diff options
Diffstat (limited to 'src/share/algebra')
| -rw-r--r-- | src/share/algebra/browse.daase | 312 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 8 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1308 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 7342 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 25334 |
5 files changed, 17153 insertions, 17151 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index af67ff62..d765e330 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2282756 . 3452610475) +(2282756 . 3452645032) (-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 @@ -56,7 +56,7 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -2308) +(-32 R -2306) ((|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 -1034) (QUOTE (-564))))) @@ -88,11 +88,11 @@ NIL ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{} [a1,{}...,{}an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-40 -2308 UP UPUP -2130) +(-40 -2306 UP UPUP -3056) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4400 |has| (-407 |#2|) (-363)) (-4405 |has| (-407 |#2|) (-363)) (-4399 |has| (-407 |#2|) (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2807 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2807 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2807 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2807 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) -(-41 R -2308) +(-41 R -2306) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))))) @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -2308) +(-54 |Base| R -2306) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -388,7 +388,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op,{} p,{} v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|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| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op,{} p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|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!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op,{} p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|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| (($ $ (|Identifier|)) "\\spad{assert(op,{} p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,{}p)} 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|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f,{} a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|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}."))) NIL NIL -(-115 -2308 UP) +(-115 -2306 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 @@ -468,11 +468,11 @@ 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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4409 "*") . T)) NIL -(-135 |minix| -3598 S T$) +(-135 |minix| -3599 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-136 |minix| -3598 R) +(-136 |minix| -3599 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 @@ -520,7 +520,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4404 . T)) NIL -(-148 -2308 UP UPUP) +(-148 -2306 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 @@ -560,7 +560,7 @@ 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 -(-158 R -2308) +(-158 R -2306) ((|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 @@ -680,7 +680,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-188 R -2308) +(-188 R -2306) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -788,11 +788,11 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -(-215 -2308 UP UPUP R) +(-215 -2306 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 -(-216 -2308 FP) +(-216 -2306 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 @@ -804,7 +804,7 @@ NIL ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-219 R -2308) +(-219 R -2306) ((|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 @@ -824,7 +824,7 @@ NIL ((|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}."))) ((-4404 . T)) NIL -(-224 R -2308) +(-224 R -2306) ((|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 @@ -876,19 +876,19 @@ NIL ((|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 -(-237 S -3598 R) +(-237 S -3599 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 (-363))) (|HasCategory| |#3| (QUOTE (-789))) (|HasCategory| |#3| (QUOTE (-844))) (|HasAttribute| |#3| (QUOTE -4404)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-722))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (QUOTE (-1094)))) -(-238 -3598 R) +(-238 -3599 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"))) ((-4401 |has| |#2| (-1045)) (-4402 |has| |#2| (-1045)) (-4404 |has| |#2| (-6 -4404)) ((-4409 "*") |has| |#2| (-172)) (-4407 . T)) NIL -(-239 -3598 A B) +(-239 -3599 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-240 -3598 R) +(-240 -3599 R) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) ((-4401 |has| |#2| (-1045)) (-4402 |has| |#2| (-1045)) (-4404 |has| |#2| (-6 -4404)) ((-4409 "*") |has| |#2| (-172)) (-4407 . T)) ((-2807 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))))) (-2807 (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1094)))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1045)))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-363))) (-2807 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1045)))) (-2807 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363)))) (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (QUOTE (-789))) (-2807 (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-172))) (-2807 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-1045)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (-2807 (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2807 (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1045)))) (-2807 (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1045)))) (-2807 (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1045)))) (-2807 (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1045)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-25)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-172)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-233)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-368)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-789)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-844)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1045)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1094))))) (-2807 (-12 (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1045))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))))) (-2807 (-12 (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| (-564) (QUOTE (-846))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1045)))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170))))) (-2807 (|HasCategory| |#2| (QUOTE (-1045))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))))) @@ -930,11 +930,11 @@ NIL NIL (-250 |n| R M S) ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) -((-4404 -2807 (-2359 (|has| |#4| (-1045)) (|has| |#4| (-233))) (-2359 (|has| |#4| (-1045)) (|has| |#4| (-896 (-1170)))) (|has| |#4| (-6 -4404)) (-2359 (|has| |#4| (-1045)) (|has| |#4| (-637 (-564))))) (-4401 |has| |#4| (-1045)) (-4402 |has| |#4| (-1045)) ((-4409 "*") |has| |#4| (-172)) (-4407 . T)) +((-4404 -2807 (-2358 (|has| |#4| (-1045)) (|has| |#4| (-233))) (-2358 (|has| |#4| (-1045)) (|has| |#4| (-896 (-1170)))) (|has| |#4| (-6 -4404)) (-2358 (|has| |#4| (-1045)) (|has| |#4| (-637 (-564))))) (-4401 |has| |#4| (-1045)) (-4402 |has| |#4| (-1045)) ((-4409 "*") |has| |#4| (-172)) (-4407 . T)) ((-2807 (-12 (|HasCategory| |#4| (QUOTE (-172))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-233))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-363))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-722))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-789))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-844))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1045))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|))) 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(QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (-252 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."))) @@ -1032,11 +1032,11 @@ 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 -(-276 R -2308) +(-276 R -2306) ((|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 -(-277 R -2308) +(-277 R -2306) ((|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 @@ -1084,7 +1084,7 @@ 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 -(-289 S R |Mod| -1408 -2063 |exactQuo|) +(-289 S R |Mod| -1812 -3669 |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"))) ((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL @@ -1116,11 +1116,11 @@ NIL ((|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 -(-297 -2308 S) +(-297 -2306 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 -(-298 E -2308) +(-298 E -2306) ((|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 @@ -1168,7 +1168,7 @@ 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 -(-310 -2308) +(-310 -2306) ((|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 @@ -1194,9 +1194,9 @@ NIL NIL (-316 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."))) -((-4404 -2807 (-2359 (|has| |#1| (-1045)) (|has| |#1| (-637 (-564)))) (-12 (|has| |#1| (-556)) (-2807 (-2359 (|has| |#1| (-1045)) (|has| |#1| (-637 (-564)))) (|has| |#1| (-1045)) (|has| |#1| (-473)))) (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) ((-4409 "*") |has| |#1| (-556)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-556)) (-4399 |has| |#1| (-556))) +((-4404 -2807 (-2358 (|has| |#1| (-1045)) (|has| |#1| (-637 (-564)))) (-12 (|has| |#1| (-556)) (-2807 (-2358 (|has| |#1| (-1045)) (|has| |#1| (-637 (-564)))) (|has| |#1| (-1045)) (|has| |#1| (-473)))) (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) ((-4409 "*") |has| |#1| (-556)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-556)) (-4399 |has| |#1| (-556))) ((-2807 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| |#1| (QUOTE (-556))) (-2807 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-2807 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2807 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1045)))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556)))) (-2807 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1106)))) (-2807 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-2807 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1106)))) (-2807 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-2807 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2807 (-12 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-564))))) -(-317 R -2308) +(-317 R -2306) ((|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 @@ -1207,7 +1207,7 @@ NIL (-319 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."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2423) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3697) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2423) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2070) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-320 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 @@ -1240,11 +1240,11 @@ NIL ((|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."))) ((-4408 . T) (-4407 . T)) ((-2807 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2807 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) -(-328 S -2308) +(-328 S -2306) ((|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 (-368)))) -(-329 -2308) +(-329 -2306) ((|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."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL @@ -1264,15 +1264,15 @@ 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 -(-334 S -2308 UP UPUP R) +(-334 S -2306 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 -(-335 -2308 UP UPUP R) +(-335 -2306 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 -(-336 -2308 UP UPUP R) +(-336 -2306 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 @@ -1292,11 +1292,11 @@ 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 -(-341 S -2308 UP UPUP) +(-341 S -2306 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-363)))) -(-342 -2308 UP UPUP) +(-342 -2306 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) ((-4400 |has| (-407 |#2|) (-363)) (-4405 |has| (-407 |#2|) (-363)) (-4399 |has| (-407 |#2|) (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL @@ -1328,7 +1328,7 @@ 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."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL -(-350 R UP -2308) +(-350 R UP -2306) ((|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 @@ -1352,7 +1352,7 @@ NIL ((|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."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) ((-2807 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) -(-356 -2308 GF) +(-356 -2306 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 @@ -1360,7 +1360,7 @@ 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 -(-358 -2308 FP FPP) +(-358 -2306 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 @@ -1496,7 +1496,7 @@ 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 -(-392 -2308 UP UPUP R) +(-392 -2306 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 @@ -1520,11 +1520,11 @@ NIL ((|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 -(-398 -2562 |returnType| -2837 |symbols|) +(-398 -2562 |returnType| -2838 |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 -(-399 -2308 UP) +(-399 -2306 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1580,11 +1580,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-413 R -2308 UP A) +(-413 R -2306 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4404 . T)) NIL -(-414 R -2308 UP A |ibasis|) +(-414 R -2306 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 -1034) (|devaluate| |#2|)))) @@ -1632,7 +1632,7 @@ NIL ((|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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4407 . T) (-4397 . T) (-4408 . T)) NIL -(-426 R -2308) +(-426 R -2306) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1640,7 +1640,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) ((-4394 -12 (|has| |#1| (-6 -4394)) (|has| |#2| (-6 -4394))) (-4401 . T) (-4402 . T) (-4404 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4394)) (|HasAttribute| |#2| (QUOTE -4394)))) -(-428 R -2308) +(-428 R -2306) ((|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 @@ -1652,15 +1652,15 @@ NIL ((|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}."))) ((-4404 -2807 (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) ((-4409 "*") |has| |#1| (-556)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-556)) (-4399 |has| |#1| (-556))) NIL -(-431 R -2308) +(-431 R -2306) ((|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 -(-432 R -2308) +(-432 R -2306) ((|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)))) -(-433 R -2308) +(-433 R -2306) ((|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 @@ -1668,7 +1668,7 @@ 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 -(-435 R -2308 UP) +(-435 R -2306 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 -1034) (QUOTE (-48))))) @@ -1700,7 +1700,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,{}sqf,{}pd,{}r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,{}sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r,{}sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,{}p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\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 -(-443 R UP -2308) +(-443 R UP -2306) ((|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 @@ -1812,7 +1812,7 @@ 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 -(-471 |lv| -2308 R) +(-471 |lv| -2306 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 @@ -1827,7 +1827,7 @@ NIL (-474 |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."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . 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T)) ((|HasCategory| |#2| (QUOTE (-905))) (-2807 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2807 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2807 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2807 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2807 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) -(-482 -3598 S) +(-482 -3599 S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered first by the sum of their components,{} and then refined using a reverse lexicographic ordering. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) ((-4401 |has| |#2| (-1045)) (-4402 |has| |#2| (-1045)) (-4404 |has| |#2| (-6 -4404)) ((-4409 "*") |has| |#2| (-172)) (-4407 . T)) ((-2807 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST 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(LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| (-564) (QUOTE (-846))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1045)))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170))))) (-2807 (|HasCategory| |#2| (QUOTE (-1045))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))))) @@ -1868,7 +1868,7 @@ NIL ((|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}."))) ((-4407 . T) (-4408 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) -(-485 -2308 UP UPUP R) +(-485 -2306 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 @@ -1904,7 +1904,7 @@ 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 -(-494 -2308 UP |AlExt| |AlPol|) +(-494 -2306 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 @@ -1924,7 +1924,7 @@ NIL ((|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 -(-499 R UP -2308) +(-499 R UP -2306) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1944,7 +1944,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-504 -2308 |Expon| |VarSet| |DPoly|) +(-504 -2306 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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 -612) (QUOTE (-1170))))) @@ -2056,7 +2056,7 @@ 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 -(-532 K -2308 |Par|) +(-532 K -2306 |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 @@ -2080,7 +2080,7 @@ 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 -(-538 K -2308 |Par|) +(-538 K -2306 |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 @@ -2132,11 +2132,11 @@ NIL ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4407 . T) (-4408 . T)) ((-12 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1901) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3813) (|devaluate| |#2|)))))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) -(-551 R -2308) +(-551 R -2306) ((|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 -(-552 R0 -2308 UP UPUP R) +(-552 R0 -2306 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 @@ -2156,7 +2156,7 @@ 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."))) ((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL -(-557 R -2308) +(-557 R -2306) ((|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 @@ -2168,7 +2168,7 @@ 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 -(-560 R -2308 L) +(-560 R -2306 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 -652) (|devaluate| |#2|)))) @@ -2176,11 +2176,11 @@ 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 -(-562 -2308 UP UPUP R) +(-562 -2306 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 -(-563 -2308 UP) +(-563 -2306 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 @@ -2192,15 +2192,15 @@ 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 -(-566 R -2308 L) +(-566 R -2306 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 -652) (|devaluate| |#2|)))) -(-567 R -2308) +(-567 R -2306) ((|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 -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1133)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-627))))) -(-568 -2308 UP) +(-568 -2306 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 @@ -2208,7 +2208,7 @@ 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 -(-570 -2308) +(-570 -2306) ((|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 @@ -2220,15 +2220,15 @@ NIL ((|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 -(-573 R -2308) +(-573 R -2306) ((|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 -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-627))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-284)))) (|HasCategory| |#1| (QUOTE (-556)))) -(-574 -2308 UP) +(-574 -2306 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 -(-575 R -2308) +(-575 R -2306) ((|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 @@ -2260,15 +2260,15 @@ 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 -(-583 R -2308) +(-583 R -2306) ((|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 -(-584 E -2308) +(-584 E -2306) ((|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 -(-585 -2308) +(-585 -2306) ((|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}."))) ((-4402 . T) (-4401 . T)) ((|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-1170))))) @@ -2320,7 +2320,7 @@ 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 -(-598 R -2308 FG) +(-598 R -2306 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 @@ -2350,7 +2350,7 @@ NIL NIL (-605 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)."))) -((-4404 -2807 (-2359 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4402 . T) (-4401 . T)) +((-4404 -2807 (-2358 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4402 . T) (-4401 . T)) ((-2807 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-606 |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."))) @@ -2380,7 +2380,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-613 -2308 UP) +(-613 -2306 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2408,7 +2408,7 @@ 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}."))) ((-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| |#1| (QUOTE (-844)))) -(-620 R -2308) +(-620 R -2306) ((|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 @@ -2440,11 +2440,11 @@ 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 -(-628 R -2308) +(-628 R -2306) ((|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 -(-629 |lv| -2308) +(-629 |lv| -2306) ((|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 @@ -2462,7 +2462,7 @@ NIL NIL (-633 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)."))) -((-4404 -2807 (-2359 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4402 . T) (-4401 . T)) +((-4404 -2807 (-2358 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4402 . T) (-4401 . T)) ((-2807 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-634 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))}."))) @@ -2520,7 +2520,7 @@ NIL ((|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})}."))) NIL NIL -(-648 R -2308 L) +(-648 R -2306 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 @@ -2540,11 +2540,11 @@ 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}."))) ((-4401 . T) (-4402 . T) (-4404 . T)) NIL -(-653 -2308 UP) +(-653 -2306 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)))) -(-654 A -3865) +(-654 A -4234) ((|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}}"))) ((-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) @@ -2580,11 +2580,11 @@ NIL ((|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}."))) ((-4408 . T) (-4407 . T)) NIL -(-663 -2308) +(-663 -2306) ((|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 -(-664 -2308 |Row| |Col| M) +(-664 -2306 |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 @@ -2680,7 +2680,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value \\spad{`x'} into \\%."))) NIL NIL -(-688 S -2308 FLAF FLAS) +(-688 S -2306 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 @@ -2704,7 +2704,7 @@ 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 -(-694 OV E -2308 PG) +(-694 OV E -2306 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 @@ -2756,7 +2756,7 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-707 R |Mod| -1408 -2063 |exactQuo|) +(-707 R |Mod| -1812 -3669 |exactQuo|) ((|constructor| (NIL "\\indented{1}{These domains are used for the factorization and gcds} of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL @@ -2772,7 +2772,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-711 R |Mod| -1408 -2063 |exactQuo|) +(-711 R |Mod| -1812 -3669 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4404 . T)) NIL @@ -2784,7 +2784,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4402 . T) (-4401 . T)) NIL -(-714 -2308) +(-714 -2306) ((|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]]}."))) ((-4404 . T)) NIL @@ -2820,7 +2820,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-723 -2308 UP) +(-723 -2306 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 @@ -2972,11 +2972,11 @@ 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 -(-761 -2308) +(-761 -2306) ((|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 -(-762 P -2308) +(-762 P -2306) ((|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 @@ -2984,7 +2984,7 @@ NIL NIL NIL NIL -(-764 UP -2308) +(-764 UP -2306) ((|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 @@ -3000,7 +3000,7 @@ 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."))) (((-4409 "*") . T)) NIL -(-768 R -2308) +(-768 R -2306) ((|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 @@ -3020,7 +3020,7 @@ 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 -(-773 -2308 |ExtF| |SUEx| |ExtP| |n|) +(-773 -2306 |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 @@ -3116,11 +3116,11 @@ NIL ((|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 -(-797 R -2308 L) +(-797 R -2306 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 -(-798 R -2308) +(-798 R -2306) ((|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 @@ -3128,7 +3128,7 @@ 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 -(-800 R -2308) +(-800 R -2306) ((|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 @@ -3136,11 +3136,11 @@ 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 -(-802 -2308 UP UPUP R) +(-802 -2306 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 -(-803 -2308 UP L LQ) +(-803 -2306 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 @@ -3148,31 +3148,31 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|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 -(-805 -2308 UP L LQ) +(-805 -2306 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 -(-806 -2308 UP) +(-806 -2306 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 -(-807 -2308 L UP A LO) +(-807 -2306 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 -(-808 -2308 UP) +(-808 -2306 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)))) -(-809 -2308 LO) +(-809 -2306 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m,{} v)} returns \\spad{[m_0,{} v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") 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(LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| (-564) (QUOTE (-846))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1045)))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170))))) (-2807 (|HasCategory| |#2| (QUOTE (-1045))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))))) @@ -3292,7 +3292,7 @@ NIL ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-841 -3598 S) +(-841 -3599 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 @@ -3496,7 +3496,7 @@ 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 -(-892 UP -2308) +(-892 UP -2306) ((|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 @@ -3556,7 +3556,7 @@ 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."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-368)))) -(-907 R0 -2308 UP UPUP R) +(-907 R0 -2306 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 @@ -3584,7 +3584,7 @@ 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 -(-914 -2308) +(-914 -2306) ((|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 @@ -3600,11 +3600,11 @@ 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}."))) (((-4409 "*") . T)) NIL -(-918 -2308 P) +(-918 -2306 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-919 |xx| -2308) +(-919 |xx| -2306) ((|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 @@ -3628,7 +3628,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-925 R -2308) +(-925 R -2306) ((|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| (|Identifier|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3640,7 +3640,7 @@ 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 -(-928 S R -2308) +(-928 S R -2306) ((|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 @@ -3660,7 +3660,7 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -882) (|devaluate| |#1|)))) -(-933 R -2308 -4063) +(-933 R -2306 -4063) ((|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 @@ -3712,7 +3712,7 @@ 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}."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) NIL -(-946 E V R P -2308) +(-946 E V R P -2306) ((|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 @@ -3724,7 +3724,7 @@ NIL ((|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}."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) ((|HasCategory| |#1| (QUOTE (-905))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-949 E V R P -2308) +(-949 E V R P -2306) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,{}n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-452)))) @@ -3752,7 +3752,7 @@ NIL ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -(-956 -2308) +(-956 -2306) ((|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 @@ -3852,7 +3852,7 @@ 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 -(-981 K R UP -2308) +(-981 K R UP -2306) ((|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 @@ -3924,7 +3924,7 @@ 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 -(-999 -2308 UP UPUP |radicnd| |n|) +(-999 -2306 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4400 |has| (-407 |#2|) (-363)) (-4405 |has| (-407 |#2|) (-363)) (-4399 |has| (-407 |#2|) (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2807 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2807 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2807 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2807 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) @@ -3964,19 +3964,19 @@ 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}}"))) ((-4400 . T) (-4405 . T) (-4399 . T) (-4402 . T) (-4401 . T) ((-4409 "*") . T) (-4404 . T)) NIL -(-1009 R -2308) +(-1009 R -2306) ((|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 -(-1010 R -2308) +(-1010 R -2306) ((|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 -(-1011 -2308 UP) +(-1011 -2306 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 -(-1012 -2308 UP) +(-1012 -2306 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 @@ -4012,7 +4012,7 @@ NIL ((|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"))) ((-4400 . T) (-4405 . T) (-4399 . T) (-4402 . T) (-4401 . T) ((-4409 "*") . T) (-4404 . T)) ((-2807 (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (QUOTE (-564))))) -(-1021 -2308 L) +(-1021 -2306 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 @@ -4048,7 +4048,7 @@ 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 -(-1030 -2308 |Expon| |VarSet| |FPol| |LFPol|) +(-1030 -2306 |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"))) (((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL @@ -4112,7 +4112,7 @@ 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\"}.")) (|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."))) ((-4404 . T)) NIL -(-1046 |xx| -2308) +(-1046 |xx| -2306) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4208,11 +4208,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1070 |Base| R -2308) +(-1070 |Base| R -2306) ((|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 -(-1071 |Base| R -2308) +(-1071 |Base| R -2306) ((|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 @@ -4368,7 +4368,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,{}s,{}t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1110 R -2308) +(-1110 R -2306) ((|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 @@ -4416,7 +4416,7 @@ NIL ((|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}"))) ((-4408 . T) (-4407 . T)) NIL -(-1122 UP -2308) +(-1122 UP -2306) ((|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 @@ -4574,9 +4574,9 @@ NIL NIL (-1161 |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."))) -(((-4409 "*") -2807 (-2359 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-816))) (|has| |#1| (-172)) (-2359 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-905)))) (-4400 -2807 (-2359 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-816))) (|has| |#1| (-556)) (-2359 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-905)))) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . 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We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|)))) (|HasCategory| (-767) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -2423) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-2807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3697) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|)))) (|HasCategory| (-767) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -2423) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-2807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2070) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-1169) ((|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 @@ -4720,7 +4720,7 @@ 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 -(-1198 R -2308) +(-1198 R -2306) ((|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 @@ -4728,7 +4728,7 @@ 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 -(-1200 R -2308) +(-1200 R -2306) ((|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 -612) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -882) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -882) (|devaluate| |#1|))))) @@ -4756,7 +4756,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,{}n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) -(-1207 -2308) +(-1207 -2306) ((|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}."))) 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(-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2070) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|)))))) (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-905))) (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-145))) (-2807 (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-816))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-556)))) (-2807 (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2807 (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-816))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-172)))) (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-363)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1224 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 @@ -4903,11 +4903,11 @@ NIL (-1243 |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)}."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2423) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3697) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) +((|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2423) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2070) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-1244 |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}."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2423) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3697) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2423) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2070) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-1245 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") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,{}f(var))}."))) (((-4409 "*") |has| (-1244 |#2| |#3| |#4|) (-172)) (-4400 |has| (-1244 |#2| |#3| |#4|) (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) @@ -4927,7 +4927,7 @@ NIL (-1249 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-564)))) (|HasCategory| |#2| (QUOTE (-955))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasSignature| |#2| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3697) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1170))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-955))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasSignature| |#2| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2070) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1170))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363)))) (-1250 |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."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) @@ -4935,12 +4935,12 @@ NIL (-1251 |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}."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|)))) (|HasCategory| (-767) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -2423) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-2807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3697) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|)))) (|HasCategory| (-767) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -2423) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-2807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2070) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-1252 |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 -(-1253 -2308 UP L UTS) +(-1253 -2306 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 (-556)))) @@ -5000,7 +5000,7 @@ 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 -(-1268 K R UP -2308) +(-1268 K R UP -2306) ((|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 @@ -5036,11 +5036,11 @@ 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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T)) NIL -(-1277 S -2308) +(-1277 S -2306) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) -(-1278 -2308) +(-1278 -2306) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 5436af06..28532714 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,5 +1,5 @@ -(161804 . 3452610480) +(161804 . 3452645038) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) #0#) |has| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (-309 (-2 (|:| -1901 |#1|) (|:| -3813 |#2|))))) ((((-564)) . T) (($) -2807 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) (((-407 (-564))) -2807 (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-1034 (-407 (-564))))) ((|#1|) . T)) (((|#2| |#2|) . T)) @@ -70,7 +70,7 @@ ((((-564)) . T) (((-407 (-564))) -2807 (|has| |#2| (-38 (-407 (-564)))) (|has| |#2| (-1034 (-407 (-564))))) ((|#2|) . T) (($) -2807 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) (((-860 |#1|)) . T)) (-2807 (|has| |#1| (-363)) (|has| |#1| (-556))) (-2807 (|has| |#1| (-363)) (|has| |#1| (-556))) -((((-2 (|:| -2083 |#1|) (|:| -1410 |#2|))) . T)) +((((-2 (|:| -2083 |#1|) (|:| -1838 |#2|))) . T)) ((($) . T)) ((((-564)) . T) (((-407 (-564))) -2807 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) ((|#1|) . T) (($) -2807 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((-1170)) . T)) ((((-858)) -2807 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) @@ -266,11 +266,11 @@ ((((-536)) |has| |#2| (-612 (-536))) (((-888 (-379))) |has| |#2| (-612 (-888 (-379)))) (((-888 (-564))) |has| |#2| (-612 (-888 (-564))))) ((((-858)) . T)) (((|#1| |#2| |#3| |#4|) . T)) -((((-2 (|:| -2083 |#1|) (|:| -1410 |#2|))) . T) (((-858)) . T)) +((((-2 (|:| -2083 |#1|) (|:| -1838 |#2|))) . T) (((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536))) (((-888 (-379))) |has| |#1| (-612 (-888 (-379)))) (((-888 (-564))) |has| |#1| (-612 (-888 (-564))))) (((|#4|) -2807 (|has| |#4| (-172)) (|has| |#4| (-363)) (|has| |#4| (-1045))) (($) |has| |#4| (-172))) (((|#3|) -2807 (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-1045))) (($) |has| |#3| (-172))) -((((-2 (|:| -2083 |#1|) (|:| -1410 |#2|))) . T)) +((((-2 (|:| -2083 |#1|) (|:| -1838 |#2|))) . T)) ((((-858)) . T)) ((((-858)) . T)) ((((-536)) . T) (((-564)) . T) (((-888 (-564))) . T) (((-379)) . T) (((-225)) . T)) diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 35ac95fd..39afecb3 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3452610474) +(30 . 3452645031) (4410 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -477,658 +477,660 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |cAcsch| |height| |scalarMatrix| |stronglyReduce| - |KrullNumber| |inf| |basis| |po| |simplify| |inverseLaplace| |rroot| - |e02daf| |continuedFraction| |lift| |redPol| |untab| |Si| |lex| - |primitivePart!| |convert| |myDegree| |rewriteIdealWithRemainder| - |s17dcf| |diagonalProduct| |reduce| |clipSurface| - |removeSuperfluousQuasiComponents| |asimpson| |surface| |enterInCache| - |janko2| |rewriteSetWithReduction| |nilFactor| |orbits| - |basisOfRightAnnihilator| |clip| |df2st| |pdf2ef| |leftFactor| - |e04ycf| |subSet| |tab| |powerSum| |pastel| |maximumExponent| - |writeByte!| |dAndcExp| |squareFreePrim| |df2fi| |symbol| - |meshPar1Var| |OMopenString| |repSq| |eulerE| |autoReduced?| - |topFortranOutputStack| |lazyPseudoQuotient| |zeroDimensional?| - |expression| |rCoord| |subResultantChain| |symmetricPower| - |stopTableInvSet!| |insert!| |exprHasAlgebraicWeight| |modularGcd| - |innerSolve1| |integer| |accuracyIF| |trivialIdeal?| - |solveLinearPolynomialEquationByFractions| |solveInField| |harmonic| - |rightTrace| |pureLex| |floor| |cExp| |rischDE| |cyclicSubmodule| - |viewSizeDefault| |iteratedInitials| |partialQuotients| |wholeRagits| - |d02gaf| |factorials| |algint| |perfectSquare?| |randomR| |axes| - |binaryTournament| |littleEndian| |leftOne| |blankSeparate| - |someBasis| |leftScalarTimes!| |OMgetEndBind| |monicLeftDivide| - |legendreP| |declare| |sequence| |Nul| |rdregime| |critMonD1| |style| - |checkRur| |postfix| |totalDegree| |pol| |charpol| - |ScanFloatIgnoreSpaces| |diagonal| |tail| - |indiceSubResultantEuclidean| |port| |horizConcat| |factorFraction| - |reduction| |normalizedDivide| |exponent| |OMreadStr| |tanQ| - |readInt16!| |critB| ** |basisOfMiddleNucleus| |mergeDifference| - |numerators| |remove!| |byte| |minIndex| |roughUnitIdeal?| - |roughBasicSet| |prevPrime| |alternating| |getDatabase| |t| - |outputList| |label| |moduloP| |patternMatchTimes| |rules| |error| - |fixedPointExquo| |eigenMatrix| |listOfLists| |expIfCan| |makeMulti| - |divideIfCan| |ScanFloatIgnoreSpacesIfCan| |antisymmetricTensors| - |leftRank| |trueEqual| |assert| |symbolIfCan| |unknown| |reindex| - |bipolarCylindrical| |rationalFunction| |multiple?| |characteristic| - |int| |leader| |stopTableGcd!| |doubleDisc| |pToDmp| |chebyshevU| - |lSpaceBasis| |optional?| |zeroMatrix| |infLex?| |poisson| |sorted?| - |mulmod| |triangularSystems| |f01rdf| - |unprotectedRemoveRedundantFactors| |associatedEquations| - |deepestTail| |hasHi| |sinhIfCan| |tubeRadiusDefault| - |nextsousResultant2| |roughEqualIdeals?| |typeList| |equality| - |ramified?| |square?| |f2st| |unparse| LODO2FUN |invmod| |nlde| - |regularRepresentation| |e01saf| |ocf2ocdf| |cCot| - |stoseInvertibleSetreg| |li| |scanOneDimSubspaces| |constructor| - |graphStates| |numberOfChildren| |nativeModuleExtension| - |principalAncestors| |expenseOfEvaluationIF| |max| |minus!| |d01gbf| - |nary?| |mix| |univcase| |option| |lifting| |d01fcf| |moebiusMu| - |removeCosSq| |f02aaf| |quadraticNorm| |printingInfo?| |seed| |s17aff| - |selectPDERoutines| |expPot| |s18aef| |integers| |normal?| |limit| - |e04gcf| |solveid| |resultantEuclidean| |shade| |float?| - |GospersMethod| |lazy?| |leftRemainder| |distance| |checkPrecision| - |homogeneous?| |interpretString| |flagFactor| |iFTable| |atrapezoidal| - |inconsistent?| |printTypes| |createZechTable| |rightTrim| - |primaryDecomp| |f01qef| |simpsono| |insertionSort!| |augment| |cCsc| - |gramschmidt| |explimitedint| |leftTrim| |parents| |generalPosition| - |tubePointsDefault| |sumOfDivisors| |viewWriteAvailable| - |noncommutativeJordanAlgebra?| |computeCycleLength| |exptMod| - |LyndonWordsList1| |ParCondList| |bounds| |laguerreL| - |expandTrigProducts| |isMult| |chiSquare1| |nextColeman| |mapExpon| - |integralMatrix| |printInfo| |maxrow| |closedCurve?| |realSolve| - |weakBiRank| |iisin| |subresultantSequence| |signatureAst| |test| - |bernoulliB| |quoByVar| |approximants| |integralBasis| |intcompBasis| - |packageCall| |OMreceive| |trim| |functionIsFracPolynomial?| |e04fdf| - |maxrank| |rational| |leftGcd| |permutationGroup| |rootDirectory| - RF2UTS |viewWriteDefault| |iiasec| |stoseInvertibleSet| |newLine| - |minordet| |removeDuplicates!| |OMputAttr| |singularAtInfinity?| - |laurentRep| |clipWithRanges| |setPosition| |divideIfCan!| - |LagrangeInterpolation| |back| |generate| |close| |eq| - |stoseIntegralLastSubResultant| |resetAttributeButtons| |ptFunc| - |linearAssociatedOrder| |kind| |OMgetObject| |makeViewport2D| |c05adf| - |ridHack1| |iter| |lyndon| |prefix| |goodnessOfFit| |nullity| - |cylindrical| |exprToUPS| |incrementBy| |f01maf| |f04mcf| |op| - |pattern| |OMputEndApp| |display| |cos2sec| |flatten| |read!| - |nextPrimitivePoly| |infieldint| |numberOfNormalPoly| |laplace| - |computeCycleEntry| |genericLeftDiscriminant| |crushedSet| |f04asf| - |expand| |cAsec| |s17ahf| |cyclotomicFactorization| |iicsc| |iiabs| - |resetVariableOrder| |reducedDiscriminant| |filterWhile| |f04axf| - |partialDenominators| |purelyAlgebraic?| |basisOfLeftNucloid| - |filterUntil| |partialFraction| |redpps| |shallowCopy| |headReduced?| - |getlo| |insertBottom!| |reducedQPowers| |numberOfComponents| |bits| - |message| |isOp| |curve| |internalDecompose| |select| - |factorSquareFreePolynomial| |functionIsOscillatory| |weierstrass| - |f02bjf| |input| |difference| |cyclicCopy| |nonLinearPart| - |outputSpacing| |symbolTable| |semiResultantEuclidean1| - |lastSubResultant| |socf2socdf| |eof?| |union| |reductum| |integral?| - |library| |round| |exp| |htrigs| |OMputEndObject| |mathieu23| |iisec| - |tablePow| |tan2cot| |block| |listYoungTableaus| |clipParametric| - |shufflein| |hasPredicate?| |composite| |leftCharacteristicPolynomial| - |iExquo| |subQuasiComponent?| |sh| |pushucoef| |nonQsign| - |genericLeftNorm| |rightRankPolynomial| |makeResult| |exprToXXP| - |pToHdmp| |outerProduct| |reducedForm| |iiacot| |c06fuf| |e02ahf| - |coordinate| |cons| |radPoly| |cosIfCan| |fortranLiteralLine| - |makeRecord| |e02dff| |set| |matrixConcat3D| |f04faf| |rational?| - |getGoodPrime| |getMeasure| |shanksDiscLogAlgorithm| |addMatch| - |hyperelliptic| |cot2trig| |clearDenominator| |balancedBinaryTree| - |hcrf| |beauzamyBound| |mindeg| |coerceP| |reflect| |asinhIfCan| - |nonSingularModel| |dimensionOfIrreducibleRepresentation| |f04maf| - |dioSolve| |commutator| |setMinPoints| |fortranDoubleComplex| - |resultantReduitEuclidean| |drawComplexVectorField| |bombieriNorm| - |binary| |laguerre| |c06gcf| |setProperties| |d02cjf| |rootRadius| - |jacobiIdentity?| |stop| |algDsolve| |qinterval| |abs| |updateStatus!| - |argumentList!| |prepareDecompose| |shiftLeft| - |branchPointAtInfinity?| |setEmpty!| |iicosh| |getStream| |s14aaf| - |second| |OMgetAttr| |returns| |list?| |showAllElements| - |createPrimitiveElement| |localIntegralBasis| |ipow| |vedf2vef| - |reduced?| |tan2trig| |third| |mainDefiningPolynomial| - |generalLambert| |iroot| |pmComplexintegrate| |lazyPrem| |signature| - |s14baf| |nextPartition| |distribute| |sumSquares| |s18dcf| - |internalSubQuasiComponent?| |purelyTranscendental?| |addPoint2| - |numericalOptimization| |integralLastSubResultant| |definingEquations| - |algebraicDecompose| |binding| |createLowComplexityTable| - |zeroDimPrimary?| |changeVar| |pushuconst| |limitPlus| |iilog| - |modularFactor| |palglimint| |extendedint| |bottom!| |backOldPos| - |lhs| |conjugates| |dmpToHdmp| |critMTonD1| |torsionIfCan| - |getMultiplicationTable| |genericLeftTraceForm| |optimize| |sqfree| - |atom?| |rightMult| |associator| |acscIfCan| |rhs| |presub| - |outlineRender| |algebraicOf| |setAdaptive| |biRank| |leadingTerm| - |leftLcm| |mapDown!| |void| |generators| |mapUp!| |fortranLiteral| - |constantOpIfCan| |palgextint0| |belong?| |numberOfVariables| - |systemCommand| |sincos| |divideExponents| |cothIfCan| |monomRDEsys| - |Aleph| |copies| |variable?| |leastMonomial| |setelt!| - |numericalIntegration| |d02gbf| |insertMatch| |gethi| - |reduceBasisAtInfinity| |LiePoly| |deleteRoutine!| |script| |zeroDim?| - |prolateSpheroidal| |weight| |createNormalPoly| |rightScalarTimes!| - |firstDenom| |overlabel| |moreAlgebraic?| |errorKind| |redPo| - |makeGraphImage| |d03eef| |nodes| |isImplies| |relationsIdeal| - |elseBranch| |hasSolution?| |part?| |taylorQuoByVar| |coth2trigh| - |vark| |doublyTransitive?| |f07aef| |withPredicates| |airyBi| |normal| - |symFunc| |normalDeriv| |elem?| |writeLine!| |graphCurves| |makeTerm| - |numberOfMonomials| |mat| |arity| |closedCurve| |setStatus!| |tex| - |localAbs| |key| |convergents| |totalfract| |low| |f02abf| |mr| |pade| - |findBinding| |host| |coerceImages| |OMcloseConn| |OMgetSymbol| - |skewSFunction| |createPrimitivePoly| |f02adf| |recoverAfterFail| - |graphs| |s19adf| |latex| |qfactor| |f02xef| |numberOfCycles| - |RittWuCompare| |delta| |filename| |denominator| - |generalizedContinuumHypothesisAssumed?| |monomialIntegrate| |depth| - |cartesian| |pdf2df| |leastPower| |symmetricTensors| |cond| - |readUInt16!| |baseRDE| |ode2| |dimensions| |f04jgf| |rootProduct| - |LyndonBasis| |fi2df| |multiset| |hermite| |truncate| |lfinfieldint| - |d01anf| |inputBinaryFile| |multiplyExponents| |generic?| |parse| - |leadingIdeal| |setlast!| |e04dgf| |s20acf| |compactFraction| - |dequeue!| |algintegrate| |nextItem| |lfintegrate| |transcendent?| - |primPartElseUnitCanonical| |drawComplex| |singularitiesOf| - |prefixRagits| |repeating| |extendedSubResultantGcd| - |pointSizeDefault| |curveColor| |createNormalPrimitivePoly| - |stirling1| |diagonalMatrix| |getZechTable| |duplicates?| - |minimumDegree| |factorSquareFreeByRecursion| |alternatingGroup| - |radicalSolve| |scripted?| |normalizeAtInfinity| |listConjugateBases| - |karatsubaOnce| |powmod| |substring?| |limitedIntegrate| |randomLC| - |pow| |OMgetEndError| |setStatus| |rightGcd| |complexNormalize| - |factorList| |f02aef| |delete!