552 717924 718065 "FCOMP" 718315 NIL FCOMP (NIL T) -8 NIL NIL) (-311 701187 704601 708162 "FC" 714011 T FC (NIL) -8 NIL NIL) (-310 693783 697829 697869 "FAXF" 699671 NIL FAXF (NIL T) -9 NIL 700362) (-309 691062 691717 692542 "FAXF-" 693007 NIL FAXF- (NIL T T) -8 NIL NIL) (-308 686162 690438 690614 "FARRAY" 690919 NIL FARRAY (NIL T) -8 NIL NIL) (-307 681553 683624 683676 "FAMR" 684688 NIL FAMR (NIL T T) -9 NIL 685148) (-306 680444 680746 681180 "FAMR-" 681185 NIL FAMR- (NIL T T T) -8 NIL NIL) (-305 679640 680366 680419 "FAMONOID" 680424 NIL FAMONOID (NIL T) -8 NIL NIL) (-304 677473 678157 678210 "FAMONC" 679151 NIL FAMONC (NIL T T) -9 NIL 679536) (-303 676165 677227 677364 "FAGROUP" 677369 NIL FAGROUP (NIL T) -8 NIL NIL) (-302 673968 674287 674689 "FACUTIL" 675846 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-301 673067 673252 673474 "FACTFUNC" 673778 NIL FACTFUNC (NIL T) -7 NIL NIL) (-300 665387 672318 672530 "EXPUPXS" 672923 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-299 662870 663410 663996 "EXPRTUBE" 664821 T EXPRTUBE (NIL) -7 NIL NIL) (-298 659064 659656 660393 "EXPRODE" 662209 NIL EXPRODE (NIL T T) -7 NIL NIL) (-297 644223 657723 658149 "EXPR" 658670 NIL EXPR (NIL T) -8 NIL NIL) (-296 638651 639238 640050 "EXPR2UPS" 643521 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-295 638287 638344 638451 "EXPR2" 638588 NIL EXPR2 (NIL T T) -7 NIL NIL) (-294 629641 637424 637719 "EXPEXPAN" 638125 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-293 629468 629598 629627 "EXIT" 629632 T EXIT (NIL) -8 NIL NIL) (-292 629095 629157 629270 "EVALCYC" 629400 NIL EVALCYC (NIL T) -7 NIL NIL) (-291 628636 628754 628795 "EVALAB" 628965 NIL EVALAB (NIL T) -9 NIL 629069) (-290 628117 628239 628460 "EVALAB-" 628465 NIL EVALAB- (NIL T T) -8 NIL NIL) (-289 625580 626892 626920 "EUCDOM" 627475 T EUCDOM (NIL) -9 NIL 627825) (-288 623985 624427 625017 "EUCDOM-" 625022 NIL EUCDOM- (NIL T) -8 NIL NIL) (-287 611563 614311 617051 "ESTOOLS" 621265 T ESTOOLS (NIL) -7 NIL NIL) (-286 611199 611256 611363 "ESTOOLS2" 611500 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-285 610950 610992 611072 "ESTOOLS1" 611151 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-284 604888 606612 606640 "ES" 609404 T ES (NIL) -9 NIL 610810) (-283 599835 601122 602939 "ES-" 603103 NIL ES- (NIL T) -8 NIL NIL) (-282 596210 596970 597750 "ESCONT" 599075 T ESCONT (NIL) -7 NIL NIL) (-281 595955 595987 596069 "ESCONT1" 596172 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-280 595630 595680 595780 "ES2" 595899 NIL ES2 (NIL T T) -7 NIL NIL) (-279 595260 595318 595427 "ES1" 595566 NIL ES1 (NIL T T) -7 NIL NIL) (-278 594476 594605 594781 "ERROR" 595104 T ERROR (NIL) -7 NIL NIL) (-277 587979 594335 594426 "EQTBL" 594431 NIL EQTBL (NIL T T) -8 NIL NIL) (-276 580416 583297 584744 "EQ" 586565 NIL -3806 (NIL T) -8 NIL NIL) (-275 580048 580105 580214 "EQ2" 580353 NIL EQ2 (NIL T T) -7 NIL NIL) (-274 575340 576386 577479 "EP" 578987 NIL EP (NIL T) -7 NIL NIL) (-273 573922 574223 574540 "ENV" 575043 T ENV (NIL) -8 NIL NIL) (-272 573082 573646 573674 "ENTIRER" 573679 T ENTIRER (NIL) -9 NIL 573724) (-271 569538 571037 571407 "EMR" 572881 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-270 568682 568867 568921 "ELTAGG" 569301 NIL ELTAGG (NIL T T) -9 NIL 569512) (-269 568401 568463 568604 "ELTAGG-" 568609 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-268 568190 568219 568273 "ELTAB" 568357 NIL ELTAB (NIL T T) -9 NIL NIL) (-267 567316 567462 567661 "ELFUTS" 568041 NIL ELFUTS (NIL T T) -7 NIL NIL) (-266 567058 567114 567142 "ELEMFUN" 567247 T ELEMFUN (NIL) -9 NIL NIL) (-265 566928 566949 567017 "ELEMFUN-" 567022 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-264 561820 565029 565070 "ELAGG" 566010 NIL ELAGG (NIL T) -9 NIL 566473) (-263 560105 560539 561202 "ELAGG-" 561207 NIL ELAGG- (NIL T T) -8 NIL NIL) (-262 558762 559042 559337 "ELABEXPR" 559830 T ELABEXPR (NIL) -8 NIL NIL) (-261 551628 553429 554256 "EFUPXS" 558038 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-260 545078 546879 547689 "EFULS" 550904 NIL EFULS (NIL T T T) -8 NIL NIL) (-259 542509 542867 543345 "EFSTRUC" 544710 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-258 531581 533146 534706 "EF" 541024 NIL EF (NIL T T) -7 NIL NIL) (-257 530682 531066 531215 "EAB" 531452 T EAB (NIL) -8 NIL NIL) (-256 529895 530641 530669 "E04UCFA" 530674 T E04UCFA (NIL) -8 NIL NIL) (-255 529108 529854 529882 "E04NAFA" 529887 T E04NAFA (NIL) -8 NIL NIL) (-254 528321 529067 529095 "E04MBFA" 529100 T E04MBFA (NIL) -8 NIL NIL) (-253 527534 528280 528308 "E04JAFA" 528313 T E04JAFA (NIL) -8 NIL NIL) (-252 526749 527493 527521 "E04GCFA" 527526 T E04GCFA (NIL) -8 NIL NIL) (-251 525964 526708 526736 "E04FDFA" 526741 T E04FDFA (NIL) -8 NIL NIL) (-250 525177 525923 525951 "E04DGFA" 525956 T E04DGFA (NIL) -8 NIL NIL) (-249 519362 520707 522069 "E04AGNT" 523835 T E04AGNT (NIL) -7 NIL NIL) (-248 518089 518569 518609 "DVARCAT" 519084 NIL DVARCAT (NIL T) -9 NIL 519282) (-247 517293 517505 517819 "DVARCAT-" 517824 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-246 510155 517095 517222 "DSMP" 517227 NIL DSMP (NIL T T T) -8 NIL NIL) (-245 504965 506100 507168 "DROPT" 509107 T DROPT (NIL) -8 NIL NIL) (-244 504630 504689 504787 "DROPT1" 504900 NIL DROPT1 (NIL T) -7 NIL NIL) (-243 499745 500871 502008 "DROPT0" 503513 T DROPT0 (NIL) -7 NIL NIL) (-242 498090 498415 498801 "DRAWPT" 499379 T DRAWPT (NIL) -7 NIL NIL) (-241 492677 493600 494679 "DRAW" 497064 NIL DRAW (NIL T) -7 NIL NIL) (-240 492310 492363 492481 "DRAWHACK" 492618 NIL DRAWHACK (NIL T) -7 NIL NIL) (-239 491041 491310 491601 "DRAWCX" 492039 T DRAWCX (NIL) -7 NIL NIL) (-238 490559 490627 490777 "DRAWCURV" 490967 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-237 481030 482989 485104 "DRAWCFUN" 488464 T DRAWCFUN (NIL) -7 NIL NIL) (-236 477844 479726 479767 "DQAGG" 480396 NIL DQAGG (NIL T) -9 NIL 480669) (-235 466351 473089 473171 "DPOLCAT" 475009 NIL DPOLCAT (NIL T T T T) -9 NIL 475553) (-234 461191 462537 464494 "DPOLCAT-" 464499 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-233 453987 461053 461150 "DPMO" 461155 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-232 446686 453768 453934 "DPMM" 453939 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-231 446106 446309 446423 "DOMAIN" 446592 T DOMAIN (NIL) -8 NIL NIL) (-230 439818 445743 445894 "DMP" 446007 NIL DMP (NIL NIL T) -8 NIL NIL) (-229 439418 439474 439618 "DLP" 439756 NIL DLP (NIL T) -7 NIL NIL) (-228 433062 438519 438746 "DLIST" 439223 NIL DLIST (NIL T) -8 NIL NIL) (-227 429909 431918 431959 "DLAGG" 432509 NIL DLAGG (NIL T) -9 NIL 432738) (-226 428619 429311 429339 "DIVRING" 429489 T DIVRING (NIL) -9 NIL 429597) (-225 427607 427860 428253 "DIVRING-" 428258 NIL DIVRING- (NIL T) -8 NIL NIL) (-224 425709 426066 426472 "DISPLAY" 427221 T DISPLAY (NIL) -7 NIL NIL) (-223 419598 425623 425686 "DIRPROD" 425691 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-222 418446 418649 418914 "DIRPROD2" 419391 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-221 407965 413970 414023 "DIRPCAT" 414431 NIL DIRPCAT (NIL NIL T) -9 NIL 415270) (-220 405291 405933 406814 "DIRPCAT-" 407151 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-219 404578 404738 404924 "DIOSP" 405125 T DIOSP (NIL) -7 NIL NIL) (-218 401281 403491 403532 "DIOPS" 403966 NIL DIOPS (NIL T) -9 NIL 404195) (-217 400830 400944 401135 "DIOPS-" 401140 NIL DIOPS- (NIL T T) -8 NIL NIL) (-216 399702 400340 400368 "DIFRING" 400555 T DIFRING (NIL) -9 NIL 400664) (-215 399348 399425 399577 "DIFRING-" 399582 NIL DIFRING- (NIL T) -8 NIL NIL) (-214 397138 398420 398460 "DIFEXT" 398819 NIL DIFEXT (NIL T) -9 NIL 399112) (-213 395424 395852 396517 "DIFEXT-" 396522 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-212 392747 394957 394998 "DIAGG" 395003 NIL DIAGG (NIL T) -9 NIL 395023) (-211 392131 392288 392540 "DIAGG-" 392545 NIL DIAGG- (NIL T T) -8 NIL NIL) (-210 387596 391090 391367 "DHMATRIX" 391900 NIL DHMATRIX (NIL T) -8 NIL NIL) (-209 383208 384117 385127 "DFSFUN" 386606 T DFSFUN (NIL) -7 NIL NIL) (-208 377994 381922 382287 "DFLOAT" 382863 T DFLOAT (NIL) -8 NIL NIL) (-207 376227 376508 376903 "DFINTTLS" 377702 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-206 373260 374262 374660 "DERHAM" 375894 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-205 371109 373035 373124 "DEQUEUE" 373204 NIL DEQUEUE (NIL T) -8 NIL NIL) (-204 370327 370460 370655 "DEGRED" 370971 NIL DEGRED (NIL T T) -7 NIL NIL) (-203 366727 367472 368324 "DEFINTRF" 369555 NIL DEFINTRF (NIL T) -7 NIL NIL) (-202 364258 364727 365325 "DEFINTEF" 366246 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-201 358088 363699 363865 "DECIMAL" 364112 T DECIMAL (NIL) -8 NIL NIL) (-200 355600 356058 356564 "DDFACT" 357632 NIL DDFACT (NIL T T) -7 NIL NIL) (-199 355196 355239 355390 "DBLRESP" 355551 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-198 352906 353240 353609 "DBASE" 354954 NIL DBASE (NIL T) -8 NIL NIL) (-197 352175 352386 352532 "DATABUF" 352805 NIL DATABUF (NIL NIL T) -8 NIL NIL) (-196 351310 352134 352162 "D03FAFA" 352167 T D03FAFA (NIL) -8 NIL NIL) (-195 350446 351269 351297 "D03EEFA" 351302 T D03EEFA (NIL) -8 NIL NIL) (-194 348396 348862 349351 "D03AGNT" 349977 T D03AGNT (NIL) -7 NIL NIL) (-193 347714 348355 348383 "D02EJFA" 348388 T D02EJFA (NIL) -8 NIL NIL) (-192 347032 347673 347701 "D02CJFA" 347706 T D02CJFA (NIL) -8 NIL NIL) (-191 346350 346991 347019 "D02BHFA" 347024 T D02BHFA (NIL) -8 NIL NIL) (-190 345668 346309 346337 "D02BBFA" 346342 T D02BBFA (NIL) -8 NIL NIL) (-189 338866 340454 342060 "D02AGNT" 344082 T D02AGNT (NIL) -7 NIL NIL) (-188 336635 337157 337703 "D01WGTS" 338340 T D01WGTS (NIL) -7 NIL NIL) (-187 335738 336594 336622 "D01TRNS" 336627 T D01TRNS (NIL) -8 NIL NIL) (-186 334841 335697 335725 "D01GBFA" 335730 T D01GBFA (NIL) -8 NIL NIL) (-185 333944 334800 334828 "D01FCFA" 334833 T D01FCFA (NIL) -8 NIL NIL) (-184 333047 333903 333931 "D01ASFA" 333936 T D01ASFA (NIL) -8 NIL NIL) (-183 332150 333006 333034 "D01AQFA" 333039 T D01AQFA (NIL) -8 NIL NIL) (-182 331253 332109 332137 "D01APFA" 332142 T D01APFA (NIL) -8 NIL NIL) (-181 330356 331212 331240 "D01ANFA" 331245 T D01ANFA (NIL) -8 NIL NIL) (-180 329459 330315 330343 "D01AMFA" 330348 T D01AMFA (NIL) -8 NIL NIL) (-179 328562 329418 329446 "D01ALFA" 329451 T D01ALFA (NIL) -8 NIL NIL) (-178 327665 328521 328549 "D01AKFA" 328554 T D01AKFA (NIL) -8 NIL NIL) (-177 326768 327624 327652 "D01AJFA" 327657 T D01AJFA (NIL) -8 NIL NIL) (-176 320072 321621 323180 "D01AGNT" 325229 T D01AGNT (NIL) -7 NIL NIL) (-175 319409 319537 319689 "CYCLOTOM" 319940 T CYCLOTOM (NIL) -7 NIL NIL) (-174 316144 316857 317584 "CYCLES" 318702 T CYCLES (NIL) -7 NIL NIL) (-173 315456 315590 315761 "CVMP" 316005 NIL CVMP (NIL T) -7 NIL NIL) (-172 313237 313495 313870 "CTRIGMNP" 315184 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-171 312748 312937 313036 "CTORCALL" 313158 T CTORCALL (NIL) -8 NIL NIL) (-170 312122 312221 312374 "CSTTOOLS" 312645 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-169 307921 308578 309336 "CRFP" 311434 NIL CRFP (NIL T T) -7 NIL NIL) (-168 306968 307153 307381 "CRAPACK" 307725 NIL CRAPACK (NIL T) -7 NIL NIL) (-167 306352 306453 306657 "CPMATCH" 306844 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-166 306077 306105 306211 "CPIMA" 306318 NIL CPIMA (NIL T T T) -7 NIL NIL) (-165 302441 303113 303831 "COORDSYS" 305412 NIL COORDSYS (NIL T) -7 NIL NIL) (-164 301825 301954 302104 "CONTOUR" 302311 T CONTOUR (NIL) -8 NIL NIL) (-163 297686 299828 300320 "CONTFRAC" 301365 NIL CONTFRAC (NIL T) -8 NIL NIL) (-162 296840 297404 297432 "COMRING" 297437 T COMRING (NIL) -9 NIL 297488) (-161 295921 296198 296382 "COMPPROP" 296676 T COMPPROP (NIL) -8 NIL NIL) (-160 295582 295617 295745 "COMPLPAT" 295880 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-159 285563 295391 295500 "COMPLEX" 295505 NIL COMPLEX (NIL T) -8 NIL NIL) (-158 285199 285256 285363 "COMPLEX2" 285500 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-157 284917 284952 285050 "COMPFACT" 285158 NIL COMPFACT (NIL T T) -7 NIL NIL) (-156 269252 279546 279586 "COMPCAT" 280588 NIL COMPCAT (NIL T) -9 NIL 281981) (-155 258767 261691 265318 "COMPCAT-" 265674 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-154 258498 258526 258628 "COMMUPC" 258733 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-153 258293 258326 258385 "COMMONOP" 258459 T COMMONOP (NIL) -7 NIL NIL) (-152 257876 258044 258131 "COMM" 258226 T COMM (NIL) -8 NIL NIL) (-151 257125 257319 257347 "COMBOPC" 257685 T COMBOPC (NIL) -9 NIL 257860) (-150 256021 256231 256473 "COMBINAT" 256915 NIL COMBINAT (NIL T) -7 NIL NIL) (-149 252219 252792 253432 "COMBF" 255443 NIL COMBF (NIL T T) -7 NIL NIL) (-148 251005 251335 251570 "COLOR" 252004 T COLOR (NIL) -8 NIL NIL) (-147 250645 250692 250817 "CMPLXRT" 250952 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-146 246147 247175 248255 "CLIP" 249585 T CLIP (NIL) -7 NIL NIL) (-145 244485 245255 245493 "CLIF" 245975 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-144 240708 242632 242673 "CLAGG" 243602 NIL CLAGG (NIL T) -9 NIL 244138) (-143 239130 239587 240170 "CLAGG-" 240175 NIL CLAGG- (NIL T T) -8 NIL NIL) (-142 238674 238759 238899 "CINTSLPE" 239039 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-141 236175 236646 237194 "CHVAR" 238202 NIL CHVAR (NIL T T T) -7 NIL NIL) (-140 235398 235962 235990 "CHARZ" 235995 T CHARZ (NIL) -9 NIL 236009) (-139 235152 235192 235270 "CHARPOL" 235352 NIL CHARPOL (NIL T) -7 NIL NIL) (-138 234259 234856 234884 "CHARNZ" 234931 T CHARNZ (NIL) -9 NIL 234986) (-137 232284 232949 233284 "CHAR" 233944 T CHAR (NIL) -8 NIL NIL) (-136 232010 232071 232099 "CFCAT" 232210 T CFCAT (NIL) -9 NIL NIL) (-135 231255 231366 231548 "CDEN" 231894 NIL CDEN (NIL T T T) -7 NIL NIL) (-134 227247 230408 230688 "CCLASS" 230995 T CCLASS (NIL) -8 NIL NIL) (-133 227166 227192 227227 "CATEGORY" 227232 T -10 (NIL) -8 NIL NIL) (-132 222218 223195 223948 "CARTEN" 226469 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-131 221326 221474 221695 "CARTEN2" 222065 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-130 219624 220478 220734 "CARD" 221090 T CARD (NIL) -8 NIL NIL) (-129 218997 219325 219353 "CACHSET" 219485 T CACHSET (NIL) -9 NIL 219562) (-128 218494 218790 218818 "CABMON" 218868 T CABMON (NIL) -9 NIL 218924) (-127 217662 218041 218184 "BYTE" 218371 T BYTE (NIL) -8 NIL NIL) (-126 213610 217609 217643 "BYTEARY" 217648 T BYTEARY (NIL) -8 NIL NIL) (-125 211167 213302 213409 "BTREE" 213536 NIL BTREE (NIL T) -8 NIL NIL) (-124 208665 210815 210937 "BTOURN" 211077 NIL BTOURN (NIL T) -8 NIL NIL) (-123 206084 208137 208178 "BTCAT" 208246 NIL BTCAT (NIL T) -9 NIL 208323) (-122 205751 205831 205980 "BTCAT-" 205985 NIL BTCAT- (NIL T T) -8 NIL NIL) (-121 201044 204895 204923 "BTAGG" 205145 T BTAGG (NIL) -9 NIL 205306) (-120 200534 200659 200865 "BTAGG-" 200870 NIL