| |cAcosh| |HenselLift| |mapMatrixIfCan| - |exQuo| |divisors| |diag| |ode| |OMUnknownCD?| |setButtonValue| - |lambda| |reducedSystem| |c05pbf| |complexExpand| |suffix?| - |firstSubsetGray| |call| |doubleComplex?| |patternVariable| - |cyclicGroup| |fintegrate| |explicitlyEmpty?| |usingTable?| |expt| - |resize| |push| |isPlus| |rk4| |super| |totalDifferential| - |definingInequation| |printCode| |testModulus| |perfectSqrt| |slash| - |fTable| |paren| |lo| |f02wef| |imagK| |iidprod| EQ |rootPoly| |lfunc| - |linearMatrix| |sequences| |select!| |thetaCoord| |iiacsc| |s17dhf| - |OMgetVariable| |patternMatch| |taylorRep| |monicCompleteDecompose| - |sizePascalTriangle| |integral| |hessian| |hdmpToDmp| |column| - |principalIdeal| |fill!| |leftExtendedGcd| |OMputBVar| |cotIfCan| - |selectfirst| |integralAtInfinity?| |dn| |f04mbf| |wholeRadix| |merge| - |is?| |normal01| |arg1| |att2Result| - |removeIrreducibleRedundantFactors| |reorder| |getCurve| |setOrder| - |selectFiniteRoutines| |rspace| |colorDef| |operators| |externalList| - |arg2| |copyInto!| |cSech| |expenseOfEvaluation| |addMatchRestricted| - |sqfrFactor| |index| |lcm| |An| |useEisensteinCriterion| |palgRDE| - |identitySquareMatrix| |minPoints| |figureUnits| |modularGcdPrimitive| - |maxint| |acothIfCan| |highCommonTerms| |polar| |divisorCascade| - |changeMeasure| |selectODEIVPRoutines| |RemainderList| |conditions| - |zeroOf| |companionBlocks| |frobenius| |child?| |errorInfo| |write!| - |append| |revert| |headAst| |lquo| |dimensionsOf| |oddintegers| - |match| |delete| |genericRightTrace| |OMmakeConn| |specialTrigs| - |indicialEquation| |pair| |completeSmith| |safetyMargin| |supersub| - |gcd| |squareFreePolynomial| |aLinear| |OMputEndBVar| |permutations| - |value| |result| |modulus| |purelyAlgebraicLeadingMonomial?| |eq?| - |increase| |addiag| |UpTriBddDenomInv| |false| |dihedral| - |getProperty| |kroneckerDelta| |headRemainder| |initials| |zoom| - |leftRankPolynomial| |Is| |clearTable!| |magnitude| |swap!| |sign| - |df2mf| |sdf2lst| |matrixGcd| |halfExtendedResultant2| |reset| - |leadingCoefficientRicDE| |closeComponent| |move| |cSin| |iisqrt2| - |symbolTableOf| |solveLinear| |polygamma| |UnVectorise| - |symmetricGroup| |positiveRemainder| |fractionFreeGauss!| - |genericRightNorm| |d02bbf| |imaginary| |getPickedPoints| |acotIfCan| - |uniform| |s17agf| |write| |tanNa| |currentScope| |loopPoints| - |internalAugment| |constantOperator| |getSyntaxFormsFromFile| |box| - |#| |compiledFunction| |atanhIfCan| |algebraicVariables| |tree| - |mkcomm| |save| |factorSquareFree| |credPol| |f02fjf| - |separateDegrees| |componentUpperBound| |digamma| |controlPanel| - |hexDigit?| |exactQuotient!| |infinityNorm| |dec| |f02akf| - |degreePartition| |minPoints3D| |linGenPos| |d01asf| |putColorInfo| - |mainExpression| |dualSignature| |setTopPredicate| |primeFactor| - |asinIfCan| |extract!| |genericLeftMinimalPolynomial| - |minimumExponent| |PollardSmallFactor| |oblateSpheroidal| |subHeight| - |dequeue| |upDateBranches| |jordanAdmissible?| |parent| |duplicates| - |normFactors| |curryLeft| |physicalLength!| |yCoordinates| - |leftMinimalPolynomial| |complexZeros| |currentSubProgram| - |setProperties!| |denomLODE| |integralDerivationMatrix| |twist| - |LazardQuotient2| |precision| |subCase?| |getMultiplicationMatrix| - |hostPlatform| |dfRange| |deepestInitial| |antiAssociative?| - |normalElement| |OMclose| |c02agf| |c06gbf| |positiveSolve| - |charClass| |tanintegrate| |degreeSubResultantEuclidean| |cfirst| - |generator| |mainVariable| |internalIntegrate| |preprocess| - |drawToScale| |midpoints| |quote| |comment| |f01qdf| |divisor| |red| - |fortranComplex| |minRowIndex| |log10| |boundOfCauchy| |algebraic?| - |complex?| |wordInStrongGenerators| |euler| |mainCoefficients| |size?| - |fortranInteger| |unravel| |primintfldpoly| |bitand| |lepol| |f01rcf| - |setAttributeButtonStep| |prem| |level| |empty?| |solve1| |e01sbf| - |monomRDE| |pop!| |bitior| |constantKernel| |s15aef| |mkPrim| |e02ajf| - |merge!| |irreducibleRepresentation| |satisfy?| |rightFactorIfCan| - |palgextint| |repeating?| |wrregime| |traverse| |interpolate| - |LiePolyIfCan| |squareMatrix| |zCoord| |checkForZero| - |raisePolynomial| |arbitrary| |pack!| |traceMatrix| |abelianGroup| - |midpoint| F |mesh?| |increment| |critpOrder| |rightNorm| - |primextendedint| |extractBottom!| |SturmHabichtCoefficients| |iitanh| - |quasiRegular?| |generalSqFr| |open| |particularSolution| |polyPart| - |matrix| |triangulate| |numer| |intPatternMatch| |removeSquaresIfCan| - |search| |d01gaf| |nthFactor| |isobaric?| |quadraticForm| - |countRealRootsMultiple| |repeatUntilLoop| |null| |ddFact| |denom| - |fortran| |prime?| |factorPolynomial| |sech2cosh| - |numberOfPrimitivePoly| |cTanh| |stopMusserTrials| |simpson| - |euclideanNormalForm| |nullary| |rootNormalize| |getCode| - |rowEchLocal| |semiResultantEuclidean2| |not| |linSolve| - |structuralConstants| |clearTheIFTable| |selectOptimizationRoutines| - |schwerpunkt| |deepExpand| |rangePascalTriangle| |and| |pair?| - |atanIfCan| |bumptab1| |members| |implies| |permanent| |operations| - |OMlistSymbols| |firstNumer| |string?| |OMlistCDs| |or| |imagJ| - |categories| |OMgetBind| |lazyPseudoDivide| |cyclicEqual?| |trunc| - |mapCoef| |any| |rowEchelon| |prinb| |stFunc2| |elColumn2!| |xor| - |listLoops| |rst| |semiDiscriminantEuclidean| |permutation| |badNum| - |frst| |systemSizeIF| |solid?| |absolutelyIrreducible?| |setnext!| - |transpose| |case| |genus| |cosh2sech| |integralCoordinates| |ran| - |reopen!| |mpsode| |Zero| |conditionP| |readLine!| |external?| FG2F - |critT| |f02bbf| |sort!| |shift| |e04naf| |OMbindTCP| - |firstUncouplingMatrix| |leftUnit| |rightRecip| |One| |s19acf| - |rightExactQuotient| |f01mcf| |OMputEndAttr| |f2df| |coerce| - |bezoutMatrix| Y |npcoef| |tanh2coth| |byteBuffer| |one?| |zerosOf| - |showFortranOutputStack| |elliptic?| |primPartElseUnitCanonical!| - |outputFloating| |construct| |decrease| |curry| |cycles| |printHeader| - |inputOutputBinaryFile| |stopTable!| |setright!| |viewDeltaYDefault| - |bfEntry| |basisOfCentroid| |discreteLog| |eulerPhi| |antisymmetric?| - |basisOfCenter| |plotPolar| |fullPartialFraction| |setPredicates| - |sizeLess?| |leftAlternative?| |datalist| |extractIfCan| |evaluate| - |lazyIntegrate| |returnType!| |functionIsContinuousAtEndPoints| - |cSinh| |top| |tryFunctionalDecomposition?| |endSubProgram| - |extendedEuclidean| |lyndon?| |basisOfNucleus| - |genericRightMinimalPolynomial| |inc| |numberOfIrreduciblePoly| - |iiGamma| |lllp| |removeSinSq| |indicialEquationAtInfinity| - |resultantReduit| |f02axf| |imagE| |showSummary| |makeSin| - |linearPart| |imagj| |rightUnit| |viewThetaDefault| |sort| - |exponential| |simplifyLog| |high| |branchIfCan| |drawStyle| |obj| - |leadingSupport| |seriesSolve| |adjoint| |findConstructor| |Vectorise| - |continue| |e02def| |eyeDistance| |changeThreshhold| - |viewDeltaXDefault| |deepCopy| |showAttributes| |setref| |nthRoot| - |cache| |removeSinhSq| |concat!| |measure| |monicModulo| |imagi| - |tableau| |singular?| |compound?| |applyRules| |rank| - |polynomialZeros| |c06ecf| |real?| |linearDependenceOverZ| |rootSimp| - |norm| |list| |spherical| |B1solve| |measure2Result| |idealiser| - |consnewpol| |digit?| |collect| |isNot| - |rewriteIdealWithHeadRemainder| |groebnerFactorize| |sinh2csch| - |random| |car| |iicos| |presuper| |c06fqf| |createRandomElement| - |getBadValues| |mapGen| |bfKeys| |mainValue| |fmecg| |resultant| |cdr| - |zag| |mathieu24| |doubleFloatFormat| |buildSyntax| |makeSUP| - |mightHaveRoots| |orbit| |reduceLODE| |sinhcosh| |xn| |d02raf| - |setDifference| |subst| |c06ebf| |scan| |name| |c06frf| |rootOf| - |zeroDimPrime?| |isConnected?| |ODESolve| |factorsOfCyclicGroupSize| - |lazyGintegrate| |position!| |mathieu11| |setIntersection| - |irreducibleFactor| |besselK| |body| |toScale| |factorSFBRlcUnit| - |selectIntegrationRoutines| |nthExponent| |subNode?| |inHallBasis?| - |length| |bsolve| |isOr| |setUnion| |toroidal| |e02agf| - |clipPointsDefault| |moebius| |central?| |remove| |copy!| |scripts| - |selectAndPolynomials| |setrest!| |coerceListOfPairs| |rischDEsys| - |apply| |octon| |cyclicEntries| |mapExponents| |makeCrit| |iisqrt3| - |lists| |coleman| |semiSubResultantGcdEuclidean2| |coefficient| - |ranges| |constantLeft| |ref| |viewport2D| |leftRegularRepresentation| - |youngGroup| |exprHasLogarithmicWeights| |last| |SFunction| |formula| - |e02gaf| |lprop| |corrPoly| |composites| |size| |localReal?| - |setLegalFortranSourceExtensions| |swapColumns!| |commonDenominator| - |subNodeOf?| |assoc| |droot| |fortranTypeOf| |output| |simplifyExp| - |denomRicDE| |unrankImproperPartitions1| |primes| |maxColIndex| - |objects| |interval| |rename| |unvectorise| |leftUnits| - |constantToUnaryFunction| |nthFlag| |extendedIntegrate| - |cyclePartition| |colorFunction| |base| |userOrdered?| - |nextPrimitiveNormalPoly| |evenlambert| |cSec| |qelt| |laurentIfCan| - |nthFractionalTerm| |components| |OMencodingXML| |schema| |first| - |complexLimit| |front| |unaryFunction| |ScanRoman| |OMconnInDevice| - |qsetelt| |brillhartTrials| |thenBranch| |prinpolINFO| |nrows| - |vconcat| |deriv| |rest| |basisOfCommutingElements| |noLinearFactor?| - |polarCoordinates| |rdHack1| |leftQuotient| |xRange| |setRow!| - |coth2tanh| |OMgetString| |ncols| |linkToFortran| |OMopenFile| - |substitute| |iterationVar| |showIntensityFunctions| |lieAlgebra?| - |genericLeftTrace| |degreeSubResultant| |yRange| |rootPower| - |viewPhiDefault| |qualifier| |unary?| |degree| |removeDuplicates| - |setRealSteps| |rationalApproximation| |triangular?| |makeViewport3D| - |rarrow| |zRange| |minrank| |monomialIntPoly| |collectUnder| - |exportedOperators| |shiftRight| |listRepresentation| |fractionPart| - |forLoop| |createIrreduciblePoly| |maxPoints| |next| |map!| - |whileLoop| |rotate| |nodeOf?| |replace| BY |powern| |plus!| - |hasTopPredicate?| |linears| |whatInfinity| |setLabelValue| |qsetelt!| - |iicoth| |OMgetEndAtp| |discriminantEuclidean| |leaves| |dictionary| - |s17adf| |sin2csc| |viewpoint| |eigenvalues| |OMsend| F2FG |scopes| - |paraboloidal| |halfExtendedSubResultantGcd2| |OMputAtp| |realZeros| - |initializeGroupForWordProblem| |monomial?| |subtractIfCan| - |axesColorDefault| |c06fpf| |applyQuote| |parametersOf| |BasicMethod| - |OMconnectTCP| |lowerPolynomial| |setchildren!| |content| - |monicRightFactorIfCan| |iiperm| |e02bbf| |refine| - |stiffnessAndStabilityFactor| |lfextlimint| |internalIntegrate0| - |univariatePolynomialsGcds| |radicalEigenvector| |epilogue| |isPower| - |elements| |recur| |stoseInvertibleSetsqfreg| |point| - |characteristicSerie| |safeFloor| |pole?| |algebraicSort| - |SturmHabicht| |clearTheSymbolTable| |iiacoth| |assign| |previous| - |ksec| |tensorProduct| |validExponential| |mainVariable?| |close!| - |acsch| |getProperties| |f04arf| |useSingleFactorBound?| |ruleset| - |contours| |internalInfRittWu?| |leadingIndex| |multiplyCoefficients| - |exponentialOrder| |prologue| |recip| NOT |isAbsolutelyIrreducible?| - |aromberg| |sinIfCan| |eisensteinIrreducible?| |headReduce| - |multinomial| |notelem| |mvar| |internalZeroSetSplit| |nextSublist| OR - |series| |changeName| |intermediateResultsIF| |computeInt| |factorset| - |quasiAlgebraicSet| |rotatex| |represents| |capacity| |exactQuotient| - |gbasis| AND |compdegd| |OMputError| |probablyZeroDim?| |suchThat| - |just| |nextPrime| |OMputEndError| |phiCoord| |Ci| |expint| |sec2cos| - |associatedSystem| |calcRanges| |stronglyReduced?| |getGraph| - |musserTrials| |prefix?| |arguments| |top!| |fortranLogical| |rk4a| - |monicRightDivide| |setMaxPoints| |semiSubResultantGcdEuclidean1| - |cAsech| |cycleElt| |equiv| |ScanArabic| |setClosed| - |squareFreeLexTriangular| |normalize| |fixedDivisor| |incr| |iisinh| - |legendre| |min| |enqueue!| |showAll?| |expandLog| |swap| |makeSeries| - |failed?| |csc2sin| |newTypeLists| |setVariableOrder| - |quasiMonicPolynomials| |inGroundField?| |prindINFO| |unknownEndian| - |complete| |nextsubResultant2| |complexElementary| |graphImage| - |cschIfCan| |leadingBasisTerm| |hi| |monicDecomposeIfCan| |edf2efi| - |realRoots| |curve?| |identification| |jacobian| |bumprow| |subMatrix| - |separate| |reciprocalPolynomial| |critM| |partitions| |powers| - |critBonD| |fortranCompilerName| |rightRank| |basisOfLeftAnnihilator| - |halfExtendedResultant1| |char| |indicialEquations| |d03edf| - |OMputBind| |FormatArabic| |asechIfCan| |showTheSymbolTable| |more?| - |setFormula!| |makeop| |e02dcf| |euclideanGroebner| - |rightAlternative?| |mainForm| |slex| |pseudoRemainder| |e01bff| - |infix?| |bag| |plusInfinity| |directory| |readByte!| |elRow2!| UP2UTS - |trapezoidalo| |pointLists| |minPoly| |clearFortranOutputStack| |mask| - |extensionDegree| |f02awf| |constantCoefficientRicDE| |minusInfinity| - |integralBasisAtInfinity| |possiblyNewVariety?| |expextendedint| - |supRittWu?| |setFieldInfo| * |compBound| |entries| |quoted?| |f01brf| - |lineColorDefault| |print| |toseLastSubResultant| - |rightMinimalPolynomial| |condition| |cubic| |uniform01| - |quotedOperators| |getIdentifier| |rem| |expintfldpoly| - |uncouplingMatrices| |normInvertible?| |separateFactors| |OMserve| - |resolve| |numFunEvals3D| |elementary| - |removeRoughlyRedundantFactorsInContents| |maxRowIndex| |eigenvectors| - |Lazard| |constant| |quo| |cPower| |float| |mapUnivariate| - |symmetricDifference| |bipolar| |mapmult| |e02aef| |positive?| - |double?| |removeZero| |leftTrace| |iprint| |chineseRemainder| = - |startPolynomial| |OMputSymbol| |cap| |symmetricSquare| |padecf| - |selectsecond| |stirling2| |setScreenResolution3D| |div| - |mainCharacterization| |torsion?| |commaSeparate| |nullary?| |e01bgf| - |fillPascalTriangle| |geometric| |iiacos| |type| |OMputApp| - |var1StepsDefault| |sin?| |llprop| |updatD| |exquo| < |upperCase!| - |f04atf| |viewPosDefault| |leftMult| |bandedHessian| |setProperty| ~= - |tValues| |idealSimplify| > |viewport3D| |orthonormalBasis| |sn| - |primextintfrac| |radicalSimplify| |point?| |e01bef| |fprindINFO| - |f01bsf| |enterPointData| ~ |e01daf| <= |mainVariables| |testDim| - |var2StepsDefault| |light| |aCubic| |prinshINFO| |setClipValue| - |cyclotomic| |partition| >= |dmpToP| |generalInfiniteProduct| |parts| - |setleaves!| |OMgetFloat| |minColIndex| |empty| |aQuadratic| - |palgintegrate| |f02agf| |hypergeometric0F1| |atoms| |Beta| - |genericPosition| |showTheRoutinesTable| |writable?| - |rightRegularRepresentation| |cardinality| |genericRightDiscriminant| - |generateIrredPoly| |status| |palginfieldint| |/\\| - |expressIdealMember| |collectUpper| |varList| GE |besselI| |bumptab| - |minGbasis| |cCosh| |\\/| |s17acf| |wronskianMatrix| - |leftExactQuotient| |hspace| + |algebraicCoefficients?| |isTimes| GT - |doubleRank| |irreducible?| |d01alf| |setleft!| |const| UTS2UP - |groebnerIdeal| |defineProperty| - |addPoint| |OMputString| LE - |totalGroebner| |getVariableOrder| |pushFortranOutputStack| |lighting| - |tracePowMod| |range| |commutative?| |hasoln| / |innerSolve| LT - |outputFixed| |extension| |showTypeInOutput| |popFortranOutputStack| - |leftZero| |factorsOfDegree| |resultantEuclideannaif| |constant?| - |sturmSequence| |sylvesterSequence| |roman| |palgRDE0| |setValue!| - |compile| |outputAsFortran| |initiallyReduce| |strongGenerators| - |invertible?| |mapSolve| |recolor| |tRange| |limitedint| |coshIfCan| - |jordanAlgebra?| |power!| |retract| |exprex| |contractSolve| - |BumInSepFFE| |radicalEigenvectors| |OMconnOutDevice| - |showArrayValues| |inR?| |setCondition!| |s15adf| |knownInfBasis| - |maxdeg| |transform| |graeffe| |cycleRagits| |any?| |OMsetEncoding| - |rk4qc| |acosIfCan| |property| |mathieu12| |iiacosh| |karatsubaDivide| - |pdct| |readable?| |invmultisect| |predicates| |pointPlot| |pushdterm| - |zero?| |pushdown| |balancedFactorisation| |groebner| |nthCoef| - |iiatan| |trigs| |PDESolve| |splitDenominator| |ef2edf| |lexico| - |perfectNthRoot| |hMonic| |OMwrite| |digit| |readInt32!| - |bezoutDiscriminant| |semicolonSeparate| |null?| |printStats!| |units| - |LowTriBddDenomInv| |complexEigenvalues| |readIfCan!| - |partialNumerators| |root?| |definingPolynomial| - |removeRedundantFactors| |startTableGcd!| |rightFactorCandidate| - |froot| |middle| |processTemplate| |basisOfRightNucloid| |omError| - |reducedContinuedFraction| |conical| |jacobi| |edf2df| |s17def| |sup| - |upperCase| |normalizedAssociate| |simplifyPower| |e04mbf| |number?| - |lazyIrreducibleFactors| |primlimintfrac| |normalise| |primintegrate| - |cAcsc| |reverse| |plus| |clearCache| |findCycle| |setLength!| - |quasiComponent| |radicalOfLeftTraceForm| |mapdiv| |univariateSolve| - |nextNormalPoly| |remainder| |sample| |addBadValue| |moduleSum| - |s01eaf| |changeBase| |putGraph| |readUInt8!| |integerIfCan| - |subresultantVector| |binaryFunction| |finiteBound| - |internalSubPolSet?| |divergence| |removeSuperfluousCases| |gensym| - |closed?| |code| |coordinates| |indices| |s18adf| |e02akf| - |modifyPointData| |superscript| |powerAssociative?| |decomposeFunc| - |certainlySubVariety?| |getOperands| |evenInfiniteProduct| |vector| - |bright| |superHeight| |odd?| |leftNorm| |comp| |simpleBounds?| - |times| |toseInvertible?| |hitherPlane| |readBytes!| |airyAi| - |brillhartIrreducible?| |differentiate| |dot| |initial| |cAtan| - |approxNthRoot| |minPol| |multMonom| |modifyPoint| |iipow| - |restorePrecision| |lexTriangular| |kovacic| |reverseLex| |overlap| - |palglimint0| |nthr| |function| |s18acf| |removeConstantTerm| - |initiallyReduced?| |basisOfLeftNucleus| |OMencodingBinary| |tube| - |padicFraction| |showRegion| |stoseInvertible?| |connect| |mainKernel| - |c06gqf| |sortConstraints| |increasePrecision| |complexRoots| |failed| - |maxPoints3D| |component| |makeUnit| |connectTo| |monom| |eval| - |iiexp| |less?| |dom| |resultantnaif| |cCos| |exprToGenUPS| - |setOfMinN| |f04adf| |sylvesterMatrix| |wordInGenerators| - |adaptive3D?| |rule| |trailingCoefficient| |csch2sinh| - |setMaxPoints3D| |f07adf| |parseString| |identityMatrix| - |createLowComplexityNormalBasis| |bytes| |categoryFrame| |elliptic| - |indiceSubResultant| |deref| |infRittWu?| |expintegrate| |rightLcm| - |isEquiv| |bit?| |common| |possiblyInfinite?| |normalDenom| - |writeUInt8!| |rootSplit| |parabolic| |splitNodeOf!| |inverseColeman| - |neglist| |leftFactorIfCan| |setPoly| |points| |makeFR| - |complexNumericIfCan| |completeHensel| |viewDefaults| |lagrange| - |OMputVariable| |associative?| |permutationRepresentation| |yCoord| - |numberOfOperations| |product| |complexEigenvectors| |movedPoints| - |doubleResultant| |removeRedundantFactorsInPols| |title| - |removeZeroes| |infinite?| |space| |oddlambert| |OMgetEndBVar| |expr| - |showTheFTable| |Frobenius| |bitTruth| |perfectNthPower?| |makeCos| - |pmintegrate| |explogs2trigs| |quickSort| |prod| |prepareSubResAlgo| - |insertRoot!| |factorAndSplit| |cAcot| |explicitEntries?| |leaf?| - |OMgetEndAttr| |twoFactor| |inverseIntegralMatrixAtInfinity| - |mathieu22| |clipBoolean| |mapBivariate| |createNormalElement| - |derivationCoordinates| |rightTraceMatrix| |writeBytes!| |e| - |cycleEntry| |factorial| |tryFunctionalDecomposition| |computeBasis| - |iitan| |unmakeSUP| |aQuartic| |birth| |complementaryBasis| - |rightExtendedGcd| |multiEuclideanTree| |linearPolynomials| - |setPrologue!| |radicalEigenvalues| |variable| |extractTop!| |true| - |parabolicCylindrical| |computePowers| |lintgcd| |exponential1| - |linear| |principal?| |ReduceOrder| |pointColorDefault| |d02bhf| - |iterators| |reduceByQuasiMonic| |escape| |iiasinh| - |rightCharacteristicPolynomial| |getExplanations| |nothing| - |stripCommentsAndBlanks| |lastSubResultantEuclidean| |polygon?| - |create| |useNagFunctions| |d01apf| |rk4f| |acschIfCan| |extractIndex| - |polynomial| |iflist2Result| |d02kef| |dimension| |representationType| - |factorOfDegree| |signAround| |init| |csubst| - |tableForDiscreteLogarithm| |rename!| |deleteProperty!| - |multiEuclidean| |tanIfCan| |discriminant| - |generalizedContinuumHypothesisAssumed| |OMUnknownSymbol?| - |completeEval| |getRef| |ip4Address| |OMgetBVar| |dominantTerm| - |algSplitSimple| |complexSolve| |subResultantsChain| |primitive?| - |secIfCan| |s17aef| |OMencodingUnknown| |primitiveElement| - |rectangularMatrix| |keys| |roughBase?| |symmetricProduct| |cscIfCan| - |unitNormalize| |ellipticCylindrical| |updatF| |e01sff| - |shallowExpand| |relativeApprox| |properties| |romberg| - |toseSquareFreePart| |numberOfImproperPartitions| |rightQuotient| - |width| |appendPoint| |d01akf| |extendedResultant| |padicallyExpand| - |flexibleArray| |unitNormal| |translate| |perspective| |s21bcf| - |makingStats?| |check| |operation| |physicalLength| |s14abf| - |setAdaptive3D| |Gamma| |cCsch| |argscript| |d01bbf| |comparison| - |push!| |OMputObject| |leftTraceMatrix| |fortranLinkerArgs| |UP2ifCan| - |coHeight| |pomopo!| |s19abf| |fixPredicate| |logGamma| |OMgetEndApp| - |goodPoint| |d01ajf| |nextSubsetGray| |bandedJacobian| |iiatanh| - |mesh| |fortranReal| |minimize| |overbar| |mergeFactors| |extend| - |ideal| |quotientByP| |bitCoef| |outputBinaryFile| |varselect| - |tubePoints| |trapezoidal| |conjug| |alternative?| |lflimitedint| - |s18def| |iiacsch| |subscript| |hex| |pascalTriangle| |getMatch| - |startTableInvSet!| |univariatePolynomials| |trigs2explogs| - |semiResultantEuclideannaif| |variationOfParameters| - |coercePreimagesImages| |fixedPoint| |alphanumeric| |e02bef| |solve| - |optional| |zeroVector| |opeval| |delay| |integralRepresents| - |polyRDE| |swapRows!| |antiCommutator| |asecIfCan| |approxSqrt| - |power| |innerEigenvectors| |triangSolve| |ratPoly| |binomThmExpt| - |lookup| |interpret| |s21bbf| |hdmpToP| |stack| |wreath| - |sumOfKthPowerDivisors| |integerBound| |badValues| |unit?| |routines| - |constDsolve| |qroot| |multisect| |decompose| |ratDsolve| |setColumn!| - |mainContent| |mainMonomial| |enumerate| |rightOne| |primeFrobenius| - |lazyPquo| |d02ejf| |tower| |isOpen?| |ParCond| |cLog| - |nextLatticePermutation| |numeric| |element?| |seriesToOutputForm| - |argumentListOf| |polyred| |key?| |e01bhf| |radicalRoots| |pquo| - |zeroSetSplitIntoTriangularSystems| |radical| |numberOfDivisors| - |dflist| |cAsin| |lfextendedint| |bubbleSort!| |dim| |chebyshevT| - |semiIndiceSubResultantEuclidean| |OMgetInteger| |charthRoot| - |denominators| |extractProperty| |outputForm| |f07fef| |inrootof| - |OMputEndBind| |completeHermite| |integer?| |polygon| SEGMENT - |changeNameToObjf| |rationalPoint?| |nil| |reverse!| - |differentialVariables| |stiffnessAndStabilityOfODEIF| |cycleSplit!| - |distFact| |nthRootIfCan| |tanh2trigh| |subscriptedVariables| - |cot2tan| |normalized?| |ricDsolve| |localUnquote| |LyndonCoordinates| - |complexNumeric| |s17akf| |radix| |fortranCarriageReturn| |iidsum| - |linear?| |nsqfree| |setEpilogue!| |gcdPolynomial| |parametric?| - |center| |weights| |leastAffineMultiple| |shrinkable| |makeEq| |hue| - |psolve| |approximate| |lllip| |kernels| |c02aff| |redmat| |head| - |iCompose| |mainMonomials| |complex| |plot| |c06gsf| |log| |cAsinh| - |setScreenResolution| |univariate| |integralMatrixAtInfinity| - |outputAsTex| |univariatePolynomial| |unitCanonical| |unexpand| - |eigenvector| |node| |fullDisplay| |solid| |bringDown| |c05nbf| - |besselJ| |trace2PowMod| |lowerCase?| |pseudoQuotient| - |LyndonWordsList| |before?| |lieAdmissible?| |retractable?| |erf| - |meshFun2Var| |leftDivide| |lazyPremWithDefault| |whitePoint| - |linearDependence| |leftDiscriminant| |totolex| |factor| |digits| - |invertibleElseSplit?| |numFunEvals| |binomial| |choosemon| - |numberOfFractionalTerms| |numberOfComputedEntries| |concat| - |integrate| |listOfMonoms| |e02adf| |sqrt| |basisOfRightNucleus| - |standardBasisOfCyclicSubmodule| |chiSquare| |createThreeSpace| - |bivariate?| |medialSet| |transcendentalDecompose| |leviCivitaSymbol| - |OMputInteger| |monomials| |dilog| |real| |meatAxe| |symbol?| - |createMultiplicationTable| |LazardQuotient| |viewZoomDefault| |qqq| - |tanAn| |rightDivide| |allRootsOf| |sin| |imag| |iiasech| - |characteristicSet| |saturate| |mantissa| |directProduct| - |normalizeIfCan| |associatorDependence| |log2| |direction| - |mindegTerm| |elRow1!| |cos| |option?| |rotate!| |pushNewContour| - |getOrder| |numberOfHues| |oddInfiniteProduct| |d01aqf| |s21bdf| - |e01sef| |tan| |OMread| |nthExpon| |split| |sparsityIF| |isTerm| - |zeroSquareMatrix| |palgint| |OMsupportsSymbol?| |divide| |brace| - |cot| |relerror| |makeSketch| |rootKerSimp| |callForm?| |rightUnits| - |getOperator| |stosePrepareSubResAlgo| |crest| |destruct| |sec| - |queue| |palgLODE0| |endOfFile?| |hconcat| |source| |tubeRadius| - |rootBound| |s18aff| |determinant| |bat1| |csc| |getButtonValue| - |binaryTree| |ldf2lst| |dark| |qPot| |stFunc1| |mappingAst| |f01qcf| - |taylorIfCan| |asin| |category| |OMgetError| |curryRight| |dmp2rfi| - |node?| |iibinom| |semiDegreeSubResultantEuclidean| |OMReadError?| - |infix| |equation| |squareFreeFactors| |acos| |domain| |internal?| - |screenResolution3D| |order| |lazyVariations| |outputMeasure| - |lazyEvaluate| |extractSplittingLeaf| |invertIfCan| |c06eaf| - |monomial| |atan| |package| |entry| |topPredicate| |fibonacci| - |bothWays| |logIfCan| |c06ekf| |halfExtendedSubResultantGcd1| - |intersect| |show| |expandPower| |cosSinInfo| |multivariate| |acot| - |sizeMultiplication| |subResultantGcdEuclidean| |incrementKthElement| - |pushup| |target| |scalarTypeOf| |quotient| |imagk| |diagonals| - |returnTypeOf| |variables| |asec| |invertibleSet| |s20adf| - |rewriteIdealWithQuasiMonicGenerators| |hclf| |realElementary| - |hermiteH| |semiLastSubResultantEuclidean| |blue| |quasiRegular| - |trace| |acsc| |edf2ef| |yellow| |bindings| |tab1| - |inverseIntegralMatrix| |rombergo| |palgint0| |OMgetType| |coord| - |sinh| |solveLinearPolynomialEquation| |reify| |makeVariable| |iicsch| - |cn| |s21baf| |diff| |polyRicDE| |quasiMonic?| - |selectMultiDimensionalRoutines| |cosh| |mainPrimitivePart| |sPol| - |terms| |alphabetic?| |ravel| |inspect| |intensity| |optpair| - |lazyResidueClass| |coefficients| |tanh| |cyclic?| |rightDiscriminant| - |baseRDEsys| |iifact| |summation| |reshape| |var1Steps| - |infieldIntegrate| |e02ddf| |OMParseError?| |coth| |taylor| |shuffle| - |in?| |negative?| |setprevious!| |palgLODE| |f04qaf| |member?| - |stoseLastSubResultant| |cyclicParents| |sech| |laurent| |setelt| - |isExpt| |cAcoth| |semiResultantReduitEuclidean| |mkAnswer| |rootsOf| - |nor| |iiasin| |inRadical?| |f01ref| |csch| |puiseux| - |transcendenceDegree| |separant| |minimalPolynomial| |setMinPoints3D| - |plenaryPower| |lambert| |OMputFloat| |OMsupportsCD?| |areEquivalent?| - |asinh| |copy| |ratDenom| |fortranDouble| |factorGroebnerBasis| - |split!| |conditionsForIdempotents| |groebSolve| |polCase| |pile| - |solveRetract| |inv| |acosh| |createMultiplicationMatrix| |xCoord| - |vectorise| |setTex!| |pleskenSplit| |update| |ground?| - |rationalIfCan| |contains?| |irreducibleFactors| |complexIntegrate| - |atanh| |decreasePrecision| |contract| |subset?| |extendIfCan| - |curveColorPalette| |tubePlot| |primitivePart| |ground| |logpart| - |d03faf| |acoth| |autoCoerce| |btwFact| |antiCommutative?| |s17dgf| - |removeRedundantFactorsInContents| |fortranCharacter| |lexGroebner| - |squareFreePart| |internalLastSubResultant| - |unrankImproperPartitions0| |leadingMonomial| |asech| |addPointLast| - |messagePrint| |region| |squareFree| |splitLinear| |normDeriv2| - |vspace| |gderiv| |mainSquareFreePart| |leadingCoefficient| - |finiteBasis| |makeprod| |sts2stst| |gcdcofact| |ramifiedAtInfinity?| - |unit| |maxIndex| |realEigenvectors| |setvalue!| |multiple| - |primitiveMonomials| |ffactor| |numericIfCan| |rationalPower| - |hostByteOrder| |position| |clearTheFTable| |cycleLength| |cross| - |complement| |removeRoughlyRedundantFactorsInPol| |readUInt32!| - |splitSquarefree| |supDimElseRittWu?| |say| |build| |outputAsScript| - |generalizedInverse| |imports| |color| |green| |outputArgs| - |FormatRoman| |singRicDE| |cycle| |match?| |ignore?| |kmax| - |Hausdorff| |ldf2vmf| |heap| |subTriSet?| |rationalPoints| |anticoord| - |fractRadix| |numberOfFactors| |evaluateInverse| |rur| |rightZero| - |e02zaf| |create3Space| |gcdcofactprim| |scale| |quartic| - |constantIfCan| |selectOrPolynomials| |subPolSet?| |addmod| - |SturmHabichtSequence| |find| |symmetricRemainder| |cAcos| |directSum| - |fractRagits| |scaleRoots| |cCoth| |rischNormalize| - |lastSubResultantElseSplit| |debug| |hash| |roughSubIdeal?| |df2ef| - |makeYoungTableau| |printInfo!| |identity| |listBranches| - |numberOfComposites| |intChoose| |lazyPseudoRemainder| |count| D - |double| |morphism| |modTree| |Lazard2| |cyclotomicDecomposition| - |nullSpace| |upperCase?| |ListOfTerms| |linearlyDependent?| - |newSubProgram| |realEigenvalues| |setProperty!| - |stoseInvertible?sqfreg| |countRealRoots| |every?| - |exteriorDifferential| |quadratic?| |cAtanh| |screenResolution| - |generalizedEigenvector| |exprHasWeightCosWXorSinWX| - |unitsColorDefault| |heapSort| |makeFloatFunction| |shiftRoots| - |monicDivide| |e02baf| |resetNew| |karatsuba| |lifting1| |e02bcf| - |readInt8!| |binarySearchTree| |shellSort| |imagI| |complexForm| - |collectQuasiMonic| |rowEchelonLocal| |pointColor| |exp1| |groebgen| - |createGenericMatrix| |alphanumeric?| |explicitlyFinite?| |index?| - |factors| |bernoulli| |safeCeiling| |dihedralGroup| |interactiveEnv| - |nextIrreduciblePoly| |matrixDimensions| |gcdPrimitive| - |commutativeEquality| |rquo| |gradient| |largest| |initTable!| |zero| - |euclideanSize| |aspFilename| |numerator| |ode1| |smith| |drawCurves| - |declare!| |sumOfSquares| |has?| |decimal| |exists?| |chvar| - |setImagSteps| |freeOf?| |OMputEndAtp| |predicate| |compose| - |pointColorPalette| |argument| |s13acf| |And| |noKaratsuba| |listexp| - GF2FG |stoseInvertible?reg| |character?| |constantRight| |s17dlf| - |selectSumOfSquaresRoutines| |writeInt8!| |Or| |logical?| |pr2dmp| - |finite?| |tanSum| |iisech| |s13adf| |exponents| |sncndn| |Not| - |generalTwoFactor| |e04jaf| |row| |rangeIsFinite| |normalForm| - |mkIntegral| |e02bdf| |cRationalPower| |lyndonIfCan| |se2rfi| - |rubiksGroup| |domainOf| |stoseSquareFreePart| |OMunhandledSymbol| - |wholePart| |overset?| |useEisensteinCriterion?| - |currentCategoryFrame| |operator| |symmetric?| - |selectNonFiniteRoutines| |bitLength| |setfirst!| |mirror| - |extractClosed| |extractPoint| |pseudoDivide| |minset| |subspace| - |f07fdf| |conjugate| |segment| |alphabetic| |OMgetApp| |prime| - |rightPower| |innerint| |SturmHabichtMultiple| |cup| |OMgetEndObject| - |rowEch| |child| |OMreadFile| |hexDigit| |insertTop!| |open?| - |flexible?| |parameters| |lowerCase| |nil?| |startStats!| |id| - |s19aaf| |goto| |entry?| |e04ucf| |bat| |ceiling| |sayLength| - |squareTop| |nand| |coerceL| |showClipRegion| |ord| |cTan| |pointData| - |root| |fixedPoints| |generic| |table| |completeEchelonBasis| - |basicSet| |unitVector| |countable?| |linearAssociatedExp| |new| - |weighted| |adaptive?| |univariate?| |s13aaf| |startTable!| - |bivariatePolynomials| |optAttributes| |nextNormalPrimitivePoly| - |loadNativeModule| |insert| |meshPar2Var| |bigEndian| |sub| - |combineFeatureCompatibility| |universe| |over| - |removeRoughlyRedundantFactorsInPols| |henselFact| |removeCoshSq| - |laplacian| |inverse| |derivative| |isAnd| |zeroSetSplit| |lowerCase!| - |options| |besselY| |iicot| |bracket| |anfactor| |f02aff| |even?| - |createPrimitiveNormalPoly| |randnum| |diagonal?| |pi| - |readLineIfCan!| |generalizedEigenvectors| |stFuncN| |bivariateSLPEBR| - |replaceKthElement| |genericRightTraceForm| |selectPolynomials| - |infinity| |linearlyDependentOverZ?| |groebner?| |retractIfCan| - |primlimitedint| |clikeUniv| |factor1| |monic?| |printStatement| - |fracPart| |module| |string| |mdeg| |virtualDegree| |subResultantGcd| - |f02ajf| |mapUnivariateIfCan| |sturmVariationsOf| |distdfact| |submod| - |fglmIfCan| |Ei| |times!| |sum| |ptree| |kernel| |toseInvertibleSet| - |sechIfCan| |cycleTail| |showScalarValues| - |solveLinearPolynomialEquationByRecursion| |acoshIfCan| |coerceS| - |graphState| |draw| |quatern| |gcdprim| |children| - |rootOfIrreduciblePoly| |vertConcat| |tanhIfCan| |idealiserMatrix| - |OMencodingSGML| |arrayStack| |edf2fi| |s17ajf| |left| |setErrorBound| - |factorByRecursion| |getConstant| |infiniteProduct| |resetBadValues| - |singleFactorBound| |isList| |rotatey| |right| |e01baf| - |showTheIFTable| |isQuotient| |oneDimensionalArray| |iomode| - |rightRemainder| |leadingExponent| - |rewriteSetByReducingWithParticularGenerators| |leftPower| |lp| - |associates?| |characteristicPolynomial| |debug3D| - |stoseInternalLastSubResultant| |makeObject| |typeLists| |ratpart| - |coefChoose| |chainSubResultants| |map| |totalLex| |interReduce| - |objectOf| |wordsForStrongGenerators| |setsubMatrix!| |newReduc| - |reseed| |var2Steps| |elt| |cyclic| |problemPoints| |adaptive| - |currentEnv| |regime| |d01amf| |HermiteIntegrate| |solveLinearlyOverQ| - |leftRecip| |coef| |diophantineSystem| |branchPoint?| - |changeWeightLevel| |rotatez| |quadratic| |useSingleFactorBound| - |outputGeneral| |bezoutResultant| |linearAssociatedLog| |OMgetAtp| - |splitConstant| |nil| |infinite| |arbitraryExponent| |approximate| - |complex| |shallowMutable| |canonical| |noetherian| |central| + |Record| |Union| |height| |inR?| |complexLimit| |s21bdf| + |splitConstant| |coordinate| |deleteProperty!| |quadraticForm| + |quadratic?| |isPlus| |setCondition!| |e01sef| |front| |lift| + |radPoly| |leftOne| |multiEuclidean| |countRealRootsMultiple| |cAtanh| + |convert| |s15adf| |rk4| |unaryFunction| |OMread| |reduce| + |subResultantChain| |cosIfCan| |repeatUntilLoop| |tanIfCan| + |screenResolution| |knownInfBasis| |totalDifferential| |ScanRoman| + |nthExpon| |symmetricPower| |fortranLiteralLine| |blankSeparate| + |ddFact| |discriminant| |generalizedEigenvector| |definingInequation| + |maxdeg| |OMconnInDevice| |split| |someBasis| |e02dff| + |generalizedContinuumHypothesisAssumed| |prime?| + |exprHasWeightCosWXorSinWX| |symbol| |printCode| |transform| + |brillhartTrials| |sparsityIF| |matrixConcat3D| |OMUnknownSymbol?| + |factorPolynomial| |unitsColorDefault| |expression| |graeffe| + |testModulus| |thenBranch| |isTerm| |f04faf| |completeEval| + |sech2cosh| |heapSort| |integer| |perfectSqrt| |cycleRagits| + |zeroSquareMatrix| |prinpolINFO| |rational?| |numberOfPrimitivePoly| + |getRef| |makeFloatFunction| |any?| |slash| |palgint| |vconcat| + |getGoodPrime| |ip4Address| |cTanh| |shiftRoots| |fTable| + |OMsetEncoding| |OMsupportsSymbol?| |deriv| |simplify| |getMeasure| + |stopMusserTrials| |OMgetBVar| |monicDivide| + |basisOfCommutingElements| |rk4qc| |paren| |inverseLaplace| |divide| + |declare| |shanksDiscLogAlgorithm| |simpson| |dominantTerm| |e02baf| + |f02wef| |acosIfCan| |noLinearFactor?| |relerror| |algSplitSimple| + |addMatch| |randomR| |euclideanNormalForm| |tail| |resetNew| |port| + |mathieu12| |imagK| |makeSketch| |polarCoordinates| |hyperelliptic| + |axes| |complexSolve| |nullary| |karatsuba| ** |iidprod| |iiacosh| + |rootKerSimp| |rdHack1| |byte| |cot2trig| |rootNormalize| + |subResultantsChain| |lifting1| |rootPoly| |callForm?| |t| + |outputList| |karatsubaDivide| |leftQuotient| |label| |rules| |error| + |clearDenominator| |getCode| |primitive?| |e02bcf| |lfunc| |pdct| + |setRow!| |rightUnits| |balancedBinaryTree| |unknown| |assert| + |rowEchLocal| |secIfCan| |readInt8!| |linearMatrix| |readable?| + |getOperator| |coth2tanh| |int| |leader| |hcrf| |s17aef| + |semiResultantEuclidean2| |binarySearchTree| |sequences| + |invmultisect| |OMgetString| |stosePrepareSubResAlgo| |beauzamyBound| + |linSolve| |OMencodingUnknown| |shellSort| |select!| |predicates| + |linkToFortran| |crest| |mindeg| |primitiveElement| + |structuralConstants| |imagI| |pointPlot| |thetaCoord| |OMopenFile| + |queue| |coerceP| |clearTheIFTable| |rectangularMatrix| |complexForm| + |iiacsc| |pushdterm| |iterationVar| |palgLODE0| |binaryTournament| + |reflect| |li| |roughBase?| |selectOptimizationRoutines| |constructor| + |collectQuasiMonic| |s17dhf| |zero?| |showIntensityFunctions| + |endOfFile?| |max| |littleEndian| |asinhIfCan| |schwerpunkt| + |symmetricProduct| |rowEchelonLocal| |option| |OMgetVariable| + |pushdown| |lieAlgebra?| |hconcat| |nonSingularModel| |deepExpand| + |cscIfCan| |pointColor| |balancedFactorisation| |patternMatch| + |tubeRadius| |genericLeftTrace| |dimensionOfIrreducibleRepresentation| + |unitNormalize| |rangePascalTriangle| |exp1| |groebner| |taylorRep| + |rootBound| |degreeSubResultant| |f04maf| |ellipticCylindrical| + |pair?| |groebgen| |checkPrecision| |nthCoef| |monicCompleteDecompose| + |rootPower| |s18aff| |dioSolve| |updatF| |atanIfCan| + |createGenericMatrix| |rightTrim| |iiatan| |sizePascalTriangle| + |determinant| |viewPhiDefault| |commutator| |e01sff| |bumptab1| + |alphanumeric?| |leftTrim| |parents| |integral| |trigs| |bat1| + |qualifier| |setMinPoints| |shallowExpand| |members| + |explicitlyFinite?| |hessian| |PDESolve| |getButtonValue| |unary?| + |fortranDoubleComplex| |implies| |relativeApprox| |index?| |hdmpToDmp| + |printInfo| |splitDenominator| |binaryTree| |degree| + |resultantReduitEuclidean| |romberg| |permanent| |factors| |test| + |ef2edf| |column| |setRealSteps| |ldf2lst| |drawComplexVectorField| + |OMlistSymbols| |toseSquareFreePart| |bernoulli| |lexico| + |principalIdeal| |rationalApproximation| |dark| + |exprHasAlgebraicWeight| |bombieriNorm| |firstNumer| + |numberOfImproperPartitions| |safeCeiling| |perfectNthRoot| |fill!| + |qPot| |triangular?| |binary| |modularGcd| |rightQuotient| |string?| + |dihedralGroup| |hMonic| |generate| |stFunc1| |leftExtendedGcd| + |close| |makeViewport3D| |eq| |laguerre| |appendPoint| |OMlistCDs| + |interactiveEnv| |kind| |OMputBVar| |OMwrite| |mappingAst| |rarrow| + |iter| |c06gcf| |d01akf| |prefix| |imagJ| |nextIrreduciblePoly| + |zeroDimensional?| |digit| |incrementBy| |f01qcf| |op| |minrank| + |cotIfCan| |pattern| |display| |flatten| |setProperties| + |extendedResultant| |OMgetBind| |matrixDimensions| |rCoord| + |readInt32!| |monomialIntPoly| |selectfirst| |taylorIfCan| |expand| + |padicallyExpand| |lazyPseudoDivide| |gcdPrimitive| + |bezoutDiscriminant| |integralAtInfinity?| |OMgetError| |collectUnder| + |filterWhile| |f04mcf| |flexibleArray| |cyclicEqual?| + |commutativeEquality| |exportedOperators| |dn| |semicolonSeparate| + |curryRight| |filterUntil| |OMputEndApp| |unitNormal| |trunc| |rquo| + |f04mbf| |message| |dmp2rfi| |null?| |select| |shiftRight| |cos2sec| + |mapCoef| |perspective| |gradient| |input| |listRepresentation| + |node?| |read!| |s21bcf| |symbolTable| |rowEchelon| |largest| |fi2df| + |union| |aQuadratic| |reductum| |iibinom| |library| |fractionPart| + |nextPrimitivePoly| |exp| |prinb| |makingStats?| |initTable!| + |palgintegrate| |multiset| |forLoop| |semiDegreeSubResultantEuclidean| + |infieldint| |check| |stFunc2| |euclideanSize| |f02agf| |hermite| + |createIrreduciblePoly| |OMReadError?| |numberOfNormalPoly| |style| + |aspFilename| |hypergeometric0F1| |truncate| |infix| |maxPoints| + |outerProduct| |laplace| |bitTruth| |preprocess| |checkRur| + |numerator| |cons| |lfinfieldint| |atoms| |whileLoop| |makeRecord| + |squareFreeFactors| |set| |computeCycleEntry| |drawToScale| + |perfectNthPower?| |postfix| |ode1| |d01anf| |Beta| |internal?| + |rotate| |genericLeftDiscriminant| |makeCos| |midpoints| |totalDegree| + |smith| |genericPosition| |inputBinaryFile| |crushedSet| |pmintegrate| + |quote| |pol| |drawCurves| |showTheRoutinesTable| |multiplyExponents| + |eigenvector| |nthExponent| |f04asf| |explogs2trigs| |f01qdf| + |charpol| |sumOfSquares| |writable?| |generic?| |fullDisplay| + |subNode?| |stop| |cAsec| |divisor| |quickSort| + |ScanFloatIgnoreSpaces| |has?| |rightRegularRepresentation| + |leadingIdeal| |solid| |inHallBasis?| |s17ahf| |prod| |red| |second| + |diagonal| |rightTrace| |cardinality| |setlast!| |bringDown| |bsolve| + |cyclotomicFactorization| |fortranComplex| |e02dcf| + |prepareSubResAlgo| |third| |indiceSubResultantEuclidean| |color| + |genericRightDiscriminant| |c05nbf| |e04dgf| |signature| |isOr| + |pureLex| |insertRoot!| |iicsc| |euclideanGroebner| |minRowIndex| + |horizConcat| |green| |generateIrredPoly| |s20acf| |toroidal| + |besselJ| |factorAndSplit| |iiabs| |rightAlternative?| |boundOfCauchy| + |outputArgs| |factorFraction| |palginfieldint| |compactFraction| + |trace2PowMod| |e02agf| |reduction| |lhs| |resetVariableOrder| |cAcot| + |algebraic?| |FormatRoman| |mainForm| |lowerCase?| + |expressIdealMember| |dequeue!| |clipPointsDefault| |optimize| + |rootOfIrreduciblePoly| |complex?| |reducedDiscriminant| |rhs| + |explicitEntries?| |normalizedDivide| |singRicDE| |slex| + |algintegrate| |moebius| |collectUpper| |pseudoQuotient| |void| + |vertConcat| |exponent| |f04axf| |wordInStrongGenerators| |leaf?| + |cycle| |pseudoRemainder| |central?| |besselI| |nextItem| + |LyndonWordsList| |systemCommand| |tanhIfCan| |partialDenominators| + |ignore?| |innerSolve1| |OMgetEndAttr| |euler| |e01bff| |OMreadStr| + |lfintegrate| |copy!| |bumptab| |before?| |script| |idealiserMatrix| + |bag| |accuracyIF| |purelyAlgebraic?| |mainCoefficients| |twoFactor| + |tanQ| |kmax| |sequence| |minGbasis| |transcendent?| |lieAdmissible?| + |selectAndPolynomials| |OMencodingSGML| |size?| |basisOfLeftNucloid| + |inverseIntegralMatrixAtInfinity| |readInt16!| |readByte!| |Hausdorff| + |Nul| |cCosh| |retractable?| |primPartElseUnitCanonical| |setrest!| + |normal| |arrayStack| |ldf2vmf| |partialFraction| |fortranInteger| + |mathieu22| |critB| |elRow2!| |drawComplex| |meshFun2Var| |s17acf| + |coerceListOfPairs| |tex| |edf2fi| |key| |basisOfMiddleNucleus| + |unravel| |redpps| |clipBoolean| |heap| |mr| UP2UTS |singularitiesOf| + |wronskianMatrix| |leftDivide| |rischDEsys| |s17ajf| |mapBivariate| + |shallowCopy| |primintfldpoly| |mergeDifference| |trapezoidalo| + |subTriSet?| |octon| |leftExactQuotient| |prefixRagits| + |lazyPremWithDefault| |delta| |setErrorBound| |filename| |numerators| + |depth| |headReduced?| |createNormalElement| |lepol| |rationalPoints| + |pointLists| |cond| |hspace| |repeating| |whitePoint| |cyclicEntries| + |factorByRecursion| |minPoly| |getlo| |derivationCoordinates| |f01rcf| + |anticoord| |remove!| |extendedSubResultantGcd| + |algebraicCoefficients?| |mapExponents| |linearDependence| + |getConstant| |parse| |setAttributeButtonStep| |insertBottom!| + |clearFortranOutputStack| |rightTraceMatrix| |minIndex| |fractRadix| + |isTimes| |pointSizeDefault| |leftDiscriminant| |makeCrit| + |infiniteProduct| |reducedQPowers| |numberOfFactors| |writeBytes!| + |prem| |extensionDegree| |roughUnitIdeal?| |doubleRank| |curveColor| + |iisqrt3| |totolex| |resetBadValues| |f02awf| |numberOfComponents| + |empty?| |cycleEntry| |evaluateInverse| |roughBasicSet| |irreducible?| + |createNormalPrimitivePoly| |digits| |coleman| |substring?| + |singleFactorBound| |factorial| |bits| |solve1| + |constantCoefficientRicDE| |rur| |prevPrime| |stirling1| |d01alf| + |semiSubResultantGcdEuclidean2| |invertibleElseSplit?| |isList| + |alternating| |isOp| |tryFunctionalDecomposition| |e01sbf| |rightZero| + |integralBasisAtInfinity| |setleft!| |lambda| |numFunEvals| + |diagonalMatrix| |coefficient| |suffix?| |rotatey| |call| + |computeBasis| |curve| |e02zaf| |monomRDE| |possiblyNewVariety?| + |getDatabase| |getZechTable| |const| |ranges| |binomial| |e01baf| + |super| |iitan| |internalDecompose| |expextendedint| |pop!| + |create3Space| |moduloP| |duplicates?| |lo| UTS2UP |choosemon| + |constantLeft| |showTheIFTable| EQ |gcdcofactprim| + |factorSquareFreePolynomial| |constantKernel| |unmakeSUP| |supRittWu?| + |patternMatchTimes| |groebnerIdeal| |minimumDegree| + |numberOfFractionalTerms| |ref| |oneDimensionalArray| |basis| + |functionIsOscillatory| |setFieldInfo| |s15aef| |aQuartic| |scale| + |fixedPointExquo| |factorSquareFreeByRecursion| |defineProperty| + |numberOfComputedEntries| |viewport2D| |iomode| |po| |compBound| + |weierstrass| |mkPrim| |birth| |quartic| |eigenMatrix| |arg1| + |alternatingGroup| |addPoint| |leftRegularRepresentation| |integrate| + |rightRemainder| |f02bjf| |complementaryBasis| |e02ajf| |entries| + |constantIfCan| |arg2| |OMputString| |radicalSolve| |listOfMonoms| + |youngGroup| |leadingExponent| |index| |lcm| |difference| + |rightExtendedGcd| |merge!| |quoted?| |selectOrPolynomials| + |totalGroebner| |scripted?| |exprHasLogarithmicWeights| |e02adf| + |rewriteSetByReducingWithParticularGenerators| |cyclicCopy| + |multiEuclideanTree| |irreducibleRepresentation| |f01brf| |subPolSet?| + |conditions| |normalizeAtInfinity| |getVariableOrder| + |basisOfRightNucleus| |SFunction| |leftPower| |nonLinearPart| |append| + |KrullNumber| |satisfy?| |linearPolynomials| |addmod| + |lineColorDefault| |match| |delete| |listConjugateBases| |lighting| + |e02gaf| |standardBasisOfCyclicSubmodule| |associates?| |pair| + |outputSpacing| |inf| |gcd| |setPrologue!| |rightFactorIfCan| + |toseLastSubResultant| |SturmHabichtSequence| |value| |result| + |tracePowMod| |karatsubaOnce| |chiSquare| |lprop| + |characteristicPolynomial| |semiResultantEuclidean1| |false| + |palgextint| |radicalEigenvalues| |find| |rightMinimalPolynomial| + |range| |powmod| |corrPoly| |createThreeSpace| |debug3D| + |lastSubResultant| |extractTop!| |repeating?| |symmetricRemainder| + |cubic| |commutative?| |limitedIntegrate| |reset| |bivariate?| + |composites| |stoseInternalLastSubResultant| |socf2socdf| + |parabolicCylindrical| |wrregime| |cAcos| |uniform01| |randomLC| + |hasoln| |localReal?| |medialSet| |typeLists| |eof?| |computePowers| + |traverse| |directSum| |quotedOperators| |innerSolve| |pow| |write| + |setLegalFortranSourceExtensions| |transcendentalDecompose| |ratpart| + |getIdentifier| |integral?| |box| |#| |lintgcd| |interpolate| + |fractRagits| |tree| |save| |outputFixed| |OMgetEndError| + |leviCivitaSymbol| |swapColumns!| |coefChoose| |round| |exponential1| + |LiePolyIfCan| |scaleRoots| |expintfldpoly| |extension| |dec| + |setStatus| |OMputInteger| |commonDenominator| |chainSubResultants| + |htrigs| |principal?| |squareMatrix| |uncouplingMatrices| |cCoth| + |showTypeInOutput| |rightGcd| |monomials| |subNodeOf?| |totalLex| + |OMputEndObject| |zCoord| |ReduceOrder| |rischNormalize| + |normInvertible?| |leftZero| |complexNormalize| |droot| |meatAxe| + |interReduce| |mathieu23| |checkForZero| |pointColorDefault| + |separateFactors| |lastSubResultantElseSplit| |factorsOfDegree| + |factorList| |symbol?| |fortranTypeOf| |objectOf| |iisec| |precision| + |raisePolynomial| |d02bhf| |OMserve| |roughSubIdeal?| + |createMultiplicationTable| |f02aef| |resultantEuclideannaif| + |legendreP| |simplifyExp| |wordsForStrongGenerators| |arbitrary| + |tablePow| |df2ef| |reduceByQuasiMonic| |generator| |numFunEvals3D| + |delete!| |constant?| |denomRicDE| |LazardQuotient| |setsubMatrix!| + |escape| |tan2cot| |comment| |pack!| |elementary| |makeYoungTableau| + |log10| |cAcosh| |sturmSequence| |unrankImproperPartitions1| + |viewZoomDefault| |newReduc| |block| |iiasinh| |traceMatrix| + |removeRoughlyRedundantFactorsInContents| |printInfo!| |bitand| + |HenselLift| |sylvesterSequence| |primes| |qqq| |level| |reseed| + |rightCharacteristicPolynomial| |abelianGroup| |identity| + |maxRowIndex| |bitior| |mapMatrixIfCan| |roman| |maxColIndex| |tanAn| + |var2Steps| |isMult| |midpoint| |getExplanations| |eigenvectors| + |listBranches| |palgRDE0| |exQuo| |interval| |rightDivide| |cyclic| + |chiSquare1| |mesh?| |stripCommentsAndBlanks| |Lazard| + |numberOfComposites| |divisors| F |setValue!| |allRootsOf| |rename| + |problemPoints| |nextColeman| |increment| |lastSubResultantEuclidean| + |cPower| |intChoose| |iiasech| |unvectorise| |adaptive| |open| + |mapExpon| |critpOrder| |matrix| |numer| |polygon?| |mapUnivariate| + |lazyPseudoRemainder| |search| |chineseRemainder| |hasSolution?| + |leftUnits| |characteristicSet| |regime| |morphism| |integralMatrix| + |rightNorm| |denom| |create| |fortran| |null| |symmetricDifference| + |startPolynomial| |part?| |constantToUnaryFunction| |saturate| + |d01amf| |maxrow| |bipolar| |useNagFunctions| |primextendedint| + |modTree| |not| |taylorQuoByVar| |OMputSymbol| |nthFlag| + |normalizeIfCan| |HermiteIntegrate| |closedCurve?| |and| |Lazard2| + |mapmult| |cap| |coth2trigh| |associatorDependence| + |extendedIntegrate| |solveLinearlyOverQ| |operations| |realSolve| + |exprToGenUPS| |digamma| |cyclotomicDecomposition| |e02aef| |or| + |vark| |categories| |symmetricSquare| |log2| |cyclePartition| + |leftRecip| |weakBiRank| |any| |setOfMinN| |controlPanel| |nullSpace| + |positive?| |xor| |doublyTransitive?| |padecf| |colorFunction| + |direction| |diophantineSystem| |iisin| |hexDigit?| |f04adf| + |upperCase?| |double?| |case| |f07aef| |selectsecond| |branchPoint?| + |subresultantSequence| |sylvesterMatrix| |exactQuotient!| |Zero| + |ListOfTerms| |removeZero| |stirling2| |withPredicates| |singular?| + |OMgetInteger| |shift| |changeWeightLevel| |signatureAst| + |infinityNorm| |wordInGenerators| |leftTrace| |linearlyDependent?| + |One| |setScreenResolution3D| |airyBi| |charthRoot| |compound?| + |rotatez| |coerce| |bernoulliB| Y |f02akf| |adaptive3D?| |iprint| + |newSubProgram| |mainCharacterization| |symFunc| |applyRules| + |denominators| |quadratic| |construct| |degreePartition| |quoByVar| + |trailingCoefficient| |viewSizeDefault| |normalDeriv| |torsion?| + |polynomialZeros| |extractProperty| |useSingleFactorBound| + |approximants| |minPoints3D| |iteratedInitials| |csch2sinh| |cAsech| + |rationalIfCan| |elem?| |commaSeparate| |c06ecf| |outputForm| + |datalist| |outputGeneral| |integralBasis| |linGenPos| + |setMaxPoints3D| |cycleElt| |contains?| |top| |nullary?| |writeLine!| + |f07fef| |real?| |bezoutResultant| |inc| |intcompBasis| |d01asf| + |f07adf| |equiv| |irreducibleFactors| |e01bgf| |graphCurves| + |inrootof| |linearDependenceOverZ| |showSummary| |packageCall| + |putColorInfo| |parseString| |complexIntegrate| |ScanArabic| |sort| + |fillPascalTriangle| |makeTerm| |rootSimp| |OMputEndBind| + |removeRoughlyRedundantFactorsInPols| |obj| |OMreceive| + |identityMatrix| |mainExpression| |decreasePrecision| |setClosed| + |continue| |numberOfMonomials| |geometric| |norm| |completeHermite| + |henselFact| |partialQuotients| |dualSignature| + |createLowComplexityNormalBasis| |trim| |contract| |cache| + |showAttributes| |squareFreeLexTriangular| |iiacos| |mat| |spherical| + |integer?| |rank| |removeCoshSq| |functionIsFracPolynomial?| |bytes| + |setTopPredicate| |wholeRagits| |normalize| |subset?| |list| + |OMputApp| |arity| |B1solve| |polygon| |laplacian| |digit?| |e04fdf| + |categoryFrame| |primeFactor| |fixedDivisor| |extendIfCan| |random| + |car| |closedCurve| |var1StepsDefault| |changeNameToObjf| + |measure2Result| |inverse| |maxrank| |elliptic| |asinIfCan| + |curveColorPalette| |iisinh| |cdr| |sin?| |setStatus!| + |rationalPoint?| |idealiser| |derivative| |stopTableInvSet!| + |rational| |extract!| |indiceSubResultant| |tubePlot| |legendre| + |setDifference| |subst| |localAbs| |llprop| |name| |reverse!| + |consnewpol| |isAnd| |insert!| |leftGcd| + |genericLeftMinimalPolynomial| |deref| |enqueue!| |primitivePart| + |setIntersection| |convergents| |updatD| |body| + |differentialVariables| |collect| |zeroSetSplit| |minimumExponent| + |permutationGroup| |length| |infRittWu?| |logpart| |showAll?| + |setUnion| |totalfract| |upperCase!| |stiffnessAndStabilityOfODEIF| + |isNot| |lowerCase!| |remove| |PollardSmallFactor| |rootDirectory| + |expintegrate| |scripts| |d03faf| |expandLog| |apply| |f04atf| |low| + |rewriteIdealWithHeadRemainder| |cycleSplit!| |lists| |besselY| RF2UTS + |oblateSpheroidal| |rightLcm| |swap| |btwFact| |f02abf| + |viewPosDefault| |groebnerFactorize| |distFact| |iicot| |last| + |formula| |viewWriteDefault| |subHeight| |isEquiv| |antiCommutative?| + |makeSeries| |size| |leftMult| |pade| |nthRootIfCan| |sinh2csch| + |bracket| |assoc| |dequeue| |iiasec| |bit?| |output| |s17dgf| + |failed?| |bandedHessian| |findBinding| |objects| |iicos| |tanh2trigh| + |anfactor| |stoseInvertibleSet| |upDateBranches| |possiblyInfinite?| + |removeRedundantFactorsInContents| |csc2sin| |setProperty| |host| + |base| |subscriptedVariables| |presuper| |f02aff| |qelt| |newLine| + |jordanAdmissible?| |normalDenom| |fortranCharacter| |newTypeLists| + |first| |coerceImages| |tValues| |c06fqf| |cot2tan| |even?| |qsetelt| + |minordet| |writeUInt8!| |nrows| |parent| |lexGroebner| + |setVariableOrder| |rest| |OMcloseConn| |idealSimplify| + |createRandomElement| |normalized?| |createPrimitiveNormalPoly| + |xRange| |rootSplit| |removeDuplicates!| |duplicates| |ncols| + |quasiMonicPolynomials| |squareFreePart| |substitute| |OMgetSymbol| + |viewport3D| |ricDsolve| |getBadValues| |randnum| |yRange| |OMputAttr| + |parabolic| |normFactors| |internalLastSubResultant| |inGroundField?| + |removeDuplicates| |skewSFunction| |orthonormalBasis| |localUnquote| + |mapGen| |diagonal?| |zRange| |singularAtInfinity?| |curryLeft| + |splitNodeOf!| |prindINFO| |unrankImproperPartitions0| |sn| + |createPrimitivePoly| |bfKeys| |LyndonCoordinates| |readLineIfCan!| + |unknownEndian| |map!| |next| |laurentRep| |physicalLength!| + |inverseColeman| BY |addPointLast| |primextintfrac| |f02adf| |s17akf| + |mainValue| |generalizedEigenvectors| |qsetelt!| |clipWithRanges| + |neglist| |yCoordinates| |leaves| |messagePrint| |complete| + |radicalSimplify| |recoverAfterFail| |radix| |fmecg| |stFuncN| + |setPosition| |leftMinimalPolynomial| |leftFactorIfCan| + |nextsubResultant2| |region| |point?| |graphs| |fortranCarriageReturn| + |resultant| |bivariateSLPEBR| |complexZeros| |divideIfCan!| + |applyQuote| |setPoly| |complexElementary| |squareFree| |e01bef| + |s19adf| |iidsum| |zag| |replaceKthElement| |d02gaf| + |LagrangeInterpolation| |currentSubProgram| |points| |splitLinear| + |graphImage| |fprindINFO| |latex| |mathieu24| |linear?| + |genericRightTraceForm| |point| |factorials| |setProperties!| |back| + |makeFR| |monicLeftDivide| |normDeriv2| |cschIfCan| |previous| + |qfactor| |f01bsf| |nsqfree| |doubleFloatFormat| |selectPolynomials| + |acsch| |complexNumericIfCan| |stoseIntegralLastSubResultant| + |denomLODE| |ruleset| |leadingBasisTerm| |vspace| |f02xef| + |enterPointData| |buildSyntax| |setEpilogue!| NOT + |linearlyDependentOverZ?| |resetAttributeButtons| + |integralDerivationMatrix| |completeHensel| |gderiv| + |monicDecomposeIfCan| |groebner?| |e01daf| |numberOfCycles| + |gcdPolynomial| |makeSUP| OR |series| |ptFunc| |twist| |viewDefaults| + |edf2efi| |mainSquareFreePart| |mainVariables| |RittWuCompare| + |parametric?| |mightHaveRoots| |primlimitedint| AND + |linearAssociatedOrder| |LazardQuotient2| |lagrange| |suchThat| + |finiteBasis| |realRoots| |testDim| |denominator| |weights| |orbit| + |clikeUniv| |OMputVariable| |OMgetObject| |subCase?| |prefix?| + |makeprod| |curve?| |generalizedContinuumHypothesisAssumed?| + |arguments| |algint| |var2StepsDefault| |leastAffineMultiple| + |reduceLODE| |factor1| |makeViewport2D| |getMultiplicationMatrix| + |associative?| |identification| |sts2stst| |monomialIntegrate| + |perfectSquare?| |light| |incr| |shrinkable| |sinhcosh| |min| |monic?| + |s17dcf| |c05adf| |permutationRepresentation| |hostPlatform| + |gcdcofact| |jacobian| |cartesian| |aCubic| |xn| |makeEq| + |printStatement| |diagonalProduct| |ridHack1| |dfRange| |yCoord| + |ramifiedAtInfinity?| |bumprow| |pdf2df| |prinshINFO| |hi| |d02raf| + |hue| |fracPart| |clipSurface| |lyndon| |floor| |numberOfOperations| + |deepestInitial| |unit| |subMatrix| |setClipValue| |leastPower| + |c06ebf| |psolve| |module| |char| |removeSuperfluousQuasiComponents| + |cExp| |goodnessOfFit| |antiAssociative?| |product| |maxIndex| + |separate| |cyclotomic| |symmetricTensors| |lllip| |scan| |mdeg| + |asimpson| |reciprocalPolynomial| |nullity| |normalElement| + |complexEigenvectors| |realEigenvectors| |infix?| |directory| + |plusInfinity| |readUInt16!| |partition| |c02aff| |c06frf| + |virtualDegree| |surface| |cylindrical| |critM| |OMclose| + |movedPoints| |mask| |setvalue!| |minusInfinity| |dmpToP| |baseRDE| + |redmat| |rootOf| |subResultantGcd| * |enterInCache| |doubleResultant| + |exprToUPS| |ffactor| |c02agf| |print| |partitions| |condition| + |generalInfiniteProduct| |ode2| |zeroDimPrime?| |head| |f02ajf| |rem| + |janko2| |resolve| |f01maf| |c06gbf| |removeRedundantFactorsInPols| + |numericIfCan| |powers| |setleaves!| |mapUnivariateIfCan| |dimensions| + |iCompose| |isConnected?| |constant| |quo| |rewriteSetWithReduction| + |float| |removeZeroes| |positiveSolve| |critBonD| |rationalPower| + |f04jgf| |OMgetFloat| |ODESolve| |mainMonomials| |nilFactor| + |sturmVariationsOf| |d01gbf| = |charClass| |infinite?| + |fortranCompilerName| |hostByteOrder| |rootProduct| |minColIndex| + |factorsOfCyclicGroupSize| |plot| |distdfact| |div| |nary?| |orbits| + |space| |tanintegrate| |rightRank| |clearTheFTable| + |basisOfRightAnnihilator| |type| |LyndonBasis| |empty| |c06gsf| + |lazyGintegrate| |submod| |exquo| < |mix| + |degreeSubResultantEuclidean| |oddlambert| |basisOfLeftAnnihilator| + |cycleLength| |clip| |position!| |cAsinh| |fglmIfCan| ~= |univcase| > + |OMgetEndBVar| |cfirst| |halfExtendedResultant1| |cross| |critMTonD1| + |df2st| |mathieu11| |setScreenResolution| |Ei| ~ |lifting| <= + |showTheFTable| |mainVariable| |complement| |indicialEquations| + |torsionIfCan| |integralMatrixAtInfinity| |irreducibleFactor| |pdf2ef| + |times!| |d01fcf| >= |parts| |internalIntegrate| |Frobenius| |d03edf| + |removeRoughlyRedundantFactorsInPol| |getMultiplicationTable| + |outputAsTex| |besselK| |toseInvertibleSet| |moebiusMu| |leftFactor| + |readUInt32!| |OMputBind| |toScale| |genericLeftTraceForm| |indices| + |/\\| |univariatePolynomial| |status| |e04ycf| |sechIfCan| |modulus| + |removeCosSq| |varList| GE |splitSquarefree| |FormatArabic| |sqfree| + |unitCanonical| |\\/| |f02aaf| |factorSFBRlcUnit| |s18adf| |cycleTail| + |subSet| + |purelyAlgebraicLeadingMonomial?| GT |asechIfCan| + |supDimElseRittWu?| |atom?| |eq?| |selectIntegrationRoutines| + |unexpand| |quadraticNorm| |showScalarValues| |tab| - |e02akf| LE + |build| |showTheSymbolTable| |pushFortranOutputStack| |rightMult| + |increase| |powerSum| |solveLinearPolynomialEquationByRecursion| / + |printingInfo?| |modifyPointData| LT |outputAsScript| |more?| + |popFortranOutputStack| |associator| |zeroVector| |eulerPhi| + |acoshIfCan| |pastel| |seed| |addiag| |superscript| |setFormula!| + |generalizedInverse| |compile| |acscIfCan| |outputAsFortran| |opeval| + |antisymmetric?| |coerceS| |maximumExponent| |s17aff| + |powerAssociative?| |UpTriBddDenomInv| |imports| |retract| |makeop| + |presub| |basisOfCenter| |delay| |graphState| |writeByte!| + |selectPDERoutines| |dihedral| |decomposeFunc| |outlineRender| + |integralRepresents| |plotPolar| |quatern| |dAndcExp| |expPot| + |getProperty| |certainlySubVariety?| |alphabetic?| |ksec| |property| + |algebraicOf| |fullPartialFraction| |polyRDE| |gcdprim| + |squareFreePrim| |s18aef| |kroneckerDelta| |getOperands| |inspect| + |tensorProduct| |setAdaptive| |swapRows!| |setPredicates| |children| + |df2fi| |integers| |headRemainder| |evenInfiniteProduct| + |validExponential| |intensity| |biRank| |sizeLess?| |antiCommutator| + |normal?| |meshPar1Var| |superHeight| |initials| |optpair| + |mainVariable?| |units| |leadingTerm| |leftAlternative?| |asecIfCan| + |f07fdf| |limit| |OMopenString| |odd?| |zoom| |close!| + |lazyResidueClass| |rdregime| |leftLcm| |approxSqrt| |extractIfCan| + |conjugate| |repSq| |e04gcf| |leftNorm| |leftRankPolynomial| + |getProperties| |coefficients| |critMonD1| |mapDown!| |alphabetic| + |evaluate| |power| |simpleBounds?| |solveInField| |solveid| |reverse| + |plus| |eulerE| |Is| |clearCache| |f04arf| |cyclic?| |generators| + |innerEigenvectors| |lazyIntegrate| |harmonic| |OMgetApp| + |autoReduced?| |resultantEuclidean| |toseInvertible?| |clearTable!| + |rightDiscriminant| |useSingleFactorBound?| |mapUp!| |returnType!| + |triangSolve| |prime| |topFortranOutputStack| |shade| |magnitude| + |hitherPlane| |baseRDEsys| |contours| |code| |fortranLiteral| + |ratPoly| |functionIsContinuousAtEndPoints| |rightPower| + |lazyPseudoQuotient| |float?| |readBytes!| |swap!| |iifact| + |internalInfRittWu?| |constantOpIfCan| |vector| |bright| + |binomThmExpt| |cSinh| |innerint| |comp| |GospersMethod| |times| + |airyAi| |sign| |summation| |leadingIndex| |initial| |palgextint0| + |differentiate| |tryFunctionalDecomposition?| |lookup| + |SturmHabichtMultiple| |lazy?| |brillhartIrreducible?| |df2mf| + |var1Steps| |multiplyCoefficients| |belong?| |s21bbf| |endSubProgram| + |cup| |sdf2lst| |leftRemainder| |function| |dot| |exponentialOrder| + |infieldIntegrate| |numberOfVariables| |extendedEuclidean| |hdmpToP| + |OMgetEndObject| |distance| |matrixGcd| |cAtan| |e02ddf| |prologue| + |wreath| |sincos| |lyndon?| |failed| |rowEch| |homogeneous?| + |approxNthRoot| |halfExtendedResultant2| |monom| |eval| + |OMParseError?| |recip| |dom| |rroot| |divideExponents| + |basisOfNucleus| |sumOfKthPowerDivisors| |child| |minPol| + |interpretString| |leadingCoefficientRicDE| |rule| |shuffle| + |isAbsolutelyIrreducible?| |e02daf| |cothIfCan| |integerBound| + |genericRightMinimalPolynomial| |OMreadFile| |flagFactor| |multMonom| + |closeComponent| |in?| |aromberg| |continuedFraction| |monomRDEsys| + |numberOfIrreduciblePoly| |badValues| |hexDigit| |common| |iFTable| + |modifyPoint| |move| |sinIfCan| |negative?| |redPol| |Aleph| |iiGamma| + |unit?| |insertTop!| |atrapezoidal| |iipow| |cSin| |setprevious!| + |eisensteinIrreducible?| |untab| |copies| |routines| |lllp| |open?| + |trivialIdeal?| |inconsistent?| |iisqrt2| |restorePrecision| + |palgLODE| |headReduce| |title| |Si| |variable?| |constDsolve| + |removeSinSq| |flexible?| |expr| + |solveLinearPolynomialEquationByFractions| |printTypes| + |lexTriangular| |symbolTableOf| |multinomial| |f04qaf| |leastMonomial| + |indicialEquationAtInfinity| |qroot| |lowerCase| |createZechTable| + |kovacic| |solveLinear| |notelem| |member?| |rischDE| |setelt!| + |resultantReduit| |multisect| |nil?| |primaryDecomp| |reverseLex| + |polygamma| |mvar| |stoseLastSubResultant| |e| |cyclicSubmodule| + |numericalIntegration| |f02axf| |decompose| |startStats!| |f01qef| + |UnVectorise| |overlap| |internalZeroSetSplit| |cyclicParents| + |d02gbf| |imagE| |ratDsolve| |s19aaf| |variable| |true| |simpsono| + |palglimint0| |symmetricGroup| |nextSublist| |isExpt| |linear| + |insertMatch| |setColumn!| |makeSin| |goto| |iterators| + |insertionSort!| |positiveRemainder| |nthr| |changeName| |cAcoth| + |nothing| |gethi| |linearPart| |mainContent| |entry?| |augment| + |fractionFreeGauss!| |s18acf| |intermediateResultsIF| + |semiResultantReduitEuclidean| |polynomial| |reduceBasisAtInfinity| + |imagj| |mainMonomial| |e04ucf| |genericRightNorm| |cCsc| + |removeConstantTerm| |init| |computeInt| |mkAnswer| |lex| |LiePoly| + |rightUnit| |enumerate| |bat| |gramschmidt| |d02bbf| + |initiallyReduced?| |rootsOf| |factorset| |primitivePart!| + |deleteRoutine!| |rightOne| |viewThetaDefault| |ceiling| + |explimitedint| |basisOfLeftNucleus| |imaginary| |nor| + |quasiAlgebraicSet| |keys| |zeroDim?| |primeFrobenius| |exponential| + |sayLength| |generalPosition| |OMencodingBinary| |getPickedPoints| + |rotatex| |iiasin| |properties| |prolateSpheroidal| |lazyPquo| + |simplifyLog| |squareTop| |width| |cAcsch| |tubePointsDefault| + |acotIfCan| |tube| |represents| |inRadical?| |weight| |translate| + |d02ejf| |high| |nand| |operation| |sumOfDivisors| |scalarMatrix| + |padicFraction| |uniform| |capacity| |f01ref| |createNormalPoly| + |isOpen?| |branchIfCan| |coerceL| |s17agf| |viewWriteAvailable| + |stronglyReduce| |showRegion| |exactQuotient| |transcendenceDegree| + |rightScalarTimes!| |ParCond| |drawStyle| |showClipRegion| + |noncommutativeJordanAlgebra?| |stoseInvertible?| |tanNa| |separant| + |gbasis| |firstDenom| |leadingSupport| |cLog| |ord| + |computeCycleLength| |currentScope| |connect| |minimalPolynomial| + |compdegd| |overlabel| |seriesSolve| |nextLatticePermutation| |cTan| + |exptMod| |mainKernel| |loopPoints| |OMputError| |setMinPoints3D| + |moreAlgebraic?| |element?| |adjoint| |pointData| |LyndonWordsList1| + |c06gqf| |internalAugment| |plenaryPower| |probablyZeroDim?| + |errorKind| |findConstructor| |seriesToOutputForm| |root| |optional| + |ParCondList| |constantOperator| |sortConstraints| |just| |lambert| + |redPo| |Vectorise| |argumentListOf| |fixedPoints| |bounds| + |increasePrecision| |getSyntaxFormsFromFile| |OMputFloat| |nextPrime| + |makeGraphImage| |interpret| |e02def| |polyred| |stack| |generic| + |laguerreL| |complexRoots| |compiledFunction| |OMputEndError| + |OMsupportsCD?| |d03eef| |key?| |eyeDistance| |completeEchelonBasis| + |expandTrigProducts| |maxPoints3D| |atanhIfCan| |phiCoord| + |areEquivalent?| |nodes| |e01bhf| |changeThreshhold| |basicSet| + |tower| |component| |algebraicVariables| |ratDenom| |Ci| |numeric| + |isImplies| |radicalRoots| |viewDeltaXDefault| |unitVector| + |listOfLists| |mkcomm| |makeUnit| |fortranDouble| |expint| |radical| + |relationsIdeal| |pquo| |deepCopy| |countable?| |expIfCan| |connectTo| + |dim| |factorSquareFree| |factorGroebnerBasis| |sec2cos| |elseBranch| + |setref| |zeroSetSplitIntoTriangularSystems| |linearAssociatedExp| + |makeMulti| |iiexp| |credPol| |associatedSystem| |split!| SEGMENT + |numberOfDivisors| |nthRoot| |nil| |weighted| |divideIfCan| |f02fjf| + |less?| |conditionsForIdempotents| |calcRanges| |d02cjf| |dflist| + |removeSinhSq| |adaptive?| |ScanFloatIgnoreSpacesIfCan| + |separateDegrees| |complexNumeric| |resultantnaif| |groebSolve| + |stronglyReduced?| |rootRadius| |cAsin| |concat!| |univariate?| + |antisymmetricTensors| |cCos| |componentUpperBound| |center| |polCase| + |getGraph| |jacobiIdentity?| |lfextendedint| |measure| |s13aaf| + |approximate| |leftRank| |kernels| |musserTrials| |pile| |algDsolve| + |monicModulo| |bubbleSort!| |complex| |startTable!| |trueEqual| |log| + |wholeRadix| |printStats!| |univariate| |top!| |solveRetract| + |qinterval| |imagi| |chebyshevT| |bivariatePolynomials| |node| + |symbolIfCan| |merge| |LowTriBddDenomInv| |createMultiplicationMatrix| + |fortranLogical| |abs| |semiIndiceSubResultantEuclidean| |tableau| + |optAttributes| |reindex| |complexEigenvalues| |is?| |erf| |rk4a| + |xCoord| |updateStatus!| |nextNormalPrimitivePoly| + |bipolarCylindrical| |normal01| |readIfCan!| |factor| + |monicRightDivide| |vectorise| |myDegree| |argumentList!| + |physicalLength| |elColumn2!| |meshPar2Var| |concat| + |rationalFunction| |partialNumerators| |att2Result| |sqrt| + |setMaxPoints| |setTex!| |rewriteIdealWithRemainder| + |prepareDecompose| |s14abf| |listLoops| |bigEndian| |multiple?| + |removeIrreducibleRedundantFactors| |root?| |dilog| |real| + |pleskenSplit| |semiSubResultantGcdEuclidean1| |shiftLeft| |rst| + |setAdaptive3D| |sub| |characteristic| |reorder| |definingPolynomial| + |sin| |imag| |branchPointAtInfinity?| |mantissa| + |semiDiscriminantEuclidean| |Gamma| |combineFeatureCompatibility| + |directProduct| |stopTableGcd!| |screenResolution3D| + |removeRedundantFactors| |getCurve| |nodeOf?| |cos| |setEmpty!| + |permutation| |cCsch| |universe| |doubleDisc| |replace| + |startTableGcd!| |setOrder| |order| |tan| |iicosh| |badNum| + |argscript| |pToDmp| |over| |lazyVariations| |powern| + |rightFactorCandidate| |selectFiniteRoutines| |brace| |cot| + |getStream| |frst| |d01bbf| |outputMeasure| |plus!| |chebyshevU| + |rspace| |froot| |destruct| |sec| |s14aaf| |comparison| |systemSizeIF| + |decimal| |source| |lSpaceBasis| |lazyEvaluate| |middle| |colorDef| + |hasTopPredicate?| |csc| |OMgetAttr| |solid?| |push!| |exists?| + |operators| |optional?| |processTemplate| |linears| + |extractSplittingLeaf| |asin| |category| |returns| + |absolutelyIrreducible?| |OMputObject| |chvar| |basisOfRightNucloid| + |zeroMatrix| |invertIfCan| |equation| |externalList| |whatInfinity| + |acos| |domain| |list?| |setnext!| |leftTraceMatrix| |setImagSteps| + |setLabelValue| |copyInto!| |infLex?| |c06eaf| |omError| |monomial| + |atan| |package| |entry| |showAllElements| |fortranLinkerArgs| + |transpose| |freeOf?| |reducedContinuedFraction| |iicoth| |cSech| + |poisson| |topPredicate| |show| |multivariate| |acot| + |createPrimitiveElement| |genus| |UP2ifCan| |OMputEndAtp| |target| + |conical| |expenseOfEvaluation| |sorted?| |fibonacci| |OMgetEndAtp| + |variables| |asec| |localIntegralBasis| |cosh2sech| |coHeight| + |compose| |mulmod| |jacobi| |bothWays| |discriminantEuclidean| + |addMatchRestricted| |trace| |acsc| |ipow| |pomopo!| + |integralCoordinates| |pointColorPalette| |dictionary| + |triangularSystems| |edf2df| |sqfrFactor| |logIfCan| |sinh| |vedf2vef| + |ran| |s19abf| |argument| |cn| |An| |f01rdf| |c06ekf| |s17def| + |s17adf| |cosh| |reduced?| |reopen!| |fixPredicate| |s13acf| |ravel| + |useEisensteinCriterion| |unprotectedRemoveRedundantFactors| + |halfExtendedSubResultantGcd1| |sup| |sin2csc| |tanh| |tan2trig| + |logGamma| |mpsode| |noKaratsuba| |associatedEquations| |reshape| + |palgRDE| |intersect| |viewpoint| |upperCase| |coth| |taylor| + |mainDefiningPolynomial| |OMgetEndApp| |conditionP| |listexp| + |eigenvalues| |identitySquareMatrix| |deepestTail| + |normalizedAssociate| |expandPower| |sech| |laurent| |setelt| + |generalLambert| |goodPoint| |readLine!| GF2FG |simplifyPower| |hasHi| + |OMsend| |cosSinInfo| |minPoints| |csch| |puiseux| |iroot| |external?| + |d01ajf| |stoseInvertible?reg| |sizeMultiplication| |sinhIfCan| + |figureUnits| |e04mbf| F2FG |asinh| |copy| |pmComplexintegrate| + |nextSubsetGray| FG2F |character?| |scopes| |number?| + |tubeRadiusDefault| |modularGcdPrimitive| |subResultantGcdEuclidean| + |inv| |acosh| |lazyPrem| |critT| |bandedJacobian| |constantRight| + |paraboloidal| |update| |ground?| |nextsousResultant2| |maxint| + |lazyIrreducibleFactors| |incrementKthElement| |atanh| |s14baf| + |iiatanh| |f02bbf| |s17dlf| |ground| |primlimintfrac| + |roughEqualIdeals?| |pushup| |acothIfCan| + |halfExtendedSubResultantGcd2| |acoth| |autoCoerce| |nextPartition| + |sort!| |mesh| |selectSumOfSquaresRoutines| |highCommonTerms| + |scalarTypeOf| |typeList| |OMputAtp| |normalise| |leadingMonomial| + |asech| |distribute| |fortranReal| |e04naf| |writeInt8!| |equality| + |polar| |quotient| |primintegrate| |realZeros| |leadingCoefficient| + |sumSquares| |minimize| |OMbindTCP| |logical?| |divisorCascade| + |ramified?| |cAcsc| |imagk| |initializeGroupForWordProblem| |multiple| + |primitiveMonomials| |s18dcf| |overbar| |firstUncouplingMatrix| + |pr2dmp| |position| |square?| |changeMeasure| |findCycle| |diagonals| + |monomial?| |internalSubQuasiComponent?| |leftUnit| |mergeFactors| + |say| |finite?| |f2st| |setLength!| |selectODEIVPRoutines| + |subtractIfCan| |returnTypeOf| |purelyTranscendental?| |rightRecip| + |extend| |match?| |tanSum| |unparse| |quasiComponent| |RemainderList| + |invertibleSet| |axesColorDefault| |addPoint2| |ideal| |s19acf| + |iisech| LODO2FUN |zeroOf| |radicalOfLeftTraceForm| |c06fpf| |s20adf| + |numericalOptimization| |rightExactQuotient| |quotientByP| |s13adf| + |invmod| |companionBlocks| |mapdiv| + |rewriteIdealWithQuasiMonicGenerators| |parametersOf| + |integralLastSubResultant| |bitCoef| |f01mcf| |exponents| |nlde| + |frobenius| |univariateSolve| |BasicMethod| |hclf| |debug| |hash| + |definingEquations| |OMputEndAttr| |outputBinaryFile| |sncndn| + |regularRepresentation| |nextNormalPoly| |child?| |realElementary| + |OMconnectTCP| |count| D |double| |algebraicDecompose| |f2df| + |varselect| |generalTwoFactor| |e01saf| |errorInfo| |remainder| + |lowerPolynomial| |hermiteH| |binding| |bezoutMatrix| |tubePoints| + |e04jaf| |ocf2ocdf| |write!| |sample| |semiLastSubResultantEuclidean| + |setchildren!| |createLowComplexityTable| |npcoef| |trapezoidal| |row| + |cCot| |addBadValue| |revert| |content| |blue| |zeroDimPrimary?| + |conjug| |tanh2coth| |rangeIsFinite| |stoseInvertibleSetreg| |headAst| + |moduleSum| |monicRightFactorIfCan| |quasiRegular| |changeVar| + |byteBuffer| |alternative?| |normalForm| |scanOneDimSubspaces| + |s01eaf| |lquo| |iiperm| |edf2ef| |pushuconst| |lflimitedint| |one?| + |mkIntegral| |graphStates| |dimensionsOf| |changeBase| |yellow| + |e02bbf| |zerosOf| |limitPlus| |s18def| |zero| |e02bdf| + |numberOfChildren| |oddintegers| |putGraph| |bindings| |refine| + |declare!| |iilog| |iiacsch| |showFortranOutputStack| |cRationalPower| + |stiffnessAndStabilityFactor| |nativeModuleExtension| + |genericRightTrace| |readUInt8!| |predicate| |tab1| |elliptic?| + |modularFactor| |And| |subscript| |lyndonIfCan| |principalAncestors| + |integerIfCan| |OMmakeConn| |inverseIntegralMatrix| |lfextlimint| + |hex| |palglimint| |primPartElseUnitCanonical!| |Or| |se2rfi| + |expenseOfEvaluationIF| |specialTrigs| |subresultantVector| + |internalIntegrate0| |rombergo| |outputFloating| |extendedint| + |pascalTriangle| |Not| |rubiksGroup| |minus!| |binaryFunction| + |indicialEquation| |palgint0| |univariatePolynomialsGcds| |bottom!| + |decrease| |getMatch| |domainOf| |finiteBound| |completeSmith| + |OMgetType| |radicalEigenvector| |backOldPos| |curry| + |startTableInvSet!| |stoseSquareFreePart| |safetyMargin| + |internalSubPolSet?| |coord| |epilogue| |conjugates| |cycles| + |univariatePolynomials| |OMunhandledSymbol| |divergence| |supersub| + |solveLinearPolynomialEquation| |isPower| |segment| |dmpToHdmp| + |trigs2explogs| |printHeader| |wholePart| |squareFreePolynomial| + |removeSuperfluousCases| |reify| |elements| |inputOutputBinaryFile| + |semiResultantEuclideannaif| |overset?| |makeVariable| |gensym| + |aLinear| |parameters| |recur| |listYoungTableaus| + |variationOfParameters| |stopTable!| |useEisensteinCriterion?| |id| + |OMputEndBVar| |closed?| |iicsch| |stoseInvertibleSetsqfreg| + |clipParametric| |setright!| |coercePreimagesImages| + |currentCategoryFrame| |permutations| |coordinates| |s21baf| + |characteristicSerie| |shufflein| |fixedPoint| |viewDeltaYDefault| + |table| |operator| |safeFloor| |diff| |hasPredicate?| |bfEntry| + |alphanumeric| |new| |symmetric?| |diag| |initiallyReduce| |polyRicDE| + |pole?| |composite| |basisOfCentroid| |e02bef| |loadNativeModule| + |insert| |selectNonFiniteRoutines| |strongGenerators| |ode| + |quasiMonic?| |algebraicSort| |leftCharacteristicPolynomial| + |discreteLog| |solve| |bitLength| |OMUnknownCD?| |invertible?| + |leftScalarTimes!| |selectMultiDimensionalRoutines| |SturmHabicht| + |iExquo| |options| |setfirst!| |setButtonValue| |mapSolve| + |OMgetEndBind| |mainPrimitivePart| |clearTheSymbolTable| + |extractBottom!| |subQuasiComponent?| |d01apf| |pi| |mirror| |recolor| + |reducedSystem| |iiacoth| |sPol| |sh| |rk4f| |infinity| + |SturmHabichtCoefficients| |retractIfCan| |extractClosed| |c05pbf| + |tRange| |assign| |terms| |pushucoef| |iitanh| |acschIfCan| |string| + |extractPoint| |limitedint| |complexExpand| |nonQsign| |extractIndex| + |quasiRegular?| |pseudoDivide| |firstSubsetGray| |coshIfCan| + |userOrdered?| |mindegTerm| |sum| |ptree| |iflist2Result| + |genericLeftNorm| |kernel| |generalSqFr| |minset| |jordanAlgebra?| + |doubleComplex?| |nextPrimitiveNormalPoly| |elRow1!| |draw| + |rightRankPolynomial| |d02kef| |particularSolution| |subspace| + |power!| |patternVariable| |option?| |evenlambert| |makeResult| + |polyPart| |dimension| |left| |exprex| |cyclicGroup| |cSec| |rotate!| + |exprToXXP| |representationType| |triangulate| |realEigenvalues| + |right| |isQuotient| |contractSolve| |fintegrate| |pushNewContour| + |laurentIfCan| |pToHdmp| |factorOfDegree| |intPatternMatch| + |setProperty!| |lp| |explicitlyEmpty?| |BumInSepFFE| + |nthFractionalTerm| |getOrder| |reducedForm| |makeObject| |signAround| + |removeSquaresIfCan| |stoseInvertible?sqfreg| |map| + |radicalEigenvectors| |usingTable?| |numberOfHues| |components| + |iiacot| |d01gaf| |csubst| |countRealRoots| |elt| |currentEnv| + |OMconnOutDevice| |expt| |OMencodingXML| |oddInfiniteProduct| + |linearAssociatedLog| |tableForDiscreteLogarithm| |c06fuf| |nthFactor| + |coef| |every?| |showArrayValues| |resize| |d01aqf| |schema| + |OMgetAtp| |e02ahf| |isobaric?| |rename!| |exteriorDifferential| + |push| |nil| |infinite| |arbitraryExponent| |approximate| |complex| + |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index e1423d00..e2378a89 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,85 +1,85 @@ -(3205291 . 3452610493) -((-1463 (((-112) (-1 (-112) |#2| |#2|) $) 86) (((-112) $) NIL)) (-2410 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-3904 ((|#2| $ (-564) |#2|) NIL) ((|#2| $ (-1226 (-564)) |#2|) 43)) (-3616 (($ $) 80)) (-1316 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 51) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 49) ((|#2| (-1 |#2| |#2| |#2|) $) 48)) (-3998 (((-564) (-1 (-112) |#2|) $) 27) (((-564) |#2| $) NIL) (((-564) |#2| $ (-564)) 96)) (-3035 (((-641 |#2|) $) 13)) (-2063 (($ (-1 (-112) |#2| |#2|) $ $) 63) (($ $ $) NIL)) (-2714 (($ (-1 |#2| |#2|) $) 37)) (-4357 (($ (-1 |#2| |#2|) $) NIL) (($ (-1 |#2| |#2| |#2|) $ $) 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-407 (-564))) -2807 (|has| |#1| (-349)) (|has| |#1| (-363))) ((-38 |#1|) . T) ((-38 $) -2807 (|has| |#1| (-556)) (|has| |#1| (-349)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-35) |has| |#1| (-1194)) ((-95) |has| |#1| (-1194)) ((-102) . T) ((-111 #0# #0#) -2807 (|has| |#1| (-349)) (|has| |#1| (-363))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-131) . T) ((-145) -2807 (|has| |#1| (-349)) (|has| |#1| (-145))) ((-147) |has| |#1| (-147)) ((-614 #0#) -2807 (|has| |#1| (-1034 (-407 (-564)))) (|has| |#1| (-349)) (|has| |#1| (-363))) ((-614 (-564)) . T) ((-614 |#1|) . T) ((-614 $) -2807 (|has| |#1| (-556)) (|has| |#1| (-349)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-611 (-858)) . T) ((-172) . T) ((-612 (-169 (-225))) |has| |#1| (-1018)) ((-612 (-169 (-379))) |has| |#1| (-1018)) ((-612 (-536)) |has| |#1| (-612 (-536))) ((-612 (-888 (-379))) |has| |#1| (-612 (-888 (-379)))) ((-612 (-888 (-564))) |has| |#1| (-612 (-888 (-564)))) ((-612 #1=(-1166 |#1|)) . T) ((-231 |#1|) . T) ((-233) -2807 (|has| |#1| (-349)) (|has| |#1| (-233))) ((-243) -2807 (|has| |#1| (-349)) (|has| |#1| (-363))) ((-284) |has| |#1| (-1194)) ((-286 |#1| $) |has| |#1| (-286 |#1| |#1|)) ((-290) -2807 (|has| |#1| (-556)) (|has| |#1| (-349)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-307) -2807 (|has| |#1| (-349)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-309 |#1|) |has| |#1| (-309 |#1|)) ((-363) -2807 (|has| |#1| (-349)) (|has| |#1| (-363))) ((-402) |has| |#1| (-349)) ((-368) -2807 (|has| |#1| (-368)) (|has| |#1| (-349))) ((-349) |has| |#1| (-349)) ((-370 |#1| #1#) . T) ((-409 |#1| #1#) . T) ((-338 |#1|) . T) ((-377 |#1|) . T) ((-400 |#1|) . T) ((-411 |#1|) . T) ((-452) -2807 (|has| |#1| (-349)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-493) |has| |#1| (-1194)) ((-514 (-1170) |#1|) |has| |#1| (-514 (-1170) |#1|)) ((-514 |#1| |#1|) |has| |#1| (-309 |#1|)) ((-556) -2807 (|has| |#1| (-556)) (|has| |#1| (-349)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-644 #0#) -2807 (|has| |#1| (-349)) (|has| |#1| (-363))) ((-644 |#1|) . T) ((-644 $) . T) ((-637 (-564)) |has| |#1| (-637 (-564))) ((-637 |#1|) . T) ((-713 #0#) -2807 (|has| |#1| (-349)) (|has| |#1| (-363))) ((-713 |#1|) . T) ((-713 $) -2807 (|has| |#1| (-556)) (|has| |#1| (-349)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-720 |#1| #1#) . T) ((-722) . T) ((-896 (-1170)) |has| |#1| (-896 (-1170))) ((-882 (-379)) |has| |#1| (-882 (-379))) ((-882 (-564)) |has| |#1| (-882 (-564))) ((-880 |#1|) . T) ((-905) -12 (|has| |#1| (-307)) (|has| |#1| (-905))) ((-916) -2807 (|has| |#1| (-349)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-998) -12 (|has| |#1| (-998)) (|has| |#1| (-1194))) ((-1034 (-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) ((-1034 (-564)) |has| |#1| (-1034 (-564))) ((-1034 |#1|) . T) ((-1051 #0#) -2807 (|has| |#1| (-349)) (|has| |#1| (-363))) ((-1051 |#1|) . T) ((-1051 $) . T) ((-1045) . T) ((-1052) . T) ((-1106) . T) ((-1094) . T) ((-1145) |has| |#1| (-349)) ((-1194) |has| |#1| (-1194)) ((-1197) |has| |#1| (-1194)) ((-1209) . T) ((-1213) -2807 (|has| |#1| (-349)) (|has| |#1| (-363)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905))))) ((-3688 (((-418 |#2|) |#2|) 69))) (((-167 |#1| |#2|) (-10 -7 (-15 -3688 ((-418 |#2|) |#2|))) (-307) (-1235 (-169 |#1|))) (T -167)) @@ -629,7 +629,7 @@ NIL (((-168 |#1| |#2|) (-10 -7 (-15 -4357 ((-169 |#2|) (-1 |#2| |#1|) (-169 |#1|)))) (-172) (-172)) (T -168)) ((-4357 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-169 *5)) (-4 *5 (-172)) (-4 *6 (-172)) (-5 *2 (-169 *6)) (-5 *1 (-168 *5 *6))))) (-10 -7 (-15 -4357 ((-169 |#2|) (-1 |#2| |#1|) (-169 |#1|)))) -((-3006 (((-112) $ $) NIL)) (-3150 (((-112) $) 34)) (-3475 (((-2 (|:| -3988 $) (|:| -4394 $) (|:| |associate| $)) $) NIL (-2807 (-12 (|has| |#1| (-307)) (|has| |#1| (-905))) (|has| |#1| (-556))))) (-3664 (($ $) NIL (-2807 (-12 (|has| |#1| (-307)) (|has| |#1| (-905))) (|has| |#1| (-556))))) (-3562 (((-112) $) NIL (-2807 (-12 (|has| |#1| (-307)) (|has| |#1| (-905))) (|has| |#1| (-556))))) (-2305 (((-685 |#1|) (-1259 $)) NIL) (((-685 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T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1045)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1045))) ((-286 #1=(-564) |#2|) . T) ((-288 #1# |#2|) . T) ((-309 |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-368) |has| |#2| (-368)) ((-377 |#2|) |has| |#2| (-1045)) ((-411 |#2|) |has| |#2| (-1094)) ((-489 |#2|) . T) ((-602 #1# |#2|) . 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T) ((-302) . T) ((-363) |has| |#1| (-556)) ((-377 |#1|) |has| |#1| (-1045)) ((-400 |#1|) . T) ((-411 |#1|) . T) ((-452) |has| |#1| (-556)) ((-473) |has| |#1| (-473)) ((-514 (-610 $) $) . T) ((-514 $ $) . T) ((-556) |has| |#1| (-556)) ((-644 #0#) |has| |#1| (-556)) ((-644 |#1|) |has| |#1| (-172)) ((-644 $) -2807 (|has| |#1| (-1045)) (|has| |#1| (-556)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-637 (-564)) -12 (|has| |#1| (-637 (-564))) (|has| |#1| (-1045))) ((-637 |#1|) |has| |#1| (-1045)) ((-713 #0#) |has| |#1| (-556)) ((-713 |#1|) |has| |#1| (-172)) ((-713 $) |has| |#1| (-556)) ((-722) -2807 (|has| |#1| (-1106)) (|has| |#1| (-1045)) (|has| |#1| (-556)) (|has| |#1| (-473)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-896 (-1170)) |has| |#1| (-1045)) ((-882 (-379)) |has| |#1| (-882 (-379))) ((-882 (-564)) |has| |#1| (-882 (-564))) ((-880 |#1|) . 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NIL NIL NIL) (-1179 2853762 2853909 2854090 "SYSTEM" 2854381 T SYSTEM (NIL) -8 NIL NIL NIL) (-1178 2850221 2850920 2851703 "SYSSOLP" 2853013 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1177 2849265 2849770 2849889 "SYSNNI" 2850075 NIL SYSNNI (NIL NIL) -8 NIL NIL 2850160) (-1176 2848572 2849031 2849110 "SYSINT" 2849170 NIL SYSINT (NIL NIL) -8 NIL NIL 2849215) (-1175 2844904 2845850 2846560 "SYNTAX" 2847884 T SYNTAX (NIL) -8 NIL NIL NIL) (-1174 2842062 2842664 2843296 "SYMTAB" 2844294 T SYMTAB (NIL) -8 NIL NIL NIL) (-1173 2837311 2838213 2839196 "SYMS" 2841101 T SYMS (NIL) -8 NIL NIL NIL) (-1172 2834546 2836769 2836999 "SYMPOLY" 2837116 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1171 2834063 2834138 2834261 "SYMFUNC" 2834458 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1170 2830082 2831375 2832188 "SYMBOL" 2833272 T SYMBOL (NIL) -8 NIL NIL NIL) (-1169 2823621 2825310 2827030 "SWITCH" 2828384 T SWITCH (NIL) -8 NIL NIL NIL) (-1168 2816855 2822442 2822745 "SUTS" 2823376 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1167 2808921 2816102 2816375 "SUPXS" 2816640 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2800681 2808539 2808665 "SUP" 2808830 NIL SUP (NIL T) -8 NIL NIL NIL) (-1165 2799840 2799967 2800184 "SUPFRACF" 2800549 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1164 2799461 2799520 2799633 "SUP2" 2799775 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1163 2797909 2798183 2798539 "SUMRF" 2799160 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1162 2797244 2797310 2797502 "SUMFS" 2797830 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1161 2781211 2796421 2796672 "SULS" 2797051 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2780813 2781033 2781103 "SUCHTAST" 2781163 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1159 2780108 2780338 2780478 "SUCH" 2780721 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1158 2773974 2775014 2775973 "SUBSPACE" 2779196 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1157 2773404 2773494 2773658 "SUBRESP" 2773862 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1156 2766769 2768069 2769380 "STTF" 2772140 NIL STTF (NIL T) -7 NIL NIL NIL) (-1155 2760942 2762062 2763209 "STTFNC" 2765669 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1154 2752253 2754124 2755918 "STTAYLOR" 2759183 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1153 2745383 2752117 2752200 "STRTBL" 2752205 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1152 2740747 2745338 2745369 "STRING" 2745374 T STRING (NIL) -8 NIL NIL NIL) (-1151 2735608 2740120 2740150 "STRICAT" 2740209 T STRICAT (NIL) -9 NIL 2740271 NIL) (-1150 2728362 2733227 2733838 "STREAM" 2735032 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1149 2727872 2727949 2728093 "STREAM3" 2728279 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1148 2726854 2727037 2727272 "STREAM2" 2727685 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1147 2726542 2726594 2726687 "STREAM1" 2726796 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1146 2725558 2725739 2725970 "STINPROD" 2726358 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1145 2725110 2725320 2725350 "STEP" 2725430 T STEP (NIL) -9 NIL 2725508 NIL) (-1144 2718542 2725009 2725086 "STBL" 2725091 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1143 2713668 2717763 2717806 "STAGG" 2717959 NIL STAGG (NIL T) -9 NIL 2718048 NIL) (-1142 2711370 2711972 2712844 "STAGG-" 2712849 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1141 2709517 2711140 2711232 "STACK" 2711313 NIL STACK (NIL T) -8 NIL NIL NIL) (-1140 2702212 2707658 2708114 "SREGSET" 2709147 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1139 2694637 2696006 2697519 "SRDCMPK" 2700818 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2687554 2692077 2692107 "SRAGG" 2693410 T SRAGG (NIL) -9 NIL 2694018 NIL) (-1137 2686571 2686826 2687205 "SRAGG-" 2687210 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1136 2681031 2685518 2685939 "SQMATRIX" 2686197 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1135 2674716 2677749 2678476 "SPLTREE" 2680376 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1134 2670679 2671372 2672018 "SPLNODE" 2674142 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1133 2669726 2669959 2669989 "SPFCAT" 2670433 T SPFCAT (NIL) -9 NIL NIL NIL) (-1132 2668463 2668673 2668937 "SPECOUT" 2669484 T SPECOUT (NIL) -7 NIL NIL NIL) (-1131 2660089 2661859 2661889 "SPADXPT" 2666281 T SPADXPT (NIL) -9 NIL 2668315 NIL) (-1130 2659850 2659890 2659959 "SPADPRSR" 2660042 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1129 2658005 2659805 2659836 "SPADAST" 2659841 T SPADAST (NIL) -8 NIL NIL NIL) (-1128 2649950 2651723 2651766 "SPACEC" 2656139 NIL SPACEC (NIL T) -9 NIL 2657955 NIL) (-1127 2648080 2649882 2649931 "SPACE3" 2649936 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1126 2646832 2647003 2647294 "SORTPAK" 2647885 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1125 2644924 2645227 2645639 "SOLVETRA" 2646496 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1124 2643974 2644196 2644457 "SOLVESER" 2644697 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1123 2639276 2640166 2641161 "SOLVERAD" 2643026 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1122 2635091 2635700 2636429 "SOLVEFOR" 2638643 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1121 2629361 2634440 2634537 "SNTSCAT" 2634542 NIL SNTSCAT (NIL T T T T) -9 NIL 2634612 NIL) (-1120 2623467 2627684 2628075 "SMTS" 2629051 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1119 2618151 2623355 2623432 "SMP" 2623437 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1118 2616310 2616611 2617009 "SMITH" 2617848 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1117 2609170 2613361 2613464 "SMATCAT" 2614815 NIL SMATCAT (NIL NIL T T T) -9 NIL 2615365 NIL) (-1116 2606110 2606933 2608111 "SMATCAT-" 2608116 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1115 2603776 2605346 2605389 "SKAGG" 2605650 NIL SKAGG (NIL T) -9 NIL 2605785 NIL) (-1114 2600084 2603192 2603387 "SINT" 2603574 T SINT (NIL) -8 NIL NIL 2603747) (-1113 2599856 2599894 2599960 "SIMPAN" 2600040 T SIMPAN (NIL) -7 NIL NIL NIL) (-1112 2599135 2599391 2599531 "SIG" 2599738 T SIG (NIL) -8 NIL NIL NIL) (-1111 2597973 2598194 2598469 "SIGNRF" 2598894 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1110 2596806 2596957 2597241 "SIGNEF" 2597802 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1109 2596112 2596389 2596513 "SIGAST" 2596704 T SIGAST (NIL) -8 NIL NIL NIL) (-1108 2593801 2594256 2594762 "SHP" 2595653 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1107 2587653 2593702 2593778 "SHDP" 2593783 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1106 2587226 2587418 2587448 "SGROUP" 2587541 T SGROUP (NIL) -9 NIL 2587603 NIL) (-1105 2587084 2587110 2587183 "SGROUP-" 2587188 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1104 2583919 2584617 2585340 "SGCF" 2586383 T SGCF (NIL) -7 NIL NIL NIL) (-1103 2578287 2583366 2583463 "SFRTCAT" 2583468 NIL SFRTCAT (NIL T T T T) -9 NIL 2583507 NIL) (-1102 2571708 2572726 2573862 "SFRGCD" 2577270 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1101 2564834 2565907 2567093 "SFQCMPK" 2570641 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2564454 2564543 2564654 "SFORT" 2564775 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1099 2563572 2564294 2564415 "SEXOF" 2564420 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1098 2562679 2563453 2563521 "SEX" 2563526 T SEX (NIL) -8 NIL NIL NIL) (-1097 2558192 2558907 2559002 "SEXCAT" 2561939 NIL SEXCAT (NIL T T T T T) -9 NIL 2562517 NIL) (-1096 2555345 2558126 2558174 "SET" 2558179 NIL SET (NIL T) -8 NIL NIL NIL) (-1095 2553569 2554058 2554363 "SETMN" 2555086 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1094 2553065 2553217 2553247 "SETCAT" 2553423 T SETCAT (NIL) -9 NIL 2553533 NIL) (-1093 2552845 2552897 2552996 "SETCAT-" 2553001 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1092 2549206 2551306 2551349 "SETAGG" 2552219 NIL SETAGG (NIL T) -9 NIL 2552559 NIL) (-1091 2548664 2548780 2549017 "SETAGG-" 2549022 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1090 2548107 2548360 2548461 "SEQAST" 2548585 T SEQAST (NIL) -8 NIL NIL NIL) (-1089 2547306 2547600 2547661 "SEGXCAT" 2547947 NIL SEGXCAT (NIL T T) -9 NIL 2548067 NIL) (-1088 2546312 2546972 2547154 "SEG" 2547159 NIL SEG (NIL T) -8 NIL NIL NIL) (-1087 2545291 2545505 2545548 "SEGCAT" 2546070 NIL SEGCAT (NIL T) -9 NIL 2546291 NIL) (-1086 2544292 2544670 2544870 "SEGBIND" 2545126 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1085 2543913 2543972 2544085 "SEGBIND2" 2544227 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1084 2543486 2543714 2543791 "SEGAST" 2543858 T SEGAST (NIL) -8 NIL NIL NIL) (-1083 2542705 2542831 2543035 "SEG2" 2543330 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1082 2542115 2542640 2542687 "SDVAR" 2542692 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1081 2534642 2541885 2542015 "SDPOL" 2542020 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1080 2533235 2533501 2533820 "SCPKG" 2534357 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1079 2532399 2532571 2532763 "SCOPE" 2533065 T SCOPE (NIL) -8 NIL NIL NIL) (-1078 2531619 2531753 2531932 "SCACHE" 2532254 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1077 2531265 2531451 2531481 "SASTCAT" 2531486 T SASTCAT (NIL) -9 NIL 2531499 NIL) (-1076 2530752 2531100 2531176 "SAOS" 2531211 T SAOS (NIL) -8 NIL NIL NIL) (-1075 2530317 2530352 2530525 "SAERFFC" 2530711 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1074 2524256 2530214 2530294 "SAE" 2530299 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1073 2523849 2523884 2524043 "SAEFACT" 2524215 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1072 2522170 2522484 2522885 "RURPK" 2523515 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1071 2520807 2521113 2521418 "RULESET" 2522004 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1070 2518030 2518560 2519018 "RULE" 2520488 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1069 2517642 2517824 2517907 "RULECOLD" 2517982 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1068 2517432 2517460 2517531 "RTVALUE" 2517593 T RTVALUE (NIL) -8 NIL NIL NIL) (-1067 2516903 2517149 2517243 "RSTRCAST" 2517360 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1066 2511751 2512546 2513466 "RSETGCD" 2516102 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1065 2500981 2506060 2506157 "RSETCAT" 2510276 NIL RSETCAT (NIL T T T T) -9 NIL 2511373 NIL) (-1064 2498908 2499447 2500271 "RSETCAT-" 2500276 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1063 2491293 2492670 2494190 "RSDCMPK" 2497507 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1062 2489272 2489739 2489813 "RRCC" 2490899 NIL RRCC (NIL T T) -9 NIL 2491243 NIL) (-1061 2488623 2488797 2489076 "RRCC-" 2489081 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1060 2488066 2488319 2488420 "RPTAST" 2488544 T RPTAST (NIL) -8 NIL NIL NIL) (-1059 2462337 2471686 2471753 "RPOLCAT" 2482417 NIL RPOLCAT (NIL T T T) -9 NIL 2485576 NIL) (-1058 2453835 2456175 2459297 "RPOLCAT-" 2459302 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1057 2444766 2452046 2452528 "ROUTINE" 2453375 T ROUTINE (NIL) -8 NIL NIL NIL) (-1056 2441564 2444392 2444532 "ROMAN" 2444648 T ROMAN (NIL) -8 NIL NIL NIL) (-1055 2439808 2440424 2440684 "ROIRC" 2441369 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1054 2436166 2438444 2438474 "RNS" 2438778 T RNS (NIL) -9 NIL 2439051 NIL) (-1053 2434675 2435058 2435592 "RNS-" 2435667 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1052 2434098 2434506 2434536 "RNG" 2434541 T RNG (NIL) -9 NIL 2434562 NIL) (-1051 2433464 2433852 2433895 "RMODULE" 2433957 NIL RMODULE (NIL T) -9 NIL 2433999 NIL) (-1050 2432300 2432394 2432730 "RMCAT2" 2433365 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1049 2429150 2431646 2431943 "RMATRIX" 2432062 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1048 2422066 2424326 2424441 "RMATCAT" 2427800 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2428782 NIL) (-1047 2421441 2421588 2421895 "RMATCAT-" 2421900 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1046 2421008 2421083 2421211 "RINTERP" 2421360 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1045 2420101 2420655 2420685 "RING" 2420741 T RING (NIL) -9 NIL 2420833 NIL) (-1044 2419893 2419937 2420034 "RING-" 2420039 NIL RING- (NIL T) -8 NIL NIL NIL) (-1043 2418734 2418971 2419229 "RIDIST" 2419657 T RIDIST (NIL) -7 NIL NIL NIL) (-1042 2410023 2418202 2418408 "RGCHAIN" 2418582 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1041 2409373 2409779 2409820 "RGBCSPC" 2409878 NIL RGBCSPC (NIL T) -9 NIL 2409930 NIL) (-1040 2408531 2408912 2408953 "RGBCMDL" 2409185 NIL RGBCMDL (NIL T) -9 NIL 2409299 NIL) (-1039 2405525 2406139 2406809 "RF" 2407895 NIL RF (NIL T) -7 NIL NIL NIL) (-1038 2405171 2405234 2405337 "RFFACTOR" 2405456 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1037 2404896 2404931 2405028 "RFFACT" 2405130 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1036 2403013 2403377 2403759 "RFDIST" 2404536 T RFDIST (NIL) -7 NIL NIL NIL) (-1035 2402466 2402558 2402721 "RETSOL" 2402915 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1034 2402102 2402182 2402225 "RETRACT" 2402358 NIL RETRACT (NIL T) -9 NIL 2402445 NIL) (-1033 2401951 2401976 2402063 "RETRACT-" 2402068 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1032 2401553 2401773 2401843 "RETAST" 2401903 T RETAST (NIL) -8 NIL NIL NIL) (-1031 2394291 2401206 2401333 "RESULT" 2401448 T RESULT (NIL) -8 NIL NIL NIL) (-1030 2392882 2393560 2393759 "RESRING" 2394194 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1029 2392518 2392567 2392665 "RESLATC" 2392819 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1028 2392223 2392258 2392365 "REPSQ" 2392477 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1027 2389645 2390225 2390827 "REP" 2391643 T REP (NIL) -7 NIL NIL NIL) (-1026 2389342 2389377 2389488 "REPDB" 2389604 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1025 2383242 2384631 2385854 "REP2" 2388154 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1024 2379619 2380300 2381108 "REP1" 2382469 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1023 2372315 2377760 2378216 "REGSET" 2379249 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1022 2371080 2371463 2371713 "REF" 2372100 NIL REF (NIL T) -8 NIL NIL NIL) (-1021 2370457 2370560 2370727 "REDORDER" 2370964 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1020 2366425 2369670 2369897 "RECLOS" 2370285 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1019 2365477 2365658 2365873 "REALSOLV" 2366232 T REALSOLV (NIL) -7 NIL NIL NIL) (-1018 2365323 2365364 2365394 "REAL" 2365399 T REAL (NIL) -9 NIL 2365434 NIL) (-1017 2361806 2362608 2363492 "REAL0Q" 2364488 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1016 2357407 2358395 2359456 "REAL0" 2360787 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1015 2356878 2357124 2357218 "RDUCEAST" 2357335 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1014 2356283 2356355 2356562 "RDIV" 2356800 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1013 2355351 2355525 2355738 "RDIST" 2356105 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1012 2353948 2354235 2354607 "RDETRS" 2355059 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1011 2351760 2352214 2352752 "RDETR" 2353490 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1010 2350385 2350663 2351060 "RDEEFS" 2351476 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1009 2348894 2349200 2349625 "RDEEF" 2350073 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1008 2343120 2346030 2346060 "RCFIELD" 2347355 T RCFIELD (NIL) -9 NIL 2348085 NIL) (-1007 2341184 2341688 2342384 "RCFIELD-" 2342459 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1006 2337453 2339285 2339328 "RCAGG" 2340412 NIL RCAGG (NIL T) -9 NIL 2340877 NIL) (-1005 2337081 2337175 2337338 "RCAGG-" 2337343 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1004 2336416 2336528 2336693 "RATRET" 2336965 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1003 2335969 2336036 2336157 "RATFACT" 2336344 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1002 2335277 2335397 2335549 "RANDSRC" 2335839 T RANDSRC (NIL) -7 NIL NIL NIL) (-1001 2335011 2335055 2335128 "RADUTIL" 2335226 T RADUTIL (NIL) -7 NIL NIL NIL) (-1000 2328127 2333844 2334154 "RADIX" 2334735 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-999 2319748 2327971 2328099 "RADFF" 2328104 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-998 2319400 2319475 2319503 "RADCAT" 2319660 T RADCAT (NIL) -9 NIL NIL NIL) (-997 2319185 2319233 2319330 "RADCAT-" 2319335 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-996 2317288 2318960 2319049 "QUEUE" 2319129 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-995 2313829 2317225 2317270 "QUAT" 2317275 NIL QUAT (NIL T) -8 NIL NIL NIL) (-994 2313467 2313510 2313637 "QUATCT2" 2313780 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-993 2307179 2310516 2310556 "QUATCAT" 2311336 NIL QUATCAT (NIL T) -9 NIL 2312102 NIL) (-992 2303323 2304360 2305747 "QUATCAT-" 2305841 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-991 2300796 2302407 2302448 "QUAGG" 2302823 NIL QUAGG (NIL T) -9 NIL 2302998 NIL) (-990 2300401 2300621 2300689 "QQUTAST" 2300748 T QQUTAST (NIL) -8 NIL NIL NIL) (-989 2299299 2299799 2299971 "QFORM" 2300273 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-988 2290477 2295716 2295756 "QFCAT" 2296414 NIL QFCAT (NIL T) -9 NIL 2297415 NIL) (-987 2286049 2287250 2288841 "QFCAT-" 2288935 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-986 2285687 2285730 2285857 "QFCAT2" 2286000 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-985 2285147 2285257 2285387 "QEQUAT" 2285577 T QEQUAT (NIL) -8 NIL NIL NIL) (-984 2278294 2279366 2280550 "QCMPACK" 2284080 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-983 2275843 2276291 2276719 "QALGSET" 2277949 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-982 2275088 2275262 2275494 "QALGSET2" 2275663 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-981 2273778 2274002 2274319 "PWFFINTB" 2274861 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-980 2271960 2272128 2272482 "PUSHVAR" 2273592 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-979 2267878 2268932 2268973 "PTRANFN" 2270857 