BTAGG- (NIL T) -8 NIL NIL) (-119 197578 199812 200027 "BSTREE" 200351 NIL BSTREE (NIL T) -8 NIL NIL) (-118 196716 196842 197026 "BRILL" 197434 NIL BRILL (NIL T) -7 NIL NIL) (-117 193418 195445 195486 "BRAGG" 196135 NIL BRAGG (NIL T) -9 NIL 196392) (-116 191947 192353 192908 "BRAGG-" 192913 NIL BRAGG- (NIL T T) -8 NIL NIL) (-115 185155 191293 191477 "BPADICRT" 191795 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-114 183459 185092 185137 "BPADIC" 185142 NIL BPADIC (NIL NIL) -8 NIL NIL) (-113 183159 183189 183302 "BOUNDZRO" 183423 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-112 178674 179765 180632 "BOP" 182312 T BOP (NIL) -8 NIL NIL) (-111 176295 176739 177259 "BOP1" 178187 NIL BOP1 (NIL T) -7 NIL NIL) (-110 175019 175705 175905 "BOOLEAN" 176115 T BOOLEAN (NIL) -8 NIL NIL) (-109 174386 174764 174816 "BMODULE" 174821 NIL BMODULE (NIL T T) -9 NIL 174885) (-108 170216 174184 174257 "BITS" 174333 T BITS (NIL) -8 NIL NIL) (-107 169313 169748 169900 "BINFILE" 170084 T BINFILE (NIL) -8 NIL NIL) (-106 168725 168847 168989 "BINDING" 169191 T BINDING (NIL) -8 NIL NIL) (-105 162559 168169 168334 "BINARY" 168580 T BINARY (NIL) -8 NIL NIL) (-104 160387 161815 161856 "BGAGG" 162116 NIL BGAGG (NIL T) -9 NIL 162253) (-103 160218 160250 160341 "BGAGG-" 160346 NIL BGAGG- (NIL T T) -8 NIL NIL) (-102 159316 159602 159807 "BFUNCT" 160033 T BFUNCT (NIL) -8 NIL NIL) (-101 158011 158189 158476 "BEZOUT" 159140 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-100 154528 156863 157193 "BBTREE" 157714 NIL BBTREE (NIL T) -8 NIL NIL) (-99 154266 154319 154345 "BASTYPE" 154462 T BASTYPE (NIL) -9 NIL NIL) (-98 154121 154150 154220 "BASTYPE-" 154225 NIL BASTYPE- (NIL T) -8 NIL NIL) (-97 153559 153635 153785 "BALFACT" 154032 NIL BALFACT (NIL T T) -7 NIL NIL) (-96 152381 152978 153163 "AUTOMOR" 153404 NIL AUTOMOR (NIL T) -8 NIL NIL) (-95 152107 152112 152138 "ATTREG" 152143 T ATTREG (NIL) -9 NIL NIL) (-94 150386 150804 151156 "ATTRBUT" 151773 T ATTRBUT (NIL) -8 NIL NIL) (-93 149922 150035 150061 "ATRIG" 150262 T ATRIG (NIL) -9 NIL NIL) (-92 149731 149772 149859 "ATRIG-" 149864 NIL ATRIG- (NIL T) -8 NIL NIL) (-91 149457 149600 149626 "ASTCAT" 149631 T ASTCAT (NIL) -9 NIL 149661) (-90 149254 149297 149389 "ASTCAT-" 149394 NIL ASTCAT- (NIL T) -8 NIL NIL) (-89 147451 149030 149118 "ASTACK" 149197 NIL ASTACK (NIL T) -8 NIL NIL) (-88 145956 146253 146618 "ASSOCEQ" 147133 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 144988 145615 145739 "ASP9" 145863 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 144752 144936 144975 "ASP8" 144980 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 143621 144357 144499 "ASP80" 144641 NIL ASP80 (NIL NIL) -8 NIL NIL) (-84 142520 143256 143388 "ASP7" 143520 NIL ASP7 (NIL NIL) -8 NIL NIL) (-83 141474 142197 142315 "ASP78" 142433 NIL ASP78 (NIL NIL) -8 NIL NIL) (-82 140443 141154 141271 "ASP77" 141388 NIL ASP77 (NIL NIL) -8 NIL NIL) (-81 139355 140081 140212 "ASP74" 140343 NIL ASP74 (NIL NIL) -8 NIL NIL) (-80 138255 138990 139122 "ASP73" 139254 NIL ASP73 (NIL NIL) -8 NIL NIL) (-79 137210 137932 138050 "ASP6" 138168 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 136158 136887 137005 "ASP55" 137123 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 135108 135832 135951 "ASP50" 136070 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 134196 134809 134919 "ASP4" 135029 NIL ASP4 (NIL NIL) -8 NIL NIL) (-75 133284 133897 134007 "ASP49" 134117 NIL ASP49 (NIL NIL) -8 NIL NIL) (-74 132069 132823 132991 "ASP42" 133173 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130846 131602 131772 "ASP41" 131956 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-72 129796 130523 130641 "ASP35" 130759 NIL ASP35 (NIL NIL) -8 NIL NIL) (-71 129561 129744 129783 "ASP34" 129788 NIL ASP34 (NIL NIL) -8 NIL NIL) (-70 129298 129365 129441 "ASP33" 129516 NIL ASP33 (NIL NIL) -8 NIL NIL) (-69 128193 128933 129065 "ASP31" 129197 NIL ASP31 (NIL NIL) -8 NIL NIL) (-68 127958 128141 128180 "ASP30" 128185 NIL ASP30 (NIL NIL) -8 NIL NIL) (-67 127693 127762 127838 "ASP29" 127913 NIL ASP29 (NIL NIL) -8 NIL NIL) (-66 127458 127641 127680 "ASP28" 127685 NIL ASP28 (NIL NIL) -8 NIL NIL) (-65 127223 127406 127445 "ASP27" 127450 NIL ASP27 (NIL NIL) -8 NIL NIL) (-64 126307 126921 127032 "ASP24" 127143 NIL ASP24 (NIL NIL) -8 NIL NIL) (-63 125223 125948 126078 "ASP20" 126208 NIL ASP20 (NIL NIL) -8 NIL NIL) (-62 124311 124924 125034 "ASP1" 125144 NIL ASP1 (NIL NIL) -8 NIL NIL) (-61 123255 123985 124104 "ASP19" 124223 NIL ASP19 (NIL NIL) -8 NIL NIL) (-60 122992 123059 123135 "ASP12" 123210 NIL ASP12 (NIL NIL) -8 NIL NIL) (-59 121844 122591 122735 "ASP10" 122879 NIL ASP10 (NIL NIL) -8 NIL NIL) (-58 119743 121688 121779 "ARRAY2" 121784 NIL ARRAY2 (NIL T) -8 NIL NIL) (-57 115559 119391 119505 "ARRAY1" 119660 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 114591 114764 114985 "ARRAY12" 115382 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-55 108951 110822 110897 "ARR2CAT" 113527 NIL ARR2CAT (NIL T T T) -9 NIL 114285) (-54 106385 107129 108083 "ARR2CAT-" 108088 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-53 105137 105289 105594 "APPRULE" 106221 NIL APPRULE (NIL T T T) -7 NIL NIL) (-52 104790 104838 104956 "APPLYORE" 105083 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-51 103764 104055 104250 "ANY" 104613 T ANY (NIL) -8 NIL NIL) (-50 103042 103165 103322 "ANY1" 103638 NIL ANY1 (NIL T) -7 NIL NIL) (-49 100574 101492 101817 "ANTISYM" 102767 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-48 100089 100278 100375 "ANON" 100495 T ANON (NIL) -8 NIL NIL) (-47 94166 98634 99085 "AN" 99656 T AN (NIL) -8 NIL NIL) (-46 90520 91918 91968 "AMR" 92707 NIL AMR (NIL T T) -9 NIL 93306) (-45 89633 89854 90216 "AMR-" 90221 NIL AMR- (NIL T T T) -8 NIL NIL) (-44 74183 89550 89611 "ALIST" 89616 NIL ALIST (NIL T T) -8 NIL NIL) (-43 71020 73777 73946 "ALGSC" 74101 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-42 67576 68130 68737 "ALGPKG" 70460 NIL ALGPKG (NIL T T) -7 NIL NIL) (-41 66853 66954 67138 "ALGMFACT" 67462 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-40 62602 63283 63937 "ALGMANIP" 66377 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-39 53921 62228 62378 "ALGFF" 62535 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-38 53117 53248 53427 "ALGFACT" 53779 NIL ALGFACT (NIL T) -7 NIL NIL) (-37 52108 52718 52756 "ALGEBRA" 52816 NIL ALGEBRA (NIL T) -9 NIL 52874) (-36 51826 51885 52017 "ALGEBRA-" 52022 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-35 34087 49830 49882 "ALAGG" 50018 NIL ALAGG (NIL T T) -9 NIL 50179) (-34 33623 33736 33762 "AHYP" 33963 T AHYP (NIL) -9 NIL NIL) (-33 32554 32802 32828 "AGG" 33327 T AGG (NIL) -9 NIL 33606) (-32 31988 32150 32364 "AGG-" 32369 NIL AGG- (NIL T) -8 NIL NIL) (-31 29675 30093 30510 "AF" 31631 NIL AF (NIL T T) -7 NIL NIL) (-30 28944 29202 29358 "ACPLOT" 29537 T ACPLOT (NIL) -8 NIL NIL) (-29 18411 26357 26408 "ACFS" 27119 NIL ACFS (NIL T) -9 NIL 27358) (-28 16425 16915 17690 "ACFS-" 17695 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12693 14649 14675 "ACF" 15554 T ACF (NIL) -9 NIL 15966) (-26 11397 11731 12224 "ACF-" 12229 NIL ACF- (NIL T) -8 NIL NIL) (-25 10996 11165 11191 "ABELSG" 11283 T ABELSG (NIL) -9 NIL 11348) (-24 10863 10888 10954 "ABELSG-" 10959 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10233 10494 10520 "ABELMON" 10690 T ABELMON (NIL) -9 NIL 10802) (-22 9897 9981 10119 "ABELMON-" 10124 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9232 9578 9604 "ABELGRP" 9729 T ABELGRP (NIL) -9 NIL 9811) (-20 8695 8824 9040 "ABELGRP-" 9045 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 4035aa90..9be30cd2 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,191 +1,206 @@ -(727609 . 3429202590) -(((*1 *1 *1 *1) (-12 (-4 *1 (-607 *2)) (-4 *2 (-984)) (-4 *2 (-344)))) - ((*1 *2 *2 *2 *3) - (-12 (-5 *3 (-1 *4 *4)) (-4 *4 (-344)) (-5 *1 (-610 *4 *2)) - (-4 *2 (-607 *4))))) -(((*1 *2 *3) - (-12 (-5 *2 (-2 (|:| -3760 (-530)) (|:| -3494 (-597 *3)))) - (-5 *1 (-422 *3)) (-4 *3 (-1157 (-530)))))) -(((*1 *1 *2) - (|partial| -12 (-5 *2 (-1194 *3 *4)) (-4 *3 (-795)) (-4 *4 (-162)) - (-5 *1 (-615 *3 *4)))) - ((*1 *2 *1) - (|partial| -12 (-5 *2 (-615 *3 *4)) (-5 *1 (-1199 *3 *4)) - (-4 *3 (-795)) (-4 *4 (-162))))) -(((*1 *1 *2 *3) - (-12 (-5 *3 (-342 (-112))) (-4 *2 (-984)) (-5 *1 (-663 *2 *4)) - (-4 *4 (-599 *2)))) - ((*1 *1 *2 *3) - (-12 (-5 *3 (-342 (-112))) (-5 *1 (-782 *2)) (-4 *2 (-984))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 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((*1 *2 *3) - (-12 (-4 *1 (-850)) (-5 *2 (-399 (-1095 *1))) (-5 *3 (-1095 *1))))) -(((*1 *2 *3 *4 *5 *6) - (|partial| -12 (-5 *4 (-1 *8 *8)) - (-5 *5 - (-1 (-3 (-2 (|:| -1863 *7) (|:| |coeff| *7)) "failed") *7)) - (-5 *6 (-597 (-388 *8))) (-4 *7 (-344)) (-4 *8 (-1157 *7)) - (-5 *3 (-388 *8)) - (-5 *2 - (-2 - (|:| |answer| - (-2 (|:| |mainpart| *3) - (|:| |limitedlogs| - (-597 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) - (|:| |a0| *7))) - (-5 *1 (-540 *7 *8))))) -(((*1 *2 *1) (|partial| -12 (-5 *2 (-719)) (-5 *1 (-112))))) + (-5 *2 + (-597 + (-2 + (|:| -2940 + (-2 (|:| |xinit| (-208)) (|:| |xend| (-208)) + (|:| |fn| (-1181 (-297 (-208)))) + (|:| |yinit| (-597 (-208))) (|:| |intvals| (-597 (-208))) + (|:| |g| (-297 (-208))) (|:| |abserr| (-208)) + (|:| |relerr| (-208)))) + (|:| -1806 + (-2 (|:| |stiffness| (-360)) (|:| |stability| (-360)) + (|:| |expense| (-360)) (|:| |accuracy| (-360)) + (|:| |intermediateResults| (-360))))))) + (-5 *1 (-751))))) +(((*1 *2 *1) (-12 (-5 *2 (-1082)) (-5 *1 (-506))))) +(((*1 *1 *2) (-12 (-5 *2 (-171)) (-5 *1 (-231))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-786)) (-5 *4 (-996)) (-5 *2 (-973)) (-5 *1 (-785)))) ((*1 *2 *3) (-12 (-5 *3 (-786)) (-5 *2 (-973)) (-5 *1 (-785)))) @@ -1756,31 +1762,24 @@ ((*1 *2 *3 *4) (-12 (-5 *3 (-597 (-297 (-360)))) (-5 *4 (-597 (-360))) (-5 *2 (-973)) (-5 *1 (-785))))) -(((*1 *2 *3 *3 *4) - (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1157 *5)) - (-4 *5 (-13 (-344) (-140) (-975 (-530)))) - (-5 *2 - (-2 (|:| |a| *6) (|:| |b| (-388 *6)) (|:| |c| (-388 *6)) - (|:| -4037 *6))) - (-5 *1 (-954 *5 *6)) (-5 *3 (-388 *6))))) -(((*1 *2 *3 *3 *3) - (-12 (-5 *2 (-1080 (-597 (-530)))) (-5 *1 (-824)) (-5 *3 (-530)))) - ((*1 *2 *3) - (-12 (-5 *2 (-1080 (-597 (-530)))) (-5 *1 (-824)) (-5 *3 (-530)))) - ((*1 *2 *3 *3) - (-12 (-5 *2 (-1080 (-597 (-530)))) (-5 *1 (-824)) (-5 *3 (-530))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) - (-4 *2 (-13 (-411 *3) (-941)))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-815)) (-5 *3 (-597 (-245))) (-5 *1 (-243))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-719)) (-4 *1 (-1196 *3 *4)) (-4 *3 (-795)) - (-4 *4 (-984)) (-4 *4 (-162)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-1196 *2 *3)) (-4 *2 (-795)) (-4 *3 (-984)) - (-4 *3 (-162))))) -(((*1 *2 *1) (-12 (-5 *2 (-804)) (-5 *1 (-51))))) +(((*1 *1 *1 *2 *2 *2) (-12 (-5 *2 (-1022 (-208))) (-5 *1 (-867)))) + ((*1 *1 *1 *2 *2) (-12 (-5 *2 (-1022 (-208))) (-5 *1 (-868)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-1022 (-208))) (-5 *1 (-868)))) + ((*1 *2 *1 *3 *3 *3) + (-12 (-5 *3 (-360)) (-5 *2 (-1186)) (-5 *1 (-1183)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-360)) (-5 *2 (-1186)) (-5 *1 (-1183))))) +(((*1 *2 *3) + (-12 (-5 *3 (-597 (-862))) (-5 *2 (-845 (-530))) (-5 *1 (-858))))) +(((*1 *1 *1) + (-12 (-4 *1 (-998 *2 *3 *4)) (-4 *2 (-984)) (-4 *3 (-741)) + (-4 *4 (-795)) (-4 *2 (-522))))) +(((*1 *2 *1) + (-12 (-4 *1 (-643 *3)) (-4 *3 (-1027)) + (-5 *2 (-597 (-2 (|:| -1806 *3) (|:| -2494 (-719)))))))) +(((*1 *2) + (-12 (-4 *4 (-162)) (-5 *2 (-110)) (-5 *1 (-347 *3 *4)) + (-4 *3 (-348 *4)))) + ((*1 *2) (-12 (-4 *1 (-348 *3)) (-4 *3 (-162)) (-5 *2 (-110))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-1082)) (-5 *1 (-112)))) ((*1 *2 *2 *3) (-12 (-5 *3 (-1082)) (-4 *4 (-795)) (-5 *1 (-870 *4 *2)) @@ -1788,45 +1787,41 @@ ((*1 *2 *3 *4) (-12 (-5 *3 (-1099)) (-5 *4 (-1082)) (-5 *2 (-297 (-530))) (-5 *1 (-871))))) -(((*1 *2 *3) - (-12 (-4 *4 (-984)) (-5 *2 (-530)) (-5 *1 (-423 *4 *3 *5)) - (-4 *3 (-1157 *4)) - (-4 *5 (-13 (-385) (-975 *4) (-344) (-1121) (-266)))))) -(((*1 *1 *2) (-12 (-5 *2 (-597 *3)) (-4 *3 (-1027)) (-4 *1 (-218 *3)))) - ((*1 *1) (-12 (-4 *1 (-218 *2)) (-4 *2 (-1027))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-846 (-530))) (-5 *4 (-530)) (-5 *2 (-637 *4)) - (-5 *1 (-966 *5)) (-4 *5 (-984)))) - ((*1 *2 *3) - (-12 (-5 *3 (-597 (-530))) (-5 *2 (-637 (-530))) (-5 *1 (-966 *4)) - (-4 *4 (-984)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-597 (-846 (-530)))) (-5 *4 (-530)) - (-5 *2 (-597 (-637 *4))) (-5 *1 (-966 *5)) (-4 *5 (-984)))) - ((*1 *2 *3) - (-12 (-5 *3 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(-4 *3 (-741)) + (-4 *4 (-795)) (-4 *2 (-522))))) +(((*1 *2 *3 *4 *5 *5) + (-12 (-5 *5 (-719)) (-4 *6 (-1027)) (-4 *7 (-841 *6)) + (-5 *2 (-637 *7)) (-5 *1 (-640 *6 *7 *3 *4)) (-4 *3 (-354 *7)) + (-4 *4 (-13 (-354 *6) (-10 -7 (-6 -4270))))))) +(((*1 *2) + (-12 (-4 *4 (-162)) (-5 *2 (-110)) (-5 *1 (-347 *3 *4)) + (-4 *3 (-348 *4)))) + ((*1 *2) (-12 (-4 *1 (-348 *3)) (-4 *3 (-162)) (-5 *2 (-110))))) (((*1 *2 *3) (-12 (-5 *3 (-1082)) (-5 *2 (-293)) (-5 *1 (-278)))) ((*1 *2 *3) (-12 (-5 *3 (-597 (-1082))) (-5 *2 (-293)) (-5 *1 (-278)))) @@ -1834,31 +1829,14 @@ ((*1 *2 *3 *4) (-12 (-5 *4 (-597 (-1082))) (-5 *3 (-1082)) (-5 *2 (-293)) (-5 *1 (-278))))) -(((*1 *2 *3) (-12 (-5 *3 (-159 (-530))) (-5 *2 (-110)) (-5 *1 (-426)))) - ((*1 *2 *3) - (-12 - (-5 *3 - (-482 (-388 (-530)) (-223 *5 (-719)) (-806 *4) - (-230 *4 (-388 (-530))))) - (-14 *4 (-597 (-1099))) (-14 *5 (-719)) (-5 *2 (-110)) - (-5 *1 (-483 *4 *5)))) - ((*1 *2 *3) (-12 (-5 *2 (-110)) (-5 *1 (-902 *3)) (-4 *3 (-515)))) - ((*1 *2 *1) 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"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"))) - (-5 *1 (-176))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) - (-4 *2 (-13 (-411 *3) (-941)))))) -(((*1 *1 *1 *1 *2) - (-12 (-4 *1 (-998 *3 *4 *2)) (-4 *3 (-984)) (-4 *4 (-741)) - (-4 *2 (-795)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-998 *2 *3 *4)) (-4 *2 (-984)) (-4 *3 (-741)) - (-4 *4 (-795))))) -(((*1 *1 *1) (-12 (-4 *1 (-624 *2)) (-4 *2 (-1135))))) -(((*1 *2 *1) - (-12 (-5 *2 (-597 (-846 *3))) (-5 *1 (-845 *3)) (-4 *3 (-1027))))) -(((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-770))))) -(((*1 *2 *2) (-12 (-5 *2 (-360)) (-5 *1 (-1183)))) - ((*1 *2) (-12 (-5 *2 (-360)) (-5 *1 (-1183))))) -(((*1 *1 *1 *1) - (|partial| -12 (-4 *1 (-797 *2)) (-4 *2 (-984)) 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(-432))) (-5 *1 (-1127 *3 *2)) (-4 *2 (-13 (-411 *3) (-1121)))))) +(((*1 *2 *3 *4) + (|partial| -12 (-5 *3 (-112)) (-5 *4 (-597 *2)) (-5 *1 (-111 *2)) + (-4 *2 (-1027)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-112)) (-5 *3 (-1 *4 (-597 *4))) (-4 *4 (-1027)) + (-5 *1 (-111 *4)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-112)) (-5 *3 (-1 *4 *4)) (-4 *4 (-1027)) + (-5 *1 (-111 *4)))) + ((*1 *2 *3) + (|partial| -12 (-5 *3 (-112)) (-5 *2 (-1 *4 (-597 *4))) + (-5 *1 (-111 *4)) (-4 *4 (-1027)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-1 *4 *4)) (-4 *4 (-599 *3)) (-4 *3 (-984)) + (-5 *1 (-663 *3 *4)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-984)) (-5 *1 (-782 *3))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-923 *2)) (-4 *2 (-1121))))) +(((*1 *2 *3) (-12 (-5 *2 (-110)) (-5 *1 (-548 *3)) (-4 *3 (-515))))) +(((*1 *1 *1) + (|partial| -12 (-5 *1 (-276 *2)) (-4 *2 (-675)) (-4 *2 (-1135))))) (((*1 *2 *1) - (-12 (-5 *2 (-597 (-2 (|:| |integrand| *3) (|:| |intvar| *3)))) - (-5 *1 (-547 *3)) (-4 *3 (-344))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-3 (-110) "failed")) (-4 *3 (-432)) (-4 *4 (-795)) - (-4 *5 (-741)) (-5 *1 (-927 *3 *4 *5 *6)) (-4 *6 (-890 *3 *5 *4))))) -(((*1 *2 *3 *4 *3 *5 *5 *3 *5 *4) - (-12 (-5 *4 (-637 (-208))) (-5 *5 (-637 (-530))) (-5 *3 (-530)) - (-5 *2 (-973)) (-5 *1 (-705))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-110)) (-4 *6 (-432)) (-4 *7 (-741)) (-4 *8 (-795)) - (-4 *3 (-998 *6 *7 *8)) - (-5 *2 - (-2 (|:| |done| (-597 *4)) - (|:| |todo| (-597 (-2 (|:| |val| (-597 *3)) (|:| -2321 *4)))))) - (-5 *1 (-1001 *6 *7 *8 *3 *4)) (-4 *4 (-1003 *6 *7 *8 *3)))) - ((*1 *2 *3 *4) + (-12 (-4 *2 (-1027)) (-5 *1 (-905 *3 *2)) (-4 *3 (-1027))))) +(((*1 *2 *3 *4) (-12 (-4 *5 (-432)) (-4 *6 (-741)) (-4 *7 (-795)) (-4 *3 (-998 *5 *6 *7)) - (-5 *2 - (-2 (|:| |done| (-597 *4)) - (|:| |todo| (-597 (-2 (|:| |val| (-597 *3)) (|:| -2321 *4)))))) - (-5 *1 (-1069 *5 *6 *7 *3 *4)) (-4 *4 (-1036 *5 *6 *7 *3))))) -(((*1 *1 *1) - (-12 (-5 *1 (-555 *2)) (-4 *2 (-37 (-388 (-530)))) (-4 *2 (-984))))) -(((*1 *2 *2) - (-12 (-5 *2 (-1080 *3)) (-4 *3 (-984)) (-5 *1 (-1084 *3)))) - ((*1 *1 *1) - (-12 (-5 *1 (-1173 *2 *3 *4)) (-4 *2 (-984)) (-14 *3 (-1099)) - (-14 *4 *2)))) -(((*1 *2 *3 *4 *3 *4 *3) + (-5 *2 (-597 (-2 (|:| |val| (-110)) (|:| -2350 *4)))) + (-5 *1 (-1035 *5 *6 *7 *3 *4)) (-4 *4 (-1003 *5 *6 *7 *3))))) +(((*1 *2 *3 *4 *4 *4 *3 *4 *3) (-12 (-5 *3 (-530)) (-5 *4 (-637 (-208))) (-5 *2 (-973)) - (-5 *1 (-705))))) -(((*1 *1 *2 *3 *4) - (-12 - (-5 *3 - (-597 - (-2 (|:| |scalar| (-388 (-530))) (|:| |coeff| (-1095 *2)) - (|:| |logand| (-1095 *2))))) - (-5 *4 (-597 (-2 (|:| |integrand| *2) (|:| |intvar| *2)))) - (-4 *2 (-344)) (-5 *1 (-547 *2))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1060 *3)) (-4 *3 (-984)) - (-5 *2 (-597 (-597 (-597 (-719)))))))) + (-5 *1 (-700))))) +(((*1 *2 *3) (-12 (-5 *3 (-1082)) (-5 *2 (-1186)) (-5 *1 (-417))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-795) (-432))) (-5 *1 (-1127 *3 *2)) + (-4 *2 (-13 (-411 *3) (-1121)))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-1 *4 *4)) (-4 *4 (-599 *3)) (-4 *3 (-984)) + (-5 *1 (-663 *3 *4)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-984)) (-5 *1 (-782 *3))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-923 *2)) (-4 *2 (-1121))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |lfn| (-597 (-297 (-208)))) (|:| -3638 (-597 (-208))))) + (-2 (|:| |lfn| (-597 (-297 (-208)))) (|:| -3677 (-597 (-208))))) (-5 *2 (-597 (-1099))) (-5 *1 (-249)))) ((*1 *2 *3) (-12 (-5 *3 (-1095 *7)) (-4 *7 (-890 *6 *4 *5)) (-4 *4 (-741)) @@ -8927,7 +8414,7 @@ (-5 *1 (-891 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-344) - (-10 -8 (-15 -2235 ($ *7)) (-15 -1826 (*7 $)) (-15 -1835 (*7 $))))))) + (-10 -8 (-15 -2258 ($ *7)) (-15 -1848 (*7 $)) (-15 -1857 (*7 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1029 (-1099))) (-5 *1 (-907 *3)) (-4 *3 (-908)))) ((*1 *2 *1) @@ -8939,58 +8426,29 @@ ((*1 *2 *3) (-12 (-5 *3 (-388 (-893 *4))) (-4 *4 (-522)) (-5 *2 (-597 (-1099))) (-5 *1 (-980 *4))))) -(((*1 *2 *3) (-12 (-5 *2 (-1 *3)) (-5 *1 (-630 *3)) (-4 *3 (-1027))))) -(((*1 *2 *3 *4 *4 *5) - (-12 (-5 *4 (-570 *3)) (-5 *5 (-1 (-1095 *3) (-1095 *3))) - (-4 *3 (-13 (-27) (-411 *6))) (-4 *6 (-13 (-795) (-522))) - (-5 *2 (-547 *3)) (-5 *1 (-517 *6 *3))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-597 (-1104))) (-5 *1 (-1104)))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-1099)) (-5 *3 (-597 (-1104))) (-5 *1 (-1104))))) -(((*1 *2) - (-12 (-5 *2 (-1 *3 *3)) (-5 *1 (-501 *3)) (-4 *3 (-13 (-675) (-25)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1181 *1)) (-4 *1 (-348 *4)) (-4 *4 (-162)) - (-5 *2 (-597 (-893 *4))))) - ((*1 *2) - (-12 (-4 *4 (-162)) (-5 *2 (-597 (-893 *4))) (-5 *1 (-397 *3 *4)) - (-4 *3 (-398 *4)))) - ((*1 *2) - (-12 (-4 *1 (-398 *3)) (-4 *3 (-162)) (-5 *2 (-597 (-893 *3))))) - ((*1 *2) - (-12 (-5 *2 (-597 (-893 *3))) (-5 *1 (-433 *3 *4 *5 *6)) - (-4 *3 (-522)) (-4 *3 (-162)) (-14 *4 (-862)) - (-14 *5 (-597 (-1099))) (-14 *6 (-1181 (-637 *3))))) - ((*1 *2 *3) - (-12 (-5 *3 (-1181 (-433 *4 *5 *6 *7))) (-5 *2 (-597 (-893 *4))) - (-5 *1 (-433 *4 *5 *6 *7)) (-4 *4 (-522)) (-4 *4 (-162)) - (-14 *5 (-862)) (-14 *6 (-597 (-1099))) (-14 *7 (-1181 (-637 *4)))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1181 (-597 (-2 (|:| -3359 *4) (|:| -1891 (-1046)))))) - (-4 *4 (-330)) (-5 *2 (-1186)) (-5 *1 (-500 *4))))) -(((*1 *2 *3 *3 *3 *3 *4 *4 *4 *3 *5) - (-12 (-5 *3 (-530)) (-5 *4 (-637 (-208))) - (-5 *5 (-3 (|:| |fn| (-369)) (|:| |fp| (-64 FUNCT1)))) - (-5 *2 (-973)) (-5 *1 (-702))))) +(((*1 *2 *2 *3) (-12 (-5 *3 (-719)) (-5 *1 (-548 *2)) (-4 *2 (-515))))) +(((*1 *2 *1) + (-12 (-5 *2 (-597 (-276 *3))) (-5 *1 (-276 *3)) (-4 *3 (-522)) + (-4 *3 (-1135))))) +(((*1 *2 *3 *3) + (-12 (-5 *2 (-597 *3)) (-5 *1 (-902 *3)) (-4 *3 (-515))))) +(((*1 *2 *3 *3 *4) + (-12 (-4 *5 (-432)) (-4 *6 (-741)) (-4 *7 (-795)) + (-4 *3 (-998 *5 *6 *7)) + (-5 *2 (-597 (-2 (|:| |val| *3) (|:| -2350 *4)))) + (-5 *1 (-1035 *5 *6 *7 *3 *4)) (-4 *4 (-1003 *5 *6 *7 *3))))) +(((*1 *2 *3 *4 *4 *3) + (-12 (-5 *3 (-530)) (-5 *4 (-637 (-208))) (-5 *2 (-973)) + (-5 *1 (-700))))) +(((*1 *2) (-12 (-5 *2 (-1186)) (-5 *1 (-417))))) +(((*1 *2 *2) 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(-112)) (-5 *1 (-782 *2)) (-4 *2 (-984))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-923 *2)) (-4 *2 (-1121))))) (((*1 *2 *3 *4 *2) (-12 (-5 *3 (-1095 (-388 (-1095 *2)))) (-5 *4 (-570 *2)) (-4 *2 (-13 (-411 *5) (-27) (-1121))) @@ -9007,44 +8465,46 @@ (-4 *6 (-984)) (-4 *2 (-13 (-344) - (-10 -8 (-15 -2235 ($ *7)) (-15 -1826 (*7 $)) (-15 -1835 (*7 $))))) + (-10 -8 (-15 -2258 ($ *7)) (-15 -1848 (*7 $)) (-15 -1857 (*7 $))))) (-5 *1 (-891 *5 *4 *6 *7 *2)) (-4 *7 (-890 *6 *5 *4)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-388 (-1095 (-388 (-893 *5))))) (-5 *4 (-1099)) (-5 *2 (-388 (-893 *5))) (-5 *1 (-980 *5)) (-4 *5 (-522))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1095 *2)) (-4 *2 (-890 (-388 (-893 *6)) *5 *4)) - (-5 *1 (-681 *5 *4 *6 *2)) (-4 *5 (-741)) - (-4 *4 (-13 (-795) (-10 -8 (-15 -3153 ((-1099) $))))) - (-4 *6 (-522))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1099)) (-5 *2 (-1 (-1095 (-893 *4)) (-893 *4))) - (-5 *1 (-1189 *4)) (-4 *4 (-344))))) (((*1 *2 *2 *3) - (-12 (-5 *2 (-637 *3)) (-4 *3 (-289)) (-5 *1 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*7)) (-4 *6 (-344)) + (-5 *2 + (-2 (|:| |mainpart| *3) + (|:| |limitedlogs| + (-597 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) + (-5 *1 (-540 *6 *7))))) +(((*1 *2 *2 *3) + (-12 (-4 *3 (-344)) (-5 *1 (-267 *3 *2)) (-4 *2 (-1172 *3))))) (((*1 *2 *3) (-12 (-5 *3 (-51)) (-5 *1 (-50 *2)) (-4 *2 (-1135)))) ((*1 *1 *2) (-12 (-5 *2 (-893 (-360))) (-5 *1 (-320 *3 *4 *5)) @@ -9925,11 +9395,11 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1099)) (|:| |fn| (-297 (-208))) - (|:| -3723 (-1022 (-788 (-208)))) (|:| |abserr| (-208)) + (|:| -2902 (-1022 (-788 (-208)))) (|:| |abserr| (-208)) (|:| |relerr| (-208)))) (|:| |mdnia| (-2 (|:| |fn| (-297 (-208))) - (|:| -3723 (-597 (-1022 (-788 (-208))))) + (|:| -2902 (-597 (-1022 (-788 (-208))))) (|:| |abserr| (-208)) (|:| |relerr| (-208)))))) (-5 *1 (-717)))) ((*1 *2 *1) @@ -9945,13 +9415,13 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-297 (-208))) (|:| -3638 (-597 (-208))) + (-2 (|:| |fn| (-297 (-208))) (|:| -3677 (-597 (-208))) (|:| |lb| (-597 (-788 (-208)))) (|:| |cf| (-597 (-297 (-208)))) (|:| |ub| (-597 (-788 (-208)))))) (|:| |lsa| (-2 (|:| |lfn| (-597 (-297 (-208)))) - (|:| -3638 (-597 (-208))))))) + (|:| -3677 (-597 (-208))))))) (-5 *1 (-786)))) ((*1 *2 *1) (-12 @@ -9970,26 +9440,26 @@ (-4 *4 (-741)) (-4 *5 (-795)) (-4 *1 (-916 *3 *4 *5 *6)))) ((*1 *2 *1) (-12 (-4 *1 (-975 *2)) (-4 *2 (-1135)))) ((*1 *1 *2) - (-1450 + (-1476 (-12 (-5 *2 (-893 *3)) - (-12 (-3659 (-4 *3 (-37 (-388 (-530))))) - (-3659 (-4 *3 (-37 (-530)))) (-4 *5 (-572 (-1099)))) + (-12 (-3694 (-4 *3 (-37 (-388 (-530))))) + (-3694 (-4 *3 (-37 (-530)))) (-4 *5 (-572 (-1099)))) (-4 *3 (-984)) (-4 *1 (-998 *3 *4 *5)) (-4 *4 (-741)) (-4 *5 (-795))) (-12 (-5 *2 (-893 *3)) - (-12 (-3659 (-4 *3 (-515))) (-3659 (-4 *3 (-37 (-388 (-530))))) + (-12 (-3694 (-4 *3 (-515))) (-3694 (-4 *3 (-37 (-388 (-530))))) (-4 *3 (-37 (-530))) (-4 *5 (-572 (-1099)))) (-4 *3 (-984)) (-4 *1 (-998 *3 *4 *5)) (-4 *4 (-741)) (-4 *5 (-795))) (-12 (-5 *2 (-893 *3)) - (-12 (-3659 (-4 *3 (-932 (-530)))) (-4 *3 (-37 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*1 *1) (-12 (-14 *2 (-597 (-1099))) (-4 *3 (-162)) - (-4 *5 (-221 (-2144 *2) (-719))) + (-4 *5 (-221 (-2167 *2) (-719))) (-14 *6 - (-1 (-110) (-2 (|:| -1891 *4) (|:| -3731 *5)) - (-2 (|:| -1891 *4) (|:| -3731 *5)))) + (-1 (-110) (-2 (|:| -1910 *4) (|:| -3059 *5)) + (-2 (|:| -1910 *4) (|:| -3059 *5)))) (-5 *1 (-441 *2 *3 *4 *5 *6 *7)) (-4 *4 (-795)) (-4 *7 (-890 *3 *5 (-806 *2))))) ((*1 *1 *1) (-12 (-4 *1 (-486 *2 *3)) (-4 *2 (-1027)) (-4 *3 (-795)))) @@ -10182,31 +9657,47 @@ (-12 (-4 *1 (-998 *3 *4 *2)) (-4 *3 (-984)) (-4 *4 (-741)) (-4 *2 (-795)))) ((*1 *1 *1) (-12 (-5 *1 (-1202 *2 *3)) (-4 *2 (-984)) (-4 *3 (-791))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1046)) (-5 *2 (-110)) (-5 *1 (-769))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5) - (-12 (-5 *3 (-1 (-360) (-360))) (-5 *4 (-360)) - (-5 *2 - (-2 (|:| -3359 *4) (|:| -3895 *4) (|:| |totalpts| (-530)) - (|:| |success| (-110)))) - (-5 *1 (-737)) (-5 *5 (-530))))) -(((*1 *2 *3) - (|partial| -12 (-5 *3 (-570 *4)) (-4 *4 (-795)) (-4 *2 (-795)) - (-5 *1 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+ (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) + (-4 *2 (-411 *3))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-719)) (-4 *1 (-1157 *3)) (-4 *3 (-984))))) +(((*1 *2 *1) + (-12 (-4 *4 (-1027)) (-5 *2 (-110)) (-5 *1 (-826 *3 *4 *5)) + (-4 *3 (-1027)) (-4 *5 (-617 *4)))) + ((*1 *2 *1) + (-12 (-5 *2 (-110)) (-5 *1 (-830 *3 *4)) (-4 *3 (-1027)) + (-4 *4 (-1027))))) (((*1 *1 *1) (-4 *1 (-34))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) @@ -10576,9 +10049,7 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1030 *3 *4 *5 *6 *7)) (-4 *3 (-1027)) (-4 *4 (-1027)) - (-4 *5 (-1027)) (-4 *6 (-1027)) (-4 *7 (-1027)) (-5 *2 (-110))))) +(((*1 *2 *3) (-12 (-5 *3 (-884 *2)) (-5 *1 (-922 *2)) (-4 *2 (-984))))) (((*1 *1 *1) (-4 *1 (-226))) ((*1 *1 *1) (-12 (-4 *2 (-162)) (-5 *1 (-271 *2 *3 *4 *5 *6 *7)) @@ -10586,7 +10057,7 @@ (-14 *6 (-1 (-3 *4 "failed") *4 *4)) (-14 *7 (-1 (-3 *3 "failed") *3 *3 *4)))) ((*1 *1 *1) - (-1450 (-12 (-5 *1 (-276 *2)) (-4 *2 (-344)) (-4 *2 (-1135))) + (-1476 (-12 (-5 *1 (-276 *2)) (-4 *2 (-344)) (-4 *2 (-1135))) (-12 (-5 *1 (-276 *2)) (-4 *2 (-453)) (-4 *2 (-1135))))) ((*1 *1 *1) (-4 *1 (-453))) ((*1 *2 *2) (-12 (-5 *2 (-1181 *3)) (-4 *3 (-330)) (-5 *1 (-500 *3)))) @@ -10595,131 +10066,30 @@ (-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 *1) (-12 (-4 *1 (-745 *2)) (-4 *2 (-162)) (-4 *2 (-344))))) -(((*1 *2) - (-12 (-4 *4 (-162)) (-5 *2 (-110)) (-5 *1 (-347 *3 *4)) - (-4 *3 (-348 *4)))) - ((*1 *2) (-12 (-4 *1 (-348 *3)) (-4 *3 (-162)) (-5 *2 (-110))))) -(((*1 *2) - (-12 (-4 *2 (-13 (-411 *3) (-941))) (-5 *1 (-258 *3 *2)) - (-4 *3 (-13 (-795) (-522)))))) -(((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-862)) (-5 *4 (-1082)) (-5 *2 (-1186)) (-5 *1 (-1182))))) -(((*1 *2 *3) - (-12 (-5 *3 (-717)) - (-5 *2 - (-2 (|:| -2325 (-360)) (|:| -3890 (-1082)) - (|:| |explanations| (-597 (-1082))) (|:| |extra| (-973)))) - (-5 *1 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*2))) (-5 *4 (-1099)) + (-4 *2 (-13 (-27) (-1121) (-411 *5))) + (-4 *5 (-13 (-522) (-795) (-975 (-530)) (-593 (-530)))) + (-5 *1 (-259 *5 *2))))) +(((*1 *2 *1) (-12 (-5 *2 (-110)) (-5 *1 (-137))))) +(((*1 *1 *1) + (-12 (-5 *1 (-1064 *2 *3)) (-4 *2 (-13 (-1027) (-33))) + (-4 *3 (-13 (-1027) (-33)))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) + (-4 *2 (-411 *3))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-1157 *2)) (-4 *2 (-984))))) +(((*1 *2 *3 *1) + (|partial| -12 (-5 *3 (-833 *4)) (-4 *4 (-1027)) (-4 *2 (-1027)) + (-5 *1 (-830 *4 *2))))) (((*1 *2 *1) (-12 (-5 *2 (-597 (-570 *1))) (-4 *1 (-284))))) (((*1 *1 *1) (-4 *1 (-34))) ((*1 *2 *2) @@ -10737,20 +10107,56 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *2 *1) - (-12 (-5 *2 (-597 (-597 (-719)))) (-5 *1 (-845 *3)) (-4 *3 (-1027))))) -(((*1 *1 *1 *1) (-12 (-5 *1 (-730 *2)) (-4 *2 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+ (-12 (-4 *4 (-1157 *2)) (-4 *2 (-162)) (-5 *1 (-389 *3 *2 *4)) + (-4 *3 (-390 *2 *4)))) + ((*1 *2) (-12 (-4 *1 (-390 *2 *3)) (-4 *3 (-1157 *2)) (-4 *2 (-162)))) + ((*1 *2) + (-12 (-4 *3 (-1157 *2)) (-5 *2 (-530)) (-5 *1 (-716 *3 *4)) + (-4 *4 (-390 *2 *3)))) + ((*1 *1 *1 *2) + (-12 (-4 *1 (-890 *3 *4 *2)) (-4 *3 (-984)) (-4 *4 (-741)) + (-4 *2 (-795)) (-4 *3 (-162)))) + ((*1 *2 *3) + (-12 (-4 *2 (-522)) (-5 *1 (-910 *2 *3)) (-4 *3 (-1157 *2)))) + ((*1 *2 *1) (-12 (-4 *1 (-1157 *2)) (-4 *2 (-984)) (-4 *2 (-162))))) +(((*1 *1 *2 *3 *1) + (-12 (-5 *2 (-833 *4)) (-4 *4 (-1027)) (-5 *1 (-830 *4 *3)) + (-4 *3 (-1027))))) (((*1 *1 *1) (-4 *1 (-34))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) @@ -10804,45 +10210,41 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-388 (-530))) (-4 *4 (-984)) (-4 *1 (-1164 *4 *3)) (-4 *3 (-1141 *4))))) -(((*1 *1 *2 *2) (-12 (-5 *1 (-818 *2)) (-4 *2 (-1135)))) - ((*1 *1 *2 *2 *2) (-12 (-5 *1 (-820 *2)) (-4 *2 (-1135)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1060 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(-1099)) (-4 *4 (-432)) (-4 *4 (-795)) + (-5 *1 (-539 *4 *2)) (-4 *2 (-266)) (-4 *2 (-411 *4))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-1099)) + (-4 *5 (-13 (-522) (-795) (-975 (-530)) (-593 (-530)))) + (-5 *2 + (-2 (|:| |func| *3) (|:| |kers| (-597 (-570 *3))) + (|:| |vals| (-597 *3)))) + (-5 *1 (-259 *5 *3)) (-4 *3 (-13 (-27) (-1121) (-411 *5)))))) +(((*1 *2 *1 *1 *3) + (-12 (-5 *3 (-1 (-110) *5 *5)) (-4 *5 (-13 (-1027) (-33))) + (-5 *2 (-110)) (-5 *1 (-1064 *4 *5)) (-4 *4 (-13 (-1027) (-33)))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) +(((*1 *1 *2 *1) (-12 (-5 *1 (-119 *2)) (-4 *2 (-795))))) +(((*1 *1 *2 *3) + (-12 (-5 *1 (-408 *3 *2)) (-4 *3 (-13 (-162) (-37 (-388 (-530))))) + (-4 *2 (-13 (-795) (-21)))))) +(((*1 *1 *1 *1 *2) + (-12 (-4 *1 (-890 *3 *4 *2)) (-4 *3 (-984)) (-4 *4 (-741)) + (-4 *2 (-795)) (-4 *3 (-162)))) ((*1 *2 *3 *3) - (-12 (-5 *3 (-597 *4)) (-4 *4 (-1027)) (-5 *2 (-1186)) - (-5 *1 (-1136 *4))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-530)) (-4 *6 (-741)) (-4 *7 (-795)) (-4 *8 (-289)) - (-4 *9 (-890 *8 *6 *7)) - (-5 *2 (-2 (|:| -1632 (-1095 *9)) (|:| |polval| (-1095 *8)))) - (-5 *1 (-691 *6 *7 *8 *9)) (-5 *3 (-1095 *9)) (-5 *4 (-1095 *8))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1082)) (-5 *2 (-530)) (-5 *1 (-1118 *4)) - (-4 *4 (-984))))) -(((*1 *2 *3 *1) - (-12 (-4 *1 (-1003 *4 *5 *6 *3)) (-4 *4 (-432)) (-4 *5 (-741)) - (-4 *6 (-795)) (-4 *3 (-998 *4 *5 *6)) (-5 *2 (-110))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1027)) (-4 *5 (-1027)) - (-4 *6 (-1027)) (-5 *2 (-1 *6 *5 *4)) (-5 *1 (-632 *4 *5 *6))))) + (-12 (-4 *2 (-522)) (-5 *1 (-910 *2 *3)) (-4 *3 (-1157 *2)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-998 *2 *3 *4)) (-4 *2 (-984)) (-4 *3 (-741)) + (-4 *4 (-795)) (-4 *2 (-522)))) + ((*1 *2 *1 *1) (-12 (-4 *1 (-1157 *2)) (-4 *2 (-984)) (-4 *2 (-162))))) +(((*1 *1 *2 *3 *1) + (-12 (-5 *2 (-833 *4)) (-4 *4 (-1027)) (-5 *1 (-830 *4 *3)) + (-4 *3 (-1027))))) (((*1 *1 *1) (-4 *1 (-34))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) @@ -10859,47 +10261,48 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-637 *3)) - (-4 *3 (-13 (-289) (-10 -8 (-15 -1523 ((-399 $) $))))) - (-4 *4 (-1157 *3)) (-5 *1 (-477 *3 *4 *5)) (-4 *5 (-390 *3 *4)))) - ((*1 *2 *2 *2 *3) - (-12 (-5 *2 (-637 *3)) - (-4 *3 (-13 (-289) (-10 -8 (-15 -1523 ((-399 $) $))))) - (-4 *4 (-1157 *3)) (-5 *1 (-477 *3 *4 *5)) (-4 *5 (-390 *3 *4))))) -(((*1 *2 *1) (-12 (-4 *1 (-745 *2)) (-4 *2 (-162))))) -(((*1 *2) - (-12 (-4 *3 (-522)) (-5 *2 (-597 (-637 *3))) (-5 *1 (-42 *3 *4)) - (-4 *4 (-398 *3))))) -(((*1 *2) (-12 (-5 *2 (-1186)) (-5 *1 (-425 *3)) (-4 *3 (-984))))) -(((*1 *2 *1 *1) - (-12 - (-5 *2 - (-2 (|:| -1963 *3) (|:| |gap| (-719)) (|:| -3468 (-730 *3)) - (|:| -3078 (-730 *3)))) - (-5 *1 (-730 *3)) (-4 *3 (-984)))) - ((*1 *2 *1 *1 *3) - (-12 (-4 *4 (-984)) (-4 *5 (-741)) (-4 *3 (-795)) - (-5 *2 - (-2 (|:| -1963 *1) (|:| |gap| (-719)) (|:| -3468 *1) - (|:| -3078 *1))) - (-4 *1 (-998 *4 *5 *3)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-984)) (-4 *4 (-741)) (-4 *5 (-795)) - (-5 *2 - (-2 (|:| -1963 *1) (|:| |gap| (-719)) (|:| -3468 *1) - (|:| -3078 *1))) - (-4 *1 (-998 *3 *4 *5))))) -(((*1 *1 *1) (-4 *1 (-583))) +(((*1 *2 *3) + (-12 (-4 *4 (-13 (-795) (-522))) (-5 *2 (-110)) (-5 *1 (-258 *4 *3)) + (-4 *3 (-13 (-411 *4) (-941)))))) +(((*1 *2 *2) (-12 (-5 *2 (-208)) (-5 *1 (-209)))) + ((*1 *2 *2) (-12 (-5 *2 (-159 (-208))) (-5 *1 (-209)))) ((*1 *2 *2) - (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-584 *3 *2)) - (-4 *2 (-13 (-411 *3) (-941) (-1121)))))) -(((*1 *2 *3 *3 *3 *4 *4 *4 *4 *4 *5 *3 *3 *3 *6 *4 *3) - (-12 (-5 *4 (-637 (-208))) (-5 *5 (-637 (-530))) (-5 *6 (-208)) - (-5 *3 (-530)) (-5 *2 (-973)) (-5 *1 (-701))))) -(((*1 *2 *3 *4 *4 *5 *3 *3 *4 *3) - (-12 (-5 *3 (-530)) (-5 *5 (-637 (-208))) (-5 *4 (-208)) - (-5 *2 (-973)) (-5 *1 (-701))))) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) + (-4 *2 (-411 *3)))) + ((*1 *1 *1) (-4 *1 (-1063)))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) +(((*1 *2 *3) + (-12 (-5 *2 (-110)) (-5 *1 (-118 *3)) (-4 *3 (-1157 (-530)))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-1099)) + (-4 *5 (-13 (-289) (-795) (-140) (-975 (-530)) (-593 (-530)))) + (-5 *2 (-547 *3)) (-5 *1 (-407 *5 *3)) + (-4 *3 (-13 (-1121) (-29 *5)))))) +(((*1 *2 *2 *2) + (-12 (-4 *3 (-522)) (-5 *1 (-910 *3 *2)) (-4 *2 (-1157 *3)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-998 *2 *3 *4)) (-4 *2 (-984)) (-4 *3 (-741)) + (-4 *4 (-795)) (-4 *2 (-522)))) + ((*1 *1 *1 *1) (-12 (-4 *1 (-1157 *2)) (-4 *2 (-984)) (-4 *2 (-522))))) +(((*1 *1 *2 *3 *1 *3) + (-12 (-5 *2 (-833 *4)) (-4 *4 (-1027)) (-5 *1 (-830 *4 *3)) + (-4 *3 (-1027))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-637 *4)) (-5 *3 (-862)) (|has| *4 (-6 (-4272 "*"))) + (-4 *4 (-984)) (-5 *1 (-966 *4)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-597 (-637 *4))) (-5 *3 (-862)) + (|has| *4 (-6 (-4272 "*"))) (-4 *4 (-984)) (-5 *1 (-966 *4))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-1 (-884 (-208)) (-884 (-208)))) (-5 *3 (-597 (-245))) + (-5 *1 (-243)))) + ((*1 *1 *2) + (-12 (-5 *2 (-1 (-884 (-208)) (-884 (-208)))) (-5 *1 (-245)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-597 (-460 *5 *6))) (-5 *3 (-460 *5 *6)) + (-14 *5 (-597 (-1099))) (-4 *6 (-432)) (-5 *2 (-1181 *6)) + (-5 *1 (-585 *5 *6))))) (((*1 *1 *1) (-4 *1 (-34))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) @@ -10917,29 +10320,49 @@ (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) (((*1 *2 *3) - (-12 (-4 *4 (-289)) (-4 *5 (-354 *4)) (-4 *6 (-354 *4)) - (-5 *2 (-2 (|:| |Hermite| *3) (|:| |eqMat| *3))) - (-5 *1 (-1050 *4 *5 *6 *3)) (-4 *3 (-635 *4 *5 *6))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1049 *3 *4 *2 *5)) (-4 *4 (-984)) (-4 *5 (-221 *3 *4)) - (-4 *2 (-221 *3 *4))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-771)) (-5 *2 (-1186)) (-5 *1 (-770))))) -(((*1 *1 *1 *1) (-5 *1 (-804)))) -(((*1 *2 *1) - (-12 (-4 *1 (-916 *3 *4 *5 *6)) (-4 *3 (-984)) (-4 *4 (-741)) - (-4 *5 (-795)) (-4 *6 (-998 *3 *4 *5)) (-4 *3 (-522)) - (-5 *2 (-110))))) -(((*1 *2 *3 *3 *3 *3 *4 *4 *4 *5) - (-12 (-5 *3 (-208)) (-5 *4 (-530)) - (-5 *5 (-3 (|:| |fn| (-369)) (|:| |fp| (-62 -1329)))) (-5 *2 (-973)) - (-5 *1 (-697))))) + (-12 (-4 *4 (-522)) (-5 *2 (-719)) (-5 *1 (-42 *4 *3)) + (-4 *3 (-398 *4))))) +(((*1 *2 *2 *3) + (|partial| -12 + (-5 *3 (-597 (-2 (|:| |func| *2) (|:| |pole| (-110))))) + (-4 *2 (-13 (-411 *4) (-941))) (-4 *4 (-13 (-795) (-522))) + (-5 *1 (-258 *4 *2))))) +(((*1 *2 *2) (-12 (-5 *2 (-159 (-208))) (-5 *1 (-209)))) + ((*1 *2 *2) (-12 (-5 *2 (-208)) (-5 *1 (-209)))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) + (-4 *2 (-411 *3)))) + ((*1 *1 *1) (-4 *1 (-1063)))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) +(((*1 *2 *1) (-12 (-4 *1 (-406 *3)) (-4 *3 (-1027)) (-5 *2 (-719))))) +(((*1 *1 *2) (-12 (-5 *2 (-597 *1)) (-4 *1 (-1060 *3)) (-4 *3 (-984)))) + ((*1 *2 *2 *1) + (|partial| -12 (-5 *2 (-388 *1)) (-4 *1 (-1157 *3)) (-4 *3 (-984)) + (-4 *3 (-522)))) + ((*1 *1 *1 *1) + (|partial| -12 (-4 *1 (-1157 *2)) (-4 *2 (-984)) (-4 *2 (-522))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-1027)) (-4 *6 (-827 *5)) (-5 *2 (-826 *5 *6 (-597 *6))) + (-5 *1 (-828 *5 *6 *4)) (-5 *3 (-597 *6)) (-4 *4 (-572 (-833 *5))))) + ((*1 *2 *3 *4) + (-12 (-4 *5 (-1027)) (-5 *2 (-597 (-276 *3))) (-5 *1 (-828 *5 *3 *4)) + (-4 *3 (-975 (-1099))) (-4 *3 (-827 *5)) (-4 *4 (-572 (-833 *5))))) + ((*1 *2 *3 *4) + (-12 (-4 *5 (-1027)) (-5 *2 (-597 (-276 (-893 *3)))) + (-5 *1 (-828 *5 *3 *4)) (-4 *3 (-984)) + (-3694 (-4 *3 (-975 (-1099)))) (-4 *3 (-827 *5)) + (-4 *4 (-572 (-833 *5))))) + ((*1 *2 *3 *4) + (-12 (-4 *5 (-1027)) (-5 *2 (-830 *5 *3)) (-5 *1 (-828 *5 *3 *4)) + (-3694 (-4 *3 (-975 (-1099)))) (-3694 (-4 *3 (-984))) + (-4 *3 (-827 *5)) (-4 *4 (-572 (-833 *5)))))) (((*1 *2 *3) - (-12 (-4 *4 (-37 (-388 (-530)))) - (-5 *2 (-2 (|:| -2230 (-1080 *4)) (|:| -2241 (-1080 *4)))) - (-5 *1 (-1086 *4)) (-5 *3 (-1080 *4))))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-830 *4 *5)) (-5 *3 (-830 *4 *6)) (-4 *4 (-1027)) - (-4 *5 (-1027)) (-4 *6 (-617 *5)) (-5 *1 (-826 *4 *5 *6))))) + (-12 (-5 *3 (-637 (-388 (-893 (-530))))) + (-5 *2 (-597 (-637 (-297 (-530))))) (-5 *1 (-969))))) +(((*1 *2 *2) + (-12 (-5 *2 (-597 (-460 *3 *4))) (-14 *3 (-597 (-1099))) + (-4 *4 (-432)) (-5 *1 (-585 *3 *4))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) (-4 *2 (-13 (-411 *3) (-941))))) @@ -10956,39 +10379,47 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *2 *3 *3) - (-12 (-4 *3 (-1139)) (-4 *5 (-1157 *3)) (-4 *6 (-1157 (-388 *5))) - (-5 *2 (-110)) (-5 *1 (-322 *4 *3 *5 *6)) (-4 *4 (-323 *3 *5 *6)))) - ((*1 *2 *3 *3) - (-12 (-4 *1 (-323 *3 *4 *5)) (-4 *3 (-1139)) (-4 *4 (-1157 *3)) - (-4 *5 (-1157 (-388 *4))) (-5 *2 (-110))))) +(((*1 *2 *3) + (-12 (-4 *4 (-522)) (-5 *2 (-719)) (-5 *1 (-42 *4 *3)) + (-4 *3 (-398 *4))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) + (-4 *2 (-13 (-411 *3) (-941)))))) (((*1 *2 *3 *1) (|partial| -12 (-4 *1 (-35 *3 *4)) (-4 *3 (-1027)) (-4 *4 (-1027)) - (-5 *2 (-2 (|:| -2913 *3) (|:| -1782 *4)))))) -(((*1 *1 *2) (-12 (-5 *2 (-530)) (-5 *1 (-804))))) -(((*1 *1 *2 *3) - (-12 - (-5 *3 - (-597 - (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *2) - (|:| |xpnt| (-530))))) - (-4 *2 (-522)) (-5 *1 (-399 *2)))) - ((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |contp| (-530)) - (|:| -3494 (-597 (-2 (|:| |irr| *4) (|:| -1429 (-530))))))) - (-4 *4 (-1157 (-530))) (-5 *2 (-399 *4)) (-5 *1 (-422 *4))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1030 *3 *4 *5 *6 *7)) (-4 *3 (-1027)) (-4 *4 (-1027)) - (-4 *5 (-1027)) (-4 *6 (-1027)) (-4 *7 (-1027)) (-5 *2 (-110))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-795) (-432))) (-5 *1 (-1127 *3 *2)) - (-4 *2 (-13 (-411 *3) (-1121)))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-923 *2)) (-4 *2 (-1121))))) -(((*1 *2 *3 *3 *1) - (|partial| -12 (-5 *3 (-1099)) (-5 *2 (-1031)) (-5 *1 (-273))))) -(((*1 *2 *3 *3 *2) (-12 (-5 *2 (-973)) (-5 *3 (-1099)) (-5 *1 (-176))))) + (-5 *2 (-2 (|:| -2940 *3) (|:| -1806 *4)))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-208)) (-5 *1 (-209)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-159 (-208))) (-5 *1 (-209)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) + (-4 *2 (-411 *3)))) + ((*1 *1 *1 *1) (-4 *1 (-1063)))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) +(((*1 *1 *1) (-12 (-4 *1 (-406 *2)) (-4 *2 (-1027)) (-4 *2 (-349))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-1157 *2)) (-4 *2 (-984)) (-4 *2 (-522))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1099)) (-5 *2 (-110)) (-5 *1 (-112)))) + ((*1 *2 *1 *3) (-12 (-4 *1 (-284)) (-5 *3 (-1099)) (-5 *2 (-110)))) + ((*1 *2 *1 *3) (-12 (-4 *1 (-284)) (-5 *3 (-112)) (-5 *2 (-110)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-1099)) (-5 *2 (-110)) (-5 *1 (-570 *4)) (-4 *4 (-795)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-112)) (-5 *2 (-110)) (-5 *1 (-570 *4)) (-4 *4 (-795)))) + ((*1 *2 *3 *4) + (-12 (-4 *5 (-1027)) (-5 *2 (-110)) (-5 *1 (-828 *5 *3 *4)) + (-4 *3 (-827 *5)) (-4 *4 (-572 (-833 *5))))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-597 *6)) (-4 *6 (-827 *5)) (-4 *5 (-1027)) + (-5 *2 (-110)) (-5 *1 (-828 *5 *6 *4)) (-4 *4 (-572 (-833 *5)))))) +(((*1 *2 *2) (-12 (-5 *2 (-597 (-637 (-297 (-530))))) (-5 *1 (-969))))) +(((*1 *2 *3 *3 *4) + (-12 (-5 *3 (-597 (-460 *5 *6))) (-5 *4 (-806 *5)) + (-14 *5 (-597 (-1099))) (-5 *2 (-460 *5 *6)) (-5 *1 (-585 *5 *6)) + (-4 *6 (-432)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-597 (-460 *5 *6))) (-5 *4 (-806 *5)) + (-14 *5 (-597 (-1099))) (-5 *2 (-460 *5 *6)) (-5 *1 (-585 *5 *6)) + (-4 *6 (-432))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) (-4 *2 (-13 (-411 *3) (-941))))) @@ -11005,8 +10436,12 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *1 *1) (-12 (-4 *1 (-411 *2)) (-4 *2 (-795)) (-4 *2 (-984)))) - ((*1 *1 *1) (-12 (-4 *1 (-932 *2)) (-4 *2 (-522))))) +(((*1 *2 *3) + (-12 (-4 *4 (-522)) (-5 *2 (-719)) (-5 *1 (-42 *4 *3)) + (-4 *3 (-398 *4))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) + (-4 *2 (-13 (-411 *3) (-941)))))) (((*1 *2 *1) (-12 (-4 *1 (-227 *2)) (-4 *2 (-1135)))) ((*1 *2 *1) (|partial| -12 (-4 *1 (-1129 *3 *4 *5 *2)) (-4 *3 (-522)) @@ -11014,34 +10449,32 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-719)) (-4 *1 (-1169 *3)) (-4 *3 (-1135)))) ((*1 *2 *1) (-12 (-4 *1 (-1169 *2)) (-4 *2 (-1135))))) -(((*1 *1 *1 *2 *2) - (-12 (-5 *2 (-530)) (-4 *1 (-635 *3 *4 *5)) (-4 *3 (-984)) - (-4 *4 (-354 *3)) (-4 *5 (-354 *3))))) -(((*1 *2 *1) - (-12 (-5 *2 (-388 (-893 *3))) (-5 *1 (-433 *3 *4 *5 *6)) - (-4 *3 (-522)) (-4 *3 (-162)) (-14 *4 (-862)) - (-14 *5 (-597 (-1099))) (-14 *6 (-1181 (-637 *3)))))) -(((*1 *2 *1 *3) - (-12 (-4 *1 (-323 *4 *3 *5)) (-4 *4 (-1139)) (-4 *3 (-1157 *4)) - (-4 *5 (-1157 (-388 *3))) (-5 *2 (-110)))) - ((*1 *2 *1 *3) - (-12 (-4 *1 (-323 *3 *4 *5)) (-4 *3 (-1139)) (-4 *4 (-1157 *3)) - (-4 *5 (-1157 (-388 *4))) (-5 *2 (-110)))) - ((*1 *2 *1) - (-12 (-4 *1 (-323 *3 *4 *5)) (-4 *3 (-1139)) (-4 *4 (-1157 *3)) - (-4 *5 (-1157 (-388 *4))) (-5 *2 (-110))))) -(((*1 *1) (-5 *1 (-137))) - ((*1 *2 *3) - (-12 (-5 *3 (-597 (-245))) (-5 *2 (-1059 (-208))) (-5 *1 (-243)))) - ((*1 *1 *2) (-12 (-5 *2 (-1059 (-208))) (-5 *1 (-245))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-208)) (-5 *1 (-209)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-159 (-208))) (-5 *1 (-209)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) + (-4 *2 (-411 *3)))) + ((*1 *1 *1 *1) (-4 *1 (-1063)))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-522)) + (-5 *2 (-2 (|:| -1981 *4) (|:| -3624 *3) (|:| -3088 *3))) + (-5 *1 (-910 *4 *3)) (-4 *3 (-1157 *4)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-984)) (-4 *4 (-741)) (-4 *5 (-795)) + (-5 *2 (-2 (|:| -3624 *1) (|:| -3088 *1))) (-4 *1 (-998 *3 *4 *5)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-522)) (-4 *3 (-984)) + (-5 *2 (-2 (|:| -1981 *3) (|:| -3624 *1) (|:| -3088 *1))) + (-4 *1 (-1157 *3))))) +(((*1 *1 *2 *3) + (-12 (-5 *2 (-830 *4 *5)) (-5 *3 (-830 *4 *6)) (-4 *4 (-1027)) + (-4 *5 (-1027)) (-4 *6 (-617 *5)) (-5 *1 (-826 *4 *5 *6))))) +(((*1 *2 *2) (-12 (-5 *2 (-637 (-297 (-530)))) (-5 *1 (-969))))) (((*1 *2 *3) - (-12 (-5 *3 (-637 (-297 (-208)))) - (-5 *2 - (-2 (|:| |stiffnessFactor| (-360)) (|:| |stabilityFactor| (-360)))) - (-5 *1 (-189))))) -(((*1 *2) - (-12 (-4 *3 (-522)) (-5 *2 (-597 (-637 *3))) (-5 *1 (-42 *3 *4)) - (-4 *4 (-398 *3))))) + (-12 (-5 *3 (-597 (-460 *4 *5))) (-14 *4 (-597 (-1099))) + (-4 *5 (-432)) (-5 *2 (-597 (-230 *4 *5))) (-5 *1 (-585 *4 *5))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) (-4 *2 (-13 (-411 *3) (-941))))) @@ -11058,25 +10491,45 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-110)) (-5 *1 (-415))))) -(((*1 *2) (-12 (-5 *2 (-110)) (-5 *1 (-708))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-530)) (|has| *1 (-6 -4271)) (-4 *1 (-1169 *3)) - (-4 *3 (-1135))))) +(((*1 *2 *3 *2 *4) + (-12 (-5 *3 (-112)) (-5 *4 (-719)) (-4 *5 (-432)) (-4 *5 (-795)) + (-4 *5 (-975 (-530))) (-4 *5 (-522)) (-5 *1 (-40 *5 *2)) + (-4 *2 (-411 *5)) + (-4 *2 + (-13 (-344) (-284) + (-10 -8 (-15 -1848 ((-1051 *5 (-570 $)) $)) + (-15 -1857 ((-1051 *5 (-570 $)) $)) + (-15 -2258 ($ (-1051 *5 (-570 $)))))))))) (((*1 *2 *2) - (-12 (-4 *3 (-13 (-795) (-432))) (-5 *1 (-1127 *3 *2)) - (-4 *2 (-13 (-411 *3) (-1121)))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-862)) (-5 *1 (-970 *2)) - (-4 *2 (-13 (-1027) (-10 -8 (-15 * ($ $ $)))))))) -(((*1 *2 *1 *3) (-12 (-4 *1 (-33)) (-5 *3 (-719)) (-5 *2 (-110)))) - ((*1 *2 *3 *3) - (|partial| -12 (-5 *2 (-110)) (-5 *1 (-1136 *3)) (-4 *3 (-1027)))) - ((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-1 (-110) *3 *3)) (-4 *3 (-1027)) (-5 *2 (-110)) - (-5 *1 (-1136 *3))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-815)) (-5 *3 (-597 (-245))) (-5 *1 (-243))))) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) + (-4 *2 (-13 (-411 *3) (-941)))))) +(((*1 *2) (-12 (-5 *2 (-110)) (-5 *1 (-708))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-208)) (-5 *1 (-209)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-159 (-208))) (-5 *1 (-209)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) + (-4 *2 (-411 *3)))) + ((*1 *1 *1 *1) (-4 *1 (-1063)))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) +(((*1 *2 *3 *4 *5 *6) + (-12 (-5 *6 (-862)) (-4 *5 (-289)) (-4 *3 (-1157 *5)) + (-5 *2 (-2 (|:| |plist| (-597 *3)) (|:| |modulo| *5))) + (-5 *1 (-440 *5 *3)) (-5 *4 (-597 *3))))) +(((*1 *2 *3) + (-12 (-4 *4 (-344)) (-4 *4 (-522)) (-4 *5 (-1157 *4)) + (-5 *2 (-2 (|:| -3149 (-578 *4 *5)) (|:| -3138 (-388 *5)))) + (-5 *1 (-578 *4 *5)) (-5 *3 (-388 *5)))) + ((*1 *2 *1) + (-12 (-5 *2 (-597 (-1088 *3 *4))) (-5 *1 (-1088 *3 *4)) + (-14 *3 (-862)) (-4 *4 (-984)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-432)) (-4 *3 (-984)) + (-5 *2 (-2 (|:| |primePart| *1) (|:| |commonPart| *1))) + (-4 *1 (-1157 *3))))) +(((*1 *2 *1) + (-12 (-4 *4 (-1027)) (-5 *2 (-830 *3 *4)) (-5 *1 (-826 *3 *4 *5)) + (-4 *3 (-1027)) (-4 *5 (-617 *4))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-804) (-804))) (-5 *1 (-112)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-804) (-597 (-804)))) (-5 *1 (-112)))) ((*1 *2 *1) @@ -11085,20 +10538,17 @@ (-12 (-5 *2 (-1186)) (-5 *1 (-198 *3)) (-4 *3 (-13 (-795) - (-10 -8 (-15 -1808 ((-1082) $ (-1099))) (-15 -2256 (*2 $)) - (-15 -2510 (*2 $))))))) + (-10 -8 (-15 -1832 ((-1082) $ (-1099))) (-15 -2278 (*2 $)) + (-15 -1671 (*2 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-375)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-530)) (-5 *2 (-1186)) (-5 *1 (-375)))) ((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-480)))) ((*1 *2 *3) (-12 (-5 *3 (-1082)) (-5 *2 (-1186)) (-5 *1 (-659)))) ((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-1116)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-530)) (-5 *2 (-1186)) (-5 *1 (-1116))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-530)) (-4 *1 (-55 *4 *2 *5)) (-4 *4 (-1135)) - (-4 *5 (-354 *4)) (-4 *2 (-354 *4)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-530)) (-4 *1 (-987 *4 *5 *6 *2 *7)) (-4 *6 (-984)) - (-4 *7 (-221 *4 *6)) (-4 *2 (-221 *5 *6))))) +(((*1 *2 *3) + (|partial| -12 (-5 *3 (-637 (-388 (-893 (-530))))) + (-5 *2 (-637 (-297 (-530)))) (-5 *1 (-969))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) (-4 *2 (-13 (-411 *3) (-941))))) @@ -11118,16 +10568,14 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-597 *7)) (-4 *7 (-795)) (-4 *5 (-850)) (-4 *6 (-741)) - (-4 *8 (-890 *5 *6 *7)) (-5 *2 (-399 (-1095 *8))) - (-5 *1 (-847 *5 *6 *7 *8)) (-5 *4 (-1095 *8)))) - ((*1 *2 *3) - (-12 (-4 *4 (-850)) (-4 *5 (-1157 *4)) (-5 *2 (-399 (-1095 *5))) - (-5 *1 (-848 *4 *5)) (-5 *3 (-1095 *5))))) -(((*1 *1 *1 *1 *2) - (-12 (-5 *2 (-719)) (-4 *1 (-307 *3 *4)) (-4 *3 (-984)) - (-4 *4 (-740)) (-4 *3 (-162))))) +(((*1 *2 *3) + (-12 (-14 *4 (-597 (-1099))) (-4 *5 (-432)) + (-5 *2 + (-2 (|:| |glbase| (-597 (-230 *4 *5))) (|:| |glval| (-597 (-530))))) + (-5 *1 (-585 *4 *5)) (-5 *3 (-597 (-230 *4 *5)))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) + (-4 *2 (-13 (-411 *3) (-941)))))) (((*1 *1 *1) (-12 (-4 *1 (-235 *2 *3 *4 *5)) (-4 *2 (-984)) (-4 *3 (-795)) (-4 *4 (-248 *3)) (-4 *5 (-741))))) @@ -11147,24 +10595,27 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1064 *3 *4)) (-4 *3 (-13 (-1027) (-33))) (-4 *4 (-13 (-1027) (-33))) (-5 *1 (-1065 *3 *4))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1 *6 *4)) (-4 *4 (-1027)) (-4 *6 (-1027)) - (-5 *2 (-1 *6 *4 *5)) (-5 *1 (-632 *4 *5 *6)) (-4 *5 (-1027))))) -(((*1 *2 *3) - (-12 (-5 *3 (-530)) (|has| *1 (-6 -4261)) (-4 *1 (-385)) - (-5 *2 (-862))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-399 *3)) (-4 *3 (-522)) (-5 *1 (-400 *3))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-208)) (-5 *1 (-209)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-159 (-208))) (-5 *1 (-209)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) + (-4 *2 (-411 *3)))) + ((*1 *1 *1 *1) (-4 *1 (-1063)))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-597 *5)) (-4 *5 (-1157 *3)) (-4 *3 (-289)) + (-5 *2 (-110)) (-5 *1 (-435 *3 *5))))) (((*1 *1 *2) (-12 (-5 *2 (-597 *3)) (-4 *3 (-1135)) (-4 *1 (-144 *3)))) ((*1 *1 *2) (-12 - (-5 *2 (-597 (-2 (|:| -3731 (-719)) (|:| -3689 *4) (|:| |num| *4)))) + (-5 *2 (-597 (-2 (|:| -3059 (-719)) (|:| -3721 *4) (|:| |num| *4)))) (-4 *4 (-1157 *3)) (-4 *3 (-13 (-344) (-140))) (-5 *1 (-380 *3 *4)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-415)) (|:| -2840 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) (-5 *3 (-597 (-893 (-530)))) (-5 *4 (-110)) (-5 *1 (-418)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-415)) (|:| -2840 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) (-5 *3 (-597 (-1099))) (-5 *4 (-110)) (-5 *1 (-418)))) ((*1 *2 *1) (-12 (-5 *2 (-1080 *3)) (-5 *1 (-560 *3)) (-4 *3 (-1135)))) @@ -11184,23 +10635,23 @@ ((*1 *1 *2 *3) (-12 (-5 *1 (-662 *2 *3 *4)) (-4 *2 (-795)) (-4 *3 (-1027)) (-14 *4 - (-1 (-110) (-2 (|:| -1891 *2) (|:| -3731 *3)) - (-2 (|:| -1891 *2) (|:| -3731 *3)))))) + (-1 (-110) (-2 (|:| -1910 *2) (|:| -3059 *3)) + (-2 (|:| -1910 *2) (|:| -3059 *3)))))) ((*1 *1 *2 *3) (-12 (-5 *1 (-814 *2 *3)) (-4 *2 (-1135)) (-4 *3 (-1135)))) ((*1 *1 *2) - (-12 (-5 *2 (-597 (-2 (|:| -2913 (-1099)) (|:| -1782 *4)))) + (-12 (-5 *2 (-597 (-2 (|:| -2940 (-1099)) (|:| -1806 *4)))) (-4 *4 (-1027)) (-5 *1 (-830 *3 *4)) (-4 *3 (-1027)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-597 *5)) (-4 *5 (-13 (-1027) (-33))) (-5 *2 (-597 (-1064 *3 *5))) (-5 *1 (-1064 *3 *5)) (-4 *3 (-13 (-1027) (-33))))) ((*1 *2 *3) - (-12 (-5 *3 (-597 (-2 (|:| |val| *4) (|:| -2321 *5)))) + (-12 (-5 *3 (-597 (-2 (|:| |val| *4) (|:| -2350 *5)))) (-4 *4 (-13 (-1027) (-33))) (-4 *5 (-13 (-1027) (-33))) (-5 *2 (-597 (-1064 *4 *5))) (-5 *1 (-1064 *4 *5)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -2321 *4))) + (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -2350 *4))) (-4 *3 (-13 (-1027) (-33))) (-4 *4 (-13 (-1027) (-33))) (-5 *1 (-1064 *3 *4)))) ((*1 *1 *2 *3) @@ -11223,24 +10674,21 @@ (-4 *4 (-13 (-1027) (-33))) (-5 *1 (-1065 *3 *4)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-1089 *2 *3)) (-4 *2 (-1027)) (-4 *3 (-1027))))) -(((*1 *2 *1) (-12 (-5 *2 (-772)) (-5 *1 (-773))))) -(((*1 *2 *1) (-12 (-4 *1 (-289)) (-5 *2 (-719))))) -(((*1 *2 *3 *4 *2) - (-12 (-5 *3 (-1 *2 (-719) *2)) (-5 *4 (-719)) (-4 *2 (-1027)) - (-5 *1 (-627 *2)))) - ((*1 *2 *2) - (-12 (-5 *2 (-1 *3 (-719) *3)) (-4 *3 (-1027)) (-5 *1 (-630 *3))))) -(((*1 *2 *3 *4 *5 *6 *7 *6) - (|partial| -12 - (-5 *5 - (-2 (|:| |contp| *3) - (|:| -3494 (-597 (-2 (|:| |irr| *10) (|:| -1429 (-530))))))) - (-5 *6 (-597 *3)) (-5 *7 (-597 *8)) (-4 *8 (-795)) (-4 *3 (-289)) - (-4 *10 (-890 *3 *9 *8)) (-4 *9 (-741)) - (-5 *2 - (-2 (|:| |polfac| (-597 *10)) (|:| |correct| *3) - (|:| |corrfact| (-597 (-1095 *3))))) - (-5 *1 (-580 *8 *9 *3 *10)) (-5 *4 (-597 (-1095 *3)))))) +(((*1 *2 *2 *2 *3 *3) + (-12 (-5 *3 (-719)) (-4 *4 (-984)) (-5 *1 (-1153 *4 *2)) + (-4 *2 (-1157 *4))))) +(((*1 *2 *3) + (-12 (-5 *2 (-1080 (-597 (-530)))) (-5 *1 (-824)) (-5 *3 (-530))))) +(((*1 *2 *3) + (-12 (-5 *3 (-637 (-388 (-893 (-530))))) (-5 *2 (-597 (-297 (-530)))) + (-5 *1 (-969))))) +(((*1 *2 *3) + (-12 (-5 *3 (-597 (-460 *4 *5))) (-14 *4 (-597 (-1099))) + (-4 *5 (-432)) + (-5 *2 + (-2 (|:| |gblist| (-597 (-230 *4 *5))) + (|:| |gvlist| (-597 (-530))))) + (-5 *1 (-585 *4 *5))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) (-4 *2 (-13 (-411 *3) (-941))))) @@ -11260,31 +10708,24 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *2 *1) - (-12 (-4 *3 (-344)) (-4 *4 (-1157 *3)) (-4 *5 (-1157 (-388 *4))) - (-5 *2 (-1181 *6)) (-5 *1 (-317 *3 *4 *5 *6)) - (-4 *6 (-323 *3 *4 *5))))) -(((*1 *2 *1) - (-12 (-4 *4 (-1027)) (-5 *2 (-830 *3 *5)) (-5 *1 (-826 *3 *4 *5)) - (-4 *3 (-1027)) (-4 *5 (-617 *4))))) -(((*1 *2 *1) (-12 (-5 *2 (-110)) (-5 *1 (-415))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |var| (-1099)) (|:| |fn| (-297 (-208))) - (|:| -3723 (-1022 (-788 (-208)))) (|:| |abserr| (-208)) - (|:| |relerr| (-208)))) - (-5 *2 (-360)) (-5 *1 (-176))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) + (-4 *2 (-13 (-411 *3) (-941)))))) +(((*1 *1 *1) (-5 *1 (-208))) + ((*1 *2 *2) (-12 (-5 *2 (-208)) (-5 *1 (-209)))) + ((*1 *2 *2) (-12 (-5 *2 (-159 (-208))) (-5 *1 (-209)))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) + (-4 *2 (-411 *3)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) + (-4 *2 (-411 *3)))) + ((*1 *1 *1) (-4 *1 (-1063))) ((*1 *1 *1 *1) (-4 *1 (-1063)))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) (((*1 *2 *3 *4 *5) - (-12 (-4 *6 (-1157 *9)) (-4 *7 (-741)) (-4 *8 (-795)) (-4 *9 (-289)) - (-4 *10 (-890 *9 *7 *8)) - (-5 *2 - (-2 (|:| |deter| (-597 (-1095 *10))) - (|:| |dterm| - (-597 (-597 (-2 (|:| -2259 (-719)) (|:| |pcoef| *10))))) - (|:| |nfacts| (-597 *6)) (|:| |nlead| (-597 *10)))) - (-5 *1 (-726 *6 *7 *8 *9 *10)) (-5 *3 (-1095 *10)) (-5 *4 (-597 *6)) - (-5 *5 (-597 *10))))) + (|partial| -12 (-5 *5 (-1181 (-597 *3))) (-4 *4 (-289)) + (-5 *2 (-597 *3)) (-5 *1 (-435 *4 *3)) (-4 *3 (-1157 *4))))) (((*1 *1 *2) (-12 (-4 *1 (-37 *2)) (-4 *2 (-162)))) ((*1 *1 *2) (-12 (-5 *2 (-1181 *3)) (-4 *3 (-344)) (-14 *6 (-1181 (-637 *3))) @@ -11292,69 +10733,69 @@ ((*1 *1 *2) (-12 (-5 *2 (-1051 (-530) (-570 (-47)))) (-5 *1 (-47)))) ((*1 *2 *3) (-12 (-5 *2 (-51)) (-5 *1 (-50 *3)) (-4 *3 (-1135)))) ((*1 *1 *2) - (-12 (-5 *2 (-1181 (-320 (-2246 'JINT 'X 'ELAM) (-2246) (-647)))) + (-12 (-5 *2 (-1181 (-320 (-2268 'JINT 'X 'ELAM) (-2268) (-647)))) (-5 *1 (-59 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-1181 (-320 (-2246) (-2246 'XC) (-647)))) + (-12 (-5 *2 (-1181 (-320 (-2268) (-2268 'XC) (-647)))) (-5 *1 (-61 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-320 (-2246 'X) (-2246) (-647))) (-5 *1 (-62 *3)) + (-12 (-5 *2 (-320 (-2268 'X) (-2268) (-647))) (-5 *1 (-62 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-637 (-320 (-2246) (-2246 'X 'HESS) (-647)))) + (-12 (-5 *2 (-637 (-320 (-2268) (-2268 'X 'HESS) (-647)))) (-5 *1 (-63 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-320 (-2246) (-2246 'XC) (-647))) (-5 *1 (-64 *3)) + (-12 (-5 *2 (-320 (-2268) (-2268 'XC) (-647))) (-5 *1 (-64 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-1181 (-320 (-2246 'X) (-2246 '-4125) (-647)))) + (-12 (-5 *2 (-1181 (-320 (-2268 'X) (-2268 '-4114) (-647)))) (-5 *1 (-69 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-1181 (-320 (-2246) (-2246 'X) (-647)))) + (-12 (-5 *2 (-1181 (-320 (-2268) (-2268 'X) (-647)))) (-5 *1 (-72 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-1181 (-320 (-2246 'X 'EPS) (-2246 '-4125) (-647)))) + (-12 (-5 *2 (-1181 (-320 (-2268 'X 'EPS) (-2268 '-4114) (-647)))) (-5 *1 (-73 *3 *4 *5)) (-14 *3 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(-320 (-2268) (-2268 'X) (-647)))) (-5 *1 (-79 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-1181 (-320 (-2246 'X '-4125) (-2246) (-647)))) + (-12 (-5 *2 (-1181 (-320 (-2268 'X '-4114) (-2268) (-647)))) (-5 *1 (-80 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-637 (-320 (-2246 'X '-4125) (-2246) (-647)))) + (-12 (-5 *2 (-637 (-320 (-2268 'X '-4114) (-2268) (-647)))) (-5 *1 (-81 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-637 (-320 (-2246 'X) (-2246) (-647)))) (-5 *1 (-82 *3)) + (-12 (-5 *2 (-637 (-320 (-2268 'X) (-2268) (-647)))) (-5 *1 (-82 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-1181 (-320 (-2246 'X) (-2246) (-647)))) + (-12 (-5 *2 (-1181 (-320 (-2268 'X) (-2268) (-647)))) (-5 *1 (-83 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-1181 (-320 (-2246 'X) (-2246 '-4125) (-647)))) + (-12 (-5 *2 (-1181 (-320 (-2268 'X) (-2268 '-4114) (-647)))) (-5 *1 (-84 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-637 (-320 (-2246 'XL 'XR 'ELAM) (-2246) (-647)))) + (-12 (-5 *2 (-637 (-320 (-2268 'XL 'XR 'ELAM) (-2268) (-647)))) (-5 *1 (-85 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-320 (-2246 'X) (-2246 '-4125) (-647))) (-5 *1 (-87 *3)) + (-12 (-5 *2 (-320 (-2268 'X) (-2268 '-4114) (-647))) (-5 *1 (-87 *3)) (-14 *3 (-1099)))) ((*1 *2 *1) (-12 (-5 *2 (-943 2)) (-5 *1 (-105)))) ((*1 *2 *1) (-12 (-5 *2 (-388 (-530))) (-5 *1 (-105)))) @@ -11378,8 +10819,8 @@ (-12 (-5 *2 (-597 *3)) (-4 *3 (-13 (-795) - (-10 -8 (-15 -1808 ((-1082) $ (-1099))) (-15 -2256 ((-1186) $)) - (-15 -2510 ((-1186) $))))) + (-10 -8 (-15 -1832 ((-1082) $ (-1099))) (-15 -2278 ((-1186) $)) + (-15 -1671 ((-1186) $))))) (-5 *1 (-198 *3)))) ((*1 *2 *1) (-12 (-5 *2 (-943 10)) (-5 *1 (-201)))) ((*1 *2 *1) (-12 (-5 *2 (-388 (-530))) (-5 *1 (-201)))) @@ -11420,14 +10861,14 @@ ((*1 *1 *2) (-12 (-4 *1 (-355 *2 *3)) (-4 *2 (-795)) (-4 *3 (-162)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1803 (-597 (-311))))) + (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1827 (-597 (-311))))) (-4 *1 (-364)))) ((*1 *1 *2) (-12 (-5 *2 (-311)) (-4 *1 (-364)))) ((*1 *1 *2) (-12 (-5 *2 (-597 (-311))) (-4 *1 (-364)))) ((*1 *1 *2) (-12 (-5 *2 (-637 (-647))) (-4 *1 (-364)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1803 (-597 (-311))))) + (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1827 (-597 (-311))))) (-4 *1 (-365)))) ((*1 *1 *2) (-12 (-5 *2 (-311)) (-4 *1 (-365)))) ((*1 *1 *2) (-12 (-5 *2 (-597 (-311))) (-4 *1 (-365)))) @@ -11437,71 +10878,71 @@ ((*1 *1 *2) (-12 (-5 *2 (-804)) (-5 *1 (-375)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1803 (-597 (-311))))) + (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1827 (-597 (-311))))) (-4 *1 (-377)))) ((*1 *1 *2) (-12 (-5 *2 (-311)) (-4 *1 (-377)))) ((*1 *1 *2) (-12 (-5 *2 (-597 (-311))) (-4 *1 (-377)))) ((*1 *1 *2) (-12 (-5 *2 (-276 (-297 (-159 (-360))))) (-5 *1 (-379 *3 *4 *5 *6)) - (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2840 "void"))) + 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(-415)) (|:| -2840 "void"))) + (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) (-14 *5 (-597 (-1099))) (-14 *6 (-1103)))) ((*1 *1 *2) (-12 (-5 *2 (-297 (-530))) (-5 *1 (-379 *3 *4 *5 *6)) - (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2840 "void"))) + (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) (-14 *5 (-597 (-1099))) (-14 *6 (-1103)))) ((*1 *1 *2) (-12 (-5 *2 (-276 (-297 (-642)))) (-5 *1 (-379 *3 *4 *5 *6)) - (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2840 "void"))) + (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) (-14 *5 (-597 (-1099))) (-14 *6 (-1103)))) ((*1 *1 *2) (-12 (-5 *2 (-276 (-297 (-647)))) (-5 *1 (-379 *3 *4 *5 *6)) - (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2840 "void"))) + (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) (-14 *5 (-597 (-1099))) (-14 *6 (-1103)))) ((*1 *1 *2) (-12 (-5 *2 (-276 (-297 (-649)))) (-5 *1 (-379 *3 *4 *5 *6)) - (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2840 "void"))) + (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) (-14 *5 (-597 (-1099))) (-14 *6 (-1103)))) ((*1 *1 *2) (-12 (-5 *2 (-297 (-642))) (-5 *1 (-379 *3 *4 *5 *6)) - (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2840 "void"))) + (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) (-14 *5 (-597 (-1099))) (-14 *6 (-1103)))) ((*1 *1 *2) (-12 (-5 *2 (-297 (-647))) (-5 *1 (-379 *3 *4 *5 *6)) - (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2840 "void"))) + (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) (-14 *5 (-597 (-1099))) (-14 *6 (-1103)))) ((*1 *1 *2) (-12 (-5 *2 (-297 (-649))) (-5 *1 (-379 *3 *4 *5 *6)) - (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2840 "void"))) + (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) (-14 *5 (-597 (-1099))) (-14 *6 (-1103)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1803 (-597 (-311))))) + (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1827 (-597 (-311))))) (-5 *1 (-379 *3 *4 *5 *6)) (-14 *3 (-1099)) - (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2840 "void"))) + (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) (-14 *5 (-597 (-1099))) (-14 *6 (-1103)))) ((*1 *1 *2) (-12 (-5 *2 (-597 (-311))) (-5 *1 (-379 *3 *4 *5 *6)) - (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2840 "void"))) + (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) (-14 *5 (-597 (-1099))) (-14 *6 (-1103)))) ((*1 *1 *2) (-12 (-5 *2 (-311)) (-5 *1 (-379 *3 *4 *5 *6)) (-14 *3 (-1099)) - (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2840 "void"))) + (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) (-14 *5 (-597 (-1099))) (-14 *6 (-1103)))) ((*1 *1 *2) (-12 (-5 *2 (-312 *4)) (-4 *4 (-13 (-795) (-21))) @@ -11529,14 +10970,14 @@ ((*1 *2 *1) (-12 (-5 *2 (-804)) (-5 *1 (-418)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1803 (-597 (-311))))) + (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1827 (-597 (-311))))) (-4 *1 (-420)))) ((*1 *1 *2) (-12 (-5 *2 (-311)) (-4 *1 (-420)))) ((*1 *1 *2) (-12 (-5 *2 (-597 (-311))) (-4 *1 (-420)))) ((*1 *1 *2) (-12 (-5 *2 (-1181 (-647))) (-4 *1 (-420)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1803 (-597 (-311))))) + (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1827 (-597 (-311))))) (-4 *1 (-421)))) ((*1 *1 *2) (-12 (-5 *2 (-311)) (-4 *1 (-421)))) ((*1 *1 *2) (-12 (-5 *2 (-597 (-311))) (-4 *1 (-421)))) @@ -11605,18 +11046,18 @@ ((*1 *1 *2) (-12 (-4 *3 (-984)) (-5 *1 (-661 *3 *2)) (-4 *2 (-1157 *3)))) ((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| -1891 *3) (|:| -3731 *4))) + (-12 (-5 *2 (-2 (|:| -1910 *3) (|:| -3059 *4))) (-5 *1 (-662 *3 *4 *5)) (-4 *3 (-795)) (-4 *4 (-1027)) (-14 *5 (-1 (-110) *2 *2)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| -1891 *3) (|:| -3731 *4))) (-4 *3 (-795)) + (-12 (-5 *2 (-2 (|:| -1910 *3) (|:| -3059 *4))) (-4 *3 (-795)) (-4 *4 (-1027)) (-5 *1 (-662 *3 *4 *5)) (-14 *5 (-1 (-110) *2 *2)))) ((*1 *2 *1) (-12 (-4 *2 (-162)) (-5 *1 (-664 *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 (-597 (-2 (|:| -1963 *3) (|:| -3922 *4)))) (-4 *3 (-984)) + (-12 (-5 *2 (-597 (-2 (|:| -1981 *3) (|:| -3931 *4)))) (-4 *3 (-984)) (-4 *4 (-675)) (-5 *1 (-684 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-530)) (-4 *1 (-712)))) ((*1 *1 *2) @@ -11625,25 +11066,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1099)) (|:| |fn| (-297 (-208))) - (|:| -3723 (-1022 (-788 (-208)))) (|:| |abserr| (-208)) + (|:| -2902 (-1022 (-788 (-208)))) (|:| |abserr| (-208)) (|:| |relerr| (-208)))) (|:| |mdnia| (-2 (|:| |fn| (-297 (-208))) - (|:| -3723 (-597 (-1022 (-788 (-208))))) + (|:| -2902 (-597 (-1022 (-788 (-208))))) (|:| |abserr| (-208)) (|:| |relerr| (-208)))))) (-5 *1 (-717)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-297 (-208))) - (|:| -3723 (-597 (-1022 (-788 (-208))))) (|:| |abserr| (-208)) + (|:| -2902 (-597 (-1022 (-788 (-208))))) (|:| |abserr| (-208)) (|:| |relerr| (-208)))) (-5 *1 (-717)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1099)) (|:| |fn| (-297 (-208))) - (|:| -3723 (-1022 (-788 (-208)))) (|:| |abserr| (-208)) + (|:| -2902 (-1022 (-788 (-208)))) (|:| |abserr| (-208)) (|:| |relerr| (-208)))) (-5 *1 (-717)))) ((*1 *2 *1) (-12 (-5 *2 (-804)) (-5 *1 (-717)))) @@ -11669,23 +11110,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-297 (-208))) (|:| -3638 (-597 (-208))) + (-2 (|:| |fn| (-297 (-208))) (|:| -3677 (-597 (-208))) (|:| |lb| (-597 (-788 (-208)))) (|:| |cf| (-597 (-297 (-208)))) (|:| |ub| (-597 (-788 (-208)))))) (|:| |lsa| (-2 (|:| |lfn| (-597 (-297 (-208)))) - (|:| -3638 (-597 (-208))))))) + (|:| -3677 (-597 (-208))))))) (-5 *1 (-786)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-597 (-297 (-208)))) (|:| -3638 (-597 (-208))))) + (-2 (|:| |lfn| (-597 (-297 (-208)))) (|:| -3677 (-597 (-208))))) (-5 *1 (-786)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-297 (-208))) (|:| -3638 (-597 (-208))) + (-2 (|:| |fn| (-297 (-208))) (|:| -3677 (-597 (-208))) (|:| |lb| (-597 (-788 (-208)))) (|:| |cf| (-597 (-297 (-208)))) (|:| |ub| (-597 (-788 (-208)))))) (-5 *1 (-786)))) @@ -11849,7 +11290,7 @@ (-4 *2 (-344)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-530)) (-5 *1 (-208)))) ((*1 *1 *1 *1) - (-1450 (-12 (-5 *1 (-276 *2)) (-4 *2 (-344)) (-4 *2 (-1135))) + (-1476 (-12 (-5 *1 (-276 *2)) (-4 *2 (-344)) (-4 *2 (-1135))) (-12 (-5 *1 (-276 *2)) (-4 *2 (-453)) (-4 *2 (-1135))))) ((*1 *1 *1 *1) (-4 *1 (-344))) ((*1 *1 *1 *2) (-12 (-5 *2 (-530)) (-5 *1 (-360)))) @@ -11897,6 +11338,8 @@ ((*1 *1 *1 *2) (-12 (-5 *1 (-1202 *2 *3)) (-4 *2 (-344)) (-4 *2 (-984)) (-4 *3 (-791))))) +(((*1 *2 *2 *2) + (-12 (-4 *3 (-984)) (-5 *1 (-1153 *3 *2)) (-4 *2 (-1157 *3))))) (((*1 *2 *3 *2 *3) (-12 (-5 *2 (-418)) (-5 *3 (-1099)) (-5 *1 (-1102)))) ((*1 *2 *3 *2) (-12 (-5 *2 (-418)) (-5 *3 (-1099)) (-5 *1 (-1102)))) @@ -11909,19 +11352,12 @@ (-12 (-5 *2 (-418)) (-5 *3 (-1099)) (-5 *1 (-1103)))) ((*1 *2 *3 *2 *1) (-12 (-5 *2 (-418)) (-5 *3 (-597 (-1099))) (-5 *1 (-1103))))) -(((*1 *2 *2) - (-12 (-4 *3 (-975 (-530))) (-4 *3 (-13 (-795) (-522))) - (-5 *1 (-31 *3 *2)) (-4 *2 (-411 *3)))) - ((*1 *2) - (-12 (-4 *4 (-162)) (-5 *2 (-1095 *4)) (-5 *1 (-155 *3 *4)) - (-4 *3 (-156 *4)))) - ((*1 *1 *1) (-12 (-4 *1 (-984)) (-4 *1 (-284)))) - ((*1 *2) (-12 (-4 *1 (-310 *3)) (-4 *3 (-344)) (-5 *2 (-1095 *3)))) - ((*1 *2) (-12 (-4 *1 (-673 *3 *2)) (-4 *3 (-162)) (-4 *2 (-1157 *3)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1000 *3 *2)) (-4 *3 (-13 (-793) (-344))) - (-4 *2 (-1157 *3))))) -(((*1 *2 *3) (-12 (-5 *3 (-884 *2)) (-5 *1 (-922 *2)) (-4 *2 (-984))))) +(((*1 *2 *3 *3) + (-12 (-5 *2 (-1080 (-597 (-530)))) (-5 *1 (-824)) + (-5 *3 (-597 (-530))))) + ((*1 *2 *3) + (-12 (-5 *2 (-1080 (-597 (-530)))) (-5 *1 (-824)) + (-5 *3 (-597 (-530)))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) (-4 *2 (-13 (-411 *3) (-941))))) @@ -11941,42 +11377,29 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *2 *2) (-12 (-5 *2 (-360)) (-5 *1 (-1183)))) - ((*1 *2) (-12 (-5 *2 (-360)) (-5 *1 (-1183))))) (((*1 *2 *1 *2) (-12 (-5 *2 (-110)) (-5 *1 (-161)))) ((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-1182)))) ((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-1183))))) -(((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-530)) (-4 *1 (-55 *4 *3 *5)) (-4 *4 (-1135)) - (-4 *3 (-354 *4)) (-4 *5 (-354 *4))))) -(((*1 *2 *2 *1) - (-12 (-5 *2 (-1203 *3 *4)) (-4 *1 (-355 *3 *4)) (-4 *3 (-795)) - (-4 *4 (-162)))) - ((*1 *1 *1 *1) (|partial| -12 (-5 *1 (-367 *2)) (-4 *2 (-1027)))) - ((*1 *1 *1 *2) (|partial| -12 (-5 *1 (-767 *2)) (-4 *2 (-795)))) - ((*1 *1 *1 *1) (|partial| -12 (-5 *1 (-767 *2)) (-4 *2 (-795)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-1196 *2 *3)) (-4 *2 (-795)) (-4 *3 (-984)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-767 *3)) (-4 *1 (-1196 *3 *4)) (-4 *3 (-795)) - (-4 *4 (-984)))) - ((*1 *1 *1 *2) - (-12 (-4 *1 (-1196 *2 *3)) (-4 *2 (-795)) (-4 *3 (-984))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-530)) (-4 *1 (-1141 *4)) (-4 *4 (-984)) (-4 *4 (-522)) - (-5 *2 (-388 (-893 *4))))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-530)) (-4 *1 (-1141 *4)) (-4 *4 (-984)) (-4 *4 (-522)) - (-5 *2 (-388 (-893 *4)))))) -(((*1 *2 *1) - (-12 (-4 *1 (-307 *3 *4)) (-4 *3 (-984)) (-4 *4 (-740)) - (-5 *2 (-719)))) - ((*1 *2 *1) - (-12 (-4 *1 (-363 *3 *4)) (-4 *3 (-984)) (-4 *4 (-1027)) - (-5 *2 (-719)))) - ((*1 *2 *1) - (-12 (-5 *2 (-719)) (-5 *1 (-684 *3 *4)) (-4 *3 (-984)) - (-4 *4 (-675))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-637 (-388 (-893 (-530))))) + (-5 *2 (-597 (-637 (-297 (-530))))) (-5 *1 (-969)) + (-5 *3 (-297 (-530)))))) +(((*1 *1 *1) (-4 *1 (-583))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-584 *3 *2)) + (-4 *2 (-13 (-411 *3) (-941) (-1121)))))) +(((*1 *2 *3 *2) (-12 (-5 *2 (-208)) (-5 *3 (-719)) (-5 *1 (-209)))) + ((*1 *2 *3 *2) + (-12 (-5 *2 (-159 (-208))) (-5 *3 (-719)) (-5 *1 (-209)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) + (-4 *2 (-411 *3)))) + ((*1 *1 *1 *1) (-4 *1 (-1063)))) +(((*1 *2 *3 *3 *3 *4) + (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) +(((*1 *2 *3 *4 *5) + (|partial| -12 (-5 *3 (-719)) (-4 *4 (-289)) (-4 *6 (-1157 *4)) + (-5 *2 (-1181 (-597 *6))) (-5 *1 (-435 *4 *6)) (-5 *5 (-597 *6))))) (((*1 *2 *1 *1) (-12 (-4 *1 (-99)) (-5 *2 (-110)))) ((*1 *1 *1 *1) (-5 *1 (-804)))) (((*1 *1 *1 *1) (-4 *1 (-21))) ((*1 *1 *1) (-4 *1 (-21))) @@ -11985,8 +11408,8 @@ (-12 (-5 *1 (-198 *2)) (-4 *2 (-13 (-795) - (-10 -8 (-15 -1808 ((-1082) $ (-1099))) (-15 -2256 ((-1186) $)) - (-15 -2510 ((-1186) $))))))) + (-10 -8 (-15 -1832 ((-1082) $ (-1099))) (-15 -2278 ((-1186) $)) + (-15 -1671 ((-1186) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-276 *2)) (-4 *2 (-21)) (-4 *2 (-1135)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-276 *2)) (-4 *2 (-21)) (-4 *2 (-1135)))) ((*1 *1 *1 *1) @@ -12006,22 +11429,18 @@ ((*1 *2 *2 *2) (-12 (-5 *2 (-884 (-208))) (-5 *1 (-1132)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1179 *2)) (-4 *2 (-1135)) (-4 *2 (-21)))) ((*1 *1 *1) (-12 (-4 *1 (-1179 *2)) (-4 *2 (-1135)) (-4 *2 (-21))))) +(((*1 *2 *2 *2) + (-12 (-4 *3 (-984)) (-5 *1 (-1153 *3 *2)) (-4 *2 (-1157 *3))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-1080 (-597 (-530)))) (-5 *3 (-597 (-530))) + (-5 *1 (-824))))) (((*1 *2 *3) - (-12 (-4 *4 (-13 (-344) (-10 -8 (-15 ** ($ $ (-388 (-530))))))) - (-5 *2 (-597 *4)) (-5 *1 (-1054 *3 *4)) (-4 *3 (-1157 *4)))) - ((*1 *2 *3 *3 *3 *3) - (-12 (-4 *3 (-13 (-344) (-10 -8 (-15 ** ($ $ (-388 (-530))))))) - (-5 *2 (-597 *3)) (-5 *1 (-1054 *4 *3)) (-4 *4 (-1157 *3))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-208)) (-5 *1 (-209)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-159 (-208))) (-5 *1 (-209)))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) - (-4 *2 (-411 *3)))) - ((*1 *1 *1 *1) (-4 *1 (-1063)))) -(((*1 *2 *3 *4 *4 *4 *3 *4 *3) - (-12 (-5 *3 (-530)) (-5 *4 (-637 (-208))) (-5 *2 (-973)) - (-5 *1 (-700))))) -(((*1 *2) (-12 (-5 *2 (-530)) (-5 *1 (-867))))) + (-12 (-5 *3 (-637 (-388 (-893 (-530))))) + (-5 *2 + (-597 + (-2 (|:| |radval| (-297 (-530))) (|:| |radmult| (-530)) + (|:| |radvect| (-597 (-637 (-297 (-530)))))))) + (-5 *1 (-969))))) (((*1 *1 *1) (-4 *1 (-93))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) @@ -12041,25 +11460,29 @@ (((*1 *2 *3 *4) (-12 (-5 *2 (-2 (|:| |part1| *3) (|:| |part2| *4))) (-5 *1 (-654 *3 *4)) (-4 *3 (-1135)) (-4 *4 (-1135))))) -(((*1 *2 *2 *2 *2) - (-12 (-5 *2 (-637 *3)) (-4 *3 (-984)) (-5 *1 (-638 *3))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-637 *4)) (-5 *3 (-862)) (-4 *4 (-984)) - (-5 *1 (-966 *4)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-597 (-637 *4))) (-5 *3 (-862)) (-4 *4 (-984)) - (-5 *1 (-966 *4))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-597 *1)) (|has| *1 (-6 -4271)) (-4 *1 (-949 *3)) - (-4 *3 (-1135))))) -(((*1 *2 *1) (-12 (-5 *2 (-110)) (-5 *1 (-833 *3)) (-4 *3 (-1027))))) +(((*1 *1 *1) (-4 *1 (-583))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-584 *3 *2)) + (-4 *2 (-13 (-411 *3) (-941) (-1121)))))) +(((*1 *1 *2 *1) (-12 (-5 *2 (-1098)) (-5 *1 (-311))))) +(((*1 *2 *2) (-12 (-5 *2 (-208)) (-5 *1 (-209)))) + ((*1 *2 *2) (-12 (-5 *2 (-159 (-208))) (-5 *1 (-209)))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) + (-4 *2 (-411 *3)))) + ((*1 *1 *1) (-4 *1 (-1063)))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-597 *3)) (-4 *3 (-1157 *5)) (-4 *5 (-289)) + (-5 *2 (-719)) (-5 *1 (-435 *5 *3))))) (((*1 *1 *1 *1) (-4 *1 (-25))) ((*1 *1 *1 *1) (-5 *1 (-148))) ((*1 *1 *1 *1) (-12 (-5 *1 (-198 *2)) (-4 *2 (-13 (-795) - (-10 -8 (-15 -1808 ((-1082) $ (-1099))) (-15 -2256 ((-1186) $)) - (-15 -2510 ((-1186) $))))))) + (-10 -8 (-15 -1832 ((-1082) $ (-1099))) (-15 -2278 ((-1186) $)) + (-15 -1671 ((-1186) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-276 *2)) (-4 *2 (-25)) (-4 *2 (-1135)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-276 *2)) (-4 *2 (-25)) (-4 *2 (-1135)))) ((*1 *1 *2 *1) @@ -12082,18 +11505,14 @@ (-12 (-5 *2 (-1080 *3)) (-4 *3 (-984)) (-5 *1 (-1084 *3)))) ((*1 *2 *2 *2) (-12 (-5 *2 (-884 (-208))) (-5 *1 (-1132)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1179 *2)) (-4 *2 (-1135)) (-4 *2 (-25))))) -(((*1 *2 *1 *1) - (-12 (-4 *1 (-221 *3 *2)) (-4 *2 (-1135)) (-4 *2 (-984)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-719)) (-5 *1 (-804)))) - ((*1 *1 *1) (-5 *1 (-804))) - ((*1 *2 *3 *3) - (-12 (-5 *3 (-884 (-208))) (-5 *2 (-208)) (-5 *1 (-1132)))) - ((*1 *2 *1 *1) - (-12 (-4 *1 (-1179 *2)) (-4 *2 (-1135)) (-4 *2 (-984))))) -(((*1 *2) (-12 (-5 *2 (-1186)) (-5 *1 (-1184))))) -(((*1 *2 *3 *3 *3 *4 *4 *3) - (-12 (-5 *3 (-530)) (-5 *4 (-637 (-208))) (-5 *2 (-973)) - (-5 *1 (-704))))) +(((*1 *2 *3 *3) + (|partial| -12 (-4 *4 (-522)) + (-5 *2 (-2 (|:| -3624 *3) (|:| -3088 *3))) (-5 *1 (-1152 *4 *3)) + (-4 *3 (-1157 *4))))) +(((*1 *2 *3 *3) + (-12 (-5 *2 (-1080 (-597 (-530)))) (-5 *1 (-824)) + (-5 *3 (-597 (-530)))))) +(((*1 *1 *2) (-12 (-5 *1 (-964 *2)) (-4 *2 (-1135))))) (((*1 *1 *1) (-4 *1 (-93))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) @@ -12110,41 +11529,62 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-719)) (-5 *5 (-597 *3)) (-4 *3 (-289)) (-4 *6 (-795)) - (-4 *7 (-741)) (-5 *2 (-110)) (-5 *1 (-580 *6 *7 *3 *8)) - (-4 *8 (-890 *3 *7 *6))))) -(((*1 *1 *1 *2 *1) (-12 (-5 *1 (-125 *2)) (-4 *2 (-1027)))) - ((*1 *1 *2) (-12 (-5 *1 (-125 *2)) (-4 *2 (-1027))))) -(((*1 *2 *2) (-12 (-5 *2 (-530)) (-5 *1 (-527))))) -(((*1 *1) (-5 *1 (-134)))) -(((*1 *2 *3) - (-12 (-4 *4 (-850)) (-4 *5 (-741)) (-4 *6 (-795)) - (-4 *7 (-890 *4 *5 *6)) (-5 *2 (-399 (-1095 *7))) - (-5 *1 (-847 *4 *5 *6 *7)) (-5 *3 (-1095 *7)))) - ((*1 *2 *3) - (-12 (-4 *4 (-850)) (-4 *5 (-1157 *4)) (-5 *2 (-399 (-1095 *5))) - (-5 *1 (-848 *4 *5)) (-5 *3 (-1095 *5))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-795) (-432))) (-5 *1 (-1127 *3 *2)) - (-4 *2 (-13 (-411 *3) (-1121)))))) +(((*1 *1 *1) (-4 *1 (-583))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-584 *3 *2)) + (-4 *2 (-13 (-411 *3) (-941) (-1121)))))) +(((*1 *1 *2) (-12 (-5 *2 (-1046)) (-5 *1 (-311))))) +(((*1 *1 *1 *1) (-5 *1 (-208))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-208)) (-5 *1 (-209)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-159 (-208))) (-5 *1 (-209)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) + (-4 *2 (-411 *3)))) + ((*1 *2 *3 *3) + (-12 (-5 *3 (-719)) (-5 *2 (-1 (-360))) (-5 *1 (-977)))) + ((*1 *1 *1 *1) (-4 *1 (-1063)))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) (((*1 *2) (|partial| -12 (-4 *3 (-522)) (-4 *3 (-162)) - (-5 *2 (-2 (|:| |particular| *1) (|:| -3386 (-597 *1)))) + (-5 *2 (-2 (|:| |particular| *1) (|:| -3853 (-597 *1)))) (-4 *1 (-348 *3)))) ((*1 *2) (|partial| -12 (-5 *2 (-2 (|:| |particular| (-433 *3 *4 *5 *6)) - (|:| -3386 (-597 (-433 *3 *4 *5 *6))))) + (|:| -3853 (-597 (-433 *3 *4 *5 *6))))) (-5 *1 (-433 *3 *4 *5 *6)) (-4 *3 (-162)) (-14 *4 (-862)) (-14 *5 (-597 (-1099))) (-14 *6 (-1181 (-637 *3)))))) -(((*1 *2 *1 *2) (-12 (-5 *2 (-597 (-1082))) (-5 *1 (-375)))) - ((*1 *2 *1 *2) (-12 (-5 *2 (-597 (-1082))) (-5 *1 (-1116))))) (((*1 *2 *3) - (-12 (-5 *2 (-110)) (-5 *1 (-118 *3)) (-4 *3 (-1157 (-530))))) - ((*1 *2 *3 *2) - (-12 (-5 *2 (-110)) (-5 *1 (-118 *3)) (-4 *3 (-1157 (-530)))))) + (-12 (-4 *4 (-13 (-522) (-140))) (-5 *2 (-597 *3)) + (-5 *1 (-1151 *4 *3)) (-4 *3 (-1157 *4))))) +(((*1 *2 *2) (-12 (-5 *2 (-1080 (-597 (-530)))) (-5 *1 (-824))))) +(((*1 *2 *1) (-12 (-5 *1 (-964 *2)) (-4 *2 (-1135))))) +(((*1 *2 *2) + (-12 (-5 *2 (-112)) (-4 *3 (-13 (-795) (-522))) (-5 *1 (-31 *3 *4)) + (-4 *4 (-411 *3)))) + ((*1 *1 *2 *3) (-12 (-5 *2 (-1099)) (-5 *3 (-719)) (-5 *1 (-112)))) + ((*1 *1 *2) (-12 (-5 *2 (-1099)) (-5 *1 (-112)))) + ((*1 *2 *2) + (-12 (-5 *2 (-112)) (-4 *3 (-13 (-795) (-522))) (-5 *1 (-149 *3 *4)) + (-4 *4 (-411 *3)))) + ((*1 *2 *3) (-12 (-5 *3 (-1099)) (-5 *2 (-112)) (-5 *1 (-153)))) + ((*1 *2 *2) + (-12 (-5 *2 (-112)) (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *4)) + (-4 *4 (-13 (-411 *3) (-941))))) + ((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-283 *3)) (-4 *3 (-284)))) + ((*1 *2 *2) (-12 (-4 *1 (-284)) (-5 *2 (-112)))) + ((*1 *2 *2) + (-12 (-5 *2 (-112)) (-4 *4 (-795)) (-5 *1 (-410 *3 *4)) + (-4 *3 (-411 *4)))) + ((*1 *2 *2) + (-12 (-5 *2 (-112)) (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *4)) + (-4 *4 (-411 *3)))) + ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-570 *3)) (-4 *3 (-795)))) + ((*1 *2 *2) + (-12 (-5 *2 (-112)) (-4 *3 (-13 (-795) (-522))) (-5 *1 (-584 *3 *4)) + (-4 *4 (-13 (-411 *3) (-941) (-1121)))))) (((*1 *1 *1) (-4 *1 (-93))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) @@ -12161,53 +11601,69 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *1 *1) - (|partial| -12 (-5 *1 (-276 *2)) (-4 *2 (-675)) (-4 *2 (-1135))))) -(((*1 *2 *1 *1 *3 *4) - (-12 (-5 *3 (-1 (-110) *5 *5)) (-5 *4 (-1 (-110) *6 *6)) - (-4 *5 (-13 (-1027) (-33))) (-4 *6 (-13 (-1027) (-33))) - (-5 *2 (-110)) (-5 *1 (-1064 *5 *6))))) -(((*1 *2 *3 *3 *3 *3 *3 *4 *4 *4 *5) - (-12 (-5 *3 (-208)) (-5 *4 (-530)) - (-5 *5 (-3 (|:| |fn| (-369)) (|:| |fp| (-62 G)))) (-5 *2 (-973)) - (-5 *1 (-697))))) -(((*1 *2 *2) - (|partial| -12 (-4 *3 (-1135)) (-5 *1 (-170 *3 *2)) - (-4 *2 (-624 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-110)) (-5 *1 (-1104))))) +(((*1 *1 *2) (-12 (-5 *2 (-297 (-159 (-360)))) (-5 *1 (-311)))) + ((*1 *1 *2) (-12 (-5 *2 (-297 (-530))) (-5 *1 (-311)))) + ((*1 *1 *2) (-12 (-5 *2 (-297 (-360))) (-5 *1 (-311)))) + ((*1 *1 *2) (-12 (-5 *2 (-297 (-642))) (-5 *1 (-311)))) + ((*1 *1 *2) (-12 (-5 *2 (-297 (-649))) (-5 *1 (-311)))) + ((*1 *1 *2) (-12 (-5 *2 (-297 (-647))) (-5 *1 (-311)))) + ((*1 *1) (-5 *1 (-311)))) +(((*1 *1 *1) (-12 (-4 *1 (-156 *2)) (-4 *2 (-162)) (-4 *2 (-993)))) + ((*1 *1 *1) + (-12 (-5 *1 (-320 *2 *3 *4)) (-14 *2 (-597 (-1099))) + (-14 *3 (-597 (-1099))) (-4 *4 (-368)))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) + (-4 *2 (-411 *3)))) + ((*1 *2 *1) (-12 (-4 *1 (-745 *2)) (-4 *2 (-162)) (-4 *2 (-993)))) + ((*1 *1 *1) (-4 *1 (-793))) + ((*1 *2 *1) (-12 (-4 *1 (-936 *2)) (-4 *2 (-162)) (-4 *2 (-993)))) + ((*1 *1 *1) (-4 *1 (-993))) ((*1 *1 *1) (-4 *1 (-1063)))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) +(((*1 *2) + (|partial| -12 (-4 *3 (-522)) (-4 *3 (-162)) + (-5 *2 (-2 (|:| |particular| *1) (|:| -3853 (-597 *1)))) + (-4 *1 (-348 *3)))) + ((*1 *2) + (|partial| -12 + (-5 *2 + (-2 (|:| |particular| (-433 *3 *4 *5 *6)) + (|:| -3853 (-597 (-433 *3 *4 *5 *6))))) + (-5 *1 (-433 *3 *4 *5 *6)) (-4 *3 (-162)) (-14 *4 (-862)) + (-14 *5 (-597 (-1099))) (-14 *6 (-1181 (-637 *3)))))) (((*1 *2 *3) - (-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| (-1080 (-208))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -3723 - (-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 (-973)) (-5 *1 (-287))))) -(((*1 *1 *1 *2) - (|partial| -12 (-5 *2 (-862)) (-5 *1 (-1028 *3 *4)) (-14 *3 *2) - (-14 *4 *2)))) -(((*1 *2 *1) (-12 (-5 *2 (-110)) (-5 *1 (-907 *3)) (-4 *3 (-908))))) -(((*1 *2 *3 *2) - (-12 (-5 *3 (-719)) (-5 *1 (-731 *2)) (-4 *2 (-37 (-388 (-530)))) - (-4 *2 (-162))))) + (|partial| -12 (-4 *4 (-13 (-522) (-140))) + (-5 *2 (-2 (|:| -3648 *3) (|:| -3657 *3))) (-5 *1 (-1151 *4 *3)) + (-4 *3 (-1157 *4))))) +(((*1 *2 *3 *3 *3) + (-12 (-5 *2 (-1080 (-597 (-530)))) (-5 *1 (-824)) (-5 *3 (-530)))) + ((*1 *2 *3) + (-12 (-5 *2 (-1080 (-597 (-530)))) (-5 *1 (-824)) (-5 *3 (-530)))) + ((*1 *2 *3 *3) + (-12 (-5 *2 (-1080 (-597 (-530)))) (-5 *1 (-824)) (-5 *3 (-530))))) +(((*1 *2 *1 *2) (-12 (-5 *1 (-964 *2)) (-4 *2 (-1135))))) +(((*1 *2 *3) + (-12 (-5 *3 (-112)) (-4 *4 (-13 (-795) (-522))) (-5 *2 (-110)) + (-5 *1 (-31 *4 *5)) (-4 *5 (-411 *4)))) + ((*1 *2 *3) + (-12 (-5 *3 (-112)) (-4 *4 (-13 (-795) (-522))) (-5 *2 (-110)) + (-5 *1 (-149 *4 *5)) (-4 *5 (-411 *4)))) + ((*1 *2 *3) + (-12 (-5 *3 (-112)) (-4 *4 (-13 (-795) (-522))) (-5 *2 (-110)) + (-5 *1 (-258 *4 *5)) (-4 *5 (-13 (-411 *4) (-941))))) + ((*1 *2 *3) + (-12 (-5 *3 (-112)) (-5 *2 (-110)) (-5 *1 (-283 *4)) (-4 *4 (-284)))) + ((*1 *2 *3) (-12 (-4 *1 (-284)) (-5 *3 (-112)) (-5 *2 (-110)))) + ((*1 *2 *3) + (-12 (-5 *3 (-112)) (-4 *5 (-795)) (-5 *2 (-110)) + (-5 *1 (-410 *4 *5)) (-4 *4 (-411 *5)))) + ((*1 *2 *3) + (-12 (-5 *3 (-112)) (-4 *4 (-13 (-795) (-522))) (-5 *2 (-110)) + (-5 *1 (-412 *4 *5)) (-4 *5 (-411 *4)))) + ((*1 *2 *3) + (-12 (-5 *3 (-112)) (-4 *4 (-13 (-795) (-522))) (-5 *2 (-110)) + (-5 *1 (-584 *4 *5)) (-4 *5 (-13 (-411 *4) (-941) (-1121)))))) (((*1 *1 *1) (-4 *1 (-93))) ((*1 *1 *1 *1) (-5 *1 (-208))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) @@ -12228,29 +11684,47 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *2 *3 *3 *2) - (-12 (-5 *2 (-1080 *4)) (-5 *3 (-530)) (-4 *4 (-984)) - (-5 *1 (-1084 *4)))) - ((*1 *1 *2 *2 *1) - (-12 (-5 *2 (-530)) (-5 *1 (-1173 *3 *4 *5)) (-4 *3 (-984)) - (-14 *4 (-1099)) (-14 *5 *3)))) -(((*1 *2 *1) - (-12 (-4 *2 (-13 (-793) (-344))) (-5 *1 (-994 *2 *3)) - (-4 *3 (-1157 *2))))) -(((*1 *2 *3 *1) (-12 (-5 *3 (-1099)) (-5 *2 (-418)) (-5 *1 (-1103))))) -(((*1 *2) - (-12 - (-5 *2 (-2 (|:| -4059 (-597 (-1099))) (|:| -1789 (-597 (-1099))))) - (-5 *1 (-1137))))) -(((*1 *2 *3) - (-12 (-4 *4 (-1157 (-388 *2))) (-5 *2 (-530)) (-5 *1 (-854 *4 *3)) - (-4 *3 (-1157 (-388 *4)))))) +(((*1 *1 *2) (-12 (-5 *2 (-597 (-311))) (-5 *1 (-311))))) +(((*1 *2 *3) (-12 (-5 *3 (-804)) (-5 *2 (-1186)) (-5 *1 (-1062)))) + ((*1 *2 *3) + (-12 (-5 *3 (-597 (-804))) (-5 *2 (-1186)) (-5 *1 (-1062))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) +(((*1 *1 *2 *3) + (-12 (-5 *2 (-1181 (-1099))) (-5 *3 (-1181 (-433 *4 *5 *6 *7))) + (-5 *1 (-433 *4 *5 *6 *7)) (-4 *4 (-162)) (-14 *5 (-862)) + (-14 *6 (-597 (-1099))) (-14 *7 (-1181 (-637 *4))))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1099)) (-5 *3 (-1181 (-433 *4 *5 *6 *7))) + (-5 *1 (-433 *4 *5 *6 *7)) (-4 *4 (-162)) (-14 *5 (-862)) + (-14 *6 (-597 *2)) (-14 *7 (-1181 (-637 *4))))) + ((*1 *1 *2) + (-12 (-5 *2 (-1181 (-433 *3 *4 *5 *6))) (-5 *1 (-433 *3 *4 *5 *6)) + (-4 *3 (-162)) (-14 *4 (-862)) (-14 *5 (-597 (-1099))) + (-14 *6 (-1181 (-637 *3))))) + ((*1 *1 *2) + (-12 (-5 *2 (-1181 (-1099))) (-5 *1 (-433 *3 *4 *5 *6)) + (-4 *3 (-162)) (-14 *4 (-862)) (-14 *5 (-597 (-1099))) + (-14 *6 (-1181 (-637 *3))))) + ((*1 *1 *2) + (-12 (-5 *2 (-1099)) (-5 *1 (-433 *3 *4 *5 *6)) (-4 *3 (-162)) + (-14 *4 (-862)) (-14 *5 (-597 *2)) (-14 *6 (-1181 (-637 *3))))) + ((*1 *1) + (-12 (-5 *1 (-433 *2 *3 *4 *5)) (-4 *2 (-162)) (-14 *3 (-862)) + (-14 *4 (-597 (-1099))) (-14 *5 (-1181 (-637 *2)))))) +(((*1 *2 *2 *2) + (|partial| -12 (-4 *3 (-13 (-522) (-140))) (-5 *1 (-1151 *3 *2)) + (-4 *2 (-1157 *3))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-719)) (-5 *1 (-818 *2)) (-4 *2 (-1135)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-719)) (-5 *1 (-820 *2)) (-4 *2 (-1135)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-719)) (-5 *1 (-823 *2)) (-4 *2 (-1135))))) (((*1 *2 *1 *1) (-12 (-4 *1 (-795)) (-5 *2 (-110)))) ((*1 *1 *1 *1) (-5 *1 (-804)))) -(((*1 *2 *1) - (-12 (-4 *3 (-344)) (-4 *4 (-1157 *3)) (-4 *5 (-1157 (-388 *4))) - (-5 *2 (-1181 *6)) (-5 *1 (-317 *3 *4 *5 *6)) - (-4 *6 (-323 *3 *4 *5))))) +(((*1 *2 *2 *3) + (-12 (-4 *3 (-344)) (-5 *1 (-963 *3 *2)) (-4 *2 (-607 *3)))) + ((*1 *2 *3 *4) + (-12 (-4 *5 (-344)) (-5 *2 (-2 (|:| -2623 *3) (|:| -4135 (-597 *5)))) + (-5 *1 (-963 *5 *3)) (-5 *4 (-597 *5)) (-4 *3 (-607 *5))))) (((*1 *1 *1) (-4 *1 (-93))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) @@ -12270,79 +11744,38 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-597 (-276 *4))) (-5 *1 (-581 *3 *4 *5)) (-4 *3 (-795)) - (-4 *4 (-13 (-162) (-666 (-388 (-530))))) (-14 *5 (-862))))) -(((*1 *2 *3 *4 *5 *5 *6) - (-12 (-5 *4 (-1099)) (-5 *6 (-110)) - (-4 *7 (-13 (-289) (-795) (-140) (-975 (-530)) (-593 (-530)))) - (-4 *3 (-13 (-1121) (-900) (-29 *7))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-597 (-728 *5 (-806 *6)))) (-5 *4 (-110)) (-4 *5 (-432)) + (-14 *6 (-597 (-1099))) (-5 *2 - (-3 (|:| |f1| (-788 *3)) (|:| |f2| (-597 (-788 *3))) - (|:| |fail| "failed") (|:| |pole| "potentialPole"))) - (-5 *1 (-202 *7 *3)) (-5 *5 (-788 *3))))) -(((*1 *2 *1) - (-12 (-5 *2 (-719)) (-5 *1 (-132 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(-724 *5 *6 *7 *3 *4)) (-4 *4 (-1003 *5 *6 *7 *3))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-795) (-432))) (-5 *1 (-1127 *3 *2)) - (-4 *2 (-13 (-411 *3) (-1121)))))) -(((*1 *1 *2) - (-12 (-5 *2 (-597 (-846 *3))) (-4 *3 (-1027)) (-5 *1 (-845 *3))))) + (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) +(((*1 *2) + (-12 (-4 *4 (-162)) (-5 *2 (-1095 (-893 *4))) (-5 *1 (-397 *3 *4)) + (-4 *3 (-398 *4)))) + ((*1 *2) + (-12 (-4 *1 (-398 *3)) (-4 *3 (-162)) (-4 *3 (-344)) + (-5 *2 (-1095 (-893 *3))))) + ((*1 *2) + (-12 (-5 *2 (-1095 (-388 (-893 *3)))) (-5 *1 (-433 *3 *4 *5 *6)) + (-4 *3 (-522)) (-4 *3 (-162)) (-14 *4 (-862)) + (-14 *5 (-597 (-1099))) (-14 *6 (-1181 (-637 *3)))))) +(((*1 *2 *2 *3 *4) + (|partial| -12 (-5 *3 (-719)) (-4 *4 (-13 (-522) (-140))) + (-5 *1 (-1151 *4 *2)) (-4 *2 (-1157 *4))))) (((*1 *2 *1 *1) (-12 (-4 *1 (-795)) (-5 *2 (-110)))) ((*1 *1 *1 *1) (-5 *1 (-804))) ((*1 *2 *1 *1) (-12 (-5 *2 (-110)) (-5 *1 (-845 *3)) (-4 *3 (-1027))))) -(((*1 *2 *3) - (-12 (-5 *3 (-208)) (-5 *2 (-110)) (-5 *1 (-281 *4 *5)) (-14 *4 *3) - (-14 *5 *3))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-1022 (-788 (-208)))) (-5 *3 (-208)) (-5 *2 (-110)) - (-5 *1 (-287)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-344)) (-4 *4 (-741)) (-4 *5 (-795)) (-5 *2 (-110)) - (-5 *1 (-482 *3 *4 *5 *6)) (-4 *6 (-890 *3 *4 *5))))) +(((*1 *1 *2 *2 *2) (-12 (-5 *1 (-823 *2)) (-4 *2 (-1135))))) +(((*1 *1 *2 *3) + (-12 (-5 *2 (-994 (-962 *4) (-1095 (-962 *4)))) (-5 *3 (-804)) + (-5 *1 (-962 *4)) (-4 *4 (-13 (-793) (-344) (-960)))))) (((*1 *1 *1) (-4 *1 (-93))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) @@ -12362,46 +11795,39 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) - (-4 *2 (-411 *3))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-597 *3)) (-4 *3 (-289)) (-5 *1 (-168 *3))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-637 *4)) (-5 *3 (-862)) (|has| *4 (-6 (-4272 "*"))) - (-4 *4 (-984)) (-5 *1 (-966 *4)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-597 (-637 *4))) (-5 *3 (-862)) - (|has| *4 (-6 (-4272 "*"))) (-4 *4 (-984)) (-5 *1 (-966 *4))))) -(((*1 *2 *1) (-12 (-5 *2 (-110)) (-5 *1 (-833 *3)) (-4 *3 (-1027))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-597 (-728 *5 (-806 *6)))) (-5 *4 (-110)) (-4 *5 (-432)) + (-14 *6 (-597 (-1099))) (-5 *2 (-597 (-981 *5 *6))) + (-5 *1 (-582 *5 *6))))) +(((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-311))))) (((*1 *1 *2) - (-12 (-5 *2 (-1 *3 *3 (-530))) (-4 *3 (-984)) (-5 *1 (-96 *3)))) - ((*1 *1 *2 *2) - (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-984)) (-5 *1 (-96 *3)))) - ((*1 *1 *2) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-984)) (-5 *1 (-96 *3))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-597 *1)) (-5 *3 (-597 *7)) (-4 *1 (-1003 *4 *5 *6 *7)) - (-4 *4 (-432)) (-4 *5 (-741)) (-4 *6 (-795)) - (-4 *7 (-998 *4 *5 *6)))) - ((*1 *2 *3 *1) - (-12 (-5 *3 (-597 *7)) (-4 *7 (-998 *4 *5 *6)) (-4 *4 (-432)) - (-4 *5 (-741)) (-4 *6 (-795)) (-5 *2 (-597 *1)) - (-4 *1 (-1003 *4 *5 *6 *7)))) - ((*1 *2 *3 *2) - (-12 (-5 *2 (-597 *1)) (-4 *1 (-1003 *4 *5 *6 *3)) (-4 *4 (-432)) - (-4 *5 (-741)) (-4 *6 (-795)) (-4 *3 (-998 *4 *5 *6)))) - ((*1 *2 *3 *1) - (-12 (-4 *4 (-432)) (-4 *5 (-741)) (-4 *6 (-795)) - (-4 *3 (-998 *4 *5 *6)) (-5 *2 (-597 *1)) - (-4 *1 (-1003 *4 *5 *6 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 |RationalNumber|) (-5 *2 (-1 (-530))) (-5 *1 (-982))))) + (-12 (-5 *2 (-1088 3 *3)) (-4 *3 (-984)) (-4 *1 (-1060 *3)))) + ((*1 *1) (-12 (-4 *1 (-1060 *2)) (-4 *2 (-984))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-159 (-208))) (-5 *4 (-530)) (-5 *2 (-973)) + (-5 *1 (-707))))) +(((*1 *2 *1) + (-12 (-5 *2 (-1095 (-388 (-893 *3)))) (-5 *1 (-433 *3 *4 *5 *6)) + (-4 *3 (-522)) (-4 *3 (-162)) (-14 *4 (-862)) + (-14 *5 (-597 (-1099))) (-14 *6 (-1181 (-637 *3)))))) +(((*1 *2 *2 *3) + (|partial| -12 (-5 *3 (-719)) (-4 *4 (-13 (-522) (-140))) + (-5 *1 (-1151 *4 *2)) (-4 *2 (-1157 *4))))) (((*1 *2 *3 *2) (-12 (-5 *3 (-862)) (-5 *1 (-968 *2)) - (-4 *2 (-13 (-1027) (-10 -8 (-15 -2211 ($ $ $)))))))) + (-4 *2 (-13 (-1027) (-10 -8 (-15 -2234 ($ $ $)))))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-597 (-804))) (-5 *1 (-804)))) + ((*1 *2 *1) + (-12 + (-5 *2 + (-2 (|:| -1908 (-597 (-804))) (|:| -3821 (-597 (-804))) + (|:| |presup| (-597 (-804))) (|:| -1891 (-597 (-804))) + (|:| |args| (-597 (-804))))) + (-5 *1 (-1099))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1082)) (-5 *2 (-597 (-1104))) (-5 *1 (-821))))) (((*1 *2 *1 *1) (-12 (-4 *1 (-795)) (-5 *2 (-110)))) ((*1 *1 *1 *1) (-5 *1 (-804)))) -(((*1 *2 *2) (-12 (-5 *1 (-902 *2)) (-4 *2 (-515))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) (-4 *2 (-13 (-411 *3) (-941))))) @@ -12430,93 +11856,85 @@ (-4 *5 (-741)) (-4 *3 (-795)) (-4 *2 (-998 *4 *5 *3)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-719)) (-5 *1 (-1133 *2)) (-4 *2 (-1135))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-637 (-159 (-388 (-530))))) (-5 *2 (-597 (-159 *4))) - (-5 *1 (-713 *4)) (-4 *4 (-13 (-344) (-793)))))) -(((*1 *1 *2) (-12 (-5 *2 (-719)) (-5 *1 (-130))))) -(((*1 *2 *3) - (-12 (-4 *2 (-1157 *4)) (-5 *1 (-757 *4 *2 *3 *5)) - (-4 *4 (-13 (-344) (-140) (-975 (-388 (-530))))) (-4 *3 (-607 *2)) - (-4 *5 (-607 (-388 *2)))))) -(((*1 *2 *3) - (-12 (-14 *4 (-597 (-1099))) (-14 *5 (-719)) - (-5 *2 - (-597 - (-482 (-388 (-530)) (-223 *5 (-719)) (-806 *4) - (-230 *4 (-388 (-530)))))) - (-5 *1 (-483 *4 *5)) - (-5 *3 - (-482 (-388 (-530)) (-223 *5 (-719)) (-806 *4) - (-230 *4 (-388 (-530)))))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-597 (-570 (-47)))) (-5 *1 (-47)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-570 (-47))) (-5 *1 (-47)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-1095 (-47))) (-5 *3 (-597 (-570 (-47)))) (-5 *1 (-47)))) +(((*1 *2 *1) + (|partial| -12 (-5 *2 (-994 (-962 *3) (-1095 (-962 *3)))) + (-5 *1 (-962 *3)) (-4 *3 (-13 (-793) (-344) (-960)))))) +(((*1 *2 *2) + (-12 (-5 *2 (-597 (-893 *3))) (-4 *3 (-432)) (-5 *1 (-341 *3 *4)) + (-14 *4 (-597 (-1099))))) + ((*1 *2 *2) + (-12 (-5 *2 (-597 *6)) (-4 *6 (-890 *3 *4 *5)) (-4 *3 (-432)) + (-4 *4 (-741)) (-4 *5 (-795)) (-5 *1 (-430 *3 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((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-110) *3)) (-4 *3 (-1135)) (-5 *1 (-1080 *3))))) -(((*1 *2 *3 *4 *5 *4) - (-12 (-5 *3 (-637 (-208))) (-5 *4 (-530)) (-5 *5 (-110)) - (-5 *2 (-973)) (-5 *1 (-694))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-597 (-2 (|:| -2436 (-1095 *6)) (|:| -3731 (-530))))) - (-4 *6 (-289)) (-4 *4 (-741)) (-4 *5 (-795)) (-5 *2 (-110)) - (-5 *1 (-691 *4 *5 *6 *7)) (-4 *7 (-890 *6 *4 *5)))) - ((*1 *1 *1) (-12 (-4 *1 (-1060 *2)) (-4 *2 (-984))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-597 (-2 (|:| -3648 (-388 (-530))) (|:| -3657 (-388 (-530)))))) + (-5 *2 (-597 (-388 (-530)))) (-5 *1 (-958 *4)) + (-4 *4 (-1157 (-530)))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) (-4 *2 (-13 (-411 *3) (-941))))) @@ -12596,27 +12066,44 @@ (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3)))) ((*1 *1 *1) (-4 *1 (-1124)))) -(((*1 *1 *1) (-4 *1 (-583))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-584 *3 *2)) - (-4 *2 (-13 (-411 *3) (-941) (-1121)))))) -(((*1 *1 *1) - (-12 (-4 *1 (-998 *2 *3 *4)) (-4 *2 (-984)) (-4 *3 (-741)) - (-4 *4 (-795))))) (((*1 *2 *3) - (|partial| -12 - (-5 *3 - (-2 (|:| |var| (-1099)) (|:| |fn| (-297 (-208))) - (|:| -3723 (-1022 (-788 (-208)))) (|:| |abserr| (-208)) - (|:| |relerr| (-208)))) - (-5 *2 (-2 (|:| -4144 (-112)) (|:| |w| (-208)))) (-5 *1 (-188))))) -(((*1 *2 *2) (-12 (-5 *2 (-110)) (-5 *1 (-868))))) + (-12 (-5 *3 (-597 (-893 *4))) (-4 *4 (-432)) (-5 *2 (-110)) + (-5 *1 (-341 *4 *5)) (-14 *5 (-597 (-1099))))) + ((*1 *2 *3) + (-12 (-5 *3 (-597 (-728 *4 (-806 *5)))) (-4 *4 (-432)) + (-14 *5 (-597 (-1099))) (-5 *2 (-110)) (-5 *1 (-582 *4 *5))))) +(((*1 *1) (-12 (-4 *1 (-310 *2)) (-4 *2 (-349)) (-4 *2 (-344))))) +(((*1 *2 *1) (-12 (-4 *3 (-984)) (-5 *2 (-597 *1)) (-4 *1 (-1060 *3))))) +(((*1 *2 *3 *4 *4 *5 *4 *6 *4 *5) + (-12 (-5 *3 (-1082)) (-5 *5 (-637 (-208))) (-5 *6 (-637 (-530))) + (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-706))))) +(((*1 *2) + (-12 (-4 *4 (-162)) (-5 *2 (-1095 (-893 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(-1135))))) -(((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-770))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-862)) (-4 *6 (-13 (-522) (-795))) (-5 *2 (-597 (-297 *6))) (-5 *1 (-204 *5 *6)) (-5 *3 (-297 *6)) @@ -12643,9 +12130,10 @@ ((*1 *2 *1) (-12 (-5 *2 (-1194 *3 *4)) (-5 *1 (-1203 *3 *4)) (-4 *3 (-795)) (-4 *4 (-984))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-637 (-388 (-530)))) (-5 *2 (-597 *4)) (-5 *1 (-727 *4)) - (-4 *4 (-13 (-344) (-793)))))) +(((*1 *2 *3) + (-12 (-5 *3 (-2 (|:| -3648 (-388 (-530))) (|:| -3657 (-388 (-530))))) + (-5 *2 (-388 (-530))) (-5 *1 (-958 *4)) (-4 *4 (-1157 (-530)))))) +(((*1 *1 *2) (-12 (-5 *2 (-148)) (-5 *1 (-815))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) (-4 *2 (-13 (-411 *3) (-941))))) @@ -12665,66 +12153,54 @@ (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3)))) ((*1 *1 *1) (-4 *1 (-1124)))) -(((*1 *2 *3 *4 *5 *6 *5) - (-12 (-5 *4 (-159 (-208))) (-5 *5 (-530)) (-5 *6 (-1082)) - (-5 *3 (-208)) (-5 *2 (-973)) (-5 *1 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(|:| |todo| (-597 (-2 (|:| |val| *3) (|:| -2321 *11)))))) - (-5 *6 (-719)) - (-5 *2 (-597 (-2 (|:| |val| (-597 *10)) (|:| -2321 *11)))) - (-5 *3 (-597 *10)) (-5 *4 (-597 *11)) (-4 *10 (-998 *7 *8 *9)) - (-4 *11 (-1036 *7 *8 *9 *10)) (-4 *7 (-432)) (-4 *8 (-741)) - (-4 *9 (-795)) (-5 *1 (-1069 *7 *8 *9 *10 *11))))) -(((*1 *2 *1) (-12 (-5 *2 (-1080 *3)) (-5 *1 (-163 *3)) (-4 *3 (-289))))) -(((*1 *2) - (-12 (-5 *2 (-110)) (-5 *1 (-1113 *3 *4)) (-4 *3 (-1027)) - (-4 *4 (-1027))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-597 *2)) (-4 *2 (-890 *4 *5 *6)) (-4 *4 (-289)) - (-4 *5 (-741)) (-4 *6 (-795)) (-5 *1 (-427 *4 *5 *6 *2))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1082)) (-5 *2 (-1186)) (-5 *1 (-1183))))) -(((*1 *2 *3 *3 *3 *4 *5 *6) - (-12 (-5 *3 (-297 (-530))) (-5 *4 (-1 (-208) (-208))) - (-5 *5 (-1022 (-208))) (-5 *6 (-597 (-245))) (-5 *2 (-1059 (-208))) - (-5 *1 (-645))))) + (-12 (-5 *2 (-163 (-388 (-530)))) (-5 *1 (-812 *3)) (-14 *3 (-530)))) + ((*1 *2 *1) + (-12 (-14 *3 (-530)) (-5 *2 (-163 (-388 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*2))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-597 (-804))) (-5 *1 (-1099))))) + (-12 (-4 *2 (-23)) (-5 *1 (-664 *3 *2 *4 *5 *6)) (-4 *3 (-162)) + (-14 *4 (-1 *3 *3 *2)) (-14 *5 (-1 (-3 *2 "failed") *2 *2)) + (-14 *6 (-1 (-3 *3 "failed") *3 *3 *2)))) + ((*1 *2) (-12 (-4 *1 (-810 *3)) (-5 *2 (-530))))) (((*1 *2 *3 *3) (-12 (-5 *3 (-719)) (-5 *2 (-1181 (-597 (-530)))) (-5 *1 (-459)))) ((*1 *1 *2 *3) @@ -12838,11 +12328,25 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1135)) (-5 *1 (-1080 *3)))) ((*1 *1 *2) (-12 (-5 *2 (-1 *3)) (-4 *3 (-1135)) (-5 *1 (-1080 *3))))) -(((*1 *2 *3) (-12 (-5 *3 (-530)) (-5 *2 (-1186)) (-5 *1 (-945))))) +(((*1 *2 *3 *3 *3) + (|partial| -12 (-4 *4 (-13 (-344) (-140) (-975 (-530)))) + (-4 *5 (-1157 *4)) (-5 *2 (-597 (-388 *5))) (-5 *1 (-955 *4 *5)) + (-5 *3 (-388 *5))))) (((*1 *1 *1) (-4 *1 (-583))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-584 *3 *2)) (-4 *2 (-13 (-411 *3) (-941) (-1121)))))) +(((*1 *2 *3 *4 *5 *6 *7 *6) + (|partial| -12 + (-5 *5 + (-2 (|:| |contp| *3) + (|:| -4162 (-597 (-2 (|:| |irr| *10) (|:| -3001 (-530))))))) + (-5 *6 (-597 *3)) (-5 *7 (-597 *8)) (-4 *8 (-795)) (-4 *3 (-289)) + (-4 *10 (-890 *3 *9 *8)) (-4 *9 (-741)) + (-5 *2 + (-2 (|:| |polfac| (-597 *10)) (|:| |correct| *3) + (|:| |corrfact| (-597 (-1095 *3))))) + (-5 *1 (-580 *8 *9 *3 *10)) (-5 *4 (-597 (-1095 *3)))))) (((*1 *1 *2) (-12 (-5 *2 (-597 *1)) (-4 *1 (-432)))) ((*1 *1 *1 *1) (-4 *1 (-432))) ((*1 *2 *3) @@ -12871,24 +12375,24 @@ ((*1 *2 *2 *1) (-12 (-4 *1 (-998 *2 *3 *4)) (-4 *2 (-984)) (-4 *3 (-741)) (-4 *4 (-795)) (-4 *2 (-432))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-795) (-522))) (-5 *2 (-110)) (-5 *1 (-258 *4 *3)) - (-4 *3 (-13 (-411 *4) (-941)))))) -(((*1 *1 *2) - (-12 (-5 *2 (-862)) (-4 *1 (-221 *3 *4)) (-4 *4 (-984)) - (-4 *4 (-1135)))) +(((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *4 *4)) (-4 *1 (-307 *3 *4)) (-4 *3 (-984)) + (-4 *4 (-740))))) +(((*1 *1 *2 *2) (-12 (-5 *1 (-818 *2)) (-4 *2 (-1135)))) + ((*1 *1 *2 *2 *2) (-12 (-5 *1 (-820 *2)) (-4 *2 (-1135)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1060 *3)) (-4 *3 (-984)) (-5 *2 (-597 (-884 *3))))) ((*1 *1 *2) - (-12 (-14 *3 (-597 (-1099))) (-4 *4 (-162)) - (-4 *5 (-221 (-2144 *3) (-719))) - (-14 *6 - (-1 (-110) (-2 (|:| -1891 *2) (|:| -3731 *5)) - (-2 (|:| -1891 *2) (|:| -3731 *5)))) - (-5 *1 (-441 *3 *4 *2 *5 *6 *7)) (-4 *2 (-795)) - (-4 *7 (-890 *4 *5 (-806 *3))))) - ((*1 *2 *2) (-12 (-5 *2 (-884 (-208))) (-5 *1 (-1132))))) -(((*1 *2 *3 *3 *3 *4 *4 *4 *4 *5 *6 *5 *4 *7 *3) - (-12 (-5 *4 (-637 (-530))) (-5 *5 (-110)) (-5 *7 (-637 (-208))) - (-5 *3 (-530)) (-5 *6 (-208)) (-5 *2 (-973)) (-5 *1 (-703))))) + (-12 (-5 *2 (-597 (-884 *3))) (-4 *3 (-984)) (-4 *1 (-1060 *3)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-597 (-597 *3))) (-4 *1 (-1060 *3)) (-4 *3 (-984)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-597 (-884 *3))) (-4 *1 (-1060 *3)) (-4 *3 (-984))))) +(((*1 *2 *3 *4 *5 *6 *3 *3 *3 *3 *6 *3 *7 *8) + (-12 (-5 *3 (-530)) (-5 *4 (-637 (-208))) (-5 *5 (-110)) + (-5 *6 (-208)) (-5 *7 (-3 (|:| |fn| (-369)) (|:| |fp| (-66 APROD)))) + (-5 *8 (-3 (|:| |fn| (-369)) (|:| |fp| (-71 MSOLVE)))) + (-5 *2 (-973)) (-5 *1 (-705))))) (((*1 *2 *1) (|partial| -12 (-4 *3 (-432)) (-4 *4 (-795)) (-4 *5 (-741)) (-5 *2 (-110)) (-5 *1 (-927 *3 *4 *5 *6)) @@ -12896,28 +12400,54 @@ ((*1 *2 *1) (-12 (-5 *2 (-110)) (-5 *1 (-1064 *3 *4)) (-4 *3 (-13 (-1027) (-33))) (-4 *4 (-13 (-1027) (-33)))))) -(((*1 *2 *3 *3 *4 *4 *4 *4 *3 *3 *3 *3 *5 *3 *6) - (-12 (-5 *3 (-530)) (-5 *5 (-637 (-208))) - (-5 *6 (-3 (|:| |fn| (-369)) (|:| |fp| (-68 APROD)))) (-5 *4 (-208)) - (-5 *2 (-973)) (-5 *1 (-705))))) +(((*1 *2 *1 *1) + (-12 (-5 *2 (-388 (-893 *3))) (-5 *1 (-433 *3 *4 *5 *6)) + (-4 *3 (-522)) (-4 *3 (-162)) (-14 *4 (-862)) + (-14 *5 (-597 (-1099))) (-14 *6 (-1181 (-637 *3)))))) (((*1 *2 *3) (-12 (-5 *3 (-597 (-51))) (-5 *2 (-1186)) (-5 *1 (-805))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-597 (-1099))) (-5 *1 (-506))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-1080 *3)) (-4 *3 (-344)) (-4 *3 (-984)) - (-5 *1 (-1084 *3))))) -(((*1 *1 *2) - 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top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))) + (-5 *2 (-973)) (-5 *1 (-287))))) +(((*1 *2 *3 *2) + (|partial| -12 (-5 *2 (-1181 *4)) (-5 *3 (-637 *4)) (-4 *4 (-344)) + (-5 *1 (-618 *4)))) + ((*1 *2 *3 *2) + (|partial| -12 (-4 *4 (-344)) + (-4 *5 (-13 (-354 *4) (-10 -7 (-6 -4271)))) + (-4 *2 (-13 (-354 *4) (-10 -7 (-6 -4271)))) + (-5 *1 (-619 *4 *5 *2 *3)) (-4 *3 (-635 *4 *5 *2)))) + ((*1 *2 *3 *2 *4 *5) + (|partial| -12 (-5 *4 (-597 *2)) (-5 *5 (-1 *2 *2)) (-4 *2 (-344)) + (-5 *1 (-762 *2 *3)) (-4 *3 (-607 *2)))) + ((*1 *2 *3) + (-12 (-4 *2 (-13 (-344) (-10 -8 (-15 ** ($ $ (-388 (-530))))))) + (-5 *1 (-1054 *3 *2)) (-4 *3 (-1157 *2))))) +(((*1 *2 *3 *3 *4 *4 *5 *4 *5 *4 *4 *5 *4) + (-12 (-5 *3 (-1082)) (-5 *4 (-530)) (-5 *5 (-637 (-208))) + (-5 *2 (-973)) (-5 *1 (-703))))) (((*1 *2 *2 *3) - (-12 (-4 *3 (-289)) (-5 *1 (-435 *3 *2)) (-4 *2 (-1157 *3)))) - ((*1 *2 *2 *3) - (-12 (-4 *3 (-289)) (-5 *1 (-440 *3 *2)) (-4 *2 (-1157 *3)))) - ((*1 *2 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*2)) (-4 *2 (-984))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| -1523 (-360)) (|:| -3901 (-1082)) + (|:| |explanations| (-597 (-1082))))) + (-5 *2 (-973)) (-5 *1 (-287)))) + ((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| -1523 (-360)) (|:| -3901 (-1082)) + (|:| |explanations| (-597 (-1082))) (|:| |extra| (-973)))) + (-5 *2 (-973)) (-5 *1 (-287))))) (((*1 *2 *1 *3 *3 *2) (-12 (-5 *3 (-530)) (-4 *1 (-55 *2 *4 *5)) (-4 *2 (-1135)) (-4 *4 (-354 *2)) (-4 *5 (-354 *2)))) @@ -14240,14 +13934,14 @@ (-12 (-5 *3 (-1099)) (-5 *2 (-228 (-1082))) (-5 *1 (-198 *4)) (-4 *4 (-13 (-795) - (-10 -8 (-15 -1808 ((-1082) $ *3)) (-15 -2256 ((-1186) $)) - (-15 -2510 ((-1186) $))))))) + (-10 -8 (-15 -1832 ((-1082) $ *3)) (-15 -2278 ((-1186) $)) + (-15 -1671 ((-1186) $))))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-929)) (-5 *1 (-198 *3)) (-4 *3 (-13 (-795) - (-10 -8 (-15 -1808 ((-1082) $ (-1099))) (-15 -2256 ((-1186) $)) - (-15 -2510 ((-1186) $))))))) + (-10 -8 (-15 -1832 ((-1082) $ (-1099))) (-15 -2278 ((-1186) $)) + (-15 -1671 ((-1186) $))))))) ((*1 *2 *1 *3) (-12 (-5 *3 "count") (-5 *2 (-719)) (-5 *1 (-228 *4)) (-4 *4 (-795)))) ((*1 *1 *1 *2) (-12 (-5 *2 "sort") (-5 *1 (-228 *3)) (-4 *3 (-795)))) @@ -14333,11 +14027,29 @@ (-12 (-5 *2 "rest") (-4 *1 (-1169 *3)) (-4 *3 (-1135)))) ((*1 *2 *1 *3) (-12 (-5 *3 "first") (-4 *1 (-1169 *2)) (-4 *2 (-1135))))) -(((*1 *2 *2) (-12 (-5 *2 (-530)) (-5 *1 (-527))))) -(((*1 *2 *1) - (-12 (-4 *1 (-998 *3 *4 *5)) (-4 *3 (-984)) (-4 *4 (-741)) - (-4 *5 (-795)) (-5 *2 (-110))))) -(((*1 *2 *2) (-12 (-5 *2 (-530)) (-5 *1 (-239))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-597 *6)) (-5 *4 (-597 (-1080 *7))) (-4 *6 (-795)) + (-4 *7 (-890 *5 (-502 *6) *6)) (-4 *5 (-984)) + (-5 *2 (-1 (-1080 *7) *7)) (-5 *1 (-1052 *5 *6 *7))))) +(((*1 *2 *3 *3 *3 *4 *3) + (-12 (-5 *3 (-530)) (-5 *4 (-637 (-208))) (-5 *2 (-973)) + (-5 *1 (-703))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-13 (-289) (-140))) (-4 *5 (-741)) (-4 *6 (-795)) + (-4 *7 (-890 *4 *5 *6)) (-5 *2 (-597 (-597 *7))) + (-5 *1 (-428 *4 *5 *6 *7)) (-5 *3 (-597 *7)))) + ((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-110)) (-4 *5 (-13 (-289) (-140))) (-4 *6 (-741)) + (-4 *7 (-795)) (-4 *8 (-890 *5 *6 *7)) (-5 *2 (-597 (-597 *8))) + (-5 *1 (-428 *5 *6 *7 *8)) (-5 *3 (-597 *8)))) + ((*1 *2 *3) + (-12 (-4 *4 (-13 (-289) (-140))) (-4 *5 (-741)) (-4 *6 (-795)) + (-4 *7 (-890 *4 *5 *6)) (-5 *2 (-597 (-597 *7))) + (-5 *1 (-428 *4 *5 *6 *7)) (-5 *3 (-597 *7)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-110)) (-4 *5 (-13 (-289) (-140))) (-4 *6 (-741)) + (-4 *7 (-795)) (-4 *8 (-890 *5 *6 *7)) (-5 *2 (-597 (-597 *8))) + (-5 *1 (-428 *5 *6 *7 *8)) (-5 *3 (-597 *8))))) (((*1 *2) (-12 (-5 *2 (-1186)) (-5 *1 (-1013 *3)) (-4 *3 (-129))))) (((*1 *2 *1) (-12 @@ -14347,7 +14059,7 @@ (-2 (|:| |var| (-1099)) (|:| |arrayIndex| (-597 (-893 (-530)))) (|:| |rand| - (-2 (|:| |ints2Floats?| (-110)) (|:| -3949 (-804)))))) + (-2 (|:| |ints2Floats?| (-110)) (|:| -3954 (-804)))))) (|:| |arrayAssignmentBranch| (-2 (|:| |var| (-1099)) (|:| |rand| (-804)) (|:| |ints2Floats?| (-110)))) 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\ No newline at end of file |