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-978 2266280 2266571 2266893 "PTPACK" 2267589 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-977 2265912 2265969 2266078 "PTFUNC2" 2266217 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-976 2260391 2264784 2264825 "PTCAT" 2265121 NIL PTCAT (NIL T) -9 NIL 2265274 NIL) (-975 2260049 2260084 2260208 "PSQFR" 2260350 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-974 2258644 2258942 2259276 "PSEUDLIN" 2259747 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-973 2245407 2247778 2250102 "PSETPK" 2256404 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-972 2238425 2241165 2241261 "PSETCAT" 2244282 NIL PSETCAT (NIL T T T T) -9 NIL 2245096 NIL) (-971 2236261 2236895 2237716 "PSETCAT-" 2237721 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-970 2235610 2235775 2235803 "PSCURVE" 2236071 T PSCURVE (NIL) -9 NIL 2236238 NIL) (-969 2231932 2233448 2233513 "PSCAT" 2234357 NIL PSCAT (NIL T T T) -9 NIL 2234597 NIL) (-968 2230995 2231211 2231611 "PSCAT-" 2231616 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-967 2229700 2230360 2230565 "PRTITION" 2230810 T PRTITION (NIL) -8 NIL NIL NIL) (-966 2229175 2229421 2229513 "PRTDAST" 2229628 T PRTDAST (NIL) -8 NIL NIL NIL) (-965 2218265 2220479 2222667 "PRS" 2227037 NIL PRS (NIL T T) -7 NIL NIL NIL) (-964 2216076 2217615 2217655 "PRQAGG" 2217838 NIL PRQAGG (NIL T) -9 NIL 2217940 NIL) (-963 2215280 2215585 2215613 "PROPLOG" 2215860 T PROPLOG (NIL) -9 NIL 2216026 NIL) (-962 2213710 2214231 2214488 "PROPFRML" 2215056 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-961 2213179 2213286 2213414 "PROPERTY" 2213602 T PROPERTY (NIL) -8 NIL NIL NIL) (-960 2207237 2211345 2212165 "PRODUCT" 2212405 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-959 2204515 2206695 2206929 "PR" 2207048 NIL PR (NIL T T) -8 NIL NIL NIL) (-958 2204311 2204343 2204402 "PRINT" 2204476 T PRINT (NIL) -7 NIL NIL NIL) (-957 2203651 2203768 2203920 "PRIMES" 2204191 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-956 2201716 2202117 2202583 "PRIMELT" 2203230 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-955 2201445 2201494 2201522 "PRIMCAT" 2201646 T PRIMCAT (NIL) -9 NIL NIL NIL) (-954 2197560 2201383 2201428 "PRIMARR" 2201433 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-953 2196567 2196745 2196973 "PRIMARR2" 2197378 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-952 2196210 2196266 2196377 "PREASSOC" 2196505 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-951 2195685 2195818 2195846 "PPCURVE" 2196051 T PPCURVE (NIL) -9 NIL 2196187 NIL) (-950 2195280 2195480 2195563 "PORTNUM" 2195622 T PORTNUM (NIL) -8 NIL NIL NIL) (-949 2192639 2193038 2193630 "POLYROOT" 2194861 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-948 2186821 2192243 2192403 "POLY" 2192512 NIL POLY (NIL T) -8 NIL NIL NIL) (-947 2186204 2186262 2186496 "POLYLIFT" 2186757 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-946 2182479 2182928 2183557 "POLYCATQ" 2185749 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-945 2169611 2174731 2174796 "POLYCAT" 2178310 NIL POLYCAT (NIL T T T) -9 NIL 2180188 NIL) (-944 2163060 2164922 2167306 "POLYCAT-" 2167311 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-943 2162647 2162715 2162835 "POLY2UP" 2162986 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-942 2162279 2162336 2162445 "POLY2" 2162584 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-941 2160964 2161203 2161479 "POLUTIL" 2162053 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-940 2159319 2159596 2159927 "POLTOPOL" 2160686 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-939 2154786 2159255 2159301 "POINT" 2159306 NIL POINT (NIL T) -8 NIL NIL NIL) (-938 2152973 2153330 2153705 "PNTHEORY" 2154431 T PNTHEORY (NIL) -7 NIL NIL NIL) (-937 2151431 2151728 2152127 "PMTOOLS" 2152671 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-936 2151024 2151102 2151219 "PMSYM" 2151347 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-935 2150534 2150603 2150777 "PMQFCAT" 2150949 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-934 2149889 2149999 2150155 "PMPRED" 2150411 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-933 2149282 2149368 2149530 "PMPREDFS" 2149790 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-932 2147946 2148154 2148532 "PMPLCAT" 2149044 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-931 2147478 2147557 2147709 "PMLSAGG" 2147861 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-930 2146951 2147027 2147209 "PMKERNEL" 2147396 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-929 2146568 2146643 2146756 "PMINS" 2146870 NIL PMINS (NIL T) -7 NIL NIL NIL) (-928 2146010 2146079 2146288 "PMFS" 2146493 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-927 2145238 2145356 2145561 "PMDOWN" 2145887 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-926 2144405 2144563 2144744 "PMASS" 2145077 T PMASS (NIL) -7 NIL NIL NIL) (-925 2143678 2143788 2143951 "PMASSFS" 2144292 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-924 2143333 2143401 2143495 "PLOTTOOL" 2143604 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-923 2137940 2139144 2140292 "PLOT" 2142205 T PLOT (NIL) -8 NIL NIL NIL) (-922 2133744 2134788 2135709 "PLOT3D" 2137039 T PLOT3D (NIL) -8 NIL NIL NIL) (-921 2132656 2132833 2133068 "PLOT1" 2133548 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-920 2108045 2112722 2117573 "PLEQN" 2127922 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-919 2107363 2107485 2107665 "PINTERP" 2107910 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-918 2107056 2107103 2107206 "PINTERPA" 2107310 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-917 2106277 2106825 2106912 "PI" 2106952 T PI (NIL) -8 NIL NIL 2107019) (-916 2104640 2105615 2105643 "PID" 2105825 T PID (NIL) -9 NIL 2105959 NIL) (-915 2104391 2104428 2104503 "PICOERCE" 2104597 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-914 2103711 2103850 2104026 "PGROEB" 2104247 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-913 2099298 2100112 2101017 "PGE" 2102826 T PGE (NIL) -7 NIL NIL NIL) (-912 2097421 2097668 2098034 "PGCD" 2099015 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-911 2096759 2096862 2097023 "PFRPAC" 2097305 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-910 2093400 2095307 2095660 "PFR" 2096438 NIL PFR (NIL T) -8 NIL NIL NIL) (-909 2091789 2092033 2092358 "PFOTOOLS" 2093147 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-908 2090322 2090561 2090912 "PFOQ" 2091546 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-907 2088823 2089035 2089391 "PFO" 2090106 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-906 2085376 2088712 2088781 "PF" 2088786 NIL PF (NIL NIL) -8 NIL NIL NIL) (-905 2082776 2084047 2084075 "PFECAT" 2084660 T PFECAT (NIL) -9 NIL 2085044 NIL) (-904 2082221 2082375 2082589 "PFECAT-" 2082594 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-903 2080824 2081076 2081377 "PFBRU" 2081970 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-902 2078689 2079042 2079474 "PFBR" 2080475 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-901 2074571 2076065 2076741 "PERM" 2078046 NIL PERM (NIL T) -8 NIL NIL NIL) (-900 2069805 2070778 2071648 "PERMGRP" 2073734 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-899 2067911 2068868 2068909 "PERMCAT" 2069355 NIL PERMCAT (NIL T) -9 NIL 2069660 NIL) (-898 2067564 2067605 2067729 "PERMAN" 2067864 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-897 2065052 2067229 2067351 "PENDTREE" 2067475 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-896 2063111 2063879 2063920 "PDRING" 2064577 NIL PDRING (NIL T) -9 NIL 2064863 NIL) (-895 2062214 2062432 2062794 "PDRING-" 2062799 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-894 2059429 2060207 2060875 "PDEPROB" 2061566 T PDEPROB (NIL) -8 NIL NIL NIL) (-893 2056974 2057478 2058033 "PDEPACK" 2058894 T PDEPACK (NIL) -7 NIL NIL NIL) (-892 2055886 2056076 2056327 "PDECOMP" 2056773 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-891 2053465 2054308 2054336 "PDECAT" 2055123 T PDECAT (NIL) -9 NIL 2055836 NIL) (-890 2053216 2053249 2053339 "PCOMP" 2053426 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-889 2051394 2052017 2052314 "PBWLB" 2052945 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-888 2043867 2045467 2046805 "PATTERN" 2050077 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-887 2043499 2043556 2043665 "PATTERN2" 2043804 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-886 2041256 2041644 2042101 "PATTERN1" 2043088 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-885 2038624 2039205 2039686 "PATRES" 2040821 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-884 2038188 2038255 2038387 "PATRES2" 2038551 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-883 2036071 2036476 2036883 "PATMATCH" 2037855 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-882 2035581 2035790 2035831 "PATMAB" 2035938 NIL PATMAB (NIL T) -9 NIL 2036021 NIL) (-881 2034099 2034435 2034693 "PATLRES" 2035386 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-880 2033645 2033768 2033809 "PATAB" 2033814 NIL PATAB (NIL T) -9 NIL 2033986 NIL) (-879 2031126 2031658 2032231 "PARTPERM" 2033092 T PARTPERM (NIL) -7 NIL NIL NIL) (-878 2030747 2030810 2030912 "PARSURF" 2031057 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-877 2030379 2030436 2030545 "PARSU2" 2030684 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-876 2030143 2030183 2030250 "PARSER" 2030332 T PARSER (NIL) -7 NIL NIL NIL) (-875 2029764 2029827 2029929 "PARSCURV" 2030074 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-874 2029396 2029453 2029562 "PARSC2" 2029701 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-873 2029035 2029093 2029190 "PARPCURV" 2029332 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-872 2028667 2028724 2028833 "PARPC2" 2028972 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-871 2028187 2028273 2028392 "PAN2EXPR" 2028568 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-870 2026964 2027308 2027536 "PALETTE" 2027979 T PALETTE (NIL) -8 NIL NIL NIL) (-869 2025357 2025969 2026329 "PAIR" 2026650 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-868 2019227 2024616 2024810 "PADICRC" 2025212 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-867 2012456 2018573 2018757 "PADICRAT" 2019075 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-866 2010771 2012393 2012438 "PADIC" 2012443 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-865 2007947 2009511 2009551 "PADICCT" 2010132 NIL PADICCT (NIL NIL) -9 NIL 2010414 NIL) (-864 2006904 2007104 2007372 "PADEPAC" 2007734 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-863 2006116 2006249 2006455 "PADE" 2006766 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-862 2004503 2005324 2005604 "OWP" 2005920 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-861 2003996 2004209 2004306 "OVERSET" 2004426 T OVERSET (NIL) -8 NIL NIL NIL) (-860 2003042 2003601 2003773 "OVAR" 2003864 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-859 2002306 2002427 2002588 "OUT" 2002901 T OUT (NIL) -7 NIL NIL NIL) (-858 1991177 1993415 1995615 "OUTFORM" 2000126 T OUTFORM (NIL) -8 NIL NIL NIL) (-857 1990513 1990774 1990901 "OUTBFILE" 1991070 T OUTBFILE (NIL) -8 NIL NIL NIL) (-856 1989820 1989985 1990013 "OUTBCON" 1990331 T OUTBCON (NIL) -9 NIL 1990497 NIL) (-855 1989421 1989533 1989690 "OUTBCON-" 1989695 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-854 1988801 1989150 1989239 "OSI" 1989352 T OSI (NIL) -8 NIL NIL NIL) (-853 1988331 1988669 1988697 "OSGROUP" 1988702 T OSGROUP (NIL) -9 NIL 1988724 NIL) (-852 1987076 1987303 1987588 "ORTHPOL" 1988078 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-851 1984627 1986911 1987032 "OREUP" 1987037 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-850 1982030 1984318 1984445 "ORESUP" 1984569 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-849 1979558 1980058 1980619 "OREPCTO" 1981519 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-848 1973348 1975549 1975590 "OREPCAT" 1977938 NIL OREPCAT (NIL T) -9 NIL 1979042 NIL) (-847 1970495 1971277 1972335 "OREPCAT-" 1972340 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-846 1969646 1969944 1969972 "ORDSET" 1970281 T ORDSET (NIL) -9 NIL 1970445 NIL) (-845 1969077 1969225 1969449 "ORDSET-" 1969454 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-844 1967677 1968468 1968496 "ORDRING" 1968698 T ORDRING (NIL) -9 NIL 1968823 NIL) (-843 1967322 1967416 1967560 "ORDRING-" 1967565 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-842 1966702 1967165 1967193 "ORDMON" 1967198 T ORDMON (NIL) -9 NIL 1967219 NIL) (-841 1965864 1966011 1966206 "ORDFUNS" 1966551 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-840 1965202 1965621 1965649 "ORDFIN" 1965714 T ORDFIN (NIL) -9 NIL 1965788 NIL) (-839 1961761 1963788 1964197 "ORDCOMP" 1964826 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-838 1961027 1961154 1961340 "ORDCOMP2" 1961621 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1957608 1958518 1959332 "OPTPROB" 1960233 T OPTPROB (NIL) -8 NIL NIL NIL) (-836 1954410 1955049 1955753 "OPTPACK" 1956924 T OPTPACK (NIL) -7 NIL NIL NIL) (-835 1952097 1952863 1952891 "OPTCAT" 1953710 T OPTCAT (NIL) -9 NIL 1954360 NIL) (-834 1951513 1951774 1951879 "OPSIG" 1952012 T OPSIG (NIL) -8 NIL NIL NIL) (-833 1951281 1951320 1951386 "OPQUERY" 1951467 T OPQUERY (NIL) -7 NIL NIL NIL) (-832 1948412 1949592 1950096 "OP" 1950810 NIL OP (NIL T) -8 NIL NIL NIL) (-831 1947921 1948118 1948159 "OPERCAT" 1948294 NIL OPERCAT (NIL T) -9 NIL 1948362 NIL) (-830 1947767 1947794 1947880 "OPERCAT-" 1947885 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-829 1944579 1946564 1946933 "ONECOMP" 1947431 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-828 1943884 1943999 1944173 "ONECOMP2" 1944451 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-827 1943303 1943409 1943539 "OMSERVER" 1943774 T OMSERVER (NIL) -7 NIL NIL NIL) (-826 1940165 1942743 1942783 "OMSAGG" 1942844 NIL OMSAGG (NIL T) -9 NIL 1942908 NIL) (-825 1938788 1939051 1939333 "OMPKG" 1939903 T OMPKG (NIL) -7 NIL NIL NIL) (-824 1938218 1938321 1938349 "OM" 1938648 T OM (NIL) -9 NIL NIL NIL) (-823 1936765 1937767 1937936 "OMLO" 1938099 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-822 1935725 1935872 1936092 "OMEXPR" 1936591 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-821 1935016 1935271 1935407 "OMERR" 1935609 T OMERR (NIL) -8 NIL NIL NIL) (-820 1934167 1934437 1934597 "OMERRK" 1934876 T OMERRK (NIL) -8 NIL NIL NIL) (-819 1933618 1933844 1933952 "OMENC" 1934079 T OMENC (NIL) -8 NIL NIL NIL) (-818 1927513 1928698 1929869 "OMDEV" 1932467 T OMDEV (NIL) -8 NIL NIL NIL) (-817 1926582 1926753 1926947 "OMCONN" 1927339 T OMCONN (NIL) -8 NIL NIL NIL) (-816 1925169 1926145 1926173 "OINTDOM" 1926178 T OINTDOM (NIL) -9 NIL 1926199 NIL) (-815 1920948 1922159 1922875 "OFMONOID" 1924485 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-814 1920359 1920885 1920930 "ODVAR" 1920935 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-813 1917782 1920104 1920259 "ODR" 1920264 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-812 1910363 1917558 1917684 "ODPOL" 1917689 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-811 1904185 1910235 1910340 "ODP" 1910345 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-810 1902951 1903166 1903441 "ODETOOLS" 1903959 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-809 1899918 1900576 1901292 "ODESYS" 1902284 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-808 1894800 1895708 1896733 "ODERTRIC" 1898993 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-807 1894226 1894308 1894502 "ODERED" 1894712 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-806 1891114 1891662 1892339 "ODERAT" 1893649 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-805 1888071 1888538 1889135 "ODEPRRIC" 1890643 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-804 1886014 1886610 1887096 "ODEPROB" 1887605 T ODEPROB (NIL) -8 NIL NIL NIL) (-803 1882534 1883019 1883666 "ODEPRIM" 1885493 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-802 1881783 1881885 1882145 "ODEPAL" 1882426 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-801 1877945 1878736 1879600 "ODEPACK" 1880939 T ODEPACK (NIL) -7 NIL NIL NIL) (-800 1877006 1877113 1877335 "ODEINT" 1877834 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-799 1871107 1872532 1873979 "ODEIFTBL" 1875579 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-798 1866505 1867291 1868243 "ODEEF" 1870266 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-797 1865854 1865943 1866166 "ODECONST" 1866410 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-796 1863979 1864640 1864668 "ODECAT" 1865273 T ODECAT (NIL) -9 NIL 1865804 NIL) (-795 1860851 1863691 1863810 "OCT" 1863892 NIL OCT (NIL T) -8 NIL NIL NIL) (-794 1860489 1860532 1860659 "OCTCT2" 1860802 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-793 1855229 1857663 1857703 "OC" 1858800 NIL OC (NIL T) -9 NIL 1859658 NIL) (-792 1852456 1853204 1854194 "OC-" 1854288 NIL OC- (NIL T T) -8 NIL NIL NIL) (-791 1851808 1852276 1852304 "OCAMON" 1852309 T OCAMON (NIL) -9 NIL 1852330 NIL) (-790 1851339 1851680 1851708 "OASGP" 1851713 T OASGP (NIL) -9 NIL 1851733 NIL) (-789 1850600 1851089 1851117 "OAMONS" 1851157 T OAMONS (NIL) -9 NIL 1851200 NIL) (-788 1850014 1850447 1850475 "OAMON" 1850480 T OAMON (NIL) -9 NIL 1850500 NIL) (-787 1849292 1849810 1849838 "OAGROUP" 1849843 T OAGROUP (NIL) -9 NIL 1849863 NIL) (-786 1848982 1849032 1849120 "NUMTUBE" 1849236 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-785 1842555 1844073 1845609 "NUMQUAD" 1847466 T NUMQUAD (NIL) -7 NIL NIL NIL) (-784 1838311 1839299 1840324 "NUMODE" 1841550 T NUMODE (NIL) -7 NIL NIL NIL) (-783 1835666 1836546 1836574 "NUMINT" 1837497 T NUMINT (NIL) -9 NIL 1838261 NIL) (-782 1834614 1834811 1835029 "NUMFMT" 1835468 T NUMFMT (NIL) -7 NIL NIL NIL) (-781 1820973 1823918 1826450 "NUMERIC" 1832121 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-780 1815343 1820422 1820517 "NTSCAT" 1820522 NIL NTSCAT (NIL T T T T) -9 NIL 1820561 NIL) (-779 1814537 1814702 1814895 "NTPOLFN" 1815182 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-778 1802614 1811362 1812174 "NSUP" 1813758 NIL NSUP (NIL T) -8 NIL NIL NIL) (-777 1802246 1802303 1802412 "NSUP2" 1802551 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-776 1792474 1802020 1802153 "NSMP" 1802158 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-775 1790906 1791207 1791564 "NREP" 1792162 NIL NREP (NIL T) -7 NIL NIL NIL) (-774 1789497 1789749 1790107 "NPCOEF" 1790649 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-773 1788563 1788678 1788894 "NORMRETR" 1789378 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-772 1786604 1786894 1787303 "NORMPK" 1788271 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-771 1786289 1786317 1786441 "NORMMA" 1786570 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-770 1786089 1786246 1786275 "NONE" 1786280 T NONE (NIL) -8 NIL NIL NIL) (-769 1785878 1785907 1785976 "NONE1" 1786053 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-768 1785375 1785437 1785616 "NODE1" 1785810 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-767 1783655 1784506 1784761 "NNI" 1785108 T NNI (NIL) -8 NIL NIL 1785343) (-766 1782075 1782388 1782752 "NLINSOL" 1783323 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-765 1778316 1779311 1780210 "NIPROB" 1781196 T NIPROB (NIL) -8 NIL NIL NIL) (-764 1777073 1777307 1777609 "NFINTBAS" 1778078 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-763 1776247 1776723 1776764 "NETCLT" 1776936 NIL NETCLT (NIL T) -9 NIL 1777018 NIL) (-762 1774955 1775186 1775467 "NCODIV" 1776015 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-761 1774717 1774754 1774829 "NCNTFRAC" 1774912 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-760 1772897 1773261 1773681 "NCEP" 1774342 NIL NCEP (NIL T) -7 NIL NIL NIL) (-759 1771768 1772541 1772569 "NASRING" 1772679 T NASRING (NIL) -9 NIL 1772759 NIL) (-758 1771563 1771607 1771701 "NASRING-" 1771706 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-757 1770690 1771215 1771243 "NARNG" 1771360 T NARNG (NIL) -9 NIL 1771451 NIL) (-756 1770382 1770449 1770583 "NARNG-" 1770588 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-755 1769261 1769468 1769703 "NAGSP" 1770167 T NAGSP (NIL) -7 NIL NIL NIL) (-754 1760533 1762217 1763890 "NAGS" 1767608 T NAGS (NIL) -7 NIL NIL NIL) (-753 1759081 1759389 1759720 "NAGF07" 1760222 T NAGF07 (NIL) -7 NIL NIL NIL) (-752 1753619 1754910 1756217 "NAGF04" 1757794 T NAGF04 (NIL) -7 NIL NIL NIL) (-751 1746587 1748201 1749834 "NAGF02" 1752006 T NAGF02 (NIL) -7 NIL NIL NIL) (-750 1741811 1742911 1744028 "NAGF01" 1745490 T NAGF01 (NIL) -7 NIL NIL NIL) (-749 1735439 1737005 1738590 "NAGE04" 1740246 T NAGE04 (NIL) -7 NIL NIL NIL) (-748 1726608 1728729 1730859 "NAGE02" 1733329 T NAGE02 (NIL) -7 NIL NIL NIL) (-747 1722561 1723508 1724472 "NAGE01" 1725664 T NAGE01 (NIL) -7 NIL NIL NIL) (-746 1720356 1720890 1721448 "NAGD03" 1722023 T NAGD03 (NIL) -7 NIL NIL NIL) (-745 1712106 1714034 1715988 "NAGD02" 1718422 T NAGD02 (NIL) -7 NIL NIL NIL) (-744 1705917 1707342 1708782 "NAGD01" 1710686 T NAGD01 (NIL) -7 NIL NIL NIL) (-743 1702126 1702948 1703785 "NAGC06" 1705100 T NAGC06 (NIL) -7 NIL NIL NIL) (-742 1700591 1700923 1701279 "NAGC05" 1701790 T NAGC05 (NIL) -7 NIL NIL NIL) (-741 1699967 1700086 1700230 "NAGC02" 1700467 T NAGC02 (NIL) -7 NIL NIL NIL) (-740 1699001 1699584 1699624 "NAALG" 1699703 NIL NAALG (NIL T) -9 NIL 1699764 NIL) (-739 1698836 1698865 1698955 "NAALG-" 1698960 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-738 1692786 1693894 1695081 "MULTSQFR" 1697732 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-737 1692105 1692180 1692364 "MULTFACT" 1692698 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-736 1685163 1689068 1689121 "MTSCAT" 1690191 NIL MTSCAT (NIL T T) -9 NIL 1690705 NIL) (-735 1684875 1684929 1685021 "MTHING" 1685103 NIL MTHING (NIL T) -7 NIL NIL NIL) (-734 1684667 1684700 1684760 "MSYSCMD" 1684835 T MSYSCMD (NIL) -7 NIL NIL NIL) (-733 1680749 1683422 1683742 "MSET" 1684380 NIL MSET (NIL T) -8 NIL NIL NIL) (-732 1677818 1680310 1680351 "MSETAGG" 1680356 NIL MSETAGG (NIL T) -9 NIL 1680390 NIL) (-731 1673659 1675197 1675942 "MRING" 1677118 NIL MRING (NIL T T) -8 NIL NIL NIL) (-730 1673225 1673292 1673423 "MRF2" 1673586 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-729 1672843 1672878 1673022 "MRATFAC" 1673184 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-728 1670455 1670750 1671181 "MPRFF" 1672548 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-727 1664752 1670309 1670406 "MPOLY" 1670411 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-726 1664242 1664277 1664485 "MPCPF" 1664711 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-725 1663756 1663799 1663983 "MPC3" 1664193 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1662951 1663032 1663253 "MPC2" 1663671 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-723 1661252 1661589 1661979 "MONOTOOL" 1662611 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-722 1660477 1660794 1660822 "MONOID" 1661041 T MONOID (NIL) -9 NIL 1661188 NIL) (-721 1660023 1660142 1660323 "MONOID-" 1660328 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-720 1650847 1656790 1656849 "MONOGEN" 1657523 NIL MONOGEN (NIL T T) -9 NIL 1657979 NIL) (-719 1648065 1648800 1649800 "MONOGEN-" 1649919 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-718 1646898 1647344 1647372 "MONADWU" 1647764 T MONADWU (NIL) -9 NIL 1648002 NIL) (-717 1646270 1646429 1646677 "MONADWU-" 1646682 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-716 1645629 1645873 1645901 "MONAD" 1646108 T MONAD (NIL) -9 NIL 1646220 NIL) (-715 1645314 1645392 1645524 "MONAD-" 1645529 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-714 1643603 1644227 1644506 "MOEBIUS" 1645067 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-713 1642969 1643373 1643413 "MODULE" 1643418 NIL MODULE (NIL T) -9 NIL 1643444 NIL) (-712 1642537 1642633 1642823 "MODULE-" 1642828 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-711 1640217 1640901 1641228 "MODRING" 1642361 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1637161 1638322 1638843 "MODOP" 1639746 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-709 1635749 1636228 1636505 "MODMONOM" 1637024 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-708 1625790 1634040 1634454 "MODMON" 1635386 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-707 1622946 1624634 1624910 "MODFIELD" 1625665 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-706 1621923 1622227 1622417 "MMLFORM" 1622776 T MMLFORM (NIL) -8 NIL NIL NIL) (-705 1621449 1621492 1621671 "MMAP" 1621874 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-704 1619632 1620399 1620440 "MLO" 1620863 NIL MLO (NIL T) -9 NIL 1621105 NIL) (-703 1616998 1617514 1618116 "MLIFT" 1619113 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-702 1616389 1616473 1616627 "MKUCFUNC" 1616909 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-701 1615988 1616058 1616181 "MKRECORD" 1616312 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-700 1615035 1615197 1615425 "MKFUNC" 1615799 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-699 1614423 1614527 1614683 "MKFLCFN" 1614918 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-698 1613700 1613802 1613987 "MKBCFUNC" 1614316 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-697 1610407 1613254 1613390 "MINT" 1613584 T MINT (NIL) -8 NIL NIL NIL) (-696 1609219 1609462 1609739 "MHROWRED" 1610162 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-695 1604599 1607754 1608159 "MFLOAT" 1608834 T MFLOAT (NIL) -8 NIL NIL NIL) (-694 1603956 1604032 1604203 "MFINFACT" 1604511 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-693 1600271 1601119 1602003 "MESH" 1603092 T MESH (NIL) -7 NIL NIL NIL) (-692 1598661 1598973 1599326 "MDDFACT" 1599958 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-691 1595456 1597820 1597861 "MDAGG" 1598116 NIL MDAGG (NIL T) -9 NIL 1598259 NIL) (-690 1585199 1594749 1594956 "MCMPLX" 1595269 T MCMPLX (NIL) -8 NIL NIL NIL) (-689 1584340 1584486 1584686 "MCDEN" 1585048 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-688 1582230 1582500 1582880 "MCALCFN" 1584070 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-687 1581155 1581395 1581628 "MAYBE" 1582036 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-686 1578767 1579290 1579852 "MATSTOR" 1580626 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-685 1574724 1578139 1578387 "MATRIX" 1578552 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-684 1570488 1571197 1571933 "MATLIN" 1574081 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-683 1560594 1563780 1563857 "MATCAT" 1568737 NIL MATCAT (NIL T T T) -9 NIL 1570154 NIL) (-682 1556950 1557971 1559327 "MATCAT-" 1559332 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-681 1555544 1555697 1556030 "MATCAT2" 1556785 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-680 1553656 1553980 1554364 "MAPPKG3" 1555219 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-679 1552637 1552810 1553032 "MAPPKG2" 1553480 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-678 1551136 1551420 1551747 "MAPPKG1" 1552343 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-677 1550215 1550542 1550719 "MAPPAST" 1550979 T MAPPAST (NIL) -8 NIL NIL NIL) (-676 1549826 1549884 1550007 "MAPHACK3" 1550151 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-675 1549418 1549479 1549593 "MAPHACK2" 1549758 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-674 1548855 1548959 1549101 "MAPHACK1" 1549309 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-673 1546934 1547555 1547859 "MAGMA" 1548583 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-672 1546413 1546658 1546749 "MACROAST" 1546863 T MACROAST (NIL) -8 NIL NIL NIL) (-671 1542831 1544652 1545113 "M3D" 1545985 NIL M3D (NIL T) -8 NIL NIL NIL) (-670 1536937 1541200 1541241 "LZSTAGG" 1542023 NIL LZSTAGG (NIL T) -9 NIL 1542318 NIL) (-669 1532894 1534068 1535525 "LZSTAGG-" 1535530 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-668 1529981 1530785 1531272 "LWORD" 1532439 NIL LWORD (NIL T) -8 NIL NIL NIL) (-667 1529557 1529785 1529860 "LSTAST" 1529926 T LSTAST (NIL) -8 NIL NIL NIL) (-666 1522723 1529328 1529462 "LSQM" 1529467 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-665 1521947 1522086 1522314 "LSPP" 1522578 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-664 1519759 1520060 1520516 "LSMP" 1521636 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-663 1516538 1517212 1517942 "LSMP1" 1519061 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-662 1510415 1515705 1515746 "LSAGG" 1515808 NIL LSAGG (NIL T) -9 NIL 1515886 NIL) (-661 1507110 1508034 1509247 "LSAGG-" 1509252 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-660 1504709 1506254 1506503 "LPOLY" 1506905 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-659 1504291 1504376 1504499 "LPEFRAC" 1504618 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-658 1502612 1503385 1503638 "LO" 1504123 NIL LO (NIL T T T) -8 NIL NIL NIL) (-657 1502264 1502376 1502404 "LOGIC" 1502515 T LOGIC (NIL) -9 NIL 1502596 NIL) (-656 1502126 1502149 1502220 "LOGIC-" 1502225 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-655 1501319 1501459 1501652 "LODOOPS" 1501982 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-654 1498742 1501235 1501301 "LODO" 1501306 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-653 1497280 1497515 1497868 "LODOF" 1498489 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-652 1493602 1496033 1496074 "LODOCAT" 1496512 NIL LODOCAT (NIL T) -9 NIL 1496723 NIL) (-651 1493335 1493393 1493520 "LODOCAT-" 1493525 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-650 1490655 1493176 1493294 "LODO2" 1493299 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-649 1488090 1490592 1490637 "LODO1" 1490642 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-648 1486971 1487136 1487441 "LODEEF" 1487913 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-647 1482210 1485101 1485142 "LNAGG" 1486089 NIL LNAGG (NIL T) -9 NIL 1486533 NIL) (-646 1481357 1481571 1481913 "LNAGG-" 1481918 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-645 1477493 1478282 1478921 "LMOPS" 1480772 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-644 1476862 1477250 1477291 "LMODULE" 1477352 NIL LMODULE (NIL T) -9 NIL 1477394 NIL) (-643 1474060 1476507 1476630 "LMDICT" 1476772 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-642 1473759 1473968 1474028 "LITERAL" 1474033 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-641 1466942 1472705 1473003 "LIST" 1473494 NIL LIST (NIL T) -8 NIL NIL NIL) (-640 1466467 1466541 1466680 "LIST3" 1466862 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-639 1465474 1465652 1465880 "LIST2" 1466285 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-638 1463608 1463920 1464319 "LIST2MAP" 1465121 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-637 1462304 1462974 1463015 "LINEXP" 1463270 NIL LINEXP (NIL T) -9 NIL 1463419 NIL) (-636 1460951 1461211 1461508 "LINDEP" 1462056 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-635 1457718 1458437 1459214 "LIMITRF" 1460206 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-634 1456021 1456317 1456726 "LIMITPS" 1457413 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-633 1450449 1455532 1455760 "LIE" 1455842 NIL LIE (NIL T T) -8 NIL NIL NIL) (-632 1449472 1449941 1449981 "LIECAT" 1450121 NIL LIECAT (NIL T) -9 NIL 1450272 NIL) (-631 1449313 1449340 1449428 "LIECAT-" 1449433 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-630 1441809 1448762 1448927 "LIB" 1449168 T LIB (NIL) -8 NIL NIL NIL) (-629 1437444 1438327 1439262 "LGROBP" 1440926 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-628 1435453 1435727 1436076 "LF" 1437165 NIL LF (NIL T T) -7 NIL NIL NIL) (-627 1434293 1434985 1435013 "LFCAT" 1435220 T LFCAT (NIL) -9 NIL 1435359 NIL) (-626 1431195 1431825 1432513 "LEXTRIPK" 1433657 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-625 1427939 1428765 1429268 "LEXP" 1430775 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-624 1427415 1427660 1427752 "LETAST" 1427867 T LETAST (NIL) -8 NIL NIL NIL) (-623 1425813 1426126 1426527 "LEADCDET" 1427097 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-622 1425003 1425077 1425306 "LAZM3PK" 1425734 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-621 1419920 1423080 1423618 "LAUPOL" 1424515 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-620 1419499 1419543 1419704 "LAPLACE" 1419870 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-619 1417438 1418600 1418851 "LA" 1419332 NIL LA (NIL T T T) -8 NIL NIL NIL) (-618 1416485 1417069 1417110 "LALG" 1417172 NIL LALG (NIL T) -9 NIL 1417231 NIL) (-617 1416199 1416258 1416394 "LALG-" 1416399 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-616 1416034 1416058 1416099 "KVTFROM" 1416161 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-615 1414957 1415401 1415586 "KTVLOGIC" 1415869 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-614 1414792 1414816 1414857 "KRCFROM" 1414919 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-613 1413696 1413883 1414182 "KOVACIC" 1414592 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-612 1413531 1413555 1413596 "KONVERT" 1413658 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-611 1413366 1413390 1413431 "KOERCE" 1413493 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-610 1411048 1411836 1412237 "KERNEL" 1412998 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-609 1410544 1410625 1410757 "KERNEL2" 1410962 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-608 1404314 1409083 1409137 "KDAGG" 1409514 NIL KDAGG (NIL T T) -9 NIL 1409720 NIL) (-607 1403843 1403967 1404172 "KDAGG-" 1404177 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-606 1396991 1403504 1403659 "KAFILE" 1403721 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-605 1391419 1396502 1396730 "JORDAN" 1396812 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-604 1390798 1391068 1391189 "JOINAST" 1391318 T JOINAST (NIL) -8 NIL NIL NIL) (-603 1390644 1390703 1390758 "JAVACODE" 1390763 T JAVACODE (NIL) -8 NIL NIL NIL) (-602 1386896 1388849 1388903 "IXAGG" 1389832 NIL IXAGG (NIL T T) -9 NIL 1390291 NIL) (-601 1385815 1386121 1386540 "IXAGG-" 1386545 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1381347 1385737 1385796 "IVECTOR" 1385801 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-599 1380113 1380350 1380616 "ITUPLE" 1381114 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-598 1378627 1378804 1379097 "ITRIGMNP" 1379935 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-597 1377372 1377576 1377859 "ITFUN3" 1378403 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-596 1377004 1377061 1377170 "ITFUN2" 1377309 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-595 1374806 1375866 1376165 "ITAYLOR" 1376738 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-594 1363751 1368943 1370106 "ISUPS" 1373676 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-593 1362855 1362995 1363231 "ISUMP" 1363598 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-592 1358069 1362656 1362735 "ISTRING" 1362808 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-591 1357545 1357790 1357882 "ISAST" 1357997 T ISAST (NIL) -8 NIL NIL NIL) (-590 1356754 1356836 1357052 "IRURPK" 1357459 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-589 1355690 1355891 1356131 "IRSN" 1356534 T IRSN (NIL) -7 NIL NIL NIL) (-588 1353761 1354116 1354545 "IRRF2F" 1355328 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-587 1353508 1353546 1353622 "IRREDFFX" 1353717 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-586 1352123 1352382 1352681 "IROOT" 1353241 NIL IROOT (NIL T) -7 NIL NIL NIL) (-585 1348727 1349807 1350499 "IR" 1351463 NIL IR (NIL T) -8 NIL NIL NIL) (-584 1346340 1346835 1347401 "IR2" 1348205 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-583 1345440 1345553 1345767 "IR2F" 1346223 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-582 1345231 1345265 1345325 "IPRNTPK" 1345400 T IPRNTPK (NIL) -7 NIL NIL NIL) (-581 1341811 1345120 1345189 "IPF" 1345194 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-580 1340138 1341736 1341793 "IPADIC" 1341798 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-579 1339450 1339698 1339828 "IP4ADDR" 1340028 T IP4ADDR (NIL) -8 NIL NIL NIL) (-578 1338923 1339154 1339264 "IOMODE" 1339360 T IOMODE (NIL) -8 NIL NIL NIL) (-577 1337996 1338520 1338647 "IOBFILE" 1338816 T IOBFILE (NIL) -8 NIL NIL NIL) (-576 1337484 1337900 1337928 "IOBCON" 1337933 T IOBCON (NIL) -9 NIL 1337954 NIL) (-575 1336995 1337053 1337236 "INVLAPLA" 1337420 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-574 1326643 1328997 1331383 "INTTR" 1334659 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-573 1322978 1323720 1324585 "INTTOOLS" 1325828 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-572 1322564 1322655 1322772 "INTSLPE" 1322881 T INTSLPE (NIL) -7 NIL NIL NIL) (-571 1320518 1322487 1322546 "INTRVL" 1322551 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-570 1318120 1318632 1319207 "INTRF" 1320003 NIL INTRF (NIL T) -7 NIL NIL NIL) (-569 1317531 1317628 1317770 "INTRET" 1318018 NIL INTRET (NIL T) -7 NIL NIL NIL) (-568 1315528 1315917 1316387 "INTRAT" 1317139 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-567 1312791 1313374 1313993 "INTPM" 1315013 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-566 1309535 1310135 1310873 "INTPAF" 1312177 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-565 1304714 1305676 1306727 "INTPACK" 1308504 T INTPACK (NIL) -7 NIL NIL NIL) (-564 1301591 1304443 1304570 "INT" 1304607 T INT (NIL) -8 NIL NIL NIL) (-563 1300843 1300995 1301203 "INTHERTR" 1301433 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-562 1300282 1300362 1300550 "INTHERAL" 1300757 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-561 1298128 1298571 1299028 "INTHEORY" 1299845 T INTHEORY (NIL) -7 NIL NIL NIL) (-560 1289534 1291155 1292927 "INTG0" 1296480 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-559 1270107 1274897 1279707 "INTFTBL" 1284744 T INTFTBL (NIL) -8 NIL NIL NIL) (-558 1269356 1269494 1269667 "INTFACT" 1269966 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-557 1266783 1267229 1267786 "INTEF" 1268910 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-556 1265216 1265955 1265983 "INTDOM" 1266284 T INTDOM (NIL) -9 NIL 1266491 NIL) (-555 1264585 1264759 1265001 "INTDOM-" 1265006 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-554 1261045 1262969 1263023 "INTCAT" 1263822 NIL INTCAT (NIL T) -9 NIL 1264142 NIL) (-553 1260517 1260620 1260748 "INTBIT" 1260937 T INTBIT (NIL) -7 NIL NIL NIL) (-552 1259216 1259370 1259677 "INTALG" 1260362 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-551 1258699 1258789 1258946 "INTAF" 1259120 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-550 1252042 1258509 1258649 "INTABL" 1258654 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-549 1251346 1251812 1251877 "INT8" 1251911 T INT8 (NIL) -8 NIL NIL 1251956) (-548 1250649 1251115 1251180 "INT64" 1251214 T INT64 (NIL) -8 NIL NIL 1251259) (-547 1249952 1250418 1250483 "INT32" 1250517 T INT32 (NIL) -8 NIL NIL 1250562) (-546 1249255 1249721 1249786 "INT16" 1249820 T INT16 (NIL) -8 NIL NIL 1249865) (-545 1244235 1246944 1246972 "INS" 1247906 T INS (NIL) -9 NIL 1248571 NIL) (-544 1241475 1242246 1243220 "INS-" 1243293 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1240250 1240477 1240775 "INPSIGN" 1241228 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1239368 1239485 1239682 "INPRODPF" 1240130 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1238262 1238379 1238616 "INPRODFF" 1239248 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1237262 1237414 1237674 "INNMFACT" 1238098 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1236459 1236556 1236744 "INMODGCD" 1237161 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1234967 1235212 1235536 "INFSP" 1236204 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1234151 1234268 1234451 "INFPROD0" 1234847 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1231006 1232216 1232731 "INFORM" 1233644 T INFORM (NIL) -8 NIL NIL NIL) (-535 1230616 1230676 1230774 "INFORM1" 1230941 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1230139 1230228 1230342 "INFINITY" 1230522 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1229315 1229859 1229960 "INETCLTS" 1230058 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1227931 1228181 1228502 "INEP" 1229063 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1227180 1227828 1227893 "INDE" 1227898 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1226744 1226812 1226929 "INCRMAPS" 1227107 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1225562 1226013 1226219 "INBFILE" 1226558 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1220862 1221798 1222742 "INBFF" 1224650 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1219770 1220039 1220067 "INBCON" 1220580 T INBCON (NIL) -9 NIL 1220846 NIL) (-526 1219022 1219245 1219521 "INBCON-" 1219526 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1218501 1218746 1218837 "INAST" 1218951 T INAST (NIL) -8 NIL NIL NIL) (-524 1217928 1218180 1218286 "IMPTAST" 1218415 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1214374 1217772 1217876 "IMATRIX" 1217881 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1213086 1213209 1213524 "IMATQF" 1214230 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1211306 1211533 1211870 "IMATLIN" 1212842 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1205884 1211230 1211288 "ILIST" 1211293 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1203789 1205744 1205857 "IIARRAY2" 1205862 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1199187 1203700 1203764 "IFF" 1203769 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1198534 1198804 1198920 "IFAST" 1199091 T IFAST (NIL) -8 NIL NIL NIL) (-516 1193529 1197826 1198014 "IFARRAY" 1198391 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1192709 1193433 1193506 "IFAMON" 1193511 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1192293 1192358 1192412 "IEVALAB" 1192619 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1191968 1192036 1192196 "IEVALAB-" 1192201 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1191599 1191882 1191945 "IDPO" 1191950 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1190849 1191488 1191563 "IDPOAMS" 1191568 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1190156 1190738 1190813 "IDPOAM" 1190818 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1189215 1189491 1189544 "IDPC" 1189957 NIL IDPC (NIL T T) -9 NIL 1190106 NIL) (-508 1188684 1189107 1189180 "IDPAM" 1189185 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1188060 1188576 1188649 "IDPAG" 1188654 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1187705 1187896 1187971 "IDENT" 1188005 T IDENT (NIL) -8 NIL NIL NIL) (-505 1183960 1184808 1185703 "IDECOMP" 1186862 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1176796 1177883 1178930 "IDEAL" 1182996 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1175960 1176072 1176271 "ICDEN" 1176680 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1175031 1175440 1175587 "ICARD" 1175833 T ICARD (NIL) -8 NIL NIL NIL) (-501 1173091 1173404 1173809 "IBPTOOLS" 1174708 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1168698 1172711 1172824 "IBITS" 1173010 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1165421 1165997 1166692 "IBATOOL" 1168115 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1163200 1163662 1164195 "IBACHIN" 1164956 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1161029 1163046 1163149 "IARRAY2" 1163154 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1157135 1160955 1161012 "IARRAY1" 1161017 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1151244 1155547 1156028 "IAN" 1156674 T IAN (NIL) -8 NIL NIL NIL) (-494 1150755 1150812 1150985 "IALGFACT" 1151181 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1150283 1150396 1150424 "HYPCAT" 1150631 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1149821 1149938 1150124 "HYPCAT-" 1150129 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1149416 1149616 1149699 "HOSTNAME" 1149758 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1149261 1149298 1149339 "HOMOTOP" 1149344 NIL HOMOTOP (NIL T) -9 NIL 1149377 NIL) (-489 1145893 1147271 1147312 "HOAGG" 1148293 NIL HOAGG (NIL T) -9 NIL 1148972 NIL) (-488 1144487 1144886 1145412 "HOAGG-" 1145417 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1138491 1144082 1144231 "HEXADEC" 1144358 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1137239 1137461 1137724 "HEUGCD" 1138268 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1136315 1137076 1137206 "HELLFDIV" 1137211 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1134494 1136092 1136180 "HEAP" 1136259 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1133757 1134046 1134180 "HEADAST" 1134380 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1127623 1133672 1133734 "HDP" 1133739 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1121611 1127258 1127410 "HDMP" 1127524 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1120935 1121075 1121239 "HB" 1121467 T HB (NIL) -7 NIL NIL NIL) (-479 1114321 1120781 1120885 "HASHTBL" 1120890 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1113797 1114042 1114134 "HASAST" 1114249 T HASAST (NIL) -8 NIL NIL NIL) (-477 1111575 1113419 1113601 "HACKPI" 1113635 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1107243 1111428 1111541 "GTSET" 1111546 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1100658 1107121 1107219 "GSTBL" 1107224 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1092936 1099689 1099954 "GSERIES" 1100449 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1092077 1092494 1092522 "GROUP" 1092725 T GROUP (NIL) -9 NIL 1092859 NIL) (-472 1091443 1091602 1091853 "GROUP-" 1091858 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1089810 1090131 1090518 "GROEBSOL" 1091120 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1088724 1089012 1089063 "GRMOD" 1089592 NIL GRMOD (NIL T T) -9 NIL 1089760 NIL) (-469 1088492 1088528 1088656 "GRMOD-" 1088661 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1083782 1084846 1085846 "GRIMAGE" 1087512 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1082248 1082509 1082833 "GRDEF" 1083478 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1081692 1081808 1081949 "GRAY" 1082127 T GRAY (NIL) -7 NIL NIL NIL) (-465 1080879 1081285 1081336 "GRALG" 1081489 NIL GRALG (NIL T T) -9 NIL 1081582 NIL) (-464 1080540 1080613 1080776 "GRALG-" 1080781 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1077317 1080125 1080303 "GPOLSET" 1080447 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1076671 1076728 1076986 "GOSPER" 1077254 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1072403 1073109 1073635 "GMODPOL" 1076370 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1071408 1071592 1071830 "GHENSEL" 1072215 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1065564 1066407 1067427 "GENUPS" 1070492 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1065261 1065312 1065401 "GENUFACT" 1065507 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1064673 1064750 1064915 "GENPGCD" 1065179 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1064147 1064182 1064395 "GENMFACT" 1064632 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1062713 1062970 1063277 "GENEEZ" 1063890 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1056858 1062324 1062486 "GDMP" 1062636 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1046200 1050629 1051735 "GCNAALG" 1055841 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1044593 1045455 1045483 "GCDDOM" 1045738 T GCDDOM (NIL) -9 NIL 1045895 NIL) (-451 1044063 1044190 1044405 "GCDDOM-" 1044410 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1042735 1042920 1043224 "GB" 1043842 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1031351 1033681 1036073 "GBINTERN" 1040426 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1029188 1029480 1029901 "GBF" 1031026 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1027969 1028134 1028401 "GBEUCLID" 1029004 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1027318 1027443 1027592 "GAUSSFAC" 1027840 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1025685 1025987 1026301 "GALUTIL" 1027037 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1023993 1024267 1024591 "GALPOLYU" 1025412 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1021358 1021648 1022055 "GALFACTU" 1023690 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1013163 1014663 1016271 "GALFACT" 1019790 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1010551 1011209 1011237 "FVFUN" 1012393 T FVFUN (NIL) -9 NIL 1013113 NIL) (-440 1009817 1009999 1010027 "FVC" 1010318 T FVC (NIL) -9 NIL 1010501 NIL) (-439 1009460 1009642 1009710 "FUNDESC" 1009769 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1009075 1009257 1009338 "FUNCTION" 1009412 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1006819 1007397 1007863 "FT" 1008629 T FT (NIL) -8 NIL NIL NIL) (-436 1005610 1006120 1006323 "FTEM" 1006636 T FTEM (NIL) -8 NIL NIL NIL) (-435 1003901 1004190 1004587 "FSUPFACT" 1005301 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1002298 1002587 1002919 "FST" 1003589 T FST (NIL) -8 NIL NIL NIL) (-433 1001497 1001603 1001791 "FSRED" 1002180 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 1000196 1000452 1000799 "FSPRMELT" 1001212 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 997502 997940 998426 "FSPECF" 999759 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 979657 987981 988022 "FS" 991906 NIL FS (NIL T) -9 NIL 994195 NIL) (-429 968300 971293 975350 "FS-" 975650 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 967828 967882 968052 "FSINT" 968241 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 966120 966821 967124 "FSERIES" 967607 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 965162 965278 965502 "FSCINT" 966000 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 961370 964106 964147 "FSAGG" 964517 NIL FSAGG (NIL T) -9 NIL 964776 NIL) (-424 959132 959733 960529 "FSAGG-" 960624 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 958174 958317 958544 "FSAGG2" 958985 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 955856 956136 956683 "FS2UPS" 957892 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 955490 955533 955662 "FS2" 955807 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 954368 954539 954841 "FS2EXPXP" 955315 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 953794 953909 954061 "FRUTIL" 954248 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 945207 949289 950647 "FR" 952468 NIL FR (NIL T) -8 NIL NIL NIL) (-417 940255 942925 942965 "FRNAALG" 944361 NIL FRNAALG (NIL T) -9 NIL 944968 NIL) (-416 935928 937004 938279 "FRNAALG-" 939029 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 935566 935609 935736 "FRNAAF2" 935879 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 933946 934420 934715 "FRMOD" 935378 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 931697 932329 932646 "FRIDEAL" 933737 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 930892 930979 931268 "FRIDEAL2" 931604 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 930025 930439 930480 "FRETRCT" 930485 NIL FRETRCT (NIL T) -9 NIL 930661 NIL) (-410 929137 929368 929719 "FRETRCT-" 929724 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 926315 927525 927584 "FRAMALG" 928466 NIL FRAMALG (NIL T T) -9 NIL 928758 NIL) (-408 924449 924904 925534 "FRAMALG-" 925757 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 918370 923924 924200 "FRAC" 924205 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 918006 918063 918170 "FRAC2" 918307 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 917642 917699 917806 "FR2" 917943 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 912280 915167 915195 "FPS" 916314 T FPS (NIL) -9 NIL 916871 NIL) (-403 911729 911838 912002 "FPS-" 912148 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 909149 910818 910846 "FPC" 911071 T FPC (NIL) -9 NIL 911213 NIL) (-401 908942 908982 909079 "FPC-" 909084 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 907732 908430 908471 "FPATMAB" 908476 NIL FPATMAB (NIL T) -9 NIL 908628 NIL) (-399 905405 905908 906334 "FPARFRAC" 907369 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 900798 901297 901979 "FORTRAN" 904837 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 898514 899014 899553 "FORT" 900279 T FORT (NIL) -7 NIL NIL NIL) (-396 896190 896752 896780 "FORTFN" 897840 T FORTFN (NIL) -9 NIL 898464 NIL) (-395 895954 896004 896032 "FORTCAT" 896091 T FORTCAT (NIL) -9 NIL 896153 NIL) (-394 894060 894570 894960 "FORMULA" 895584 T FORMULA (NIL) -8 NIL NIL NIL) (-393 893848 893878 893947 "FORMULA1" 894024 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 893371 893423 893596 "FORDER" 893790 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 892467 892631 892824 "FOP" 893198 T FOP (NIL) -7 NIL NIL NIL) (-390 891048 891747 891921 "FNLA" 892349 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 889777 890192 890220 "FNCAT" 890680 T FNCAT (NIL) -9 NIL 890940 NIL) (-388 889316 889736 889764 "FNAME" 889769 T FNAME (NIL) -8 NIL NIL NIL) (-387 887945 888908 888936 "FMTC" 888941 T FMTC (NIL) -9 NIL 888977 NIL) (-386 884278 885468 886097 "FMONOID" 887349 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 883470 884020 884169 "FM" 884174 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 880894 881540 881568 "FMFUN" 882712 T FMFUN (NIL) -9 NIL 883420 NIL) (-383 880163 880344 880372 "FMC" 880662 T FMC (NIL) -9 NIL 880844 NIL) (-382 877331 878191 878245 "FMCAT" 879440 NIL FMCAT (NIL T T) -9 NIL 879935 NIL) (-381 876197 877097 877197 "FM1" 877276 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 873971 874387 874881 "FLOATRP" 875748 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 867545 871700 872321 "FLOAT" 873370 T FLOAT (NIL) -8 NIL NIL NIL) (-378 864983 865483 866061 "FLOATCP" 867012 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 863758 864596 864637 "FLINEXP" 864642 NIL FLINEXP (NIL T) -9 NIL 864735 NIL) (-376 862912 863147 863475 "FLINEXP-" 863480 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 861988 862132 862356 "FLASORT" 862764 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 859179 860047 860099 "FLALG" 861326 NIL FLALG (NIL T T) -9 NIL 861793 NIL) (-373 852915 856665 856706 "FLAGG" 857968 NIL FLAGG (NIL T) -9 NIL 858620 NIL) (-372 851641 851980 852470 "FLAGG-" 852475 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 850683 850826 851053 "FLAGG2" 851494 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 847624 848632 848691 "FINRALG" 849819 NIL FINRALG (NIL T T) -9 NIL 850327 NIL) (-369 846784 847013 847352 "FINRALG-" 847357 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 846164 846403 846431 "FINITE" 846627 T FINITE (NIL) -9 NIL 846734 NIL) (-367 838596 840783 840823 "FINAALG" 844490 NIL FINAALG (NIL T) -9 NIL 845943 NIL) (-366 833928 834978 836122 "FINAALG-" 837501 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 833296 833683 833786 "FILE" 833858 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 831954 832292 832346 "FILECAT" 833030 NIL FILECAT (NIL T T) -9 NIL 833246 NIL) (-363 829788 831316 831344 "FIELD" 831384 T FIELD (NIL) -9 NIL 831464 NIL) (-362 828408 828793 829304 "FIELD-" 829309 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 826258 827043 827390 "FGROUP" 828094 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 825348 825512 825732 "FGLMICPK" 826090 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 821180 825273 825330 "FFX" 825335 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 820781 820842 820977 "FFSLPE" 821113 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 816770 817553 818349 "FFPOLY" 820017 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 816274 816310 816519 "FFPOLY2" 816728 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 812117 816193 816256 "FFP" 816261 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 807515 812028 812092 "FF" 812097 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 802641 806858 807048 "FFNBX" 807369 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 797570 801776 802034 "FFNBP" 802495 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 792203 796854 797065 "FFNB" 797403 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 791035 791233 791548 "FFINTBAS" 792000 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 787228 789442 789470 "FFIELDC" 790090 T FFIELDC (NIL) -9 NIL 790466 NIL) (-348 785890 786261 786758 "FFIELDC-" 786763 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 785459 785505 785629 "FFHOM" 785832 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 783154 783641 784158 "FFF" 784974 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 778772 782896 782997 "FFCGX" 783097 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 774393 778504 778611 "FFCGP" 778715 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 769576 774120 774228 "FFCG" 774329 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 751374 760447 760533 "FFCAT" 765698 NIL FFCAT (NIL T T T) -9 NIL 767149 NIL) (-341 746572 747619 748933 "FFCAT-" 750163 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 745983 746026 746261 "FFCAT2" 746523 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 735304 738955 740175 "FEXPR" 744835 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 734304 734739 734780 "FEVALAB" 734864 NIL FEVALAB (NIL T) -9 NIL 735125 NIL) (-337 733463 733673 734011 "FEVALAB-" 734016 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 732029 732846 733049 "FDIV" 733362 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 729069 729810 729925 "FDIVCAT" 731493 NIL FDIVCAT (NIL T T T T) -9 NIL 731930 NIL) (-334 728831 728858 729028 "FDIVCAT-" 729033 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 728051 728138 728415 "FDIV2" 728738 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 726737 726996 727285 "FCPAK1" 727782 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 725836 726237 726378 "FCOMP" 726628 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 709538 712986 716524 "FC" 722318 T FC (NIL) -8 NIL NIL NIL) (-329 702082 706102 706142 "FAXF" 707944 NIL FAXF (NIL T) -9 NIL 708636 NIL) (-328 699358 700016 700841 "FAXF-" 701306 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 694410 698734 698910 "FARRAY" 699215 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 689629 691695 691748 "FAMR" 692771 NIL FAMR (NIL T T) -9 NIL 693231 NIL) (-325 688519 688821 689256 "FAMR-" 689261 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 687688 688441 688494 "FAMONOID" 688499 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 685474 686184 686237 "FAMONC" 687178 NIL FAMONC (NIL T T) -9 NIL 687564 NIL) (-322 684139 685228 685365 "FAGROUP" 685370 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 681934 682253 682656 "FACUTIL" 683820 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 681033 681218 681440 "FACTFUNC" 681744 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 673455 680336 680535 "EXPUPXS" 680889 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 670938 671478 672064 "EXPRTUBE" 672889 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 667209 667801 668531 "EXPRODE" 670277 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 652694 665858 666287 "EXPR" 666813 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 647248 647835 648641 "EXPR2UPS" 651992 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 646880 646937 647046 "EXPR2" 647185 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 638271 646033 646323 "EXPEXPAN" 646717 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 638071 638228 638257 "EXIT" 638262 T EXIT (NIL) -8 NIL NIL NIL) (-311 637551 637795 637886 "EXITAST" 638000 T EXITAST (NIL) -8 NIL NIL NIL) (-310 637178 637240 637353 "EVALCYC" 637483 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 636719 636837 636878 "EVALAB" 637048 NIL EVALAB (NIL T) -9 NIL 637152 NIL) (-308 636200 636322 636543 "EVALAB-" 636548 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 633634 634936 634964 "EUCDOM" 635519 T EUCDOM (NIL) -9 NIL 635869 NIL) (-306 632039 632481 633071 "EUCDOM-" 633076 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 619577 622337 625087 "ESTOOLS" 629309 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 619209 619266 619375 "ESTOOLS2" 619514 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 618960 619002 619082 "ESTOOLS1" 619161 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 612997 614605 614633 "ES" 617401 T ES (NIL) -9 NIL 618811 NIL) (-301 607944 609231 611048 "ES-" 611212 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 604318 605079 605859 "ESCONT" 607184 T ESCONT (NIL) -7 NIL NIL NIL) (-299 604063 604095 604177 "ESCONT1" 604280 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 603738 603788 603888 "ES2" 604007 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 603368 603426 603535 "ES1" 603674 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 602584 602713 602889 "ERROR" 603212 T ERROR (NIL) -7 NIL NIL NIL) (-295 595976 602443 602534 "EQTBL" 602539 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 588479 591290 592739 "EQ" 594560 NIL -2035 (NIL T) -8 NIL NIL NIL) (-293 588111 588168 588277 "EQ2" 588416 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 583400 584449 585542 "EP" 587050 NIL EP (NIL T) -7 NIL NIL NIL) (-291 582000 582291 582597 "ENV" 583114 T ENV (NIL) -8 NIL NIL NIL) (-290 581145 581699 581727 "ENTIRER" 581732 T ENTIRER (NIL) -9 NIL 581778 NIL) (-289 577612 579100 579470 "EMR" 580944 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 576756 576941 576995 "ELTAGG" 577375 NIL ELTAGG (NIL T T) -9 NIL 577586 NIL) (-287 576475 576537 576678 "ELTAGG-" 576683 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 576264 576293 576347 "ELTAB" 576431 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 575390 575536 575735 "ELFUTS" 576115 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 575132 575188 575216 "ELEMFUN" 575321 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 575002 575023 575091 "ELEMFUN-" 575096 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 569846 573102 573143 "ELAGG" 574083 NIL ELAGG (NIL T) -9 NIL 574546 NIL) (-281 568131 568565 569228 "ELAGG-" 569233 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 566796 567074 567367 "ELABEXPR" 567858 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 559660 561463 562290 "EFUPXS" 566072 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 553110 554911 555721 "EFULS" 558936 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 550595 550953 551425 "EFSTRUC" 552742 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 540446 542012 543559 "EF" 549110 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 539520 539931 540080 "EAB" 540317 T EAB (NIL) -8 NIL NIL NIL) (-274 538702 539479 539507 "E04UCFA" 539512 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 537884 538661 538689 "E04NAFA" 538694 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 537066 537843 537871 "E04MBFA" 537876 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 536248 537025 537053 "E04JAFA" 537058 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 535432 536207 536235 "E04GCFA" 536240 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 534616 535391 535419 "E04FDFA" 535424 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 533798 534575 534603 "E04DGFA" 534608 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 527971 529323 530687 "E04AGNT" 532454 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 526651 527157 527197 "DVARCAT" 527672 NIL DVARCAT (NIL T) -9 NIL 527871 NIL) (-265 525855 526067 526381 "DVARCAT-" 526386 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 518992 525654 525783 "DSMP" 525788 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 513774 514937 516005 "DROPT" 517944 T DROPT (NIL) -8 NIL NIL NIL) (-262 513439 513498 513596 "DROPT1" 513709 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 508554 509680 510817 "DROPT0" 512322 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 506899 507224 507610 "DRAWPT" 508188 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 501486 502409 503488 "DRAW" 505873 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 501119 501172 501290 "DRAWHACK" 501427 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 499850 500119 500410 "DRAWCX" 500848 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 499365 499434 499585 "DRAWCURV" 499776 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 489833 491795 493910 "DRAWCFUN" 497270 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 486599 488528 488569 "DQAGG" 489198 NIL DQAGG (NIL T) -9 NIL 489471 NIL) (-253 475143 481604 481687 "DPOLCAT" 483539 NIL DPOLCAT (NIL T T T T) -9 NIL 484084 NIL) (-252 469979 471328 473286 "DPOLCAT-" 473291 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 463101 469840 469938 "DPMO" 469943 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 456126 462881 463048 "DPMM" 463053 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 455731 456045 456093 "DOMCTOR" 456098 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 454999 455253 455390 "DOMAIN" 455614 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 448987 454634 454786 "DMP" 454900 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 448587 448643 448787 "DLP" 448925 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 442409 447914 448104 "DLIST" 448429 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 439206 441262 441303 "DLAGG" 441853 NIL DLAGG (NIL T) -9 NIL 442083 NIL) (-243 437985 438649 438677 "DIVRING" 438769 T DIVRING (NIL) -9 NIL 438852 NIL) (-242 437222 437412 437712 "DIVRING-" 437717 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 435324 435681 436087 "DISPLAY" 436836 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 429212 435238 435301 "DIRPROD" 435306 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 428060 428263 428528 "DIRPROD2" 429005 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 417269 423275 423328 "DIRPCAT" 423738 NIL DIRPCAT (NIL NIL T) -9 NIL 424578 NIL) (-237 414595 415237 416118 "DIRPCAT-" 416455 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 413882 414042 414228 "DIOSP" 414429 T DIOSP (NIL) -7 NIL NIL NIL) (-235 410537 412794 412835 "DIOPS" 413269 NIL DIOPS (NIL T) -9 NIL 413498 NIL) (-234 410086 410200 410391 "DIOPS-" 410396 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 408944 409572 409600 "DIFRING" 409787 T DIFRING (NIL) -9 NIL 409897 NIL) (-232 408590 408667 408819 "DIFRING-" 408824 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 406361 407633 407674 "DIFEXT" 408037 NIL DIFEXT (NIL T) -9 NIL 408331 NIL) (-230 404646 405074 405740 "DIFEXT-" 405745 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 401921 404178 404219 "DIAGG" 404224 NIL DIAGG (NIL T) -9 NIL 404244 NIL) (-228 401305 401462 401714 "DIAGG-" 401719 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 396722 400264 400541 "DHMATRIX" 401074 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 392334 393243 394253 "DFSFUN" 395732 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 387412 391265 391577 "DFLOAT" 392042 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 385675 385956 386345 "DFINTTLS" 387120 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 382704 383696 384096 "DERHAM" 385341 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 380505 382479 382568 "DEQUEUE" 382648 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 379759 379892 380075 "DEGRED" 380367 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 376189 376934 377780 "DEFINTRF" 378987 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 373744 374213 374805 "DEFINTEF" 375708 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 373094 373364 373479 "DEFAST" 373649 T DEFAST (NIL) -8 NIL NIL NIL) (-217 367098 372689 372838 "DECIMAL" 372965 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 364609 365068 365574 "DDFACT" 366642 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 364205 364248 364399 "DBLRESP" 364560 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 362077 362438 362798 "DBASE" 363972 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 361319 361557 361703 "DATAARY" 361976 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 360425 361278 361306 "D03FAFA" 361311 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 359532 360384 360412 "D03EEFA" 360417 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 357482 357948 358437 "D03AGNT" 359063 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 356771 357441 357469 "D02EJFA" 357474 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 356060 356730 356758 "D02CJFA" 356763 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 355349 356019 356047 "D02BHFA" 356052 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 354638 355308 355336 "D02BBFA" 355341 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 347835 349424 351030 "D02AGNT" 353052 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 345603 346126 346672 "D01WGTS" 347309 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 344670 345562 345590 "D01TRNS" 345595 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 343738 344629 344657 "D01GBFA" 344662 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 342806 343697 343725 "D01FCFA" 343730 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 341874 342765 342793 "D01ASFA" 342798 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 340942 341833 341861 "D01AQFA" 341866 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 340010 340901 340929 "D01APFA" 340934 T D01APFA (NIL) -8 NIL NIL NIL) (-197 339078 339969 339997 "D01ANFA" 340002 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 338146 339037 339065 "D01AMFA" 339070 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 337214 338105 338133 "D01ALFA" 338138 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 336282 337173 337201 "D01AKFA" 337206 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 335350 336241 336269 "D01AJFA" 336274 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 328645 330198 331759 "D01AGNT" 333809 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 327982 328110 328262 "CYCLOTOM" 328513 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 324717 325430 326157 "CYCLES" 327275 T CYCLES (NIL) -7 NIL NIL NIL) (-189 324029 324163 324334 "CVMP" 324578 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 321870 322128 322497 "CTRIGMNP" 323757 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 321338 321664 321737 "CTOR" 321817 T CTOR (NIL) -8 NIL NIL NIL) (-186 320847 321069 321170 "CTORKIND" 321257 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 320169 320454 320482 "CTORCAT" 320664 T CTORCAT (NIL) -9 NIL 320777 NIL) (-184 319767 319878 320037 "CTORCAT-" 320042 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 319256 319470 319568 "CTORCALL" 319689 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 318630 318729 318882 "CSTTOOLS" 319153 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 314429 315086 315844 "CRFP" 317942 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 313904 314150 314242 "CRCEAST" 314357 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 312951 313136 313364 "CRAPACK" 313708 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 312335 312436 312640 "CPMATCH" 312827 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 312060 312088 312194 "CPIMA" 312301 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 308424 309096 309814 "COORDSYS" 311395 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 307836 307957 308099 "CONTOUR" 308302 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 303727 305839 306331 "CONTFRAC" 307376 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 303607 303628 303656 "CONDUIT" 303693 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 302746 303300 303328 "COMRING" 303333 T COMRING (NIL) -9 NIL 303385 NIL) (-171 301800 302104 302288 "COMPPROP" 302582 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 301461 301496 301624 "COMPLPAT" 301759 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 291755 301270 301379 "COMPLEX" 301384 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 291391 291448 291555 "COMPLEX2" 291692 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 291109 291144 291242 "COMPFACT" 291350 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 275585 285568 285608 "COMPCAT" 286612 NIL COMPCAT (NIL T) -9 NIL 287958 NIL) (-165 265095 268024 271651 "COMPCAT-" 272007 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 264824 264852 264955 "COMMUPC" 265061 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 264618 264652 264711 "COMMONOP" 264785 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 264174 264369 264456 "COMM" 264551 T COMM (NIL) -8 NIL NIL NIL) (-161 263750 263978 264053 "COMMAAST" 264119 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 262999 263193 263221 "COMBOPC" 263559 T COMBOPC (NIL) -9 NIL 263734 NIL) (-159 261895 262105 262347 "COMBINAT" 262789 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258352 258926 259553 "COMBF" 261317 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 257110 257468 257703 "COLOR" 258137 T COLOR (NIL) -8 NIL NIL NIL) (-156 256586 256831 256923 "COLONAST" 257038 T COLONAST (NIL) -8 NIL NIL NIL) (-155 256226 256273 256398 "CMPLXRT" 256533 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 255674 255926 256025 "CLLCTAST" 256147 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 251174 252204 253284 "CLIP" 254614 T CLIP (NIL) -7 NIL NIL NIL) (-152 249520 250280 250519 "CLIF" 251001 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 245695 247666 247707 "CLAGG" 248636 NIL CLAGG (NIL T) -9 NIL 249172 NIL) (-150 244117 244574 245157 "CLAGG-" 245162 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 243661 243746 243886 "CINTSLPE" 244026 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 241162 241633 242181 "CHVAR" 243189 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240371 240925 240953 "CHARZ" 240958 T CHARZ (NIL) -9 NIL 240973 NIL) (-146 240125 240165 240243 "CHARPOL" 240325 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 239218 239805 239833 "CHARNZ" 239880 T CHARNZ (NIL) -9 NIL 239936 NIL) (-144 237180 237908 238243 "CHAR" 238903 T CHAR (NIL) -8 NIL NIL NIL) (-143 236906 236967 236995 "CFCAT" 237106 T CFCAT (NIL) -9 NIL NIL NIL) (-142 236151 236262 236444 "CDEN" 236790 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 232116 235304 235584 "CCLASS" 235891 T CCLASS (NIL) -8 NIL NIL NIL) (-140 231423 231566 231729 "CATEGORY" 231973 T -10 (NIL) -8 NIL NIL NIL) (-139 231028 231342 231390 "CATCTOR" 231395 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 230479 230731 230829 "CATAST" 230950 T CATAST (NIL) -8 NIL NIL NIL) (-137 229955 230200 230292 "CASEAST" 230407 T CASEAST (NIL) -8 NIL NIL NIL) (-136 224964 225984 226737 "CARTEN" 229258 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 224072 224220 224441 "CARTEN2" 224811 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 222387 223222 223479 "CARD" 223835 T CARD (NIL) -8 NIL NIL NIL) (-133 221963 222191 222266 "CAPSLAST" 222332 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 221467 221675 221703 "CACHSET" 221835 T CACHSET (NIL) -9 NIL 221913 NIL) (-131 220937 221259 221287 "CABMON" 221337 T CABMON (NIL) -9 NIL 221393 NIL) (-130 220410 220641 220751 "BYTEORD" 220847 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 219386 219944 220086 "BYTE" 220249 T BYTE (NIL) -8 NIL NIL 220371) (-128 214736 218891 219063 "BYTEBUF" 219234 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 212245 214428 214535 "BTREE" 214662 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209694 211893 212015 "BTOURN" 212155 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 207064 209164 209205 "BTCAT" 209273 NIL BTCAT (NIL T) -9 NIL 209350 NIL) (-124 206731 206811 206960 "BTCAT-" 206965 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 201996 205874 205902 "BTAGG" 206124 T BTAGG (NIL) -9 NIL 206285 NIL) (-122 201486 201611 201817 "BTAGG-" 201822 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 198481 200764 200979 "BSTREE" 201303 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 197619 197745 197929 "BRILL" 198337 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 194271 196345 196386 "BRAGG" 197035 NIL BRAGG (NIL T) -9 NIL 197293 NIL) (-118 192800 193206 193761 "BRAGG-" 193766 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 186029 192146 192330 "BPADICRT" 192648 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184344 185966 186011 "BPADIC" 186016 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 184042 184072 184186 "BOUNDZRO" 184308 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 179134 180332 181275 "BOP" 183119 T BOP (NIL) -8 NIL NIL NIL) (-113 176915 177319 177794 "BOP1" 178692 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 175740 176489 176638 "BOOLEAN" 176786 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175076 175480 175534 "BMODULE" 175539 NIL BMODULE (NIL T T) -9 NIL 175604 NIL) (-110 170877 174874 174947 "BITS" 175023 T BITS (NIL) -8 NIL NIL NIL) (-109 170298 170417 170557 "BINDING" 170757 T BINDING (NIL) -8 NIL NIL NIL) (-108 164305 169895 170043 "BINARY" 170170 T BINARY (NIL) -8 NIL NIL NIL) (-107 162085 163560 163601 "BGAGG" 163861 NIL BGAGG (NIL T) -9 NIL 163998 NIL) (-106 161916 161948 162039 "BGAGG-" 162044 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160987 161300 161505 "BFUNCT" 161731 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159677 159855 160143 "BEZOUT" 160811 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156146 158529 158859 "BBTREE" 159380 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155880 155933 155961 "BASTYPE" 156080 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155732 155761 155834 "BASTYPE-" 155839 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155166 155242 155394 "BALFACT" 155643 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154022 154581 154767 "AUTOMOR" 155011 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153748 153753 153779 "ATTREG" 153784 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152000 152445 152797 "ATTRBUT" 153414 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151608 151828 151894 "ATTRAST" 151952 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151144 151257 151283 "ATRIG" 151484 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150953 150994 151081 "ATRIG-" 151086 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150598 150784 150810 "ASTCAT" 150815 T ASTCAT (NIL) -9 NIL 150845 NIL) (-92 150325 150384 150503 "ASTCAT-" 150508 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148474 150101 150189 "ASTACK" 150268 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146979 147276 147641 "ASSOCEQ" 148156 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146011 146638 146762 "ASP9" 146886 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145774 145959 145998 "ASP8" 146003 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144642 145379 145521 "ASP80" 145663 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143540 144277 144409 "ASP7" 144541 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142494 143217 143335 "ASP78" 143453 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141463 142174 142291 "ASP77" 142408 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140375 141101 141232 "ASP74" 141363 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139275 140010 140142 "ASP73" 140274 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138379 139101 139201 "ASP6" 139206 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137323 138056 138174 "ASP55" 138292 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136272 136997 137116 "ASP50" 137235 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135360 135973 136083 "ASP4" 136193 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134448 135061 135171 "ASP49" 135281 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133232 133987 134155 "ASP42" 134337 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132008 132765 132935 "ASP41" 133119 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130958 131685 131803 "ASP35" 131921 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130723 130906 130945 "ASP34" 130950 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130460 130527 130603 "ASP33" 130678 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129353 130095 130227 "ASP31" 130359 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129118 129301 129340 "ASP30" 129345 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128853 128922 128998 "ASP29" 129073 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128618 128801 128840 "ASP28" 128845 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128383 128566 128605 "ASP27" 128610 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127467 128081 128192 "ASP24" 128303 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126543 127269 127381 "ASP20" 127386 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125631 126244 126354 "ASP1" 126464 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124573 125305 125424 "ASP19" 125543 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124310 124377 124453 "ASP12" 124528 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123162 123909 124053 "ASP10" 124197 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121013 123006 123097 "ARRAY2" 123102 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116778 120661 120775 "ARRAY1" 120930 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 115810 115983 116204 "ARRAY12" 116601 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110122 112040 112115 "ARR2CAT" 114745 NIL ARR2CAT (NIL T T T) -9 NIL 115503 NIL) (-56 107556 108300 109254 "ARR2CAT-" 109259 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106873 107183 107308 "ARITY" 107449 T ARITY (NIL) -8 NIL NIL NIL) (-54 105649 105801 106100 "APPRULE" 106709 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105300 105348 105467 "APPLYORE" 105595 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104247 104565 104760 "ANY" 105123 T ANY (NIL) -8 NIL NIL NIL) (-51 103525 103648 103805 "ANY1" 104121 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101055 101962 102289 "ANTISYM" 103249 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 100547 100762 100858 "ANON" 100977 T ANON (NIL) -8 NIL NIL NIL) (-48 94796 99086 99540 "AN" 100111 T AN (NIL) -8 NIL NIL NIL) (-47 91018 92406 92457 "AMR" 93205 NIL AMR (NIL T T) -9 NIL 93805 NIL) (-46 90130 90351 90714 "AMR-" 90719 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74569 90047 90108 "ALIST" 90113 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71371 74163 74332 "ALGSC" 74487 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 67926 68481 69088 "ALGPKG" 70811 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67203 67304 67488 "ALGMFACT" 67812 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63154 63761 64379 "ALGMANIP" 66763 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54524 62780 62930 "ALGFF" 63087 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 53720 53851 54030 "ALGFACT" 54382 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52751 53351 53389 "ALGEBRA" 53394 NIL ALGEBRA (NIL T) -9 NIL 53435 NIL) (-37 52469 52528 52660 "ALGEBRA-" 52665 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34562 50471 50523 "ALAGG" 50659 NIL ALAGG (NIL T T) -9 NIL 50820 NIL) (-35 34098 34211 34237 "AHYP" 34438 T AHYP (NIL) -9 NIL NIL NIL) (-34 33029 33277 33303 "AGG" 33802 T AGG (NIL) -9 NIL 34081 NIL) (-33 32463 32625 32839 "AGG-" 32844 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30269 30692 31097 "AF" 32105 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29749 29994 30084 "ADDAST" 30197 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29017 29276 29432 "ACPLOT" 29611 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18557 26360 26398 "ACFS" 27005 NIL ACFS (NIL T) -9 NIL 27244 NIL) (-28 16584 17074 17836 "ACFS-" 17841 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12823 14751 14777 "ACF" 15656 T ACF (NIL) -9 NIL 16068 NIL) (-26 11527 11861 12354 "ACF-" 12359 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11099 11294 11320 "ABELSG" 11412 T ABELSG (NIL) -9 NIL 11477 NIL) (-24 10966 10991 11057 "ABELSG-" 11062 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10309 10596 10622 "ABELMON" 10792 T ABELMON (NIL) -9 NIL 10904 NIL) (-22 9973 10057 10195 "ABELMON-" 10200 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9281 9653 9679 "ABELGRP" 9804 T ABELGRP (NIL) -9 NIL 9886 NIL) (-20 8744 8873 9089 "ABELGRP-" 9094 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8083 8122 "A1AGG" 8127 NIL A1AGG (NIL T) -9 NIL 8167 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3205068 3205073 3205078 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3205053 3205058 3205063 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3205038 3205043 3205048 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3205023 3205028 3205033 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1287 3204166 3204898 3204975 "ZMOD" 3204980 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1286 3203276 3203440 3203649 "ZLINDEP" 3203998 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1285 3192576 3194344 3196316 "ZDSOLVE" 3201406 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1284 3191822 3191963 3192152 "YSTREAM" 3192422 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1283 3189596 3191123 3191327 "XRPOLY" 3191665 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1282 3186149 3187467 3188042 "XPR" 3189068 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1281 3183870 3185480 3185684 "XPOLY" 3185980 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1280 3181627 3182995 3183050 "XPOLYC" 3183338 NIL XPOLYC (NIL T T) -9 NIL 3183451 NIL) (-1279 3178002 3180144 3180532 "XPBWPOLY" 3181285 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1278 3173878 3176165 3176207 "XF" 3176828 NIL XF (NIL T) -9 NIL 3177228 NIL) (-1277 3173499 3173587 3173756 "XF-" 3173761 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1276 3168799 3170088 3170143 "XFALG" 3172315 NIL XFALG (NIL T T) -9 NIL 3173104 NIL) (-1275 3167932 3168036 3168241 "XEXPPKG" 3168691 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1274 3166041 3167782 3167878 "XDPOLY" 3167883 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1273 3164952 3165552 3165595 "XALG" 3165600 NIL XALG (NIL T) -9 NIL 3165711 NIL) (-1272 3158394 3162929 3163423 "WUTSET" 3164544 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1271 3156650 3157446 3157769 "WP" 3158205 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1270 3156252 3156472 3156542 "WHILEAST" 3156602 T WHILEAST (NIL) -8 NIL NIL NIL) (-1269 3155724 3155969 3156063 "WHEREAST" 3156180 T WHEREAST (NIL) -8 NIL NIL NIL) (-1268 3154610 3154808 3155103 "WFFINTBS" 3155521 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1267 3152514 3152941 3153403 "WEIER" 3154182 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1266 3151635 3152085 3152127 "VSPACE" 3152263 NIL VSPACE (NIL T) -9 NIL 3152337 NIL) (-1265 3151473 3151500 3151591 "VSPACE-" 3151596 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1264 3151281 3151324 3151392 "VOID" 3151427 T VOID (NIL) -8 NIL NIL NIL) (-1263 3149417 3149776 3150182 "VIEW" 3150897 T VIEW (NIL) -7 NIL NIL NIL) (-1262 3145841 3146480 3147217 "VIEWDEF" 3148702 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1261 3135145 3137389 3139562 "VIEW3D" 3143690 T VIEW3D (NIL) -8 NIL NIL NIL) (-1260 3127396 3129056 3130635 "VIEW2D" 3133588 T VIEW2D (NIL) -8 NIL NIL NIL) (-1259 3122750 3127166 3127258 "VECTOR" 3127339 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1258 3121327 3121586 3121904 "VECTOR2" 3122480 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1257 3114806 3119111 3119154 "VECTCAT" 3120147 NIL VECTCAT (NIL T) -9 NIL 3120733 NIL) (-1256 3113820 3114074 3114464 "VECTCAT-" 3114469 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1255 3113274 3113471 3113591 "VARIABLE" 3113735 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1254 3113207 3113212 3113242 "UTYPE" 3113247 T UTYPE (NIL) -9 NIL NIL NIL) (-1253 3112037 3112191 3112453 "UTSODETL" 3113033 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1252 3109477 3109937 3110461 "UTSODE" 3111578 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1251 3101314 3107103 3107592 "UTS" 3109046 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1250 3092522 3097881 3097924 "UTSCAT" 3099036 NIL UTSCAT (NIL T) -9 NIL 3099793 NIL) (-1249 3089869 3090592 3091581 "UTSCAT-" 3091586 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1248 3089496 3089539 3089672 "UTS2" 3089820 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1247 3083722 3086334 3086377 "URAGG" 3088447 NIL URAGG (NIL T) -9 NIL 3089170 NIL) (-1246 3080661 3081524 3082647 "URAGG-" 3082652 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1245 3076371 3079296 3079761 "UPXSSING" 3080325 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1244 3068437 3075618 3075891 "UPXS" 3076156 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1243 3061510 3068341 3068413 "UPXSCONS" 3068418 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1242 3051720 3058505 3058567 "UPXSCCA" 3059141 NIL UPXSCCA (NIL T T) -9 NIL 3059374 NIL) (-1241 3051358 3051443 3051617 "UPXSCCA-" 3051622 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1240 3041421 3047979 3048022 "UPXSCAT" 3048670 NIL UPXSCAT (NIL T) -9 NIL 3049278 NIL) (-1239 3040851 3040930 3041109 "UPXS2" 3041336 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1238 3039505 3039758 3040109 "UPSQFREE" 3040594 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1237 3033258 3036307 3036362 "UPSCAT" 3037523 NIL UPSCAT (NIL T T) -9 NIL 3038297 NIL) (-1236 3032462 3032669 3032996 "UPSCAT-" 3033001 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1235 3018577 3026337 3026380 "UPOLYC" 3028481 NIL UPOLYC (NIL T) -9 NIL 3029702 NIL) (-1234 3009905 3012331 3015478 "UPOLYC-" 3015483 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1233 3009532 3009575 3009708 "UPOLYC2" 3009856 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1232 3001343 3009215 3009344 "UP" 3009451 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1231 3000682 3000789 3000953 "UPMP" 3001232 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1230 3000235 3000316 3000455 "UPDIVP" 3000595 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1229 2998803 2999052 2999368 "UPDECOMP" 2999984 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1228 2998038 2998150 2998335 "UPCDEN" 2998687 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1227 2997557 2997626 2997775 "UP2" 2997963 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1226 2996024 2996761 2997038 "UNISEG" 2997315 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1225 2995239 2995366 2995571 "UNISEG2" 2995867 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1224 2994299 2994479 2994705 "UNIFACT" 2995055 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1223 2978231 2993476 2993727 "ULS" 2994106 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1222 2966230 2978135 2978207 "ULSCONS" 2978212 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1221 2948811 2960788 2960850 "ULSCCAT" 2961488 NIL ULSCCAT (NIL T T) -9 NIL 2961776 NIL) (-1220 2947861 2948106 2948494 "ULSCCAT-" 2948499 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1219 2937701 2944173 2944216 "ULSCAT" 2945079 NIL ULSCAT (NIL T) -9 NIL 2945809 NIL) (-1218 2937131 2937210 2937389 "ULS2" 2937616 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1217 2936258 2936768 2936875 "UINT8" 2936986 T UINT8 (NIL) -8 NIL NIL 2937071) (-1216 2935384 2935894 2936001 "UINT64" 2936112 T UINT64 (NIL) -8 NIL NIL 2936197) (-1215 2934510 2935020 2935127 "UINT32" 2935238 T UINT32 (NIL) -8 NIL NIL 2935323) (-1214 2933636 2934146 2934253 "UINT16" 2934364 T UINT16 (NIL) -8 NIL NIL 2934449) (-1213 2932005 2932962 2932992 "UFD" 2933204 T UFD (NIL) -9 NIL 2933318 NIL) (-1212 2931799 2931845 2931940 "UFD-" 2931945 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1211 2930881 2931064 2931280 "UDVO" 2931605 T UDVO (NIL) -7 NIL NIL NIL) (-1210 2928697 2929106 2929577 "UDPO" 2930445 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1209 2928630 2928635 2928665 "TYPE" 2928670 T TYPE (NIL) -9 NIL NIL NIL) (-1208 2928390 2928585 2928616 "TYPEAST" 2928621 T TYPEAST (NIL) -8 NIL NIL NIL) (-1207 2927361 2927563 2927803 "TWOFACT" 2928184 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1206 2926384 2926770 2927005 "TUPLE" 2927161 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1205 2924075 2924594 2925133 "TUBETOOL" 2925867 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1204 2922924 2923129 2923370 "TUBE" 2923868 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1203 2917653 2921896 2922179 "TS" 2922676 NIL TS (NIL T) -8 NIL NIL NIL) (-1202 2906293 2910412 2910509 "TSETCAT" 2915778 NIL TSETCAT (NIL T T T T) -9 NIL 2917309 NIL) (-1201 2901025 2902625 2904516 "TSETCAT-" 2904521 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1200 2895664 2896511 2897440 "TRMANIP" 2900161 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1199 2895105 2895168 2895331 "TRIMAT" 2895596 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1198 2892971 2893208 2893565 "TRIGMNIP" 2894854 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1197 2892491 2892604 2892634 "TRIGCAT" 2892847 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1196 2892160 2892239 2892380 "TRIGCAT-" 2892385 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1195 2889005 2891018 2891299 "TREE" 2891914 NIL TREE (NIL T) -8 NIL NIL NIL) (-1194 2888279 2888807 2888837 "TRANFUN" 2888872 T TRANFUN (NIL) -9 NIL 2888938 NIL) (-1193 2887558 2887749 2888029 "TRANFUN-" 2888034 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1192 2887362 2887394 2887455 "TOPSP" 2887519 T TOPSP (NIL) -7 NIL NIL NIL) (-1191 2886710 2886825 2886979 "TOOLSIGN" 2887243 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1190 2885344 2885887 2886126 "TEXTFILE" 2886493 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1189 2883256 2883797 2884226 "TEX" 2884937 T TEX (NIL) -8 NIL NIL NIL) (-1188 2883037 2883068 2883140 "TEX1" 2883219 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1187 2882685 2882748 2882838 "TEMUTL" 2882969 T TEMUTL (NIL) -7 NIL NIL NIL) (-1186 2880839 2881119 2881444 "TBCMPPK" 2882408 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1185 2872616 2878999 2879055 "TBAGG" 2879455 NIL TBAGG (NIL T T) -9 NIL 2879666 NIL) (-1184 2867686 2869174 2870928 "TBAGG-" 2870933 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1183 2867070 2867177 2867322 "TANEXP" 2867575 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1182 2860460 2866927 2867020 "TABLE" 2867025 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1181 2859872 2859971 2860109 "TABLEAU" 2860357 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1180 2854480 2855700 2856948 "TABLBUMP" 2858658 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1179 2853702 2853849 2854030 "SYSTEM" 2854321 T SYSTEM (NIL) -8 NIL NIL NIL) (-1178 2850161 2850860 2851643 "SYSSOLP" 2852953 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1177 2849205 2849710 2849829 "SYSNNI" 2850015 NIL SYSNNI (NIL NIL) -8 NIL NIL 2850100) (-1176 2848512 2848971 2849050 "SYSINT" 2849110 NIL SYSINT (NIL NIL) -8 NIL NIL 2849155) (-1175 2844844 2845790 2846500 "SYNTAX" 2847824 T SYNTAX (NIL) -8 NIL NIL NIL) (-1174 2842002 2842604 2843236 "SYMTAB" 2844234 T SYMTAB (NIL) -8 NIL NIL NIL) (-1173 2837251 2838153 2839136 "SYMS" 2841041 T SYMS (NIL) -8 NIL NIL NIL) (-1172 2834486 2836709 2836939 "SYMPOLY" 2837056 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1171 2834003 2834078 2834201 "SYMFUNC" 2834398 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1170 2830022 2831315 2832128 "SYMBOL" 2833212 T SYMBOL (NIL) -8 NIL NIL NIL) (-1169 2823561 2825250 2826970 "SWITCH" 2828324 T SWITCH (NIL) -8 NIL NIL NIL) (-1168 2816795 2822382 2822685 "SUTS" 2823316 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1167 2808861 2816042 2816315 "SUPXS" 2816580 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2800621 2808479 2808605 "SUP" 2808770 NIL SUP (NIL T) -8 NIL NIL NIL) (-1165 2799780 2799907 2800124 "SUPFRACF" 2800489 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1164 2799401 2799460 2799573 "SUP2" 2799715 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1163 2797849 2798123 2798479 "SUMRF" 2799100 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1162 2797184 2797250 2797442 "SUMFS" 2797770 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1161 2781151 2796361 2796612 "SULS" 2796991 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2780753 2780973 2781043 "SUCHTAST" 2781103 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1159 2780048 2780278 2780418 "SUCH" 2780661 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1158 2773914 2774954 2775913 "SUBSPACE" 2779136 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1157 2773344 2773434 2773598 "SUBRESP" 2773802 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1156 2766709 2768009 2769320 "STTF" 2772080 NIL STTF (NIL T) -7 NIL NIL NIL) (-1155 2760882 2762002 2763149 "STTFNC" 2765609 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1154 2752193 2754064 2755858 "STTAYLOR" 2759123 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1153 2745323 2752057 2752140 "STRTBL" 2752145 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1152 2740687 2745278 2745309 "STRING" 2745314 T STRING (NIL) -8 NIL NIL NIL) (-1151 2735548 2740060 2740090 "STRICAT" 2740149 T STRICAT (NIL) -9 NIL 2740211 NIL) (-1150 2728302 2733167 2733778 "STREAM" 2734972 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1149 2727812 2727889 2728033 "STREAM3" 2728219 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1148 2726794 2726977 2727212 "STREAM2" 2727625 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1147 2726482 2726534 2726627 "STREAM1" 2726736 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1146 2725498 2725679 2725910 "STINPROD" 2726298 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1145 2725050 2725260 2725290 "STEP" 2725370 T STEP (NIL) -9 NIL 2725448 NIL) (-1144 2718482 2724949 2725026 "STBL" 2725031 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1143 2713608 2717703 2717746 "STAGG" 2717899 NIL STAGG (NIL T) -9 NIL 2717988 NIL) (-1142 2711310 2711912 2712784 "STAGG-" 2712789 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1141 2709457 2711080 2711172 "STACK" 2711253 NIL STACK (NIL T) -8 NIL NIL NIL) (-1140 2702152 2707598 2708054 "SREGSET" 2709087 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1139 2694577 2695946 2697459 "SRDCMPK" 2700758 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2687494 2692017 2692047 "SRAGG" 2693350 T SRAGG (NIL) -9 NIL 2693958 NIL) (-1137 2686511 2686766 2687145 "SRAGG-" 2687150 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1136 2680971 2685458 2685879 "SQMATRIX" 2686137 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1135 2674656 2677689 2678416 "SPLTREE" 2680316 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1134 2670619 2671312 2671958 "SPLNODE" 2674082 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1133 2669666 2669899 2669929 "SPFCAT" 2670373 T SPFCAT (NIL) -9 NIL NIL NIL) (-1132 2668403 2668613 2668877 "SPECOUT" 2669424 T SPECOUT (NIL) -7 NIL NIL NIL) (-1131 2660029 2661799 2661829 "SPADXPT" 2666221 T SPADXPT (NIL) -9 NIL 2668255 NIL) (-1130 2659790 2659830 2659899 "SPADPRSR" 2659982 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1129 2657945 2659745 2659776 "SPADAST" 2659781 T SPADAST (NIL) -8 NIL NIL NIL) (-1128 2649890 2651663 2651706 "SPACEC" 2656079 NIL SPACEC (NIL T) -9 NIL 2657895 NIL) (-1127 2648020 2649822 2649871 "SPACE3" 2649876 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1126 2646772 2646943 2647234 "SORTPAK" 2647825 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1125 2644864 2645167 2645579 "SOLVETRA" 2646436 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1124 2643914 2644136 2644397 "SOLVESER" 2644637 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1123 2639216 2640106 2641101 "SOLVERAD" 2642966 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1122 2635031 2635640 2636369 "SOLVEFOR" 2638583 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1121 2629301 2634380 2634477 "SNTSCAT" 2634482 NIL SNTSCAT (NIL T T T T) -9 NIL 2634552 NIL) (-1120 2623407 2627624 2628015 "SMTS" 2628991 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1119 2618091 2623295 2623372 "SMP" 2623377 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1118 2616250 2616551 2616949 "SMITH" 2617788 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1117 2609110 2613301 2613404 "SMATCAT" 2614755 NIL SMATCAT (NIL NIL T T T) -9 NIL 2615305 NIL) (-1116 2606050 2606873 2608051 "SMATCAT-" 2608056 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1115 2603716 2605286 2605329 "SKAGG" 2605590 NIL SKAGG (NIL T) -9 NIL 2605725 NIL) (-1114 2600024 2603132 2603327 "SINT" 2603514 T SINT (NIL) -8 NIL NIL 2603687) (-1113 2599796 2599834 2599900 "SIMPAN" 2599980 T SIMPAN (NIL) -7 NIL NIL NIL) (-1112 2599075 2599331 2599471 "SIG" 2599678 T SIG (NIL) -8 NIL NIL NIL) (-1111 2597913 2598134 2598409 "SIGNRF" 2598834 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1110 2596746 2596897 2597181 "SIGNEF" 2597742 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1109 2596052 2596329 2596453 "SIGAST" 2596644 T SIGAST (NIL) -8 NIL NIL NIL) (-1108 2593741 2594196 2594702 "SHP" 2595593 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1107 2587593 2593642 2593718 "SHDP" 2593723 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1106 2587166 2587358 2587388 "SGROUP" 2587481 T SGROUP (NIL) -9 NIL 2587543 NIL) (-1105 2587024 2587050 2587123 "SGROUP-" 2587128 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1104 2583859 2584557 2585280 "SGCF" 2586323 T SGCF (NIL) -7 NIL NIL NIL) (-1103 2578227 2583306 2583403 "SFRTCAT" 2583408 NIL SFRTCAT (NIL T T T T) -9 NIL 2583447 NIL) (-1102 2571648 2572666 2573802 "SFRGCD" 2577210 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1101 2564774 2565847 2567033 "SFQCMPK" 2570581 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2564394 2564483 2564594 "SFORT" 2564715 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1099 2563512 2564234 2564355 "SEXOF" 2564360 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1098 2562619 2563393 2563461 "SEX" 2563466 T SEX (NIL) -8 NIL NIL NIL) (-1097 2558132 2558847 2558942 "SEXCAT" 2561879 NIL SEXCAT (NIL T T T T T) -9 NIL 2562457 NIL) (-1096 2555285 2558066 2558114 "SET" 2558119 NIL SET (NIL T) -8 NIL NIL NIL) (-1095 2553509 2553998 2554303 "SETMN" 2555026 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1094 2553005 2553157 2553187 "SETCAT" 2553363 T SETCAT (NIL) -9 NIL 2553473 NIL) (-1093 2552697 2552775 2552905 "SETCAT-" 2552910 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1092 2549058 2551158 2551201 "SETAGG" 2552071 NIL SETAGG (NIL T) -9 NIL 2552411 NIL) (-1091 2548516 2548632 2548869 "SETAGG-" 2548874 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1090 2547959 2548212 2548313 "SEQAST" 2548437 T SEQAST (NIL) -8 NIL NIL NIL) (-1089 2547158 2547452 2547513 "SEGXCAT" 2547799 NIL SEGXCAT (NIL T T) -9 NIL 2547919 NIL) (-1088 2546164 2546824 2547006 "SEG" 2547011 NIL SEG (NIL T) -8 NIL NIL NIL) (-1087 2545143 2545357 2545400 "SEGCAT" 2545922 NIL SEGCAT (NIL T) -9 NIL 2546143 NIL) (-1086 2544144 2544522 2544722 "SEGBIND" 2544978 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1085 2543765 2543824 2543937 "SEGBIND2" 2544079 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1084 2543338 2543566 2543643 "SEGAST" 2543710 T SEGAST (NIL) -8 NIL NIL NIL) (-1083 2542557 2542683 2542887 "SEG2" 2543182 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1082 2541967 2542492 2542539 "SDVAR" 2542544 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1081 2534494 2541737 2541867 "SDPOL" 2541872 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1080 2533087 2533353 2533672 "SCPKG" 2534209 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1079 2532251 2532423 2532615 "SCOPE" 2532917 T SCOPE (NIL) -8 NIL NIL NIL) (-1078 2531471 2531605 2531784 "SCACHE" 2532106 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1077 2531117 2531303 2531333 "SASTCAT" 2531338 T SASTCAT (NIL) -9 NIL 2531351 NIL) (-1076 2530604 2530952 2531028 "SAOS" 2531063 T SAOS (NIL) -8 NIL NIL NIL) (-1075 2530169 2530204 2530377 "SAERFFC" 2530563 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1074 2524108 2530066 2530146 "SAE" 2530151 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1073 2523701 2523736 2523895 "SAEFACT" 2524067 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1072 2522022 2522336 2522737 "RURPK" 2523367 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1071 2520659 2520965 2521270 "RULESET" 2521856 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1070 2517882 2518412 2518870 "RULE" 2520340 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1069 2517494 2517676 2517759 "RULECOLD" 2517834 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1068 2517284 2517312 2517383 "RTVALUE" 2517445 T RTVALUE (NIL) -8 NIL NIL NIL) (-1067 2516755 2517001 2517095 "RSTRCAST" 2517212 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1066 2511603 2512398 2513318 "RSETGCD" 2515954 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1065 2500833 2505912 2506009 "RSETCAT" 2510128 NIL RSETCAT (NIL T T T T) -9 NIL 2511225 NIL) (-1064 2498760 2499299 2500123 "RSETCAT-" 2500128 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1063 2491145 2492522 2494042 "RSDCMPK" 2497359 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1062 2489124 2489591 2489665 "RRCC" 2490751 NIL RRCC (NIL T T) -9 NIL 2491095 NIL) (-1061 2488475 2488649 2488928 "RRCC-" 2488933 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1060 2487918 2488171 2488272 "RPTAST" 2488396 T RPTAST (NIL) -8 NIL NIL NIL) (-1059 2462189 2471538 2471605 "RPOLCAT" 2482269 NIL RPOLCAT (NIL T T T) -9 NIL 2485428 NIL) (-1058 2453687 2456027 2459149 "RPOLCAT-" 2459154 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1057 2444618 2451898 2452380 "ROUTINE" 2453227 T ROUTINE (NIL) -8 NIL NIL NIL) (-1056 2441416 2444244 2444384 "ROMAN" 2444500 T ROMAN (NIL) -8 NIL NIL NIL) (-1055 2439660 2440276 2440536 "ROIRC" 2441221 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1054 2436018 2438296 2438326 "RNS" 2438630 T RNS (NIL) -9 NIL 2438903 NIL) (-1053 2434527 2434910 2435444 "RNS-" 2435519 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1052 2433950 2434358 2434388 "RNG" 2434393 T RNG (NIL) -9 NIL 2434414 NIL) (-1051 2433316 2433704 2433747 "RMODULE" 2433809 NIL RMODULE (NIL T) -9 NIL 2433851 NIL) (-1050 2432152 2432246 2432582 "RMCAT2" 2433217 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1049 2429002 2431498 2431795 "RMATRIX" 2431914 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1048 2421918 2424178 2424293 "RMATCAT" 2427652 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2428634 NIL) (-1047 2421293 2421440 2421747 "RMATCAT-" 2421752 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1046 2420860 2420935 2421063 "RINTERP" 2421212 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1045 2419953 2420507 2420537 "RING" 2420593 T RING (NIL) -9 NIL 2420685 NIL) (-1044 2419745 2419789 2419886 "RING-" 2419891 NIL RING- (NIL T) -8 NIL NIL NIL) (-1043 2418586 2418823 2419081 "RIDIST" 2419509 T RIDIST (NIL) -7 NIL NIL NIL) (-1042 2409875 2418054 2418260 "RGCHAIN" 2418434 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1041 2409225 2409631 2409672 "RGBCSPC" 2409730 NIL RGBCSPC (NIL T) -9 NIL 2409782 NIL) (-1040 2408383 2408764 2408805 "RGBCMDL" 2409037 NIL RGBCMDL (NIL T) -9 NIL 2409151 NIL) (-1039 2405377 2405991 2406661 "RF" 2407747 NIL RF (NIL T) -7 NIL NIL NIL) (-1038 2405023 2405086 2405189 "RFFACTOR" 2405308 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1037 2404748 2404783 2404880 "RFFACT" 2404982 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1036 2402865 2403229 2403611 "RFDIST" 2404388 T RFDIST (NIL) -7 NIL NIL NIL) (-1035 2402318 2402410 2402573 "RETSOL" 2402767 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1034 2401954 2402034 2402077 "RETRACT" 2402210 NIL RETRACT (NIL T) -9 NIL 2402297 NIL) (-1033 2401803 2401828 2401915 "RETRACT-" 2401920 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1032 2401405 2401625 2401695 "RETAST" 2401755 T RETAST (NIL) -8 NIL NIL NIL) (-1031 2394143 2401058 2401185 "RESULT" 2401300 T RESULT (NIL) -8 NIL NIL NIL) (-1030 2392734 2393412 2393611 "RESRING" 2394046 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1029 2392370 2392419 2392517 "RESLATC" 2392671 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1028 2392075 2392110 2392217 "REPSQ" 2392329 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1027 2389497 2390077 2390679 "REP" 2391495 T REP (NIL) -7 NIL NIL NIL) (-1026 2389194 2389229 2389340 "REPDB" 2389456 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1025 2383094 2384483 2385706 "REP2" 2388006 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1024 2379471 2380152 2380960 "REP1" 2382321 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1023 2372167 2377612 2378068 "REGSET" 2379101 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1022 2370932 2371315 2371565 "REF" 2371952 NIL REF (NIL T) -8 NIL NIL NIL) (-1021 2370309 2370412 2370579 "REDORDER" 2370816 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1020 2366277 2369522 2369749 "RECLOS" 2370137 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1019 2365329 2365510 2365725 "REALSOLV" 2366084 T REALSOLV (NIL) -7 NIL NIL NIL) (-1018 2365175 2365216 2365246 "REAL" 2365251 T REAL (NIL) -9 NIL 2365286 NIL) (-1017 2361658 2362460 2363344 "REAL0Q" 2364340 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1016 2357259 2358247 2359308 "REAL0" 2360639 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1015 2356730 2356976 2357070 "RDUCEAST" 2357187 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1014 2356135 2356207 2356414 "RDIV" 2356652 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1013 2355203 2355377 2355590 "RDIST" 2355957 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1012 2353800 2354087 2354459 "RDETRS" 2354911 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1011 2351612 2352066 2352604 "RDETR" 2353342 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1010 2350237 2350515 2350912 "RDEEFS" 2351328 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1009 2348746 2349052 2349477 "RDEEF" 2349925 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1008 2342972 2345882 2345912 "RCFIELD" 2347207 T RCFIELD (NIL) -9 NIL 2347937 NIL) (-1007 2341036 2341540 2342236 "RCFIELD-" 2342311 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1006 2337305 2339137 2339180 "RCAGG" 2340264 NIL RCAGG (NIL T) -9 NIL 2340729 NIL) (-1005 2336933 2337027 2337190 "RCAGG-" 2337195 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1004 2336268 2336380 2336545 "RATRET" 2336817 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1003 2335821 2335888 2336009 "RATFACT" 2336196 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1002 2335129 2335249 2335401 "RANDSRC" 2335691 T RANDSRC (NIL) -7 NIL NIL NIL) (-1001 2334863 2334907 2334980 "RADUTIL" 2335078 T RADUTIL (NIL) -7 NIL NIL NIL) (-1000 2327979 2333696 2334006 "RADIX" 2334587 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-999 2319600 2327823 2327951 "RADFF" 2327956 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-998 2319252 2319327 2319355 "RADCAT" 2319512 T RADCAT (NIL) -9 NIL NIL NIL) (-997 2319037 2319085 2319182 "RADCAT-" 2319187 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-996 2317140 2318812 2318901 "QUEUE" 2318981 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-995 2313681 2317077 2317122 "QUAT" 2317127 NIL QUAT (NIL T) -8 NIL NIL NIL) (-994 2313319 2313362 2313489 "QUATCT2" 2313632 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-993 2307031 2310368 2310408 "QUATCAT" 2311188 NIL QUATCAT (NIL T) -9 NIL 2311954 NIL) (-992 2303175 2304212 2305599 "QUATCAT-" 2305693 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-991 2300648 2302259 2302300 "QUAGG" 2302675 NIL QUAGG (NIL T) -9 NIL 2302850 NIL) (-990 2300253 2300473 2300541 "QQUTAST" 2300600 T QQUTAST (NIL) -8 NIL NIL NIL) (-989 2299151 2299651 2299823 "QFORM" 2300125 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-988 2290329 2295568 2295608 "QFCAT" 2296266 NIL QFCAT (NIL T) -9 NIL 2297267 NIL) (-987 2285901 2287102 2288693 "QFCAT-" 2288787 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-986 2285539 2285582 2285709 "QFCAT2" 2285852 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-985 2284999 2285109 2285239 "QEQUAT" 2285429 T QEQUAT (NIL) -8 NIL NIL NIL) (-984 2278146 2279218 2280402 "QCMPACK" 2283932 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-983 2275695 2276143 2276571 "QALGSET" 2277801 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-982 2274940 2275114 2275346 "QALGSET2" 2275515 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-981 2273630 2273854 2274171 "PWFFINTB" 2274713 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-980 2271812 2271980 2272334 "PUSHVAR" 2273444 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-979 2267730 2268784 2268825 "PTRANFN" 2270709 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-978 2266132 2266423 2266745 "PTPACK" 2267441 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-977 2265764 2265821 2265930 "PTFUNC2" 2266069 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-976 2260243 2264636 2264677 "PTCAT" 2264973 NIL PTCAT (NIL T) -9 NIL 2265126 NIL) (-975 2259901 2259936 2260060 "PSQFR" 2260202 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-974 2258496 2258794 2259128 "PSEUDLIN" 2259599 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-973 2245259 2247630 2249954 "PSETPK" 2256256 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-972 2238277 2241017 2241113 "PSETCAT" 2244134 NIL PSETCAT (NIL T T T T) -9 NIL 2244948 NIL) (-971 2236113 2236747 2237568 "PSETCAT-" 2237573 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-970 2235462 2235627 2235655 "PSCURVE" 2235923 T PSCURVE (NIL) -9 NIL 2236090 NIL) (-969 2231784 2233300 2233365 "PSCAT" 2234209 NIL PSCAT (NIL T T T) -9 NIL 2234449 NIL) (-968 2230847 2231063 2231463 "PSCAT-" 2231468 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-967 2229552 2230212 2230417 "PRTITION" 2230662 T PRTITION (NIL) -8 NIL NIL NIL) (-966 2229027 2229273 2229365 "PRTDAST" 2229480 T PRTDAST (NIL) -8 NIL NIL NIL) (-965 2218117 2220331 2222519 "PRS" 2226889 NIL PRS (NIL T T) -7 NIL NIL NIL) (-964 2215928 2217467 2217507 "PRQAGG" 2217690 NIL PRQAGG (NIL T) -9 NIL 2217792 NIL) (-963 2215132 2215437 2215465 "PROPLOG" 2215712 T PROPLOG (NIL) -9 NIL 2215878 NIL) (-962 2213562 2214083 2214340 "PROPFRML" 2214908 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-961 2213031 2213138 2213266 "PROPERTY" 2213454 T PROPERTY (NIL) -8 NIL NIL NIL) (-960 2207089 2211197 2212017 "PRODUCT" 2212257 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-959 2204367 2206547 2206781 "PR" 2206900 NIL PR (NIL T T) -8 NIL NIL NIL) (-958 2204163 2204195 2204254 "PRINT" 2204328 T PRINT (NIL) -7 NIL NIL NIL) (-957 2203503 2203620 2203772 "PRIMES" 2204043 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-956 2201568 2201969 2202435 "PRIMELT" 2203082 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-955 2201297 2201346 2201374 "PRIMCAT" 2201498 T PRIMCAT (NIL) -9 NIL NIL NIL) (-954 2197412 2201235 2201280 "PRIMARR" 2201285 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-953 2196419 2196597 2196825 "PRIMARR2" 2197230 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-952 2196062 2196118 2196229 "PREASSOC" 2196357 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-951 2195537 2195670 2195698 "PPCURVE" 2195903 T PPCURVE (NIL) -9 NIL 2196039 NIL) (-950 2195132 2195332 2195415 "PORTNUM" 2195474 T PORTNUM (NIL) -8 NIL NIL NIL) (-949 2192491 2192890 2193482 "POLYROOT" 2194713 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-948 2186673 2192095 2192255 "POLY" 2192364 NIL POLY (NIL T) -8 NIL NIL NIL) (-947 2186056 2186114 2186348 "POLYLIFT" 2186609 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-946 2182331 2182780 2183409 "POLYCATQ" 2185601 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-945 2169463 2174583 2174648 "POLYCAT" 2178162 NIL POLYCAT (NIL T T T) -9 NIL 2180040 NIL) (-944 2162912 2164774 2167158 "POLYCAT-" 2167163 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-943 2162499 2162567 2162687 "POLY2UP" 2162838 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-942 2162131 2162188 2162297 "POLY2" 2162436 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-941 2160816 2161055 2161331 "POLUTIL" 2161905 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-940 2159171 2159448 2159779 "POLTOPOL" 2160538 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-939 2154638 2159107 2159153 "POINT" 2159158 NIL POINT (NIL T) -8 NIL NIL NIL) (-938 2152825 2153182 2153557 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2030662 2030764 "PARSURF" 2030909 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-877 2030231 2030288 2030397 "PARSU2" 2030536 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-876 2029995 2030035 2030102 "PARSER" 2030184 T PARSER (NIL) -7 NIL NIL NIL) (-875 2029616 2029679 2029781 "PARSCURV" 2029926 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-874 2029248 2029305 2029414 "PARSC2" 2029553 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-873 2028887 2028945 2029042 "PARPCURV" 2029184 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-872 2028519 2028576 2028685 "PARPC2" 2028824 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-871 2028039 2028125 2028244 "PAN2EXPR" 2028420 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-870 2026816 2027160 2027388 "PALETTE" 2027831 T PALETTE (NIL) -8 NIL NIL NIL) (-869 2025209 2025821 2026181 "PAIR" 2026502 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-868 2019079 2024468 2024662 "PADICRC" 2025064 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-867 2012308 2018425 2018609 "PADICRAT" 2018927 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-866 2010623 2012245 2012290 "PADIC" 2012295 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-865 2007799 2009363 2009403 "PADICCT" 2009984 NIL PADICCT (NIL NIL) -9 NIL 2010266 NIL) (-864 2006756 2006956 2007224 "PADEPAC" 2007586 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-863 2005968 2006101 2006307 "PADE" 2006618 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-862 2004355 2005176 2005456 "OWP" 2005772 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-861 2003848 2004061 2004158 "OVERSET" 2004278 T OVERSET (NIL) -8 NIL NIL NIL) (-860 2002894 2003453 2003625 "OVAR" 2003716 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-859 2002158 2002279 2002440 "OUT" 2002753 T OUT (NIL) -7 NIL NIL NIL) (-858 1991029 1993267 1995467 "OUTFORM" 1999978 T OUTFORM (NIL) -8 NIL NIL NIL) (-857 1990365 1990626 1990753 "OUTBFILE" 1990922 T OUTBFILE (NIL) -8 NIL NIL NIL) (-856 1989672 1989837 1989865 "OUTBCON" 1990183 T OUTBCON (NIL) -9 NIL 1990349 NIL) (-855 1989273 1989385 1989542 "OUTBCON-" 1989547 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-854 1988653 1989002 1989091 "OSI" 1989204 T OSI (NIL) -8 NIL NIL NIL) (-853 1988183 1988521 1988549 "OSGROUP" 1988554 T OSGROUP (NIL) -9 NIL 1988576 NIL) (-852 1986928 1987155 1987440 "ORTHPOL" 1987930 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-851 1984479 1986763 1986884 "OREUP" 1986889 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-850 1981882 1984170 1984297 "ORESUP" 1984421 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-849 1979410 1979910 1980471 "OREPCTO" 1981371 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-848 1973200 1975401 1975442 "OREPCAT" 1977790 NIL OREPCAT (NIL T) -9 NIL 1978894 NIL) (-847 1970347 1971129 1972187 "OREPCAT-" 1972192 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-846 1969498 1969796 1969824 "ORDSET" 1970133 T ORDSET (NIL) -9 NIL 1970297 NIL) (-845 1968929 1969077 1969301 "ORDSET-" 1969306 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-844 1967529 1968320 1968348 "ORDRING" 1968550 T ORDRING (NIL) -9 NIL 1968675 NIL) (-843 1967174 1967268 1967412 "ORDRING-" 1967417 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-842 1966554 1967017 1967045 "ORDMON" 1967050 T ORDMON (NIL) -9 NIL 1967071 NIL) (-841 1965716 1965863 1966058 "ORDFUNS" 1966403 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-840 1965054 1965473 1965501 "ORDFIN" 1965566 T ORDFIN (NIL) -9 NIL 1965640 NIL) (-839 1961613 1963640 1964049 "ORDCOMP" 1964678 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-838 1960879 1961006 1961192 "ORDCOMP2" 1961473 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1957460 1958370 1959184 "OPTPROB" 1960085 T OPTPROB (NIL) -8 NIL NIL NIL) (-836 1954262 1954901 1955605 "OPTPACK" 1956776 T OPTPACK (NIL) -7 NIL NIL NIL) (-835 1951949 1952715 1952743 "OPTCAT" 1953562 T OPTCAT (NIL) -9 NIL 1954212 NIL) (-834 1951365 1951626 1951731 "OPSIG" 1951864 T OPSIG (NIL) -8 NIL NIL NIL) (-833 1951133 1951172 1951238 "OPQUERY" 1951319 T OPQUERY (NIL) -7 NIL NIL NIL) (-832 1948264 1949444 1949948 "OP" 1950662 NIL OP (NIL T) -8 NIL NIL NIL) (-831 1947773 1947970 1948011 "OPERCAT" 1948146 NIL OPERCAT (NIL T) -9 NIL 1948214 NIL) (-830 1947619 1947646 1947732 "OPERCAT-" 1947737 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-829 1944431 1946416 1946785 "ONECOMP" 1947283 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-828 1943736 1943851 1944025 "ONECOMP2" 1944303 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-827 1943155 1943261 1943391 "OMSERVER" 1943626 T OMSERVER (NIL) -7 NIL NIL NIL) (-826 1940017 1942595 1942635 "OMSAGG" 1942696 NIL OMSAGG (NIL T) -9 NIL 1942760 NIL) (-825 1938640 1938903 1939185 "OMPKG" 1939755 T OMPKG (NIL) -7 NIL NIL NIL) (-824 1938070 1938173 1938201 "OM" 1938500 T OM (NIL) -9 NIL NIL NIL) (-823 1936617 1937619 1937788 "OMLO" 1937951 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-822 1935577 1935724 1935944 "OMEXPR" 1936443 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-821 1934868 1935123 1935259 "OMERR" 1935461 T OMERR (NIL) -8 NIL NIL NIL) (-820 1934019 1934289 1934449 "OMERRK" 1934728 T OMERRK (NIL) -8 NIL NIL NIL) (-819 1933470 1933696 1933804 "OMENC" 1933931 T OMENC (NIL) -8 NIL NIL NIL) (-818 1927365 1928550 1929721 "OMDEV" 1932319 T OMDEV (NIL) -8 NIL NIL NIL) (-817 1926434 1926605 1926799 "OMCONN" 1927191 T OMCONN (NIL) -8 NIL NIL NIL) (-816 1925021 1925997 1926025 "OINTDOM" 1926030 T OINTDOM (NIL) -9 NIL 1926051 NIL) (-815 1920800 1922011 1922727 "OFMONOID" 1924337 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-814 1920211 1920737 1920782 "ODVAR" 1920787 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-813 1917634 1919956 1920111 "ODR" 1920116 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-812 1910215 1917410 1917536 "ODPOL" 1917541 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-811 1904037 1910087 1910192 "ODP" 1910197 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-810 1902803 1903018 1903293 "ODETOOLS" 1903811 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-809 1899770 1900428 1901144 "ODESYS" 1902136 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-808 1894652 1895560 1896585 "ODERTRIC" 1898845 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-807 1894078 1894160 1894354 "ODERED" 1894564 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-806 1890966 1891514 1892191 "ODERAT" 1893501 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-805 1887923 1888390 1888987 "ODEPRRIC" 1890495 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-804 1885866 1886462 1886948 "ODEPROB" 1887457 T ODEPROB (NIL) -8 NIL NIL NIL) (-803 1882386 1882871 1883518 "ODEPRIM" 1885345 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-802 1881635 1881737 1881997 "ODEPAL" 1882278 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-801 1877797 1878588 1879452 "ODEPACK" 1880791 T ODEPACK (NIL) -7 NIL NIL NIL) (-800 1876858 1876965 1877187 "ODEINT" 1877686 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-799 1870959 1872384 1873831 "ODEIFTBL" 1875431 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-798 1866357 1867143 1868095 "ODEEF" 1870118 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-797 1865706 1865795 1866018 "ODECONST" 1866262 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-796 1863831 1864492 1864520 "ODECAT" 1865125 T ODECAT (NIL) -9 NIL 1865656 NIL) (-795 1860703 1863543 1863662 "OCT" 1863744 NIL OCT (NIL T) -8 NIL NIL NIL) (-794 1860341 1860384 1860511 "OCTCT2" 1860654 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-793 1855081 1857515 1857555 "OC" 1858652 NIL OC (NIL T) -9 NIL 1859510 NIL) (-792 1852308 1853056 1854046 "OC-" 1854140 NIL OC- (NIL T T) -8 NIL NIL NIL) (-791 1851660 1852128 1852156 "OCAMON" 1852161 T OCAMON (NIL) -9 NIL 1852182 NIL) (-790 1851191 1851532 1851560 "OASGP" 1851565 T OASGP (NIL) -9 NIL 1851585 NIL) (-789 1850452 1850941 1850969 "OAMONS" 1851009 T OAMONS (NIL) -9 NIL 1851052 NIL) (-788 1849866 1850299 1850327 "OAMON" 1850332 T OAMON (NIL) -9 NIL 1850352 NIL) (-787 1849144 1849662 1849690 "OAGROUP" 1849695 T OAGROUP (NIL) -9 NIL 1849715 NIL) (-786 1848834 1848884 1848972 "NUMTUBE" 1849088 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-785 1842407 1843925 1845461 "NUMQUAD" 1847318 T NUMQUAD (NIL) -7 NIL NIL NIL) (-784 1838163 1839151 1840176 "NUMODE" 1841402 T NUMODE (NIL) -7 NIL NIL NIL) (-783 1835518 1836398 1836426 "NUMINT" 1837349 T NUMINT (NIL) -9 NIL 1838113 NIL) (-782 1834466 1834663 1834881 "NUMFMT" 1835320 T NUMFMT (NIL) -7 NIL NIL NIL) (-781 1820825 1823770 1826302 "NUMERIC" 1831973 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-780 1815195 1820274 1820369 "NTSCAT" 1820374 NIL NTSCAT (NIL T T T T) -9 NIL 1820413 NIL) (-779 1814389 1814554 1814747 "NTPOLFN" 1815034 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-778 1802466 1811214 1812026 "NSUP" 1813610 NIL NSUP (NIL T) -8 NIL NIL NIL) (-777 1802098 1802155 1802264 "NSUP2" 1802403 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-776 1792326 1801872 1802005 "NSMP" 1802010 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-775 1790758 1791059 1791416 "NREP" 1792014 NIL NREP (NIL T) -7 NIL NIL NIL) (-774 1789349 1789601 1789959 "NPCOEF" 1790501 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-773 1788415 1788530 1788746 "NORMRETR" 1789230 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-772 1786456 1786746 1787155 "NORMPK" 1788123 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-771 1786141 1786169 1786293 "NORMMA" 1786422 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-770 1785941 1786098 1786127 "NONE" 1786132 T NONE (NIL) -8 NIL NIL NIL) (-769 1785730 1785759 1785828 "NONE1" 1785905 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-768 1785227 1785289 1785468 "NODE1" 1785662 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-767 1783507 1784358 1784613 "NNI" 1784960 T NNI (NIL) -8 NIL NIL 1785195) (-766 1781927 1782240 1782604 "NLINSOL" 1783175 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-765 1778168 1779163 1780062 "NIPROB" 1781048 T NIPROB (NIL) -8 NIL NIL NIL) (-764 1776925 1777159 1777461 "NFINTBAS" 1777930 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-763 1776099 1776575 1776616 "NETCLT" 1776788 NIL NETCLT (NIL T) -9 NIL 1776870 NIL) (-762 1774807 1775038 1775319 "NCODIV" 1775867 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-761 1774569 1774606 1774681 "NCNTFRAC" 1774764 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-760 1772749 1773113 1773533 "NCEP" 1774194 NIL NCEP (NIL T) -7 NIL NIL NIL) (-759 1771620 1772393 1772421 "NASRING" 1772531 T NASRING (NIL) -9 NIL 1772611 NIL) (-758 1771415 1771459 1771553 "NASRING-" 1771558 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-757 1770542 1771067 1771095 "NARNG" 1771212 T NARNG (NIL) -9 NIL 1771303 NIL) (-756 1770234 1770301 1770435 "NARNG-" 1770440 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-755 1769113 1769320 1769555 "NAGSP" 1770019 T NAGSP (NIL) -7 NIL NIL NIL) (-754 1760385 1762069 1763742 "NAGS" 1767460 T NAGS (NIL) -7 NIL NIL NIL) (-753 1758933 1759241 1759572 "NAGF07" 1760074 T NAGF07 (NIL) -7 NIL NIL NIL) (-752 1753471 1754762 1756069 "NAGF04" 1757646 T NAGF04 (NIL) -7 NIL NIL NIL) (-751 1746439 1748053 1749686 "NAGF02" 1751858 T NAGF02 (NIL) -7 NIL NIL NIL) (-750 1741663 1742763 1743880 "NAGF01" 1745342 T NAGF01 (NIL) -7 NIL NIL NIL) (-749 1735291 1736857 1738442 "NAGE04" 1740098 T NAGE04 (NIL) -7 NIL NIL NIL) (-748 1726460 1728581 1730711 "NAGE02" 1733181 T NAGE02 (NIL) -7 NIL NIL NIL) (-747 1722413 1723360 1724324 "NAGE01" 1725516 T NAGE01 (NIL) -7 NIL NIL NIL) (-746 1720208 1720742 1721300 "NAGD03" 1721875 T NAGD03 (NIL) -7 NIL NIL NIL) (-745 1711958 1713886 1715840 "NAGD02" 1718274 T NAGD02 (NIL) -7 NIL NIL NIL) (-744 1705769 1707194 1708634 "NAGD01" 1710538 T NAGD01 (NIL) -7 NIL NIL NIL) (-743 1701978 1702800 1703637 "NAGC06" 1704952 T NAGC06 (NIL) -7 NIL NIL NIL) (-742 1700443 1700775 1701131 "NAGC05" 1701642 T NAGC05 (NIL) -7 NIL NIL NIL) (-741 1699819 1699938 1700082 "NAGC02" 1700319 T NAGC02 (NIL) -7 NIL NIL NIL) (-740 1698853 1699436 1699476 "NAALG" 1699555 NIL NAALG (NIL T) -9 NIL 1699616 NIL) (-739 1698688 1698717 1698807 "NAALG-" 1698812 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-738 1692638 1693746 1694933 "MULTSQFR" 1697584 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-737 1691957 1692032 1692216 "MULTFACT" 1692550 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-736 1685015 1688920 1688973 "MTSCAT" 1690043 NIL MTSCAT (NIL T T) -9 NIL 1690557 NIL) (-735 1684727 1684781 1684873 "MTHING" 1684955 NIL MTHING (NIL T) -7 NIL NIL NIL) (-734 1684519 1684552 1684612 "MSYSCMD" 1684687 T MSYSCMD (NIL) -7 NIL NIL NIL) (-733 1680601 1683274 1683594 "MSET" 1684232 NIL MSET (NIL T) -8 NIL NIL NIL) (-732 1677670 1680162 1680203 "MSETAGG" 1680208 NIL MSETAGG (NIL T) -9 NIL 1680242 NIL) (-731 1673511 1675049 1675794 "MRING" 1676970 NIL MRING (NIL T T) -8 NIL NIL NIL) (-730 1673077 1673144 1673275 "MRF2" 1673438 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-729 1672695 1672730 1672874 "MRATFAC" 1673036 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-728 1670307 1670602 1671033 "MPRFF" 1672400 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-727 1664604 1670161 1670258 "MPOLY" 1670263 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-726 1664094 1664129 1664337 "MPCPF" 1664563 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-725 1663608 1663651 1663835 "MPC3" 1664045 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1662803 1662884 1663105 "MPC2" 1663523 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-723 1661104 1661441 1661831 "MONOTOOL" 1662463 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-722 1660329 1660646 1660674 "MONOID" 1660893 T MONOID (NIL) -9 NIL 1661040 NIL) (-721 1659875 1659994 1660175 "MONOID-" 1660180 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-720 1650699 1656642 1656701 "MONOGEN" 1657375 NIL MONOGEN (NIL T T) -9 NIL 1657831 NIL) (-719 1647917 1648652 1649652 "MONOGEN-" 1649771 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-718 1646750 1647196 1647224 "MONADWU" 1647616 T MONADWU (NIL) -9 NIL 1647854 NIL) (-717 1646122 1646281 1646529 "MONADWU-" 1646534 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-716 1645481 1645725 1645753 "MONAD" 1645960 T MONAD (NIL) -9 NIL 1646072 NIL) (-715 1645166 1645244 1645376 "MONAD-" 1645381 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-714 1643455 1644079 1644358 "MOEBIUS" 1644919 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-713 1642821 1643225 1643265 "MODULE" 1643270 NIL MODULE (NIL T) -9 NIL 1643296 NIL) (-712 1642389 1642485 1642675 "MODULE-" 1642680 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-711 1640069 1640753 1641080 "MODRING" 1642213 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1637013 1638174 1638695 "MODOP" 1639598 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-709 1635601 1636080 1636357 "MODMONOM" 1636876 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-708 1625642 1633892 1634306 "MODMON" 1635238 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-707 1622798 1624486 1624762 "MODFIELD" 1625517 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-706 1621775 1622079 1622269 "MMLFORM" 1622628 T MMLFORM (NIL) -8 NIL NIL NIL) (-705 1621301 1621344 1621523 "MMAP" 1621726 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-704 1619484 1620251 1620292 "MLO" 1620715 NIL MLO (NIL T) -9 NIL 1620957 NIL) (-703 1616850 1617366 1617968 "MLIFT" 1618965 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-702 1616241 1616325 1616479 "MKUCFUNC" 1616761 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-701 1615840 1615910 1616033 "MKRECORD" 1616164 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-700 1614887 1615049 1615277 "MKFUNC" 1615651 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-699 1614275 1614379 1614535 "MKFLCFN" 1614770 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-698 1613552 1613654 1613839 "MKBCFUNC" 1614168 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-697 1610259 1613106 1613242 "MINT" 1613436 T MINT (NIL) -8 NIL NIL NIL) (-696 1609071 1609314 1609591 "MHROWRED" 1610014 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-695 1604451 1607606 1608011 "MFLOAT" 1608686 T MFLOAT (NIL) -8 NIL NIL NIL) (-694 1603808 1603884 1604055 "MFINFACT" 1604363 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-693 1600123 1600971 1601855 "MESH" 1602944 T MESH (NIL) -7 NIL NIL NIL) (-692 1598513 1598825 1599178 "MDDFACT" 1599810 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-691 1595308 1597672 1597713 "MDAGG" 1597968 NIL MDAGG (NIL T) -9 NIL 1598111 NIL) (-690 1585051 1594601 1594808 "MCMPLX" 1595121 T MCMPLX (NIL) -8 NIL NIL NIL) (-689 1584192 1584338 1584538 "MCDEN" 1584900 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-688 1582082 1582352 1582732 "MCALCFN" 1583922 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-687 1581007 1581247 1581480 "MAYBE" 1581888 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-686 1578619 1579142 1579704 "MATSTOR" 1580478 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-685 1574576 1577991 1578239 "MATRIX" 1578404 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-684 1570340 1571049 1571785 "MATLIN" 1573933 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-683 1560446 1563632 1563709 "MATCAT" 1568589 NIL MATCAT (NIL T T T) -9 NIL 1570006 NIL) (-682 1556802 1557823 1559179 "MATCAT-" 1559184 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-681 1555396 1555549 1555882 "MATCAT2" 1556637 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-680 1553508 1553832 1554216 "MAPPKG3" 1555071 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-679 1552489 1552662 1552884 "MAPPKG2" 1553332 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-678 1550988 1551272 1551599 "MAPPKG1" 1552195 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-677 1550067 1550394 1550571 "MAPPAST" 1550831 T MAPPAST (NIL) -8 NIL NIL NIL) (-676 1549678 1549736 1549859 "MAPHACK3" 1550003 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-675 1549270 1549331 1549445 "MAPHACK2" 1549610 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-674 1548707 1548811 1548953 "MAPHACK1" 1549161 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-673 1546786 1547407 1547711 "MAGMA" 1548435 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-672 1546265 1546510 1546601 "MACROAST" 1546715 T MACROAST (NIL) -8 NIL NIL NIL) (-671 1542683 1544504 1544965 "M3D" 1545837 NIL M3D (NIL T) -8 NIL NIL NIL) (-670 1536789 1541052 1541093 "LZSTAGG" 1541875 NIL LZSTAGG (NIL T) -9 NIL 1542170 NIL) (-669 1532746 1533920 1535377 "LZSTAGG-" 1535382 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-668 1529833 1530637 1531124 "LWORD" 1532291 NIL LWORD (NIL T) -8 NIL NIL NIL) (-667 1529409 1529637 1529712 "LSTAST" 1529778 T LSTAST (NIL) -8 NIL NIL NIL) (-666 1522575 1529180 1529314 "LSQM" 1529319 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-665 1521799 1521938 1522166 "LSPP" 1522430 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-664 1519611 1519912 1520368 "LSMP" 1521488 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-663 1516390 1517064 1517794 "LSMP1" 1518913 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-662 1510267 1515557 1515598 "LSAGG" 1515660 NIL LSAGG (NIL T) -9 NIL 1515738 NIL) (-661 1506962 1507886 1509099 "LSAGG-" 1509104 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-660 1504561 1506106 1506355 "LPOLY" 1506757 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-659 1504143 1504228 1504351 "LPEFRAC" 1504470 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-658 1502464 1503237 1503490 "LO" 1503975 NIL LO (NIL T T T) -8 NIL NIL NIL) (-657 1502116 1502228 1502256 "LOGIC" 1502367 T LOGIC (NIL) -9 NIL 1502448 NIL) (-656 1501978 1502001 1502072 "LOGIC-" 1502077 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-655 1501171 1501311 1501504 "LODOOPS" 1501834 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-654 1498594 1501087 1501153 "LODO" 1501158 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-653 1497132 1497367 1497720 "LODOF" 1498341 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-652 1493454 1495885 1495926 "LODOCAT" 1496364 NIL LODOCAT (NIL T) -9 NIL 1496575 NIL) (-651 1493187 1493245 1493372 "LODOCAT-" 1493377 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-650 1490507 1493028 1493146 "LODO2" 1493151 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-649 1487942 1490444 1490489 "LODO1" 1490494 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-648 1486823 1486988 1487293 "LODEEF" 1487765 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-647 1482062 1484953 1484994 "LNAGG" 1485941 NIL LNAGG (NIL T) -9 NIL 1486385 NIL) (-646 1481209 1481423 1481765 "LNAGG-" 1481770 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-645 1477345 1478134 1478773 "LMOPS" 1480624 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-644 1476714 1477102 1477143 "LMODULE" 1477204 NIL LMODULE (NIL T) -9 NIL 1477246 NIL) (-643 1473912 1476359 1476482 "LMDICT" 1476624 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-642 1473611 1473820 1473880 "LITERAL" 1473885 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-641 1466794 1472557 1472855 "LIST" 1473346 NIL LIST (NIL T) -8 NIL NIL NIL) (-640 1466319 1466393 1466532 "LIST3" 1466714 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-639 1465326 1465504 1465732 "LIST2" 1466137 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-638 1463460 1463772 1464171 "LIST2MAP" 1464973 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-637 1462156 1462826 1462867 "LINEXP" 1463122 NIL LINEXP (NIL T) -9 NIL 1463271 NIL) (-636 1460803 1461063 1461360 "LINDEP" 1461908 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-635 1457570 1458289 1459066 "LIMITRF" 1460058 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-634 1455873 1456169 1456578 "LIMITPS" 1457265 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-633 1450301 1455384 1455612 "LIE" 1455694 NIL LIE (NIL T T) -8 NIL NIL NIL) (-632 1449324 1449793 1449833 "LIECAT" 1449973 NIL LIECAT (NIL T) -9 NIL 1450124 NIL) (-631 1449165 1449192 1449280 "LIECAT-" 1449285 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-630 1441661 1448614 1448779 "LIB" 1449020 T LIB (NIL) -8 NIL NIL NIL) (-629 1437296 1438179 1439114 "LGROBP" 1440778 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-628 1435305 1435579 1435928 "LF" 1437017 NIL LF (NIL T T) -7 NIL NIL NIL) (-627 1434145 1434837 1434865 "LFCAT" 1435072 T LFCAT (NIL) -9 NIL 1435211 NIL) (-626 1431047 1431677 1432365 "LEXTRIPK" 1433509 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-625 1427791 1428617 1429120 "LEXP" 1430627 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-624 1427267 1427512 1427604 "LETAST" 1427719 T LETAST (NIL) -8 NIL NIL NIL) (-623 1425665 1425978 1426379 "LEADCDET" 1426949 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-622 1424855 1424929 1425158 "LAZM3PK" 1425586 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-621 1419772 1422932 1423470 "LAUPOL" 1424367 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-620 1419351 1419395 1419556 "LAPLACE" 1419722 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-619 1417290 1418452 1418703 "LA" 1419184 NIL LA (NIL T T T) -8 NIL NIL NIL) (-618 1416337 1416921 1416962 "LALG" 1417024 NIL LALG (NIL T) -9 NIL 1417083 NIL) (-617 1416051 1416110 1416246 "LALG-" 1416251 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-616 1415886 1415910 1415951 "KVTFROM" 1416013 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-615 1414809 1415253 1415438 "KTVLOGIC" 1415721 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-614 1414644 1414668 1414709 "KRCFROM" 1414771 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-613 1413548 1413735 1414034 "KOVACIC" 1414444 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-612 1413383 1413407 1413448 "KONVERT" 1413510 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-611 1413218 1413242 1413283 "KOERCE" 1413345 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-610 1410900 1411688 1412089 "KERNEL" 1412850 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-609 1410396 1410477 1410609 "KERNEL2" 1410814 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-608 1404166 1408935 1408989 "KDAGG" 1409366 NIL KDAGG (NIL T T) -9 NIL 1409572 NIL) (-607 1403695 1403819 1404024 "KDAGG-" 1404029 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-606 1396843 1403356 1403511 "KAFILE" 1403573 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-605 1391271 1396354 1396582 "JORDAN" 1396664 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-604 1390650 1390920 1391041 "JOINAST" 1391170 T JOINAST (NIL) -8 NIL NIL NIL) (-603 1390496 1390555 1390610 "JAVACODE" 1390615 T JAVACODE (NIL) -8 NIL NIL NIL) (-602 1386748 1388701 1388755 "IXAGG" 1389684 NIL IXAGG (NIL T T) -9 NIL 1390143 NIL) (-601 1385667 1385973 1386392 "IXAGG-" 1386397 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1381199 1385589 1385648 "IVECTOR" 1385653 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-599 1379965 1380202 1380468 "ITUPLE" 1380966 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-598 1378479 1378656 1378949 "ITRIGMNP" 1379787 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-597 1377224 1377428 1377711 "ITFUN3" 1378255 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-596 1376856 1376913 1377022 "ITFUN2" 1377161 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-595 1374658 1375718 1376017 "ITAYLOR" 1376590 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-594 1363603 1368795 1369958 "ISUPS" 1373528 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-593 1362707 1362847 1363083 "ISUMP" 1363450 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-592 1357921 1362508 1362587 "ISTRING" 1362660 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-591 1357397 1357642 1357734 "ISAST" 1357849 T ISAST (NIL) -8 NIL NIL NIL) (-590 1356606 1356688 1356904 "IRURPK" 1357311 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-589 1355542 1355743 1355983 "IRSN" 1356386 T IRSN (NIL) -7 NIL NIL NIL) (-588 1353613 1353968 1354397 "IRRF2F" 1355180 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-587 1353360 1353398 1353474 "IRREDFFX" 1353569 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-586 1351975 1352234 1352533 "IROOT" 1353093 NIL IROOT (NIL T) -7 NIL NIL NIL) (-585 1348579 1349659 1350351 "IR" 1351315 NIL IR (NIL T) -8 NIL NIL NIL) (-584 1346192 1346687 1347253 "IR2" 1348057 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-583 1345292 1345405 1345619 "IR2F" 1346075 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-582 1345083 1345117 1345177 "IPRNTPK" 1345252 T IPRNTPK (NIL) -7 NIL NIL NIL) (-581 1341663 1344972 1345041 "IPF" 1345046 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-580 1339990 1341588 1341645 "IPADIC" 1341650 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-579 1339302 1339550 1339680 "IP4ADDR" 1339880 T IP4ADDR (NIL) -8 NIL NIL NIL) (-578 1338775 1339006 1339116 "IOMODE" 1339212 T IOMODE (NIL) -8 NIL NIL NIL) (-577 1337848 1338372 1338499 "IOBFILE" 1338668 T IOBFILE (NIL) -8 NIL NIL NIL) (-576 1337336 1337752 1337780 "IOBCON" 1337785 T IOBCON (NIL) -9 NIL 1337806 NIL) (-575 1336847 1336905 1337088 "INVLAPLA" 1337272 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-574 1326495 1328849 1331235 "INTTR" 1334511 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-573 1322830 1323572 1324437 "INTTOOLS" 1325680 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-572 1322416 1322507 1322624 "INTSLPE" 1322733 T INTSLPE (NIL) -7 NIL NIL NIL) (-571 1320370 1322339 1322398 "INTRVL" 1322403 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-570 1317972 1318484 1319059 "INTRF" 1319855 NIL INTRF (NIL T) -7 NIL NIL NIL) (-569 1317383 1317480 1317622 "INTRET" 1317870 NIL INTRET (NIL T) -7 NIL NIL NIL) (-568 1315380 1315769 1316239 "INTRAT" 1316991 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-567 1312643 1313226 1313845 "INTPM" 1314865 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-566 1309387 1309987 1310725 "INTPAF" 1312029 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-565 1304566 1305528 1306579 "INTPACK" 1308356 T INTPACK (NIL) -7 NIL NIL NIL) (-564 1301443 1304295 1304422 "INT" 1304459 T INT (NIL) -8 NIL NIL NIL) (-563 1300695 1300847 1301055 "INTHERTR" 1301285 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-562 1300134 1300214 1300402 "INTHERAL" 1300609 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-561 1297980 1298423 1298880 "INTHEORY" 1299697 T INTHEORY (NIL) -7 NIL NIL NIL) (-560 1289386 1291007 1292779 "INTG0" 1296332 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-559 1269959 1274749 1279559 "INTFTBL" 1284596 T INTFTBL (NIL) -8 NIL NIL NIL) (-558 1269208 1269346 1269519 "INTFACT" 1269818 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-557 1266635 1267081 1267638 "INTEF" 1268762 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-556 1265068 1265807 1265835 "INTDOM" 1266136 T INTDOM (NIL) -9 NIL 1266343 NIL) (-555 1264437 1264611 1264853 "INTDOM-" 1264858 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-554 1260897 1262821 1262875 "INTCAT" 1263674 NIL INTCAT (NIL T) -9 NIL 1263994 NIL) (-553 1260369 1260472 1260600 "INTBIT" 1260789 T INTBIT (NIL) -7 NIL NIL NIL) (-552 1259068 1259222 1259529 "INTALG" 1260214 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-551 1258551 1258641 1258798 "INTAF" 1258972 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-550 1251894 1258361 1258501 "INTABL" 1258506 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-549 1251235 1251701 1251766 "INT8" 1251800 T INT8 (NIL) -8 NIL NIL 1251845) (-548 1250575 1251041 1251106 "INT64" 1251140 T INT64 (NIL) -8 NIL NIL 1251185) (-547 1249915 1250381 1250446 "INT32" 1250480 T INT32 (NIL) -8 NIL NIL 1250525) (-546 1249255 1249721 1249786 "INT16" 1249820 T INT16 (NIL) -8 NIL NIL 1249865) (-545 1244235 1246944 1246972 "INS" 1247906 T INS (NIL) -9 NIL 1248571 NIL) (-544 1241475 1242246 1243220 "INS-" 1243293 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1240250 1240477 1240775 "INPSIGN" 1241228 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1239368 1239485 1239682 "INPRODPF" 1240130 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1238262 1238379 1238616 "INPRODFF" 1239248 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1237262 1237414 1237674 "INNMFACT" 1238098 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1236459 1236556 1236744 "INMODGCD" 1237161 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1234967 1235212 1235536 "INFSP" 1236204 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1234151 1234268 1234451 "INFPROD0" 1234847 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1231006 1232216 1232731 "INFORM" 1233644 T INFORM (NIL) -8 NIL NIL NIL) (-535 1230616 1230676 1230774 "INFORM1" 1230941 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1230139 1230228 1230342 "INFINITY" 1230522 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1229315 1229859 1229960 "INETCLTS" 1230058 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1227931 1228181 1228502 "INEP" 1229063 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1227180 1227828 1227893 "INDE" 1227898 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1226744 1226812 1226929 "INCRMAPS" 1227107 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1225562 1226013 1226219 "INBFILE" 1226558 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1220862 1221798 1222742 "INBFF" 1224650 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1219770 1220039 1220067 "INBCON" 1220580 T INBCON (NIL) -9 NIL 1220846 NIL) (-526 1219022 1219245 1219521 "INBCON-" 1219526 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1218501 1218746 1218837 "INAST" 1218951 T INAST (NIL) -8 NIL NIL NIL) (-524 1217928 1218180 1218286 "IMPTAST" 1218415 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1214374 1217772 1217876 "IMATRIX" 1217881 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1213086 1213209 1213524 "IMATQF" 1214230 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1211306 1211533 1211870 "IMATLIN" 1212842 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1205884 1211230 1211288 "ILIST" 1211293 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1203789 1205744 1205857 "IIARRAY2" 1205862 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1199187 1203700 1203764 "IFF" 1203769 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1198534 1198804 1198920 "IFAST" 1199091 T IFAST (NIL) -8 NIL NIL NIL) (-516 1193529 1197826 1198014 "IFARRAY" 1198391 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1192709 1193433 1193506 "IFAMON" 1193511 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1192293 1192358 1192412 "IEVALAB" 1192619 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1191968 1192036 1192196 "IEVALAB-" 1192201 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1191599 1191882 1191945 "IDPO" 1191950 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1190849 1191488 1191563 "IDPOAMS" 1191568 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1190156 1190738 1190813 "IDPOAM" 1190818 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1189215 1189491 1189544 "IDPC" 1189957 NIL IDPC (NIL T T) -9 NIL 1190106 NIL) (-508 1188684 1189107 1189180 "IDPAM" 1189185 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1188060 1188576 1188649 "IDPAG" 1188654 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1187705 1187896 1187971 "IDENT" 1188005 T IDENT (NIL) -8 NIL NIL NIL) (-505 1183960 1184808 1185703 "IDECOMP" 1186862 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1176796 1177883 1178930 "IDEAL" 1182996 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1175960 1176072 1176271 "ICDEN" 1176680 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1175031 1175440 1175587 "ICARD" 1175833 T ICARD (NIL) -8 NIL NIL NIL) (-501 1173091 1173404 1173809 "IBPTOOLS" 1174708 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1168698 1172711 1172824 "IBITS" 1173010 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1165421 1165997 1166692 "IBATOOL" 1168115 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1163200 1163662 1164195 "IBACHIN" 1164956 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1161029 1163046 1163149 "IARRAY2" 1163154 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1157135 1160955 1161012 "IARRAY1" 1161017 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1151244 1155547 1156028 "IAN" 1156674 T IAN (NIL) -8 NIL NIL NIL) (-494 1150755 1150812 1150985 "IALGFACT" 1151181 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1150283 1150396 1150424 "HYPCAT" 1150631 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1149821 1149938 1150124 "HYPCAT-" 1150129 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1149416 1149616 1149699 "HOSTNAME" 1149758 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1149261 1149298 1149339 "HOMOTOP" 1149344 NIL HOMOTOP (NIL T) -9 NIL 1149377 NIL) (-489 1145893 1147271 1147312 "HOAGG" 1148293 NIL HOAGG (NIL T) -9 NIL 1148972 NIL) (-488 1144487 1144886 1145412 "HOAGG-" 1145417 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1138491 1144082 1144231 "HEXADEC" 1144358 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1137239 1137461 1137724 "HEUGCD" 1138268 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1136315 1137076 1137206 "HELLFDIV" 1137211 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1134494 1136092 1136180 "HEAP" 1136259 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1133757 1134046 1134180 "HEADAST" 1134380 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1127623 1133672 1133734 "HDP" 1133739 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1121611 1127258 1127410 "HDMP" 1127524 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1120935 1121075 1121239 "HB" 1121467 T HB (NIL) -7 NIL NIL NIL) (-479 1114321 1120781 1120885 "HASHTBL" 1120890 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1113797 1114042 1114134 "HASAST" 1114249 T HASAST (NIL) -8 NIL NIL NIL) (-477 1111575 1113419 1113601 "HACKPI" 1113635 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1107243 1111428 1111541 "GTSET" 1111546 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1100658 1107121 1107219 "GSTBL" 1107224 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1092936 1099689 1099954 "GSERIES" 1100449 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1092077 1092494 1092522 "GROUP" 1092725 T GROUP (NIL) -9 NIL 1092859 NIL) (-472 1091443 1091602 1091853 "GROUP-" 1091858 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1089810 1090131 1090518 "GROEBSOL" 1091120 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1088724 1089012 1089063 "GRMOD" 1089592 NIL GRMOD (NIL T T) -9 NIL 1089760 NIL) (-469 1088492 1088528 1088656 "GRMOD-" 1088661 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1083782 1084846 1085846 "GRIMAGE" 1087512 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1082248 1082509 1082833 "GRDEF" 1083478 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1081692 1081808 1081949 "GRAY" 1082127 T GRAY (NIL) -7 NIL NIL NIL) (-465 1080879 1081285 1081336 "GRALG" 1081489 NIL GRALG (NIL T T) -9 NIL 1081582 NIL) (-464 1080540 1080613 1080776 "GRALG-" 1080781 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1077317 1080125 1080303 "GPOLSET" 1080447 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1076671 1076728 1076986 "GOSPER" 1077254 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1072403 1073109 1073635 "GMODPOL" 1076370 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1071408 1071592 1071830 "GHENSEL" 1072215 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1065564 1066407 1067427 "GENUPS" 1070492 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1065261 1065312 1065401 "GENUFACT" 1065507 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1064673 1064750 1064915 "GENPGCD" 1065179 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1064147 1064182 1064395 "GENMFACT" 1064632 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1062713 1062970 1063277 "GENEEZ" 1063890 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1056858 1062324 1062486 "GDMP" 1062636 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1046200 1050629 1051735 "GCNAALG" 1055841 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1044593 1045455 1045483 "GCDDOM" 1045738 T GCDDOM (NIL) -9 NIL 1045895 NIL) (-451 1044063 1044190 1044405 "GCDDOM-" 1044410 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1042735 1042920 1043224 "GB" 1043842 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1031351 1033681 1036073 "GBINTERN" 1040426 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1029188 1029480 1029901 "GBF" 1031026 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1027969 1028134 1028401 "GBEUCLID" 1029004 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1027318 1027443 1027592 "GAUSSFAC" 1027840 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1025685 1025987 1026301 "GALUTIL" 1027037 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1023993 1024267 1024591 "GALPOLYU" 1025412 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1021358 1021648 1022055 "GALFACTU" 1023690 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1013163 1014663 1016271 "GALFACT" 1019790 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1010551 1011209 1011237 "FVFUN" 1012393 T FVFUN (NIL) -9 NIL 1013113 NIL) (-440 1009817 1009999 1010027 "FVC" 1010318 T FVC (NIL) -9 NIL 1010501 NIL) (-439 1009460 1009642 1009710 "FUNDESC" 1009769 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1009075 1009257 1009338 "FUNCTION" 1009412 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1006819 1007397 1007863 "FT" 1008629 T FT (NIL) -8 NIL NIL NIL) (-436 1005610 1006120 1006323 "FTEM" 1006636 T FTEM (NIL) -8 NIL NIL NIL) (-435 1003901 1004190 1004587 "FSUPFACT" 1005301 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1002298 1002587 1002919 "FST" 1003589 T FST (NIL) -8 NIL NIL NIL) (-433 1001497 1001603 1001791 "FSRED" 1002180 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 1000196 1000452 1000799 "FSPRMELT" 1001212 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 997502 997940 998426 "FSPECF" 999759 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 979657 987981 988022 "FS" 991906 NIL FS (NIL T) -9 NIL 994195 NIL) (-429 968300 971293 975350 "FS-" 975650 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 967828 967882 968052 "FSINT" 968241 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 966120 966821 967124 "FSERIES" 967607 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 965162 965278 965502 "FSCINT" 966000 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 961370 964106 964147 "FSAGG" 964517 NIL FSAGG (NIL T) -9 NIL 964776 NIL) (-424 959132 959733 960529 "FSAGG-" 960624 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 958174 958317 958544 "FSAGG2" 958985 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 955856 956136 956683 "FS2UPS" 957892 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 955490 955533 955662 "FS2" 955807 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 954368 954539 954841 "FS2EXPXP" 955315 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 953794 953909 954061 "FRUTIL" 954248 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 945207 949289 950647 "FR" 952468 NIL FR (NIL T) -8 NIL NIL NIL) (-417 940255 942925 942965 "FRNAALG" 944361 NIL FRNAALG (NIL T) -9 NIL 944968 NIL) (-416 935928 937004 938279 "FRNAALG-" 939029 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 935566 935609 935736 "FRNAAF2" 935879 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 933946 934420 934715 "FRMOD" 935378 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 931697 932329 932646 "FRIDEAL" 933737 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 930892 930979 931268 "FRIDEAL2" 931604 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 930025 930439 930480 "FRETRCT" 930485 NIL FRETRCT (NIL T) -9 NIL 930661 NIL) (-410 929137 929368 929719 "FRETRCT-" 929724 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 926315 927525 927584 "FRAMALG" 928466 NIL FRAMALG (NIL T T) -9 NIL 928758 NIL) (-408 924449 924904 925534 "FRAMALG-" 925757 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 918370 923924 924200 "FRAC" 924205 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 918006 918063 918170 "FRAC2" 918307 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 917642 917699 917806 "FR2" 917943 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 912280 915167 915195 "FPS" 916314 T FPS (NIL) -9 NIL 916871 NIL) (-403 911729 911838 912002 "FPS-" 912148 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 909149 910818 910846 "FPC" 911071 T FPC (NIL) -9 NIL 911213 NIL) (-401 908942 908982 909079 "FPC-" 909084 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 907732 908430 908471 "FPATMAB" 908476 NIL FPATMAB (NIL T) -9 NIL 908628 NIL) (-399 905405 905908 906334 "FPARFRAC" 907369 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 900798 901297 901979 "FORTRAN" 904837 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 898514 899014 899553 "FORT" 900279 T FORT (NIL) -7 NIL NIL NIL) (-396 896190 896752 896780 "FORTFN" 897840 T FORTFN (NIL) -9 NIL 898464 NIL) (-395 895954 896004 896032 "FORTCAT" 896091 T FORTCAT (NIL) -9 NIL 896153 NIL) (-394 894060 894570 894960 "FORMULA" 895584 T FORMULA (NIL) -8 NIL NIL NIL) (-393 893848 893878 893947 "FORMULA1" 894024 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 893371 893423 893596 "FORDER" 893790 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 892467 892631 892824 "FOP" 893198 T FOP (NIL) -7 NIL NIL NIL) (-390 891048 891747 891921 "FNLA" 892349 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 889777 890192 890220 "FNCAT" 890680 T FNCAT (NIL) -9 NIL 890940 NIL) (-388 889316 889736 889764 "FNAME" 889769 T FNAME (NIL) -8 NIL NIL NIL) (-387 887945 888908 888936 "FMTC" 888941 T FMTC (NIL) -9 NIL 888977 NIL) (-386 884278 885468 886097 "FMONOID" 887349 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 883470 884020 884169 "FM" 884174 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 880894 881540 881568 "FMFUN" 882712 T FMFUN (NIL) -9 NIL 883420 NIL) (-383 880163 880344 880372 "FMC" 880662 T FMC (NIL) -9 NIL 880844 NIL) (-382 877331 878191 878245 "FMCAT" 879440 NIL FMCAT (NIL T T) -9 NIL 879935 NIL) (-381 876197 877097 877197 "FM1" 877276 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 873971 874387 874881 "FLOATRP" 875748 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 867545 871700 872321 "FLOAT" 873370 T FLOAT (NIL) -8 NIL NIL NIL) (-378 864983 865483 866061 "FLOATCP" 867012 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 863758 864596 864637 "FLINEXP" 864642 NIL FLINEXP (NIL T) -9 NIL 864735 NIL) (-376 862912 863147 863475 "FLINEXP-" 863480 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 861988 862132 862356 "FLASORT" 862764 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 859179 860047 860099 "FLALG" 861326 NIL FLALG (NIL T T) -9 NIL 861793 NIL) (-373 852915 856665 856706 "FLAGG" 857968 NIL FLAGG (NIL T) -9 NIL 858620 NIL) (-372 851641 851980 852470 "FLAGG-" 852475 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 850683 850826 851053 "FLAGG2" 851494 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 847624 848632 848691 "FINRALG" 849819 NIL FINRALG (NIL T T) -9 NIL 850327 NIL) (-369 846784 847013 847352 "FINRALG-" 847357 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 846164 846403 846431 "FINITE" 846627 T FINITE (NIL) -9 NIL 846734 NIL) (-367 838596 840783 840823 "FINAALG" 844490 NIL FINAALG (NIL T) -9 NIL 845943 NIL) (-366 833928 834978 836122 "FINAALG-" 837501 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 833296 833683 833786 "FILE" 833858 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 831954 832292 832346 "FILECAT" 833030 NIL FILECAT (NIL T T) -9 NIL 833246 NIL) (-363 829788 831316 831344 "FIELD" 831384 T FIELD (NIL) -9 NIL 831464 NIL) (-362 828408 828793 829304 "FIELD-" 829309 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 826258 827043 827390 "FGROUP" 828094 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 825348 825512 825732 "FGLMICPK" 826090 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 821180 825273 825330 "FFX" 825335 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 820781 820842 820977 "FFSLPE" 821113 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 816770 817553 818349 "FFPOLY" 820017 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 816274 816310 816519 "FFPOLY2" 816728 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 812117 816193 816256 "FFP" 816261 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 807515 812028 812092 "FF" 812097 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 802641 806858 807048 "FFNBX" 807369 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 797570 801776 802034 "FFNBP" 802495 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 792203 796854 797065 "FFNB" 797403 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 791035 791233 791548 "FFINTBAS" 792000 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 787228 789442 789470 "FFIELDC" 790090 T FFIELDC (NIL) -9 NIL 790466 NIL) (-348 785890 786261 786758 "FFIELDC-" 786763 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 785459 785505 785629 "FFHOM" 785832 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 783154 783641 784158 "FFF" 784974 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 778772 782896 782997 "FFCGX" 783097 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 774393 778504 778611 "FFCGP" 778715 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 769576 774120 774228 "FFCG" 774329 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 751374 760447 760533 "FFCAT" 765698 NIL FFCAT (NIL T T T) -9 NIL 767149 NIL) (-341 746572 747619 748933 "FFCAT-" 750163 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 745983 746026 746261 "FFCAT2" 746523 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 735304 738955 740175 "FEXPR" 744835 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 734304 734739 734780 "FEVALAB" 734864 NIL FEVALAB (NIL T) -9 NIL 735125 NIL) (-337 733463 733673 734011 "FEVALAB-" 734016 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 732029 732846 733049 "FDIV" 733362 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 729069 729810 729925 "FDIVCAT" 731493 NIL FDIVCAT (NIL T T T T) -9 NIL 731930 NIL) (-334 728831 728858 729028 "FDIVCAT-" 729033 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 728051 728138 728415 "FDIV2" 728738 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 726737 726996 727285 "FCPAK1" 727782 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 725836 726237 726378 "FCOMP" 726628 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 709538 712986 716524 "FC" 722318 T FC (NIL) -8 NIL NIL NIL) (-329 702082 706102 706142 "FAXF" 707944 NIL FAXF (NIL T) -9 NIL 708636 NIL) (-328 699358 700016 700841 "FAXF-" 701306 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 694410 698734 698910 "FARRAY" 699215 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 689629 691695 691748 "FAMR" 692771 NIL FAMR (NIL T T) -9 NIL 693231 NIL) (-325 688519 688821 689256 "FAMR-" 689261 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 687688 688441 688494 "FAMONOID" 688499 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 685474 686184 686237 "FAMONC" 687178 NIL FAMONC (NIL T T) -9 NIL 687564 NIL) (-322 684139 685228 685365 "FAGROUP" 685370 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 681934 682253 682656 "FACUTIL" 683820 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 681033 681218 681440 "FACTFUNC" 681744 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 673455 680336 680535 "EXPUPXS" 680889 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 670938 671478 672064 "EXPRTUBE" 672889 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 667209 667801 668531 "EXPRODE" 670277 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 652694 665858 666287 "EXPR" 666813 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 647248 647835 648641 "EXPR2UPS" 651992 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 646880 646937 647046 "EXPR2" 647185 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 638271 646033 646323 "EXPEXPAN" 646717 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 638071 638228 638257 "EXIT" 638262 T EXIT (NIL) -8 NIL NIL NIL) (-311 637551 637795 637886 "EXITAST" 638000 T EXITAST (NIL) -8 NIL NIL NIL) (-310 637178 637240 637353 "EVALCYC" 637483 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 636719 636837 636878 "EVALAB" 637048 NIL EVALAB (NIL T) -9 NIL 637152 NIL) (-308 636200 636322 636543 "EVALAB-" 636548 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 633634 634936 634964 "EUCDOM" 635519 T EUCDOM (NIL) -9 NIL 635869 NIL) (-306 632039 632481 633071 "EUCDOM-" 633076 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 619577 622337 625087 "ESTOOLS" 629309 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 619209 619266 619375 "ESTOOLS2" 619514 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 618960 619002 619082 "ESTOOLS1" 619161 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 612997 614605 614633 "ES" 617401 T ES (NIL) -9 NIL 618811 NIL) (-301 607944 609231 611048 "ES-" 611212 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 604318 605079 605859 "ESCONT" 607184 T ESCONT (NIL) -7 NIL NIL NIL) (-299 604063 604095 604177 "ESCONT1" 604280 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 603738 603788 603888 "ES2" 604007 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 603368 603426 603535 "ES1" 603674 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 602584 602713 602889 "ERROR" 603212 T ERROR (NIL) -7 NIL NIL NIL) (-295 595976 602443 602534 "EQTBL" 602539 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 588479 591290 592739 "EQ" 594560 NIL -2035 (NIL T) -8 NIL NIL NIL) (-293 588111 588168 588277 "EQ2" 588416 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 583400 584449 585542 "EP" 587050 NIL EP (NIL T) -7 NIL NIL NIL) (-291 582000 582291 582597 "ENV" 583114 T ENV (NIL) -8 NIL NIL NIL) (-290 581145 581699 581727 "ENTIRER" 581732 T ENTIRER (NIL) -9 NIL 581778 NIL) (-289 577612 579100 579470 "EMR" 580944 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 576756 576941 576995 "ELTAGG" 577375 NIL ELTAGG (NIL T T) -9 NIL 577586 NIL) (-287 576475 576537 576678 "ELTAGG-" 576683 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 576264 576293 576347 "ELTAB" 576431 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 575390 575536 575735 "ELFUTS" 576115 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 575132 575188 575216 "ELEMFUN" 575321 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 575002 575023 575091 "ELEMFUN-" 575096 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 569846 573102 573143 "ELAGG" 574083 NIL ELAGG (NIL T) -9 NIL 574546 NIL) (-281 568131 568565 569228 "ELAGG-" 569233 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 566796 567074 567367 "ELABEXPR" 567858 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 559660 561463 562290 "EFUPXS" 566072 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 553110 554911 555721 "EFULS" 558936 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 550595 550953 551425 "EFSTRUC" 552742 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 540446 542012 543559 "EF" 549110 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 539520 539931 540080 "EAB" 540317 T EAB (NIL) -8 NIL NIL NIL) (-274 538702 539479 539507 "E04UCFA" 539512 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 537884 538661 538689 "E04NAFA" 538694 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 537066 537843 537871 "E04MBFA" 537876 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 536248 537025 537053 "E04JAFA" 537058 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 535432 536207 536235 "E04GCFA" 536240 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 534616 535391 535419 "E04FDFA" 535424 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 533798 534575 534603 "E04DGFA" 534608 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 527971 529323 530687 "E04AGNT" 532454 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 526651 527157 527197 "DVARCAT" 527672 NIL DVARCAT (NIL T) -9 NIL 527871 NIL) (-265 525855 526067 526381 "DVARCAT-" 526386 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 518992 525654 525783 "DSMP" 525788 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 513774 514937 516005 "DROPT" 517944 T DROPT (NIL) -8 NIL NIL NIL) (-262 513439 513498 513596 "DROPT1" 513709 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 508554 509680 510817 "DROPT0" 512322 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 506899 507224 507610 "DRAWPT" 508188 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 501486 502409 503488 "DRAW" 505873 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 501119 501172 501290 "DRAWHACK" 501427 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 499850 500119 500410 "DRAWCX" 500848 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 499365 499434 499585 "DRAWCURV" 499776 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 489833 491795 493910 "DRAWCFUN" 497270 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 486599 488528 488569 "DQAGG" 489198 NIL DQAGG (NIL T) -9 NIL 489471 NIL) (-253 475143 481604 481687 "DPOLCAT" 483539 NIL DPOLCAT (NIL T T T T) -9 NIL 484084 NIL) (-252 469979 471328 473286 "DPOLCAT-" 473291 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 463101 469840 469938 "DPMO" 469943 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 456126 462881 463048 "DPMM" 463053 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 455731 456045 456093 "DOMCTOR" 456098 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 454999 455253 455390 "DOMAIN" 455614 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 448987 454634 454786 "DMP" 454900 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 448587 448643 448787 "DLP" 448925 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 442409 447914 448104 "DLIST" 448429 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 439206 441262 441303 "DLAGG" 441853 NIL DLAGG (NIL T) -9 NIL 442083 NIL) (-243 437985 438649 438677 "DIVRING" 438769 T DIVRING (NIL) -9 NIL 438852 NIL) (-242 437222 437412 437712 "DIVRING-" 437717 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 435324 435681 436087 "DISPLAY" 436836 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 429212 435238 435301 "DIRPROD" 435306 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 428060 428263 428528 "DIRPROD2" 429005 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 417269 423275 423328 "DIRPCAT" 423738 NIL DIRPCAT (NIL NIL T) -9 NIL 424578 NIL) (-237 414595 415237 416118 "DIRPCAT-" 416455 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 413882 414042 414228 "DIOSP" 414429 T DIOSP (NIL) -7 NIL NIL NIL) (-235 410537 412794 412835 "DIOPS" 413269 NIL DIOPS (NIL T) -9 NIL 413498 NIL) (-234 410086 410200 410391 "DIOPS-" 410396 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 408944 409572 409600 "DIFRING" 409787 T DIFRING (NIL) -9 NIL 409897 NIL) (-232 408590 408667 408819 "DIFRING-" 408824 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 406361 407633 407674 "DIFEXT" 408037 NIL DIFEXT (NIL T) -9 NIL 408331 NIL) (-230 404646 405074 405740 "DIFEXT-" 405745 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 401921 404178 404219 "DIAGG" 404224 NIL DIAGG (NIL T) -9 NIL 404244 NIL) (-228 401305 401462 401714 "DIAGG-" 401719 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 396722 400264 400541 "DHMATRIX" 401074 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 392334 393243 394253 "DFSFUN" 395732 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 387412 391265 391577 "DFLOAT" 392042 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 385675 385956 386345 "DFINTTLS" 387120 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 382704 383696 384096 "DERHAM" 385341 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 380505 382479 382568 "DEQUEUE" 382648 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 379759 379892 380075 "DEGRED" 380367 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 376189 376934 377780 "DEFINTRF" 378987 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 373744 374213 374805 "DEFINTEF" 375708 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 373094 373364 373479 "DEFAST" 373649 T DEFAST (NIL) -8 NIL NIL NIL) (-217 367098 372689 372838 "DECIMAL" 372965 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 364609 365068 365574 "DDFACT" 366642 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 364205 364248 364399 "DBLRESP" 364560 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 362077 362438 362798 "DBASE" 363972 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 361319 361557 361703 "DATAARY" 361976 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 360425 361278 361306 "D03FAFA" 361311 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 359532 360384 360412 "D03EEFA" 360417 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 357482 357948 358437 "D03AGNT" 359063 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 356771 357441 357469 "D02EJFA" 357474 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 356060 356730 356758 "D02CJFA" 356763 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 355349 356019 356047 "D02BHFA" 356052 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 354638 355308 355336 "D02BBFA" 355341 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 347835 349424 351030 "D02AGNT" 353052 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 345603 346126 346672 "D01WGTS" 347309 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 344670 345562 345590 "D01TRNS" 345595 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 343738 344629 344657 "D01GBFA" 344662 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 342806 343697 343725 "D01FCFA" 343730 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 341874 342765 342793 "D01ASFA" 342798 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 340942 341833 341861 "D01AQFA" 341866 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 340010 340901 340929 "D01APFA" 340934 T D01APFA (NIL) -8 NIL NIL NIL) (-197 339078 339969 339997 "D01ANFA" 340002 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 338146 339037 339065 "D01AMFA" 339070 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 337214 338105 338133 "D01ALFA" 338138 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 336282 337173 337201 "D01AKFA" 337206 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 335350 336241 336269 "D01AJFA" 336274 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 328645 330198 331759 "D01AGNT" 333809 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 327982 328110 328262 "CYCLOTOM" 328513 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 324717 325430 326157 "CYCLES" 327275 T CYCLES (NIL) -7 NIL NIL NIL) (-189 324029 324163 324334 "CVMP" 324578 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 321870 322128 322497 "CTRIGMNP" 323757 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 321338 321664 321737 "CTOR" 321817 T CTOR (NIL) -8 NIL NIL NIL) (-186 320847 321069 321170 "CTORKIND" 321257 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 320169 320454 320482 "CTORCAT" 320664 T CTORCAT (NIL) -9 NIL 320777 NIL) (-184 319767 319878 320037 "CTORCAT-" 320042 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 319256 319470 319568 "CTORCALL" 319689 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 318630 318729 318882 "CSTTOOLS" 319153 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 314429 315086 315844 "CRFP" 317942 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 313904 314150 314242 "CRCEAST" 314357 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 312951 313136 313364 "CRAPACK" 313708 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 312335 312436 312640 "CPMATCH" 312827 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 312060 312088 312194 "CPIMA" 312301 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 308424 309096 309814 "COORDSYS" 311395 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 307836 307957 308099 "CONTOUR" 308302 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 303727 305839 306331 "CONTFRAC" 307376 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 303607 303628 303656 "CONDUIT" 303693 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 302746 303300 303328 "COMRING" 303333 T COMRING (NIL) -9 NIL 303385 NIL) (-171 301800 302104 302288 "COMPPROP" 302582 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 301461 301496 301624 "COMPLPAT" 301759 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 291755 301270 301379 "COMPLEX" 301384 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 291391 291448 291555 "COMPLEX2" 291692 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 291109 291144 291242 "COMPFACT" 291350 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 275585 285568 285608 "COMPCAT" 286612 NIL COMPCAT (NIL T) -9 NIL 287958 NIL) (-165 265095 268024 271651 "COMPCAT-" 272007 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 264824 264852 264955 "COMMUPC" 265061 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 264618 264652 264711 "COMMONOP" 264785 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 264174 264369 264456 "COMM" 264551 T COMM (NIL) -8 NIL NIL NIL) (-161 263750 263978 264053 "COMMAAST" 264119 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 262999 263193 263221 "COMBOPC" 263559 T COMBOPC (NIL) -9 NIL 263734 NIL) (-159 261895 262105 262347 "COMBINAT" 262789 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258352 258926 259553 "COMBF" 261317 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 257110 257468 257703 "COLOR" 258137 T COLOR (NIL) -8 NIL NIL NIL) (-156 256586 256831 256923 "COLONAST" 257038 T COLONAST (NIL) -8 NIL NIL NIL) (-155 256226 256273 256398 "CMPLXRT" 256533 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 255674 255926 256025 "CLLCTAST" 256147 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 251174 252204 253284 "CLIP" 254614 T CLIP (NIL) -7 NIL NIL NIL) (-152 249520 250280 250519 "CLIF" 251001 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 245695 247666 247707 "CLAGG" 248636 NIL CLAGG (NIL T) -9 NIL 249172 NIL) (-150 244117 244574 245157 "CLAGG-" 245162 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 243661 243746 243886 "CINTSLPE" 244026 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 241162 241633 242181 "CHVAR" 243189 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240371 240925 240953 "CHARZ" 240958 T CHARZ (NIL) -9 NIL 240973 NIL) (-146 240125 240165 240243 "CHARPOL" 240325 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 239218 239805 239833 "CHARNZ" 239880 T CHARNZ (NIL) -9 NIL 239936 NIL) (-144 237180 237908 238243 "CHAR" 238903 T CHAR (NIL) -8 NIL NIL NIL) (-143 236906 236967 236995 "CFCAT" 237106 T CFCAT (NIL) -9 NIL NIL NIL) (-142 236151 236262 236444 "CDEN" 236790 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 232116 235304 235584 "CCLASS" 235891 T CCLASS (NIL) -8 NIL NIL NIL) (-140 231423 231566 231729 "CATEGORY" 231973 T -10 (NIL) -8 NIL NIL NIL) (-139 231028 231342 231390 "CATCTOR" 231395 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 230479 230731 230829 "CATAST" 230950 T CATAST (NIL) -8 NIL NIL NIL) (-137 229955 230200 230292 "CASEAST" 230407 T CASEAST (NIL) -8 NIL NIL NIL) (-136 224964 225984 226737 "CARTEN" 229258 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 224072 224220 224441 "CARTEN2" 224811 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 222387 223222 223479 "CARD" 223835 T CARD (NIL) -8 NIL NIL NIL) (-133 221963 222191 222266 "CAPSLAST" 222332 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 221467 221675 221703 "CACHSET" 221835 T CACHSET (NIL) -9 NIL 221913 NIL) (-131 220937 221259 221287 "CABMON" 221337 T CABMON (NIL) -9 NIL 221393 NIL) (-130 220410 220641 220751 "BYTEORD" 220847 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 219386 219944 220086 "BYTE" 220249 T BYTE (NIL) -8 NIL NIL 220371) (-128 214736 218891 219063 "BYTEBUF" 219234 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 212245 214428 214535 "BTREE" 214662 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209694 211893 212015 "BTOURN" 212155 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 207064 209164 209205 "BTCAT" 209273 NIL BTCAT (NIL T) -9 NIL 209350 NIL) (-124 206731 206811 206960 "BTCAT-" 206965 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 201996 205874 205902 "BTAGG" 206124 T BTAGG (NIL) -9 NIL 206285 NIL) (-122 201486 201611 201817 "BTAGG-" 201822 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 198481 200764 200979 "BSTREE" 201303 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 197619 197745 197929 "BRILL" 198337 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 194271 196345 196386 "BRAGG" 197035 NIL BRAGG (NIL T) -9 NIL 197293 NIL) (-118 192800 193206 193761 "BRAGG-" 193766 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 186029 192146 192330 "BPADICRT" 192648 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184344 185966 186011 "BPADIC" 186016 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 184042 184072 184186 "BOUNDZRO" 184308 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 179134 180332 181275 "BOP" 183119 T BOP (NIL) -8 NIL NIL NIL) (-113 176915 177319 177794 "BOP1" 178692 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 175740 176489 176638 "BOOLEAN" 176786 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175076 175480 175534 "BMODULE" 175539 NIL BMODULE (NIL T T) -9 NIL 175604 NIL) (-110 170877 174874 174947 "BITS" 175023 T BITS (NIL) -8 NIL NIL NIL) (-109 170298 170417 170557 "BINDING" 170757 T BINDING (NIL) -8 NIL NIL NIL) (-108 164305 169895 170043 "BINARY" 170170 T BINARY (NIL) -8 NIL NIL NIL) (-107 162085 163560 163601 "BGAGG" 163861 NIL BGAGG (NIL T) -9 NIL 163998 NIL) (-106 161916 161948 162039 "BGAGG-" 162044 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160987 161300 161505 "BFUNCT" 161731 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159677 159855 160143 "BEZOUT" 160811 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156146 158529 158859 "BBTREE" 159380 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155880 155933 155961 "BASTYPE" 156080 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155732 155761 155834 "BASTYPE-" 155839 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155166 155242 155394 "BALFACT" 155643 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154022 154581 154767 "AUTOMOR" 155011 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153748 153753 153779 "ATTREG" 153784 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152000 152445 152797 "ATTRBUT" 153414 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151608 151828 151894 "ATTRAST" 151952 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151144 151257 151283 "ATRIG" 151484 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150953 150994 151081 "ATRIG-" 151086 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150598 150784 150810 "ASTCAT" 150815 T ASTCAT (NIL) -9 NIL 150845 NIL) (-92 150325 150384 150503 "ASTCAT-" 150508 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148474 150101 150189 "ASTACK" 150268 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146979 147276 147641 "ASSOCEQ" 148156 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146011 146638 146762 "ASP9" 146886 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145774 145959 145998 "ASP8" 146003 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144642 145379 145521 "ASP80" 145663 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143540 144277 144409 "ASP7" 144541 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142494 143217 143335 "ASP78" 143453 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141463 142174 142291 "ASP77" 142408 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140375 141101 141232 "ASP74" 141363 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139275 140010 140142 "ASP73" 140274 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138379 139101 139201 "ASP6" 139206 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137323 138056 138174 "ASP55" 138292 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136272 136997 137116 "ASP50" 137235 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135360 135973 136083 "ASP4" 136193 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134448 135061 135171 "ASP49" 135281 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133232 133987 134155 "ASP42" 134337 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132008 132765 132935 "ASP41" 133119 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130958 131685 131803 "ASP35" 131921 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130723 130906 130945 "ASP34" 130950 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130460 130527 130603 "ASP33" 130678 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129353 130095 130227 "ASP31" 130359 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129118 129301 129340 "ASP30" 129345 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128853 128922 128998 "ASP29" 129073 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128618 128801 128840 "ASP28" 128845 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128383 128566 128605 "ASP27" 128610 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127467 128081 128192 "ASP24" 128303 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126543 127269 127381 "ASP20" 127386 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125631 126244 126354 "ASP1" 126464 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124573 125305 125424 "ASP19" 125543 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124310 124377 124453 "ASP12" 124528 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123162 123909 124053 "ASP10" 124197 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121013 123006 123097 "ARRAY2" 123102 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116778 120661 120775 "ARRAY1" 120930 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 115810 115983 116204 "ARRAY12" 116601 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110122 112040 112115 "ARR2CAT" 114745 NIL ARR2CAT (NIL T T T) -9 NIL 115503 NIL) (-56 107556 108300 109254 "ARR2CAT-" 109259 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106873 107183 107308 "ARITY" 107449 T ARITY (NIL) -8 NIL NIL NIL) (-54 105649 105801 106100 "APPRULE" 106709 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105300 105348 105467 "APPLYORE" 105595 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104247 104565 104760 "ANY" 105123 T ANY (NIL) -8 NIL NIL NIL) (-51 103525 103648 103805 "ANY1" 104121 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101055 101962 102289 "ANTISYM" 103249 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 100547 100762 100858 "ANON" 100977 T ANON (NIL) -8 NIL NIL NIL) (-48 94796 99086 99540 "AN" 100111 T AN (NIL) -8 NIL NIL NIL) (-47 91018 92406 92457 "AMR" 93205 NIL AMR (NIL T T) -9 NIL 93805 NIL) (-46 90130 90351 90714 "AMR-" 90719 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74569 90047 90108 "ALIST" 90113 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71371 74163 74332 "ALGSC" 74487 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 67926 68481 69088 "ALGPKG" 70811 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67203 67304 67488 "ALGMFACT" 67812 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63154 63761 64379 "ALGMANIP" 66763 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54524 62780 62930 "ALGFF" 63087 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 53720 53851 54030 "ALGFACT" 54382 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52751 53351 53389 "ALGEBRA" 53394 NIL ALGEBRA (NIL T) -9 NIL 53435 NIL) (-37 52469 52528 52660 "ALGEBRA-" 52665 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34562 50471 50523 "ALAGG" 50659 NIL ALAGG (NIL T T) -9 NIL 50820 NIL) (-35 34098 34211 34237 "AHYP" 34438 T AHYP (NIL) -9 NIL NIL NIL) (-34 33029 33277 33303 "AGG" 33802 T AGG (NIL) -9 NIL 34081 NIL) (-33 32463 32625 32839 "AGG-" 32844 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30269 30692 31097 "AF" 32105 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29749 29994 30084 "ADDAST" 30197 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29017 29276 29432 "ACPLOT" 29611 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18557 26360 26398 "ACFS" 27005 NIL ACFS (NIL T) -9 NIL 27244 NIL) (-28 16584 17074 17836 "ACFS-" 17841 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12823 14751 14777 "ACF" 15656 T ACF (NIL) -9 NIL 16068 NIL) (-26 11527 11861 12354 "ACF-" 12359 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11099 11294 11320 "ABELSG" 11412 T ABELSG (NIL) -9 NIL 11477 NIL) (-24 10966 10991 11057 "ABELSG-" 11062 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10309 10596 10622 "ABELMON" 10792 T ABELMON (NIL) -9 NIL 10904 NIL) (-22 9973 10057 10195 "ABELMON-" 10200 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9281 9653 9679 "ABELGRP" 9804 T ABELGRP (NIL) -9 NIL 9886 NIL) (-20 8744 8873 9089 "ABELGRP-" 9094 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8083 8122 "A1AGG" 8127 NIL A1AGG (NIL T) -9 NIL 8167 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 99bd7f1e..4aeae036 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,52 +1,32 @@ -(731707 . 3452610477) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1170)) - (-4 *5 (-13 (-1034 (-564)) (-452) (-637 (-564)))) - (-5 *2 (-2 (|:| -3077 *3) (|:| |nconst| *3))) (-5 *1 (-567 *5 *3)) - (-4 *3 (-13 (-27) (-1194) (-430 *5)))))) +(731707 . 3452645034) +(((*1 *1 *2 *1) (-12 (-5 *2 (-109)) (-5 *1 (-175))))) +(((*1 *1 *1) + (-12 (-5 *1 (-223 *2 *3)) (-4 *2 (-13 (-1045) (-846))) + (-14 *3 (-641 (-1170)))))) +(((*1 *1 *1 *2) (-12 (-4 *1 (-1008)) (-5 *2 (-858))))) +(((*1 *2 *1) + (-12 (-4 *1 (-253 *3 *4 *5 *6)) (-4 *3 (-1045)) (-4 *4 (-846)) + (-4 *5 (-266 *4)) (-4 *6 (-789)) (-5 *2 (-112))))) +(((*1 *2 *3 *4 *4 *5 *3 *3 *3 *3 *3) + (-12 (-5 *3 (-564)) (-5 *5 (-685 (-225))) (-5 *4 (-225)) + (-5 *2 (-1031)) (-5 *1 (-748))))) (((*1 *2 *1) (-12 (-5 *2 (-1264)) (-5 *1 (-818))))) -(((*1 *2 *1 *1) - (|partial| -12 (-4 *1 (-329 *3)) (-4 *3 (-363)) (-4 *3 (-368)) - (-5 *2 (-1166 *3)))) - ((*1 *2 *1) - (-12 (-4 *1 (-329 *3)) (-4 *3 (-363)) (-4 *3 (-368)) - (-5 *2 (-1166 *3))))) (((*1 *2 *3 *3) - (-12 (|has| *2 (-6 (-4409 "*"))) (-4 *5 (-373 *2)) (-4 *6 (-373 *2)) - (-4 *2 (-1045)) (-5 *1 (-104 *2 *3 *4 *5 *6)) (-4 *3 (-1235 *2)) - (-4 *4 (-683 *2 *5 *6))))) -(((*1 *2 *3) (-12 (-5 *3 (-767)) (-5 *2 (-1264)) (-5 *1 (-379)))) - ((*1 *2) (-12 (-5 *2 (-1264)) (-5 *1 (-379))))) -(((*1 *2 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-442 *3)) (-4 *3 (-1235 (-564)))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-363) (-10 -8 (-15 ** ($ $ (-407 (-564))))))) - (-5 *2 (-641 *4)) (-5 *1 (-1122 *3 *4)) (-4 *3 (-1235 *4)))) - ((*1 *2 *3 *3 *3) - (-12 (-4 *3 (-13 (-363) (-10 -8 (-15 ** ($ $ (-407 (-564))))))) - (-5 *2 (-641 *3)) (-5 *1 (-1122 *4 *3)) (-4 *4 (-1235 *3))))) -(((*1 *1 *2) (-12 (-5 *1 (-227 *2)) (-4 *2 (-13 (-363) (-1194)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-767)) (-5 *2 (-1264)) (-5 *1 (-862 *4 *5 *6 *7)) - (-4 *4 (-1045)) (-14 *5 (-641 (-1170))) (-14 *6 (-641 *3)) - (-14 *7 *3))) - ((*1 *2 *3) - (-12 (-5 *3 (-767)) (-4 *4 (-1045)) (-4 *5 (-846)) (-4 *6 (-789)) - (-14 *8 (-641 *5)) (-5 *2 (-1264)) - (-5 *1 (-1271 *4 *5 *6 *7 *8 *9 *10)) (-4 *7 (-945 *4 *6 *5)) - (-14 *9 (-641 *3)) (-14 *10 *3)))) -(((*1 *2 *3) - (-12 (-4 *1 (-342 *4 *3 *5)) (-4 *4 (-1213)) (-4 *3 (-1235 *4)) - (-4 *5 (-1235 (-407 *3))) (-5 *2 (-112)))) - ((*1 *2 *3) - (-12 (-4 *1 (-342 *3 *4 *5)) (-4 *3 (-1213)) (-4 *4 (-1235 *3)) - (-4 *5 (-1235 (-407 *4))) (-5 *2 (-112))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-307)) (-4 *6 (-373 *5)) (-4 *4 (-373 *5)) - (-5 *2 - (-2 (|:| |particular| (-3 *4 "failed")) (|:| -1298 (-641 *4)))) - (-5 *1 (-1118 *5 *6 *4 *3)) (-4 *3 (-683 *5 *6 *4))))) + (-12 (-4 *4 (-556)) (-5 *2 (-641 (-767))) (-5 *1 (-965 *4 *3)) + (-4 *3 (-1235 *4))))) +(((*1 *2 *3 *3 *3 *3 *3 *4 *4 *4 *5) + (-12 (-5 *3 (-225)) (-5 *4 (-564)) + (-5 *5 (-3 (|:| |fn| (-388)) (|:| |fp| (-64 G)))) (-5 *2 (-1031)) + (-5 *1 (-744))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-917)) (-5 *2 (-1264)) (-5 *1 (-1260)))) + ((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-917)) (-5 *2 (-1264)) (-5 *1 (-1261))))) +(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-1031))))) +(((*1 *2 *3 *1) + (-12 (-5 *3 (-1 (-112) *4)) (|has| *1 (-6 -4407)) (-4 *1 (-489 *4)) + (-4 *4 (-1209)) (-5 *2 (-112))))) (((*1 *2 *3 *1) (-12 (-5 *3 (-1283 *4 *2)) (-4 *1 (-374 *4 *2)) (-4 *4 (-846)) (-4 *2 (-172)))) @@ -57,57 +37,45 @@ (-4 *2 (-1045)))) ((*1 *2 *1 *3) (-12 (-4 *2 (-1045)) (-5 *1 (-1282 *2 *3)) (-4 *3 (-842))))) -(((*1 *1 *1) - (|partial| -12 (-4 *1 (-367 *2)) (-4 *2 (-172)) (-4 *2 (-556)))) - ((*1 *1 *1) (|partial| -4 *1 (-718)))) -(((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-1259 *4)) (-4 *4 (-637 (-564))) - (-5 *2 (-1259 (-407 (-564)))) (-5 *1 (-1286 *4))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1235 *5)) (-4 *5 (-363)) - (-4 *7 (-1235 (-407 *6))) - (-5 *2 (-2 (|:| |answer| *3) (|:| -3958 *3))) - (-5 *1 (-562 *5 *6 *7 *3)) (-4 *3 (-342 *5 *6 *7)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1235 *5)) (-4 *5 (-363)) - (-5 *2 - (-2 (|:| |answer| (-407 *6)) (|:| -3958 (-407 *6)) - (|:| |specpart| (-407 *6)) (|:| |polypart| *6))) - (-5 *1 (-563 *5 *6)) (-5 *3 (-407 *6))))) -(((*1 *2 *3 *4 *3 *3 *4 *4 *4 *5) - (-12 (-5 *3 (-225)) (-5 *4 (-564)) - (-5 *5 (-3 (|:| |fn| (-388)) (|:| |fp| (-64 -2308)))) - (-5 *2 (-1031)) (-5 *1 (-744))))) -(((*1 *2 *3 *4 *5 *6 *7 *7 *8) - (-12 - (-5 *3 - (-2 (|:| |det| *12) (|:| |rows| (-641 (-564))) - (|:| |cols| (-641 (-564))))) - (-5 *4 (-685 *12)) (-5 *5 (-641 (-407 (-948 *9)))) - (-5 *6 (-641 (-641 *12))) (-5 *7 (-767)) (-5 *8 (-564)) - (-4 *9 (-13 (-307) (-147))) (-4 *12 (-945 *9 *11 *10)) - (-4 *10 (-13 (-846) (-612 (-1170)))) (-4 *11 (-789)) - (-5 *2 - (-2 (|:| |eqzro| (-641 *12)) (|:| |neqzro| (-641 *12)) - (|:| |wcond| (-641 (-948 *9))) - (|:| |bsoln| - (-2 (|:| |partsol| (-1259 (-407 (-948 *9)))) - (|:| -1298 (-641 (-1259 (-407 (-948 *9))))))))) - (-5 *1 (-920 *9 *10 *11 *12))))) -(((*1 *1) (-5 *1 (-291)))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-112)) (-5 *3 (-641 (-263))) (-5 *1 (-261)))) - ((*1 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-263)))) - ((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-467)))) - ((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-467))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-316 (-225))) (-5 *4 (-1170)) - (-5 *5 (-1088 (-839 (-225)))) (-5 *2 (-641 (-225))) (-5 *1 (-192)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-316 (-225))) (-5 *4 (-1170)) - (-5 *5 (-1088 (-839 (-225)))) (-5 *2 (-641 (-225))) (-5 *1 (-300))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-564)) (-4 *1 (-323 *2 *4)) (-4 *4 (-131)) + (-4 *2 (-1094)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-564)) (-5 *1 (-361 *2)) (-4 *2 (-1094)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-564)) (-5 *1 (-386 *2)) (-4 *2 (-1094)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-564)) (-5 *1 (-418 *2)) (-4 *2 (-556)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-564)) (-4 *2 (-1094)) (-5 *1 (-645 *2 *4 *5)) + (-4 *4 (-23)) (-14 *5 *4))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-564)) (-5 *1 (-815 *2)) (-4 *2 (-846))))) +(((*1 *2 *3 *3 *4 *5 *5 *5 *5 *3) + (-12 (-5 *3 (-564)) (-5 *4 (-1152)) (-5 *5 (-685 (-225))) + (-5 *2 (-1031)) (-5 *1 (-743))))) (((*1 *2 *3) - (-12 (-5 *2 (-1172 (-407 (-564)))) (-5 *1 (-190)) (-5 *3 (-564))))) + (-12 (-4 *1 (-349)) (-5 *3 (-564)) (-5 *2 (-1182 (-917) (-767)))))) +(((*1 *2 *1 *1) + (|partial| -12 (-4 *1 (-329 *3)) (-4 *3 (-363)) (-4 *3 (-368)) + (-5 *2 (-1166 *3)))) + ((*1 *2 *1) + (-12 (-4 *1 (-329 *3)) (-4 *3 (-363)) (-4 *3 (-368)) + (-5 *2 (-1166 *3))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-556) (-147))) (-5 *1 (-537 *3 *2)) + (-4 *2 (-1250 *3)))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-363) (-368) (-612 (-564)))) (-4 *4 (-1235 *3)) + (-4 *5 (-720 *3 *4)) (-5 *1 (-541 *3 *4 *5 *2)) (-4 *2 (-1250 *5)))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-363) (-368) (-612 (-564)))) (-5 *1 (-542 *3 *2)) + (-4 *2 (-1250 *3)))) + ((*1 *2 *2) + (-12 (-5 *2 (-1150 *3)) (-4 *3 (-13 (-556) (-147))) + (-5 *1 (-1146 *3))))) +(((*1 *1) (-5 *1 (-819)))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-917)) (-5 *1 (-1028 *2)) + (-4 *2 (-13 (-1094) (-10 -8 (-15 * ($ $ $)))))))) +(((*1 *2 *1) (-12 (-5 *2 (-818)) (-5 *1 (-817))))) +(((*1 *1) (-5 *1 (-291)))) (((*1 *2 *1 *3 *3 *2) (-12 (-5 *3 (-564)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1209)) (-4 *4 (-373 *2)) (-4 *5 (-373 *2)))) @@ -139,14 +107,14 @@ (-12 (-5 *3 (-1170)) (-5 *2 (-245 (-1152))) (-5 *1 (-214 *4)) (-4 *4 (-13 (-846) - (-10 -8 (-15 -4366 ((-1152) $ *3)) (-15 -1629 ((-1264) $)) - (-15 -3668 ((-1264) $))))))) + (-10 -8 (-15 -4366 ((-1152) $ *3)) (-15 -1630 ((-1264) $)) + (-15 -1757 ((-1264) $))))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-985)) (-5 *1 (-214 *3)) (-4 *3 (-13 (-846) - (-10 -8 (-15 -4366 ((-1152) $ (-1170))) (-15 -1629 ((-1264) $)) - (-15 -3668 ((-1264) $))))))) + (-10 -8 (-15 -4366 ((-1152) $ (-1170))) (-15 -1630 ((-1264) $)) + (-15 -1757 ((-1264) $))))))) ((*1 *2 *1 *3) (-12 (-5 *3 "count") (-5 *2 (-767)) (-5 *1 (-245 *4)) (-4 *4 (-846)))) ((*1 *1 *1 *2) (-12 (-5 *2 "sort") (-5 *1 (-245 *3)) (-4 *3 (-846)))) @@ -232,25 +200,32 @@ (-12 (-5 *2 "rest") (-4 *1 (-1247 *3)) (-4 *3 (-1209)))) ((*1 *2 *1 *3) (-12 (-5 *3 "first") (-4 *1 (-1247 *2)) (-4 *2 (-1209))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-917)) (-5 *3 (-641 (-263))) (-5 *1 (-261)))) - ((*1 *1 *2) (-12 (-5 *2 (-917)) (-5 *1 (-263))))) -(((*1 *2 *3) (-12 (-5 *3 (-564)) (-5 *2 (-1264)) (-5 *1 (-1002))))) -(((*1 *2) - (-12 (-4 *3 (-13 (-556) (-1034 (-564)))) (-5 *2 (-1264)) - (-5 *1 (-433 *3 *4)) (-4 *4 (-430 *3))))) -(((*1 *1 *1 *2 *2 *1) - (-12 (-5 *2 (-564)) (-4 *1 (-683 *3 *4 *5)) (-4 *3 (-1045)) - (-4 *4 (-373 *3)) (-4 *5 (-373 *3))))) -(((*1 *2 *1) - (-12 (-5 *2 (-641 (-641 (-767)))) (-5 *1 (-900 *3)) (-4 *3 (-1094))))) -(((*1 *2 *1) (-12 (-5 *2 (-858)) (-5 *1 (-52))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1232 *5 *4)) (-4 *4 (-816)) (-14 *5 (-1170)) + (-5 *2 (-564)) (-5 *1 (-1108 *4 *5))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-641 *6)) (-5 *4 (-641 (-1150 *7))) (-4 *6 (-846)) + (-4 *7 (-945 *5 (-531 *6) *6)) (-4 *5 (-1045)) + (-5 *2 (-1 (-1150 *7) *7)) (-5 *1 (-1120 *5 *6 *7))))) +(((*1 *2 *3 *3 *4 *4) + (-12 (-5 *3 (-685 (-225))) (-5 *4 (-564)) (-5 *2 (-1031)) + (-5 *1 (-744))))) (((*1 *2 *2) - (-12 (-5 *2 (-641 *6)) (-4 *6 (-1059 *3 *4 *5)) (-4 *3 (-556)) - (-4 *4 (-789)) (-4 *5 (-846)) (-5 *1 (-973 *3 *4 *5 *6))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-1259 *5)) (-4 *5 (-788)) (-5 *2 (-112)) - (-5 *1 (-841 *4 *5)) (-14 *4 (-767))))) + (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) + (-4 *2 (-13 (-430 *3) (-998)))))) +(((*1 *2 *1) + (-12 (-4 *3 (-1045)) (-5 *2 (-641 *1)) (-4 *1 (-1128 *3))))) +(((*1 *2) (-12 (-5 *2 (-917)) (-5 *1 (-157))))) +(((*1 *2) + (-12 (-5 *2 (-112)) (-5 *1 (-1186 *3 *4)) (-4 *3 (-1094)) + (-4 *4 (-1094))))) +(((*1 *2 *3) + (-12 (-5 *3 (-685 (-407 (-948 (-564))))) + (-5 *2 + (-641 + (-2 (|:| |radval| (-316 (-564))) (|:| |radmult| (-564)) + (|:| |radvect| (-641 (-685 (-316 (-564)))))))) + (-5 *1 (-1027))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-47 *3 *4)) (-4 *3 (-1045)) (-4 *4 (-788)))) @@ -357,9 +332,9 @@ (-4 *6 (-363)) (-5 *2 (-585 *6)) (-5 *1 (-584 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *6 *5)) - (-5 *4 (-3 (-2 (|:| -4354 *5) (|:| |coeff| *5)) "failed")) + (-5 *4 (-3 (-2 (|:| -2177 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-363)) (-4 *6 (-363)) - (-5 *2 (-2 (|:| -4354 *6) (|:| |coeff| *6))) + (-5 *2 (-2 (|:| -2177 *6) (|:| |coeff| *6))) (-5 *1 (-584 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) @@ -478,7 +453,7 @@ (-4 *8 (-1045)) (-4 *6 (-789)) (-4 *2 (-13 (-1094) - (-10 -8 (-15 -3069 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-767)))))) + (-10 -8 (-15 -3070 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-767)))))) (-5 *1 (-947 *6 *7 *8 *5 *2)) (-4 *5 (-945 *8 *6 *7)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-954 *5)) (-4 *5 (-1209)) @@ -579,22 +554,23 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1045)) (-5 *1 (-1282 *3 *4)) (-4 *4 (-842))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-556)) (-5 *2 (-641 *3)) (-5 *1 (-965 *4 *3)) - (-4 *3 (-1235 *4))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-564)) (-5 *4 (-418 *2)) (-4 *2 (-945 *7 *5 *6)) - (-5 *1 (-738 *5 *6 *7 *2)) (-4 *5 (-789)) (-4 *6 (-846)) - (-4 *7 (-307))))) -(((*1 *2 *1) (-12 (-5 *1 (-585 *2)) (-4 *2 (-363))))) -(((*1 *2 *1) - (-12 - (-5 *2 - (-641 - (-641 - (-3 (|:| -2562 (-1170)) - (|:| -1557 (-641 (-3 (|:| S (-1170)) (|:| P (-948 (-564)))))))))) - (-5 *1 (-1174))))) + (-12 (-4 *5 (-452)) (-4 *6 (-789)) (-4 *7 (-846)) + (-4 *3 (-1059 *5 *6 *7)) + (-5 *2 (-641 (-2 (|:| |val| (-112)) (|:| -3577 *4)))) + (-5 *1 (-1102 *5 *6 *7 *3 *4)) (-4 *4 (-1065 *5 *6 *7 *3))))) +(((*1 *2 *2) + (-12 (-5 *2 (-641 *6)) (-4 *6 (-1059 *3 *4 *5)) (-4 *3 (-556)) + (-4 *4 (-789)) (-4 *5 (-846)) (-5 *1 (-973 *3 *4 *5 *6))))) +(((*1 *2 *3 *2 *4) + (|partial| -12 (-5 *4 (-1 (-3 (-564) "failed") *5)) (-4 *5 (-1045)) + (-5 *2 (-564)) (-5 *1 (-543 *5 *3)) (-4 *3 (-1235 *5)))) + ((*1 *2 *3 *4 *2 *5) + (|partial| -12 (-5 *5 (-1 (-3 (-564) "failed") *4)) (-4 *4 (-1045)) + (-5 *2 (-564)) (-5 *1 (-543 *4 *3)) (-4 *3 (-1235 *4)))) + ((*1 *2 *3 *4 *5) + (|partial| -12 (-5 *5 (-1 (-3 (-564) "failed") *4)) (-4 *4 (-1045)) + (-5 *2 (-564)) (-5 *1 (-543 *4 *3)) (-4 *3 (-1235 *4))))) (((*1 *2 *3 *4 *5) (-12 (-5 *3 (-875 (-1 (-225) (-225)))) (-5 *4 (-1088 (-379))) (-5 *5 (-641 (-263))) (-5 *2 (-1127 (-225))) (-5 *1 (-255)))) @@ -648,78 +624,79 @@ (-12 (-5 *3 (-878 *5)) (-5 *4 (-1086 (-379))) (-4 *5 (-13 (-612 (-536)) (-1094))) (-5 *2 (-1127 (-225))) (-5 *1 (-259 *5))))) -(((*1 *2 *3 *3 *4 *5 *5) - (-12 (-5 *5 (-112)) (-4 *6 (-452)) (-4 *7 (-789)) (-4 *8 (-846)) - (-4 *3 (-1059 *6 *7 *8)) - (-5 *2 (-641 (-2 (|:| |val| *3) (|:| -3577 *4)))) - (-5 *1 (-1102 *6 *7 *8 *3 *4)) (-4 *4 (-1065 *6 *7 *8 *3)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-641 (-2 (|:| |val| (-641 *8)) (|:| -3577 *9)))) - (-5 *5 (-112)) (-4 *8 (-1059 *6 *7 *4)) (-4 *9 (-1065 *6 *7 *4 *8)) - (-4 *6 (-452)) (-4 *7 (-789)) (-4 *4 (-846)) - (-5 *2 (-641 (-2 (|:| |val| *8) (|:| -3577 *9)))) 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-(((*1 *2 *2) - (-12 (-4 *2 (-13 (-363) (-844))) (-5 *1 (-181 *2 *3)) - (-4 *3 (-1235 (-169 *2)))))) + (-12 (-5 *3 (-641 (-564))) (-5 *2 (-900 (-564))) (-5 *1 (-913))))) +(((*1 *2 *3) (-12 (-5 *3 (-858)) (-5 *2 (-1152)) (-5 *1 (-706))))) (((*1 *1 *1) (-12 (-4 *1 (-119 *2)) (-4 *2 (-1209)))) ((*1 *1 *1) (-12 (-5 *1 (-668 *2)) (-4 *2 (-846)))) ((*1 *1 *1) (-12 (-5 *1 (-673 *2)) (-4 *2 (-846)))) @@ -772,35 +747,82 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-844) (-363))) (-5 *1 (-1055 *2 *3)) (-4 *3 (-1235 *2))))) +(((*1 *2) + (-12 (-14 *4 (-767)) (-4 *5 (-1209)) (-5 *2 (-134)) + (-5 *1 (-237 *3 *4 *5)) (-4 *3 (-238 *4 *5)))) + ((*1 *2) + (-12 (-4 *4 (-363)) (-5 *2 (-134)) (-5 *1 (-328 *3 *4)) + (-4 *3 (-329 *4)))) + ((*1 *2) + (-12 (-5 *2 (-767)) (-5 *1 (-390 *3 *4 *5)) (-14 *3 *2) (-14 *4 *2) + (-4 *5 (-172)))) + ((*1 *2 *1) + (-12 (-4 *3 (-363)) (-4 *4 (-789)) (-4 *5 (-846)) (-5 *2 (-564)) + (-5 *1 (-504 *3 *4 *5 *6)) (-4 *6 (-945 *3 *4 *5)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-641 *6)) (-4 *6 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*6 *7))))) +(((*1 *2 *1) (-12 (-4 *1 (-326 *2 *3)) (-4 *3 (-788)) (-4 *2 (-1045)))) + ((*1 *2 *1) (-12 (-4 *1 (-430 *2)) (-4 *2 (-1094))))) +(((*1 *2 *3 *4 *5 *3 *6 *3) + (-12 (-5 *3 (-564)) (-5 *5 (-169 (-225))) (-5 *6 (-1152)) + (-5 *4 (-225)) (-5 *2 (-1031)) (-5 *1 (-754))))) +(((*1 *2 *3 *3 *4 *4 *3 *3 *5 *3) + (-12 (-5 *3 (-564)) (-5 *5 (-685 (-225))) (-5 *4 (-225)) + (-5 *2 (-1031)) (-5 *1 (-751))))) +(((*1 *2 *2) + (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) + (-4 *2 (-13 (-430 *3) (-998)))))) +(((*1 *2 *3 *3 *3 *4) + (-12 (-5 *3 (-225)) (-5 *4 (-564)) (-5 *2 (-1031)) (-5 *1 (-754))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) @@ -2657,62 +3112,46 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-1170)) - (-4 *4 (-13 (-307) (-147) (-1034 (-564)) (-637 (-564)))) - (-5 *1 (-426 *4 *2)) (-4 *2 (-13 (-1194) (-29 *4))))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-407 (-948 *5))) (-5 *4 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(|partial| -12 (-5 *3 (-685 *1)) (-4 *1 (-349)) (-5 *2 (-1259 *1)))) + ((*1 *2 *3) + (|partial| -12 (-5 *3 (-685 *1)) (-4 *1 (-145)) (-4 *1 (-905)) + (-5 *2 (-1259 *1))))) +(((*1 *2 *1) (-12 (-5 *2 (-1264)) (-5 *1 (-818))))) +(((*1 *2 *1) (|partial| -12 (-5 *2 (-1166 *1)) (-4 *1 (-1008))))) (((*1 *2 *3) (-12 (-5 *3 (-1170)) (-4 *4 (-13 (-452) (-1034 (-564)) (-637 (-564)))) (-5 *2 (-52)) @@ -3173,16 +3514,72 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-820))))) -(((*1 *2 *3 *4 *5 *5 *5 *5 *6 *4 *4 *4 *4 *4 *5 *4 *5 *5 *4) - (-12 (-5 *3 (-1152)) (-5 *4 (-564)) (-5 *5 (-685 (-225))) - (-5 *6 (-225)) (-5 *2 (-1031)) (-5 *1 (-748))))) -(((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-407 (-948 *4))) (-5 *3 (-1170)) - (-4 *4 (-13 (-556) (-1034 (-564)) (-147))) (-5 *1 (-570 *4))))) +(((*1 *1) (-5 *1 (-141))) ((*1 *1 *1) (-5 *1 (-144))) + ((*1 *1 *1) (-4 *1 (-1138)))) (((*1 *2 *3 *2) - (-12 (-5 *2 (-917)) (-5 *3 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(|:| |deltaY| (-225)))) + (-5 *2 (-1264)) (-5 *1 (-1261)))) + ((*1 *2 *1) + (-12 + (-5 *2 + (-2 (|:| |theta| (-225)) (|:| |phi| (-225)) (|:| -2052 (-225)) + (|:| |scaleX| (-225)) (|:| |scaleY| (-225)) (|:| |scaleZ| (-225)) + (|:| |deltaX| (-225)) (|:| |deltaY| (-225)))) + (-5 *1 (-1261)))) + ((*1 *2 *1 *3 *3 *3 *3 *3) + (-12 (-5 *3 (-379)) (-5 *2 (-1264)) (-5 *1 (-1261))))) +(((*1 *1 *2) + (-12 (-5 *2 (-641 (-504 *3 *4 *5 *6))) (-4 *3 (-363)) (-4 *4 (-789)) + (-4 *5 (-846)) (-5 *1 (-504 *3 *4 *5 *6)) (-4 *6 (-945 *3 *4 *5)))) + ((*1 *1 *1 *1) + (-12 (-4 *2 (-363)) (-4 *3 (-789)) (-4 *4 (-846)) + (-5 *1 (-504 *2 *3 *4 *5)) (-4 *5 (-945 *2 *3 *4)))) + ((*1 *2 *3 *2) + (-12 (-5 *2 (-641 *1)) (-4 *1 (-1065 *4 *5 *6 *3)) (-4 *4 (-452)) + (-4 *5 (-789)) (-4 *6 (-846)) (-4 *3 (-1059 *4 *5 *6)))) + ((*1 *2 *3 *2) + (-12 (-5 *2 (-641 *1)) (-5 *3 (-641 *7)) (-4 *1 (-1065 *4 *5 *6 *7)) + (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) + (-4 *7 (-1059 *4 *5 *6)))) + ((*1 *2 *3 *1) + (-12 (-5 *3 (-641 *7)) (-4 *7 (-1059 *4 *5 *6)) (-4 *4 (-452)) + (-4 *5 (-789)) (-4 *6 (-846)) (-5 *2 (-641 *1)) + (-4 *1 (-1065 *4 *5 *6 *7)))) + ((*1 *2 *3 *1) + (-12 (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) + (-4 *3 (-1059 *4 *5 *6)) (-5 *2 (-641 *1)) + (-4 *1 (-1065 *4 *5 *6 *3)))) + ((*1 *1 *1 *1) (-12 (-4 *1 (-1092 *2)) (-4 *2 (-1094))))) +(((*1 *2 *2 *2 *2 *3 *3 *4) + (|partial| -12 (-5 *3 (-610 *2)) + (-5 *4 (-1 (-3 *2 "failed") *2 *2 (-1170))) + (-4 *2 (-13 (-430 *5) (-27) (-1194))) + (-4 *5 (-13 (-452) (-1034 (-564)) (-147) (-637 (-564)))) + (-5 *1 (-566 *5 *2 *6)) (-4 *6 (-1094))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-641 *8)) (-5 *4 (-136 *5 *6 *7)) (-14 *5 (-564)) (-14 *6 (-767)) (-4 *7 (-172)) (-4 *8 (-172)) @@ -3192,25 +3589,23 @@ (-4 *8 (-1045)) (-4 *2 (-945 *9 *7 *5)) (-5 *1 (-724 *5 *6 *7 *8 *9 *4 *2)) (-4 *7 (-789)) (-4 *4 (-945 *8 *6 *5))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-1170)) (-4 *4 (-556)) (-5 *1 (-158 *4 *2)) - (-4 *2 (-430 *4)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1086 *2)) (-4 *2 (-430 *4)) (-4 *4 (-556)) - (-5 *1 (-158 *4 *2)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-1086 *1)) (-4 *1 (-160)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-160)) (-5 *2 (-1170))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-363)) (-4 *5 (-556)) + (-5 *2 + (-2 (|:| |minor| (-641 (-917))) (|:| -1606 *3) + (|:| |minors| (-641 (-641 (-917)))) (|:| |ops| (-641 *3)))) + (-5 *1 (-90 *5 *3)) (-5 *4 (-917)) (-4 *3 (-652 *5))))) +(((*1 *2 *2 *2) + (-12 (-4 *3 (-1045)) (-5 *1 (-1231 *3 *2)) (-4 *2 (-1235 *3))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-641 *5)) (-5 *4 (-641 (-1 *6 (-641 *6)))) + (-4 *5 (-38 (-407 (-564)))) (-4 *6 (-1250 *5)) (-5 *2 (-641 *6)) + (-5 *1 (-1252 *5 *6))))) +(((*1 *2 *2) (-12 (-5 *2 (-225)) (-5 *1 (-226)))) + ((*1 *2 *2) (-12 (-5 *2 (-169 (-225))) (-5 *1 (-226))))) (((*1 *2 *2) - (-12 (-4 *3 (-556)) (-5 *1 (-158 *3 *2)) (-4 *2 (-430 *3))))) -(((*1 *2 *3 *3 *3) - (|partial| -12 (-4 *4 (-13 (-363) (-147) (-1034 (-564)))) - (-4 *5 (-1235 *4)) (-5 *2 (-641 (-407 *5))) (-5 *1 (-1012 *4 *5)) - (-5 *3 (-407 *5))))) -(((*1 *2 *3) (-12 (-5 *3 (-1259 *1)) (-4 *1 (-367 *2)) (-4 *2 (-172)))) - ((*1 *2) (-12 (-4 *2 (-172)) (-5 *1 (-416 *3 *2)) (-4 *3 (-417 *2)))) - ((*1 *2) (-12 (-4 *1 (-417 *2)) (-4 *2 (-172))))) -(((*1 *2 *1) (-12 (-4 *1 (-1006 *3)) (-4 *3 (-1209)) (-5 *2 (-112)))) - ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1195 *3)) (-4 *3 (-1094))))) + (-12 (-4 *3 (-452)) (-5 *1 (-1200 *3 *2)) + (-4 *2 (-13 (-430 *3) (-1194)))))) (((*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-998))))) @@ -3230,57 +3625,45 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *2 *1) - (-12 (-4 *1 (-326 *3 *4)) (-4 *3 (-1045)) (-4 *4 (-788)) - (-5 *2 (-641 *3)))) - ((*1 *2 *1) - (-12 (-4 *1 (-382 *3 *4)) (-4 *3 (-1045)) (-4 *4 (-1094)) - (-5 *2 (-641 *3)))) - ((*1 *2 *1) - (-12 (-5 *2 (-1150 *3)) (-5 *1 (-595 *3)) (-4 *3 (-1045)))) - ((*1 *2 *1) - (-12 (-5 *2 (-641 *3)) (-5 *1 (-731 *3 *4)) (-4 *3 (-1045)) - (-4 *4 (-722)))) - ((*1 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|totdeg| (-767)) (|:| |poli| *2) - (|:| |polj| *2))) - (-4 *5 (-789)) (-4 *2 (-945 *4 *5 *6)) (-5 *1 (-449 *4 *5 *6 *2)) - (-4 *4 (-452)) (-4 *6 (-846))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1059 *2 *3 *4)) (-4 *2 (-1045)) (-4 *3 (-789)) - (-4 *4 (-846)) (-4 *2 (-452))))) + (-12 (-5 *3 (-1 (-112) *6)) (-4 *6 (-13 (-1094) (-1034 *5))) + (-4 *5 (-882 *4)) (-4 *4 (-1094)) (-5 *2 (-1 (-112) *5)) + (-5 *1 (-927 *4 *5 *6))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-1152)) (-4 *1 (-364 *3 *4)) (-4 *3 (-1094)) + (-4 *4 (-1094))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-641 *1)) (-4 *1 (-1059 *4 *5 *6)) (-4 *4 (-1045)) + (-4 *5 (-789)) (-4 *6 (-846)) (-5 *2 (-112)))) + ((*1 *2 *1 *1) + (-12 (-4 *1 (-1059 *3 *4 *5)) (-4 *3 (-1045)) (-4 *4 (-789)) + (-4 *5 (-846)) (-5 *2 (-112)))) + ((*1 *2 *3 *1 *4) + (-12 (-5 *4 (-1 (-112) *3 *3)) (-4 *1 (-1202 *5 *6 *7 *3)) + (-4 *5 (-556)) (-4 *6 (-789)) (-4 *7 (-846)) + (-4 *3 (-1059 *5 *6 *7)) (-5 *2 (-112))))) (((*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-998))))) @@ -3300,54 +3683,33 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *1 *1) (-5 *1 (-1057)))) -(((*1 *2 *1) - (-12 (-4 *1 (-1059 *3 *4 *5)) (-4 *3 (-1045)) (-4 *4 (-789)) - (-4 *5 (-846)) (-5 *2 (-112))))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-1 (-641 *5) *6)) - (-4 *5 (-13 (-363) (-147) (-1034 (-407 (-564))))) (-4 *6 (-1235 *5)) - (-5 *2 (-641 (-2 (|:| |poly| *6) (|:| -1606 *3)))) - (-5 *1 (-805 *5 *6 *3 *7)) (-4 *3 (-652 *6)) - (-4 *7 (-652 (-407 *6))))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-1 (-641 *5) *6)) - (-4 *5 (-13 (-363) (-147) (-1034 (-564)) (-1034 (-407 (-564))))) - (-4 *6 (-1235 *5)) - (-5 *2 (-641 (-2 (|:| |poly| *6) (|:| -1606 (-650 *6 (-407 *6)))))) - (-5 *1 (-808 *5 *6)) (-5 *3 (-650 *6 (-407 *6)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1170)) - (-4 *4 (-13 (-307) (-1034 (-564)) (-637 (-564)) (-147))) - (-5 *2 (-1 *5 *5)) (-5 *1 (-800 *4 *5)) - (-4 *5 (-13 (-29 *4) (-1194) (-955)))))) -(((*1 *2 *3 *3 *4) (-12 (-5 *3 (-225)) (-5 *4 (-564)) (-5 *2 (-1031)) (-5 *1 (-754))))) -(((*1 *2 *2 *3) - (-12 (-4 *3 (-363)) (-5 *1 (-285 *3 *2)) (-4 *2 (-1250 *3))))) -(((*1 *2 *2) - (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) - (-4 *2 (-13 (-430 *3) (-998)))))) +(((*1 *2 *3 *4 *5 *6 *5) + (-12 (-5 *4 (-169 (-225))) (-5 *5 (-564)) (-5 *6 (-1152)) + (-5 *3 (-225)) (-5 *2 (-1031)) (-5 *1 (-754))))) +(((*1 *2 *3 *3 *4 *4 *3) + (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *2 (-1031)) + (-5 *1 (-743))))) +(((*1 *2 *3 *3 *4 *4 *5 *4 *5 *4 *4 *5 *4) + (-12 (-5 *3 (-1152)) (-5 *4 (-564)) (-5 *5 (-685 (-169 (-225)))) + (-5 *2 (-1031)) (-5 *1 (-750))))) (((*1 *2 *1) - (-12 (-4 *3 (-233)) (-4 *3 (-1045)) (-4 *4 (-846)) (-4 *5 (-266 *4)) - (-4 *6 (-789)) (-5 *2 (-1 *1 (-767))) (-4 *1 (-253 *3 *4 *5 *6)))) - ((*1 *2 *3) - (-12 (-4 *4 (-1045)) (-4 *3 (-846)) (-4 *5 (-266 *3)) (-4 *6 (-789)) - (-5 *2 (-1 *1 (-767))) (-4 *1 (-253 *4 *3 *5 *6)))) - ((*1 *1 *2 *3) (-12 (-5 *3 (-767)) (-4 *1 (-266 *2)) (-4 *2 (-846))))) -(((*1 *2 *1) (-12 (-5 *2 (-183)) (-5 *1 (-248))))) + (-12 (-4 *3 (-1045)) (-5 *2 (-1259 *3)) (-5 *1 (-708 *3 *4)) + (-4 *4 (-1235 *3))))) (((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-641 (-1166 *5))) (-5 *3 (-1166 *5)) - (-4 *5 (-166 *4)) (-4 *4 (-545)) (-5 *1 (-149 *4 *5)))) - ((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-641 *3)) (-4 *3 (-1235 *5)) - (-4 *5 (-1235 *4)) (-4 *4 (-349)) (-5 *1 (-358 *4 *5 *3)))) - ((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-641 (-1166 (-564)))) (-5 *3 (-1166 (-564))) - (-5 *1 (-572)))) - ((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-641 (-1166 *1))) (-5 *3 (-1166 *1)) - (-4 *1 (-905))))) + (-12 (-4 *3 (-363)) (-5 *1 (-285 *3 *2)) (-4 *2 (-1250 *3))))) +(((*1 *2 *1) (-12 (-4 *1 (-166 *2)) (-4 *2 (-172)) (-4 *2 (-1194)))) + ((*1 *2 *1) (-12 (-5 *1 (-331 *2)) (-4 *2 (-846)))) + ((*1 *2 *1) (-12 (-5 *2 (-641 *3)) (-5 *1 (-610 *3)) (-4 *3 (-1094))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-225)) (-5 *4 (-564)) (-5 *2 (-1031)) (-5 *1 (-754))))) +(((*1 *2 *3) + (-12 (-5 *3 (-564)) (-4 *4 (-789)) (-4 *5 (-846)) (-4 *2 (-1045)) + (-5 *1 (-321 *4 *5 *2 *6)) (-4 *6 (-945 *2 *4 *5))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1259 (-316 (-225)))) (-5 *2 (-1259 (-316 (-379)))) + (-5 *1 (-305))))) (((*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-998))))) @@ -3367,42 +3729,25 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-979 *2)) (-4 *2 (-1194))))) +(((*1 *1 *2 *3) (-12 (-5 *3 (-564)) (-5 *1 (-418 *2)) (-4 *2 (-556))))) +(((*1 *2 *3) (-12 (-5 *3 (-316 (-225))) (-5 *2 (-225)) (-5 *1 (-305))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-641 (-407 (-948 *5)))) (-5 *4 (-641 (-1170))) + (-4 *5 (-556)) (-5 *2 (-641 (-641 (-948 *5)))) (-5 *1 (-1178 *5))))) +(((*1 *1 *2) (-12 (-5 *2 (-641 *3)) (-4 *3 (-1094)) (-4 *1 (-235 *3)))) + ((*1 *1) (-12 (-4 *1 (-235 *2)) (-4 *2 (-1094))))) (((*1 *2 *3 *2) - (-12 (-5 *2 (-1 (-939 (-225)) (-939 (-225)))) (-5 *3 (-641 (-263))) - (-5 *1 (-261)))) - ((*1 *1 *2) - (-12 (-5 *2 (-1 (-939 (-225)) (-939 (-225)))) (-5 *1 (-263)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-641 (-481 *5 *6))) (-5 *3 (-481 *5 *6)) - (-14 *5 (-641 (-1170))) (-4 *6 (-452)) (-5 *2 (-1259 *6)) - (-5 *1 (-629 *5 *6))))) -(((*1 *2 *1) (-12 (-5 *2 (-1170)) (-5 *1 (-818))))) -(((*1 *2 *3 *4 *4 *3 *5) - (-12 (-5 *4 (-610 *3)) (-5 *5 (-1166 *3)) - (-4 *3 (-13 (-430 *6) (-27) (-1194))) - (-4 *6 (-13 (-452) (-1034 (-564)) (-147) (-637 (-564)))) - (-5 *2 (-585 *3)) (-5 *1 (-560 *6 *3 *7)) (-4 *7 (-1094)))) - ((*1 *2 *3 *4 *4 *4 *3 *5) - (-12 (-5 *4 (-610 *3)) (-5 *5 (-407 (-1166 *3))) - (-4 *3 (-13 (-430 *6) (-27) (-1194))) - (-4 *6 (-13 (-452) (-1034 (-564)) (-147) (-637 (-564)))) - (-5 *2 (-585 *3)) (-5 *1 (-560 *6 *3 *7)) (-4 *7 (-1094))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5) - (-12 (-5 *3 (-1 (-379) (-379))) (-5 *4 (-379)) - (-5 *2 - (-2 (|:| -2128 *4) (|:| -1433 *4) (|:| |totalpts| (-564)) - (|:| |success| (-112)))) - (-5 *1 (-785)) (-5 *5 (-564))))) -(((*1 *2) + (-12 (-5 *2 (-870)) (-5 *3 (-641 (-263))) (-5 *1 (-261))))) +(((*1 *2 *1) (-12 (-4 *1 (-342 *3 *4 *5)) (-4 *3 (-1213)) (-4 *4 (-1235 *3)) - (-4 *5 (-1235 (-407 *4))) (-5 *2 (-685 (-407 *4)))))) -(((*1 *2 *3) - (-12 (-4 *4 (-846)) (-5 *2 (-641 (-641 (-641 *4)))) - (-5 *1 (-1180 *4)) (-5 *3 (-641 (-641 *4)))))) -(((*1 *2 *1) (-12 (-5 *2 (-641 (-109))) (-5 *1 (-175))))) -(((*1 *1) (-5 *1 (-157)))) + (-4 *5 (-1235 (-407 *4))) + (-5 *2 (-2 (|:| |num| (-1259 *4)) (|:| |den| *4)))))) +(((*1 *1 *1 *2 *3 *1) + (-12 (-4 *1 (-326 *2 *3)) (-4 *2 (-1045)) (-4 *3 (-788))))) (((*1 *2 *3) - (-12 (-5 *3 (-316 (-225))) (-5 *2 (-316 (-379))) (-5 *1 (-305))))) + (-12 (-5 *3 (-641 *2)) (-4 *2 (-430 *4)) (-5 *1 (-158 *4 *2)) + (-4 *4 (-556))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) @@ -3430,36 +3775,52 @@ ((*1 *2 *1) (-12 (-4 *1 (-1117 *3 *2 *4 *5)) (-4 *4 (-238 *3 *2)) (-4 *5 (-238 *3 *2)) (-4 *2 (-1045))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1276 *2 *3)) (-4 *2 (-846)) (-4 *3 (-1045)))) - ((*1 *1 *1) - (-12 (-5 *1 (-1282 *2 *3)) (-4 *2 (-1045)) (-4 *3 (-842))))) -(((*1 *1) (-5 *1 (-157))) - ((*1 *2 *1) (-12 (-4 *1 (-1040 *2)) (-4 *2 (-23))))) -(((*1 *2 *3 *3) +(((*1 *1 *2 *3 *1 *3) + (-12 (-5 *2 (-888 *4)) (-4 *4 (-1094)) (-5 *1 (-885 *4 *3)) + (-4 *3 (-1094))))) +(((*1 *2 *3) (-12 (-4 *4 (-556)) - (-5 *2 (-2 (|:| |coef2| *3) (|:| |subResultant| *3))) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -1330 *4))) (-5 *1 (-965 *4 *3)) (-4 *3 (-1235 *4))))) -(((*1 *2 *3 *2) (-12 (-5 *3 (-767)) (-5 *1 (-852 *2)) (-4 *2 (-172))))) +(((*1 *1) (-5 *1 (-578)))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-564)) (-5 *1 (-561))))) +(((*1 *1 *1 *1 *1) (-4 *1 (-545)))) +(((*1 *2 *2 *2) + (-12 (-4 *3 (-1045)) (-5 *1 (-890 *2 *3)) (-4 *2 (-1235 *3)))) + ((*1 *2 *2 *2) + (-12 (-5 *2 (-1150 *3)) (-4 *3 (-1045)) (-5 *1 (-1154 *3))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1202 *3 *4 *5 *6)) (-4 *3 (-556)) (-4 *4 (-789)) + (-4 *5 (-846)) (-4 *6 (-1059 *3 *4 *5)) (-4 *5 (-368)) + (-5 *2 (-767))))) (((*1 *2 *2) - (-12 (-4 *3 (-13 (-556) (-1034 (-564)) (-637 (-564)))) - (-5 *1 (-277 *3 *2)) (-4 *2 (-13 (-27) (-1194) (-430 *3))))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1170)) - (-4 *4 (-13 (-556) (-1034 (-564)) (-637 (-564)))) - (-5 *1 (-277 *4 *2)) (-4 *2 (-13 (-27) (-1194) (-430 *4)))))) -(((*1 *1 *1 *1) (-12 (-5 *1 (-386 *2)) (-4 *2 (-1094)))) - ((*1 *1 *1 *1) (-12 (-5 *1 (-815 *2)) (-4 *2 (-846))))) -(((*1 *2 *2 *3 *4) - (-12 (-5 *2 (-641 *8)) (-5 *3 (-1 (-112) *8 *8)) - (-5 *4 (-1 *8 *8 *8)) (-4 *8 (-1059 *5 *6 *7)) (-4 *5 (-556)) - (-4 *6 (-789)) (-4 *7 (-846)) (-5 *1 (-973 *5 *6 *7 *8))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-225)) (-5 *4 (-564)) (-5 *2 (-1031)) (-5 *1 (-754))))) -(((*1 *2 *3 *1) - (-12 (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) - (-4 *3 (-1059 *4 *5 *6)) (-5 *2 (-641 *1)) - (-4 *1 (-1065 *4 *5 *6 *3))))) + (-12 (-4 *3 (-452)) (-5 *1 (-1200 *3 *2)) + (-4 *2 (-13 (-430 *3) (-1194)))))) +(((*1 *2 *3) + (-12 (-4 *3 (-13 (-307) (-10 -8 (-15 -2753 ((-418 $) $))))) + (-4 *4 (-1235 *3)) + (-5 *2 + (-2 (|:| -2047 (-685 *3)) (|:| |basisDen| *3) + (|:| |basisInv| (-685 *3)))) + (-5 *1 (-350 *3 *4 *5)) (-4 *5 (-409 *3 *4)))) + ((*1 *2 *3) + (-12 (-5 *3 (-564)) (-4 *4 (-1235 *3)) + (-5 *2 + (-2 (|:| -2047 (-685 *3)) (|:| |basisDen| *3) + (|:| |basisInv| (-685 *3)))) + (-5 *1 (-764 *4 *5)) (-4 *5 (-409 *3 *4)))) + ((*1 *2 *3) + (-12 (-4 *4 (-349)) (-4 *3 (-1235 *4)) (-4 *5 (-1235 *3)) + (-5 *2 + (-2 (|:| -2047 (-685 *3)) (|:| |basisDen| *3) + (|:| |basisInv| (-685 *3)))) + (-5 *1 (-981 *4 *3 *5 *6)) (-4 *6 (-720 *3 *5)))) + ((*1 *2 *3) + (-12 (-4 *4 (-349)) (-4 *3 (-1235 *4)) (-4 *5 (-1235 *3)) + (-5 *2 + (-2 (|:| -2047 (-685 *3)) (|:| |basisDen| *3) + (|:| |basisInv| (-685 *3)))) + (-5 *1 (-1268 *4 *3 *5 *6)) (-4 *6 (-409 *3 *5))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) @@ -3479,7 +3840,7 @@ (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -3430 (-641 (-225))))) + (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -3431 (-641 (-225))))) (-5 *2 (-641 (-1170))) (-5 *1 (-267)))) ((*1 *2 *3) (-12 (-5 *3 (-1166 *7)) (-4 *7 (-945 *6 *4 *5)) (-4 *4 (-789)) @@ -3501,7 +3862,7 @@ (-5 *1 (-946 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-363) - (-10 -8 (-15 -2423 ($ *7)) (-15 -2324 (*7 $)) (-15 -2336 (*7 $))))))) + (-10 -8 (-15 -2423 ($ *7)) (-15 -2323 (*7 $)) (-15 -2336 (*7 $))))))) ((*1 *2 *1) (-12 (-4 *1 (-969 *3 *4 *5)) (-4 *3 (-1045)) (-4 *4 (-788)) (-4 *5 (-846)) (-5 *2 (-641 *5)))) @@ -3511,65 +3872,42 @@ ((*1 *2 *3) (-12 (-5 *3 (-407 (-948 *4))) (-4 *4 (-556)) (-5 *2 (-641 (-1170))) (-5 *1 (-1039 *4))))) -(((*1 *2 *3 *1) - (-12 (-5 *3 (-1170)) - (-5 *2 (-3 (|:| |fst| (-434)) (|:| -1836 "void"))) (-5 *1 (-1173))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1152)) (-5 *2 (-1264)) (-5 *1 (-1261))))) -(((*1 *2 *1) (-12 (-4 *1 (-793 *2)) (-4 *2 (-172))))) -(((*1 *1 *1 *2) - (-12 (-4 *3 (-363)) (-4 *4 (-789)) (-4 *5 (-846)) - (-5 *1 (-504 *3 *4 *5 *2)) (-4 *2 (-945 *3 *4 *5)))) - ((*1 *1 *1 *1) - (-12 (-4 *2 (-363)) (-4 *3 (-789)) (-4 *4 (-846)) - (-5 *1 (-504 *2 *3 *4 *5)) (-4 *5 (-945 *2 *3 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-1264)) (-5 *1 (-818))))) +(((*1 *2 *2) (-12 (-5 *2 (-564)) (-5 *1 (-561))))) (((*1 *2 *1) - (-12 (-5 *2 (-3 (|:| |fst| (-434)) (|:| -1836 "void"))) - (-5 *1 (-437))))) + (-12 (-4 *1 (-373 *3)) (-4 *3 (-1209)) (-4 *3 (-846)) (-5 *2 (-112)))) + ((*1 *2 *3 *1) + (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *1 (-373 *4)) (-4 *4 (-1209)) + (-5 *2 (-112))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -3431 (-641 (-225))))) + (-5 *2 (-379)) (-5 *1 (-267)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1259 (-316 (-225)))) (-5 *2 (-379)) (-5 *1 (-305))))) +(((*1 *2 *3 *3) + (-12 (-5 *2 (-1 (-939 *3) (-939 *3))) (-5 *1 (-176 *3)) + (-4 *3 (-13 (-363) (-1194) (-998)))))) (((*1 *2 *1) (-12 (-5 *2 (-1208)) (-5 *1 (-180)))) ((*1 *2 *1) (-12 (-5 *2 (-1208)) (-5 *1 (-677)))) ((*1 *2 *1) (-12 (-5 *2 (-1208)) (-5 *1 (-966)))) ((*1 *2 *1) (-12 (-5 *2 (-1208)) (-5 *1 (-1067)))) ((*1 *2 *1) (-12 (-5 *2 (-1175)) (-5 *1 (-1112))))) -(((*1 *2 *2 *3) - (-12 (-4 *4 (-789)) - (-4 *3 (-13 (-846) (-10 -8 (-15 -1311 ((-1170) $))))) (-4 *5 (-556)) - (-5 *1 (-728 *4 *3 *5 *2)) (-4 *2 (-945 (-407 (-948 *5)) *4 *3)))) - ((*1 *2 *2 *3) - (-12 (-4 *4 (-1045)) (-4 *5 (-789)) - (-4 *3 - (-13 (-846) - (-10 -8 (-15 -1311 ((-1170) $)) - (-15 -3395 ((-3 $ "failed") (-1170)))))) - (-5 *1 (-980 *4 *5 *3 *2)) (-4 *2 (-945 (-948 *4) *5 *3)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-641 *6)) - (-4 *6 - (-13 (-846) - (-10 -8 (-15 -1311 ((-1170) $)) - (-15 -3395 ((-3 $ "failed") (-1170)))))) - (-4 *4 (-1045)) (-4 *5 (-789)) (-5 *1 (-980 *4 *5 *6 *2)) - (-4 *2 (-945 (-948 *4) *5 *6))))) -(((*1 *1 *1 *2) - (|partial| -12 (-5 *2 (-917)) (-5 *1 (-1095 *3 *4)) (-14 *3 *2) - (-14 *4 *2)))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-556)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -2123 *3))) - (-5 *1 (-965 *4 *3)) (-4 *3 (-1235 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-1264)) (-5 *1 (-818))))) (((*1 *2 *3) - (-12 (-5 *3 (-1259 (-641 (-2 (|:| -2128 *4) (|:| -2083 (-1114)))))) - (-4 *4 (-349)) (-5 *2 (-767)) (-5 *1 (-346 *4)))) - ((*1 *2) - (-12 (-5 *2 (-767)) (-5 *1 (-351 *3 *4)) (-14 *3 (-917)) - (-14 *4 (-917)))) - ((*1 *2) - (-12 (-5 *2 (-767)) (-5 *1 (-352 *3 *4)) (-4 *3 (-349)) - (-14 *4 - (-3 (-1166 *3) - (-1259 (-641 (-2 (|:| -2128 *3) (|:| -2083 (-1114))))))))) + (-12 (-4 *4 (-13 (-556) (-1034 (-564)))) (-4 *5 (-430 *4)) + (-5 *2 + (-3 (|:| |overq| (-1166 (-407 (-564)))) + (|:| |overan| (-1166 (-48))) (|:| -3285 (-112)))) + (-5 *1 (-435 *4 *5 *3)) (-4 *3 (-1235 *5))))) +(((*1 *2) + (-12 (-4 *4 (-1213)) (-4 *5 (-1235 *4)) (-4 *6 (-1235 (-407 *5))) + (-5 *2 (-767)) (-5 *1 (-341 *3 *4 *5 *6)) (-4 *3 (-342 *4 *5 *6)))) ((*1 *2) - (-12 (-5 *2 (-767)) (-5 *1 (-353 *3 *4)) (-4 *3 (-349)) - (-14 *4 (-917))))) + (-12 (-4 *1 (-342 *3 *4 *5)) (-4 *3 (-1213)) (-4 *4 (-1235 *3)) + (-4 *5 (-1235 (-407 *4))) (-5 *2 (-767))))) +(((*1 *1) (-4 *1 (-349)))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) @@ -3602,61 +3940,50 @@ (-4 *6 (-1045)) (-4 *2 (-13 (-363) - (-10 -8 (-15 -2423 ($ *7)) (-15 -2324 (*7 $)) (-15 -2336 (*7 $))))) + (-10 -8 (-15 -2423 ($ *7)) (-15 -2323 (*7 $)) (-15 -2336 (*7 $))))) (-5 *1 (-946 *5 *4 *6 *7 *2)) (-4 *7 (-945 *6 *5 *4)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-407 (-1166 (-407 (-948 *5))))) (-5 *4 (-1170)) (-5 *2 (-407 (-948 *5))) (-5 *1 (-1039 *5)) (-4 *5 (-556))))) -(((*1 *2 *3) - (-12 (-5 *3 (-564)) (-5 *2 (-641 (-641 (-225)))) (-5 *1 (-1205))))) -(((*1 *2 *2) - (-12 (-4 *3 (-452)) (-5 *1 (-1200 *3 *2)) - (-4 *2 (-13 (-430 *3) (-1194)))))) (((*1 *2 *1 *3 *4) (-12 (-5 *3 (-917)) (-5 *4 (-1152)) (-5 *2 (-1264)) (-5 *1 (-1260))))) -(((*1 *1 *2) - (-12 (-5 *2 (-641 (-504 *3 *4 *5 *6))) (-4 *3 (-363)) (-4 *4 (-789)) - (-4 *5 (-846)) (-5 *1 (-504 *3 *4 *5 *6)) (-4 *6 (-945 *3 *4 *5)))) - ((*1 *1 *1 *1) - (-12 (-4 *2 (-363)) (-4 *3 (-789)) (-4 *4 (-846)) - (-5 *1 (-504 *2 *3 *4 *5)) (-4 *5 (-945 *2 *3 *4)))) - ((*1 *2 *3 *2) - (-12 (-5 *2 (-641 *1)) (-4 *1 (-1065 *4 *5 *6 *3)) (-4 *4 (-452)) - (-4 *5 (-789)) (-4 *6 (-846)) (-4 *3 (-1059 *4 *5 *6)))) - ((*1 *2 *3 *2) - (-12 (-5 *2 (-641 *1)) (-5 *3 (-641 *7)) (-4 *1 (-1065 *4 *5 *6 *7)) - (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) - (-4 *7 (-1059 *4 *5 *6)))) - ((*1 *2 *3 *1) - (-12 (-5 *3 (-641 *7)) (-4 *7 (-1059 *4 *5 *6)) (-4 *4 (-452)) - (-4 *5 (-789)) (-4 *6 (-846)) (-5 *2 (-641 *1)) - (-4 *1 (-1065 *4 *5 *6 *7)))) - ((*1 *2 *3 *1) - (-12 (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) - (-4 *3 (-1059 *4 *5 *6)) (-5 *2 (-641 *1)) - (-4 *1 (-1065 *4 *5 *6 *3)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-1092 *2)) (-4 *2 (-1094))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -2123 (-778 *3)) (|:| |coef1| (-778 *3)))) - (-5 *1 (-778 *3)) (-4 *3 (-556)) (-4 *3 (-1045)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-556)) (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *5 (-846)) - (-5 *2 (-2 (|:| -2123 *1) (|:| |coef1| *1))) - (-4 *1 (-1059 *3 *4 *5))))) -(((*1 *2 *3 *3 *4 *4 *3) - (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *2 (-1031)) - (-5 *1 (-743))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-979 *2)) (-4 *2 (-1194))))) -(((*1 *1) (-5 *1 (-578)))) -(((*1 *2 *2) (-12 (-5 *2 (-564)) (-5 *1 (-561))))) (((*1 *2 *1) (-12 (-5 *2 (-2 (|:| |var| (-641 (-1170))) (|:| |pred| (-52)))) (-5 *1 (-888 *3)) (-4 *3 (-1094))))) (((*1 *2 *3) + (-12 (-5 *3 |RationalNumber|) (-5 *2 (-1 (-564))) (-5 *1 (-1043))))) +(((*1 *1 *1) + (-12 (-5 *1 (-594 *2)) (-4 *2 (-38 (-407 (-564)))) (-4 *2 (-1045))))) +(((*1 *2 *2) + (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) + (-4 *2 (-13 (-430 *3) (-998)))))) +(((*1 *1 *2 *3) + (-12 (-5 *3 (-1150 *2)) (-4 *2 (-307)) (-5 *1 (-174 *2))))) +(((*1 *2 *1 *3) (-12 (-4 *1 (-302)) (-5 *3 (-1170)) (-5 *2 (-112)))) + ((*1 *2 *1 *1) (-12 (-4 *1 (-302)) (-5 *2 (-112))))) +(((*1 *1 *1 *2 *2) + (-12 (-5 *2 (-564)) (-5 *1 (-136 *3 *4 *5)) (-14 *3 *2) + (-14 *4 (-767)) (-4 *5 (-172)))) + ((*1 *1 *1) + (-12 (-5 *1 (-136 *2 *3 *4)) (-14 *2 (-564)) (-14 *3 (-767)) + (-4 *4 (-172)))) + ((*1 *1 *1) + (-12 (-4 *1 (-683 *2 *3 *4)) (-4 *2 (-1045)) (-4 *3 (-373 *2)) + (-4 *4 (-373 *2)))) + ((*1 *1 *2) + (-12 (-4 *3 (-1045)) (-4 *1 (-683 *3 *2 *4)) (-4 *2 (-373 *3)) + (-4 *4 (-373 *3)))) + ((*1 *1 *1) + (-12 (-5 *1 (-1136 *2 *3)) (-14 *2 (-767)) (-4 *3 (-1045))))) +(((*1 *2) (-12 (-5 *2 (-1152)) (-5 *1 (-755))))) +(((*1 *2 *1) + (-12 (-5 *2 (-858)) (-5 *1 (-1150 *3)) (-4 *3 (-1094)) + (-4 *3 (-1209))))) +(((*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) - (|:| -3090 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) + (|:| -2141 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *2 (-2 @@ -3674,7 +4001,7 @@ (-3 (|:| |str| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -3090 + (|:| -2141 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -3712,8 +4039,8 @@ (-12 (-5 *3 (-709 *5 *6 *7)) (-4 *5 (-846)) (-4 *6 (-238 (-2181 *4) (-767))) (-14 *7 - (-1 (-112) (-2 (|:| -2083 *5) (|:| -1410 *6)) - (-2 (|:| -2083 *5) (|:| -1410 *6)))) + (-1 (-112) (-2 (|:| -2083 *5) (|:| -1838 *6)) + (-2 (|:| -2083 *5) (|:| -1838 *6)))) (-14 *4 (-641 (-1170))) (-4 *2 (-172)) (-5 *1 (-461 *4 *2 *5 *6 *7 *8)) (-4 *8 (-945 *2 *6 (-860 *4))))) ((*1 *1 *2 *3) @@ -3743,75 +4070,32 @@ ((*1 *1 *1 *2 *3) (-12 (-4 *1 (-969 *4 *3 *2)) (-4 *4 (-1045)) (-4 *3 (-788)) (-4 *2 (-846))))) +(((*1 *1 *2 *3) + (-12 (-5 *2 (-820)) (-5 *3 (-641 (-1170))) (-5 *1 (-821))))) (((*1 *2 *3 *4 *3) (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *2 (-1031)) (-5 *1 (-743))))) -(((*1 *2 *2) - (|partial| -12 (-4 *3 (-556)) (-4 *3 (-172)) (-4 *4 (-373 *3)) - (-4 *5 (-373 *3)) (-5 *1 (-684 *3 *4 *5 *2)) - (-4 *2 (-683 *3 *4 *5))))) -(((*1 *1 *1) - (|partial| -12 (-5 *1 (-1135 *2 *3)) (-4 *2 (-13 (-1094) (-34))) - (-4 *3 (-13 (-1094) (-34)))))) -(((*1 *1 *1) (-12 (-4 *1 (-670 *2)) (-4 *2 (-1209))))) -(((*1 *2 *3) (-12 (-5 *3 (-379)) (-5 *2 (-1152)) (-5 *1 (-305))))) -(((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-641 *5)) (-5 *4 (-564)) (-4 *5 (-844)) (-4 *5 (-363)) - (-5 *2 (-767)) (-5 *1 (-941 *5 *6)) (-4 *6 (-1235 *5))))) -(((*1 *2 *1) - (-12 (-4 *1 (-253 *3 *4 *5 *6)) (-4 *3 (-1045)) (-4 *4 (-846)) - (-4 *5 (-266 *4)) (-4 *6 (-789)) (-5 *2 (-767)))) - ((*1 *2 *1 *3) - (-12 (-4 *1 (-253 *4 *3 *5 *6)) (-4 *4 (-1045)) (-4 *3 (-846)) - (-4 *5 (-266 *3)) (-4 *6 (-789)) (-5 *2 (-767)))) - ((*1 *2 *1) (-12 (-4 *1 (-266 *3)) (-4 *3 (-846)) (-5 *2 (-767)))) - ((*1 *2 *1) (-12 (-4 *1 (-349)) (-5 *2 (-917)))) - ((*1 *2 *3) - (-12 (-5 *3 (-336 *4 *5 *6 *7)) (-4 *4 (-13 (-368) (-363))) - (-4 *5 (-1235 *4)) (-4 *6 (-1235 (-407 *5))) (-4 *7 (-342 *4 *5 *6)) - (-5 *2 (-767)) (-5 *1 (-392 *4 *5 *6 *7)))) - ((*1 *2 *1) (-12 (-4 *1 (-402)) (-5 *2 (-829 (-917))))) - ((*1 *2 *1) (-12 (-4 *1 (-404)) (-5 *2 (-564)))) - ((*1 *2 *1 *2) (-12 (-5 *2 (-767)) (-5 *1 (-595 *3)) (-4 *3 (-1045)))) - ((*1 *2 *1) (-12 (-5 *2 (-767)) (-5 *1 (-595 *3)) (-4 *3 (-1045)))) - 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(-416 *3 *4)) + (-4 *3 (-417 *4)))) + ((*1 *2) (-12 (-4 *1 (-417 *3)) (-4 *3 (-172)) (-5 *2 (-685 *3))))) +(((*1 *1 *1 *1) + (-12 (|has| *1 (-6 -4408)) (-4 *1 (-244 *2)) (-4 *2 (-1209))))) (((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-1158 *3 *4)) (-14 *3 (-917)) - (-4 *4 (-1045))))) + (-12 (-4 *1 (-1097 *3 *4 *5 *6 *7)) (-4 *3 (-1094)) (-4 *4 (-1094)) + (-4 *5 (-1094)) (-4 *6 (-1094)) (-4 *7 (-1094)) (-5 *2 (-112))))) (((*1 *1) (-5 *1 (-186)))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) @@ -3832,46 +4116,49 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *2 *3) - (-12 (-4 *4 (-452)) (-4 *4 (-556)) (-4 *5 (-789)) (-4 *6 (-846)) - (-5 *2 (-641 *3)) (-5 *1 (-973 *4 *5 *6 *3)) - (-4 *3 (-1059 *4 *5 *6))))) +(((*1 *2 *1) (-12 (-5 *2 (-1114)) (-5 *1 (-839 *3)) (-4 *3 (-1094))))) +(((*1 *2 *1) (-12 (-5 *2 (-641 (-1170))) (-5 *1 (-1174))))) (((*1 *1 *2 *2) (-12 (-5 *1 (-294 *2)) (-4 *2 (-1209)))) ((*1 *1 *2 *3) (-12 (-5 *2 (-1170)) (-5 *3 (-1152)) 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|func| *3) (|:| |poly| *3) (|:| |c1| (-407 *5)) + (|:| |c2| (-407 *5)) (|:| |deg| (-767)))) + (-5 *1 (-148 *4 *5 *3)) (-4 *3 (-1235 (-407 *5)))))) (((*1 *2 *1) (-12 (-5 *2 (-1264)) (-5 *1 (-818))))) +(((*1 *2) + (-12 (-4 *4 (-1213)) (-4 *5 (-1235 *4)) (-4 *6 (-1235 (-407 *5))) + (-5 *2 (-112)) (-5 *1 (-341 *3 *4 *5 *6)) (-4 *3 (-342 *4 *5 *6)))) + ((*1 *2) + (-12 (-4 *1 (-342 *3 *4 *5)) (-4 *3 (-1213)) (-4 *4 (-1235 *3)) + (-4 *5 (-1235 (-407 *4))) (-5 *2 (-112))))) +(((*1 *1 *2) (-12 (-5 *2 (-316 (-169 (-379)))) (-5 *1 (-330)))) + ((*1 *1 *2) (-12 (-5 *2 (-316 (-564))) (-5 *1 (-330)))) + ((*1 *1 *2) (-12 (-5 *2 (-316 (-379))) (-5 *1 (-330)))) + ((*1 *1 *2) (-12 (-5 *2 (-316 (-690))) (-5 *1 (-330)))) + ((*1 *1 *2) (-12 (-5 *2 (-316 (-697))) (-5 *1 (-330)))) + ((*1 *1 *2) (-12 (-5 *2 (-316 (-695))) (-5 *1 (-330)))) + ((*1 *1) (-5 *1 (-330)))) (((*1 *1) (-5 *1 (-186)))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) @@ -3892,31 +4179,19 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *2 *1) - (|partial| -12 (-4 *1 (-1221 *3 *2)) (-4 *3 (-1045)) - (-4 *2 (-1250 *3))))) -(((*1 *2 *3 *3 *3 *4 *3) - (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *2 (-1031)) - (-5 *1 (-750))))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-641 (-1208))) (-5 *3 (-1208)) (-5 *1 (-677))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1 *5 *5)) (-4 *5 (-1250 *4)) - (-4 *4 (-38 (-407 (-564)))) (-5 *2 (-1 (-1150 *4) (-1150 *4))) - (-5 *1 (-1252 *4 *5))))) +(((*1 *1 *1) + (|partial| -12 (-5 *1 (-1135 *2 *3)) (-4 *2 (-13 (-1094) (-34))) + (-4 *3 (-13 (-1094) (-34)))))) (((*1 *2 *2 *3) - (-12 (-5 *2 (-1259 *4)) (-5 *3 (-564)) (-4 *4 (-349)) - (-5 *1 (-528 *4))))) -(((*1 *1 *2) (-12 (-5 *2 (-157)) (-5 *1 (-870))))) -(((*1 *2 *3) - (-12 (-5 *3 (-641 (-225))) (-5 *2 (-641 (-1152))) (-5 *1 (-192)))) - ((*1 *2 *3) - (-12 (-5 *3 (-641 (-225))) (-5 *2 (-641 (-1152))) (-5 *1 (-300)))) - ((*1 *2 *3) - (-12 (-5 *3 (-641 (-225))) (-5 *2 (-641 (-1152))) (-5 *1 (-305))))) -(((*1 *1 *1 *2 *1) (-12 (-5 *1 (-127 *2)) (-4 *2 (-1094)))) - ((*1 *1 *2) (-12 (-5 *1 (-127 *2)) (-4 *2 (-1094))))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-1152)) (-5 *2 (-379)) (-5 *1 (-97))))) + (-12 (-5 *3 (-564)) (-5 *1 (-692 *2)) (-4 *2 (-1235 *3))))) +(((*1 *2 *2) (-12 (-5 *2 (-388)) (-5 *1 (-436)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-388)) (-5 *1 (-436))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-888 *3)) (-4 *3 (-1094))))) +(((*1 *2 *1) (-12 (-4 *1 (-302)) (-5 *2 (-641 (-114)))))) +(((*1 *2 *1) (-12 (-4 *1 (-389)) (-5 *2 (-112))))) +(((*1 *2 *2 *1) (-12 (-4 *1 (-1115 *2)) (-4 *2 (-1209))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-171))))) +(((*1 *2 *1) (-12 (-5 *2 (-1264)) (-5 *1 (-818))))) (((*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-998))))) @@ -3933,50 +4208,31 @@ (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3)))) ((*1 *1 *1) (-4 *1 (-1197)))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-888 *3)) (-4 *3 (-1094))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-157)) (-5 *2 (-1264)) (-5 *1 (-1261))))) +(((*1 *2 *1) + (-12 (-4 *2 (-13 (-844) (-363))) (-5 *1 (-1055 *2 *3)) + (-4 *3 (-1235 *2))))) +(((*1 *1 *1) (-12 (-4 *1 (-670 *2)) (-4 *2 (-1209))))) +(((*1 *2 *1) + (-12 (-4 *3 (-363)) (-4 *4 (-1235 *3)) (-4 *5 (-1235 (-407 *4))) + (-5 *2 (-1259 *6)) (-5 *1 (-336 *3 *4 *5 *6)) + (-4 *6 (-342 *3 *4 *5))))) +(((*1 *2 *1) (-12 (-5 *2 (-641 (-1208))) (-5 *1 (-677)))) + ((*1 *2 *1) (-12 (-5 *2 (-641 (-1175))) (-5 *1 (-1112))))) +(((*1 *1 *2) (-12 (-5 *2 (-407 (-564))) (-5 *1 (-217))))) (((*1 *2 *3) - (-12 (-5 *3 (-641 (-641 (-641 *4)))) (-5 *2 (-641 (-641 *4))) - (-5 *1 (-1180 *4)) (-4 *4 (-846))))) -(((*1 *2 *3) - (-12 (-4 *4 (-373 *2)) (-4 *5 (-373 *2)) (-4 *2 (-363)) - (-5 *1 (-521 *2 *4 *5 *3)) (-4 *3 (-683 *2 *4 *5)))) - ((*1 *2 *1) - (-12 (-4 *1 (-683 *2 *3 *4)) (-4 *3 (-373 *2)) (-4 *4 (-373 *2)) - (|has| *2 (-6 (-4409 "*"))) (-4 *2 (-1045)))) - ((*1 *2 *3) - (-12 (-4 *4 (-373 *2)) (-4 *5 (-373 *2)) (-4 *2 (-172)) - (-5 *1 (-684 *2 *4 *5 *3)) (-4 *3 (-683 *2 *4 *5)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1117 *3 *2 *4 *5)) (-4 *4 (-238 *3 *2)) - (-4 *5 (-238 *3 *2)) (|has| *2 (-6 (-4409 "*"))) (-4 *2 (-1045))))) + (-12 + (-5 *3 + (-2 (|:| |xinit| (-225)) (|:| |xend| (-225)) + (|:| |fn| (-1259 (-316 (-225)))) (|:| |yinit| (-641 (-225))) + (|:| |intvals| (-641 (-225))) (|:| |g| (-316 (-225))) + (|:| |abserr| (-225)) (|:| |relerr| (-225)))) + (-5 *2 (-379)) (-5 *1 (-205))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-112) (-114) (-114))) (-5 *1 (-114))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-225)) (-5 *4 (-564)) (-5 *2 (-1031)) (-5 *1 (-754))))) -(((*1 *2 *3) - (-12 (-4 *4 (-1045)) (-5 *2 (-564)) (-5 *1 (-443 *4 *3 *5)) - (-4 *3 (-1235 *4)) - (-4 *5 (-13 (-404) (-1034 *4) (-363) (-1194) (-284)))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-379)) (-5 *3 (-641 (-263))) (-5 *1 (-261)))) - ((*1 *1 *2) (-12 (-5 *2 (-379)) (-5 *1 (-263))))) -(((*1 *2 *1) (-12 (-5 *2 (-641 (-1208))) (-5 *1 (-677)))) - ((*1 *2 *1) (-12 (-5 *2 (-641 (-1175))) (-5 *1 (-1112))))) -(((*1 *1 *2) (-12 (-5 *2 (-641 (-858))) (-5 *1 (-858)))) - ((*1 *1 *1 *1) (-5 *1 (-858)))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1190))))) -(((*1 *2 *3 *4 *5 *5 *4 *6) - (-12 (-5 *5 (-610 *4)) (-5 *6 (-1166 *4)) - (-4 *4 (-13 (-430 *7) (-27) (-1194))) - (-4 *7 (-13 (-452) (-1034 (-564)) (-147) (-637 (-564)))) - (-5 *2 - (-2 (|:| |particular| (-3 *4 "failed")) (|:| -1298 (-641 *4)))) - (-5 *1 (-560 *7 *4 *3)) (-4 *3 (-652 *4)) (-4 *3 (-1094)))) - ((*1 *2 *3 *4 *5 *5 *5 *4 *6) - (-12 (-5 *5 (-610 *4)) (-5 *6 (-407 (-1166 *4))) - (-4 *4 (-13 (-430 *7) (-27) (-1194))) - (-4 *7 (-13 (-452) (-1034 (-564)) (-147) (-637 (-564)))) - (-5 *2 - (-2 (|:| |particular| (-3 *4 "failed")) (|:| -1298 (-641 *4)))) - (-5 *1 (-560 *7 *4 *3)) (-4 *3 (-652 *4)) (-4 *3 (-1094))))) -(((*1 *1 *2) (-12 (-5 *2 (-641 *3)) (-4 *3 (-1094)) (-5 *1 (-996 *3))))) (((*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-998))))) @@ -3999,43 +4255,27 @@ ((*1 *2 *1) (-12 (-4 *3 (-1094)) (-4 *4 (-1094)) (-4 *5 (-1094)) (-4 *6 (-1094)) (-4 *7 (-1094)) (-5 *2 (-641 *1)) (-4 *1 (-1097 *3 *4 *5 *6 *7))))) -(((*1 *2 *3) - (-12 (-5 *3 (-767)) (-5 *2 (-1 (-1150 (-948 *4)) (-1150 (-948 *4)))) - (-5 *1 (-1267 *4)) (-4 *4 (-363))))) -(((*1 *2 *3 *3 *4) - (-12 (-4 *5 (-452)) (-4 *6 (-789)) (-4 *7 (-846)) - (-4 *3 (-1059 *5 *6 *7)) - (-5 *2 (-641 (-2 (|:| |val| (-641 *3)) (|:| -3577 *4)))) - (-5 *1 (-1102 *5 *6 *7 *3 *4)) (-4 *4 (-1065 *5 *6 *7 *3))))) -(((*1 *2 *1) (|partial| -12 (-5 *2 (-506)) (-5 *1 (-280)))) - ((*1 *2 *1) - (-12 (-5 *2 (-3 (-564) (-225) (-506) (-1152) (-1175))) - (-5 *1 (-1175))))) -(((*1 *2) - (|partial| -12 (-4 *3 (-556)) (-4 *3 (-172)) - (-5 *2 (-2 (|:| |particular| *1) (|:| -1298 (-641 *1)))) - (-4 *1 (-367 *3)))) - ((*1 *2) - (|partial| -12 - (-5 *2 - (-2 (|:| |particular| (-453 *3 *4 *5 *6)) - (|:| -1298 (-641 (-453 *3 *4 *5 *6))))) - (-5 *1 (-453 *3 *4 *5 *6)) (-4 *3 (-172)) (-14 *4 (-917)) - (-14 *5 (-641 (-1170))) (-14 *6 (-1259 (-685 *3)))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-280))))) -(((*1 *2 *3 *2 *4) - (-12 (-5 *3 (-114)) (-5 *4 (-767)) (-4 *5 (-452)) - (-4 *5 (-1034 (-564))) (-4 *5 (-556)) (-5 *1 (-41 *5 *2)) - (-4 *2 (-430 *5)) - (-4 *2 - (-13 (-363) (-302) - (-10 -8 (-15 -2324 ((-1119 *5 (-610 $)) $)) - (-15 -2336 ((-1119 *5 (-610 $)) $)) - (-15 -2423 ($ (-1119 *5 (-610 $)))))))))) -(((*1 *1 *2 *3 *3 *4 *4) - (-12 (-5 *2 (-948 (-564))) (-5 *3 (-1170)) - (-5 *4 (-1088 (-407 (-564)))) (-5 *1 (-30))))) -(((*1 *2 *1 *1) (-12 (-5 *2 (-564)) (-5 *1 (-379))))) +(((*1 *2 *3 *4) + (-12 (-4 *7 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) (-4 *7 (-556)) + (-4 *8 (-945 *7 *5 *6)) + (-5 *2 (-2 (|:| -1838 (-767)) (|:| -4376 *3) (|:| |radicand| *3))) + (-5 *1 (-949 *5 *6 *7 *8 *3)) (-5 *4 (-767)) + (-4 *3 + (-13 (-363) + (-10 -8 (-15 -2423 ($ *8)) (-15 -2323 (*8 $)) (-15 -2336 (*8 $)))))))) +(((*1 *1 *2 *2) (-12 (-5 *2 (-564)) (-5 *1 (-858))))) +(((*1 *2 *3 *2) (-12 (-5 *3 (-767)) (-5 *1 (-852 *2)) (-4 *2 (-172)))) + ((*1 *2 *3) + (-12 (-5 *2 (-1166 (-564))) (-5 *1 (-938)) (-5 *3 (-564))))) +(((*1 *2 *2 *2 *2) + (-12 (-5 *2 (-685 *3)) (-4 *3 (-1045)) (-5 *1 (-686 *3))))) +(((*1 *2 *3) (-12 (-5 *3 (-379)) (-5 *2 (-1152)) (-5 *1 (-305))))) +(((*1 *2 *3 *3 *4 *4 *4 *4) + (-12 (-5 *3 (-225)) (-5 *4 (-564)) (-5 *2 (-1031)) (-5 *1 (-744))))) +(((*1 *2 *1) (-12 (-4 *1 (-670 *2)) (-4 *2 (-1209))))) +(((*1 *2 *1) + (-12 (-5 *2 (-1150 (-2 (|:| |k| (-564)) (|:| |c| *3)))) + (-5 *1 (-594 *3)) (-4 *3 (-1045))))) (((*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-998))))) @@ -4057,62 +4297,31 @@ ((*1 *1 *2) (-12 (-5 *2 (-641 *3)) (-4 *3 (-1094)) (-4 *1 (-1092 *3)))) ((*1 *1) (-12 (-4 *1 (-1092 *2)) (-4 *2 (-1094))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -3832 *1) (|:| -3211 *1))) (-4 *1 (-307)))) - ((*1 *2 *1 *1) - (|partial| -12 (-5 *2 (-2 (|:| |lm| (-386 *3)) (|:| |rm| (-386 *3)))) - (-5 *1 (-386 *3)) (-4 *3 (-1094)))) - ((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -3832 (-767)) (|:| -3211 (-767)))) - (-5 *1 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(-556) (-1034 (-564)))) (-5 *2 (-316 *4)) @@ -4323,65 +4589,41 @@ (-12 (-4 *3 (-556)) (-5 *1 (-628 *3 *2)) (-4 *2 (-13 (-430 *3) (-998) (-1194)))))) (((*1 *2 *1) - (-12 (-4 *3 (-1045)) (-4 *4 (-1094)) (-5 *2 (-641 *1)) - (-4 *1 (-382 *3 *4)))) - ((*1 *2 *1) - (-12 (-5 *2 (-641 (-731 *3 *4))) (-5 *1 (-731 *3 *4)) (-4 *3 (-1045)) - (-4 *4 (-722)))) - ((*1 *2 *1) - (-12 (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *5 (-846)) (-5 *2 (-641 *1)) - (-4 *1 (-945 *3 *4 *5))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-564)) (-5 *2 (-1264)) (-5 *1 (-818))))) -(((*1 *1) - (-12 (-5 *1 (-136 *2 *3 *4)) (-14 *2 (-564)) (-14 *3 (-767)) - (-4 *4 (-172))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-767)) (-4 *6 (-452)) (-4 *7 (-789)) (-4 *8 (-846)) - (-4 *3 (-1059 *6 *7 *8)) - (-5 *2 - (-2 (|:| |done| (-641 *4)) - (|:| |todo| (-641 (-2 (|:| |val| (-641 *3)) (|:| -3577 *4)))))) - (-5 *1 (-1063 *6 *7 *8 *3 *4)) (-4 *4 (-1065 *6 *7 *8 *3)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-452)) (-4 *6 (-789)) (-4 *7 (-846)) - (-4 *3 (-1059 *5 *6 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*1 *1) (-12 (-5 *1 (-339 *2 *3 *4)) (-14 *2 (-641 (-1170))) (-14 *3 (-641 (-1170))) (-4 *4 (-387)))) @@ -4391,170 +4633,39 @@ ((*1 *1 *2) (-12 (-5 *2 (-407 (-564))) (-4 *1 (-1008)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-1008)) (-5 *2 (-917)))) ((*1 *1 *1) (-4 *1 (-1008)))) -(((*1 *2 *3 *3 *3 *4 *4 *4 *3) - (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *2 (-1031)) - (-5 *1 (-748))))) -(((*1 *2 *1) - (-12 (-5 *2 (-641 (-2 (|:| |gen| *3) (|:| -1688 *4)))) - (-5 *1 (-645 *3 *4 *5)) (-4 *3 (-1094)) (-4 *4 (-23)) (-14 *5 *4)))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1086 (-839 *3))) (-4 *3 (-13 (-1194) (-955) (-29 *5))) - (-4 *5 (-13 (-307) (-147) (-1034 (-564)) (-637 (-564)))) - (-5 *2 - (-3 (|:| |f1| (-839 *3)) (|:| |f2| (-641 (-839 *3))) - (|:| |fail| "failed") (|:| |pole| "potentialPole"))) - (-5 *1 (-219 *5 *3)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-1086 (-839 *3))) (-5 *5 (-1152)) - (-4 *3 (-13 (-1194) (-955) (-29 *6))) - (-4 *6 (-13 (-307) (-147) (-1034 (-564)) (-637 (-564)))) - (-5 *2 - (-3 (|:| 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"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 (-1031)) (-5 *1 (-305))))) +(((*1 *2 *1) (-12 (-5 *2 (-1150 *3)) (-5 *1 (-174 *3)) (-4 *3 (-307))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-564)) (-4 *1 (-1219 *4)) (-4 *4 (-1045)) (-4 *4 (-556)) + (-5 *2 (-407 (-948 *4))))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-564)) (-4 *1 (-1219 *4)) (-4 *4 (-1045)) (-4 *4 (-556)) + (-5 *2 (-407 (-948 *4)))))) (((*1 *2 *2 *2) (-12 (-5 *2 (-1031)) (-5 *1 (-305)))) ((*1 *2 *3) (-12 (-5 *3 (-641 (-1031))) (-5 *2 (-1031)) (-5 *1 (-305)))) @@ -4568,29 +4679,47 @@ (-4 *4 (-1209)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-1247 *2)) (-4 *2 (-1209)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1247 *2)) (-4 *2 (-1209))))) -(((*1 *2 *1) (-12 (-4 *1 (-670 *3)) (-4 *3 (-1209)) (-5 *2 (-767))))) -(((*1 *2 *1) (-12 (-5 *2 (-564)) (-5 *1 (-910 *3)) (-4 *3 (-307))))) -(((*1 *2 *2 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|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 (-192))))) +(((*1 *2 *3) + (-12 (-4 *4 (-556)) (-5 *2 (-1166 *3)) (-5 *1 (-41 *4 *3)) + (-4 *3 + (-13 (-363) (-302) + (-10 -8 (-15 -2323 ((-1119 *4 (-610 $)) $)) + (-15 -2336 ((-1119 *4 (-610 $)) $)) + (-15 -2423 ($ (-1119 *4 (-610 $)))))))))) +(((*1 *2 *3) (-12 (-5 *3 (-1152)) (-5 *2 (-1264)) (-5 *1 (-436))))) (((*1 *2 *1) (-12 (-5 *2 @@ -7392,13 +7346,13 @@ (-2 (|:| |switch| (-1169)) (|:| |thenClause| (-330)) (|:| |elseClause| (-330)))) (|:| |returnBranch| - (-2 (|:| -2279 (-112)) + (-2 (|:| -1976 (-112)) (|:| -2128 (-2 (|:| |ints2Floats?| (-112)) (|:| -3354 (-858)))))) (|:| |blockBranch| (-641 (-330))) (|:| |commentBranch| (-641 (-1152))) (|:| |callBranch| (-1152)) (|:| |forBranch| - (-2 (|:| -3090 (-1086 (-948 (-564)))) + (-2 (|:| -2141 (-1086 (-948 (-564)))) (|:| |span| (-948 (-564))) (|:| -2575 (-330)))) (|:| |labelBranch| (-1114)) (|:| |loopBranch| (-2 (|:| |switch| (-1169)) (|:| -2575 (-330)))) @@ -7406,126 +7360,117 @@ (-2 (|:| -2562 (-1170)) (|:| |contents| (-641 (-1170))))) (|:| |printBranch| (-641 (-858))))) (-5 *1 (-330))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-171)))) - ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1204 *3)) (-4 *3 (-970))))) -(((*1 *1) (-5 *1 (-506)))) -(((*1 *2 *2) - (-12 (-5 *2 (-641 (-2 (|:| |val| (-641 *6)) (|:| -3577 *7)))) - (-4 *6 (-1059 *3 *4 *5)) (-4 *7 (-1065 *3 *4 *5 *6)) (-4 *3 (-452)) - (-4 *4 (-789)) (-4 *5 (-846)) (-5 *1 (-984 *3 *4 *5 *6 *7)))) - ((*1 *2 *2) - (-12 (-5 *2 (-641 (-2 (|:| |val| (-641 *6)) (|:| -3577 *7)))) - (-4 *6 (-1059 *3 *4 *5)) (-4 *7 (-1065 *3 *4 *5 *6)) (-4 *3 (-452)) - (-4 *4 (-789)) (-4 *5 (-846)) (-5 *1 (-1101 *3 *4 *5 *6 *7))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-1094)) (-4 *2 (-896 *5)) (-5 *1 (-688 *5 *2 *3 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((*1 *1 *1 *1) (-12 (-4 *1 (-1257 *2)) (-4 *2 (-1209)) (-4 *2 (-21)))) ((*1 *1 *1) (-12 (-4 *1 (-1257 *2)) (-4 *2 (-1209)) (-4 *2 (-21))))) -(((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-641 (-767))) (-5 *3 (-171)) (-5 *1 (-1158 *4 *5)) - (-14 *4 (-917)) (-4 *5 (-1045))))) -(((*1 *1 *2) - (-12 (-5 *2 (-641 *6)) (-4 *6 (-945 *3 *4 *5)) (-4 *3 (-363)) - (-4 *4 (-789)) (-4 *5 (-846)) (-5 *1 (-504 *3 *4 *5 *6))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-767)) (-4 *5 (-1045)) (-4 *2 (-1235 *5)) - (-5 *1 (-1253 *5 *2 *6 *3)) (-4 *6 (-652 *2)) (-4 *3 (-1250 *5))))) (((*1 *2 *3) - (-12 (-5 *2 (-1 *3 *4)) (-5 *1 (-679 *4 *3)) (-4 *4 (-1094)) - (-4 *3 (-1094))))) -(((*1 *1 *1 *1) - (-12 (|has| *1 (-6 -4408)) (-4 *1 (-119 *2)) (-4 *2 (-1209))))) -(((*1 *2 *3 *3 *4 *5 *3 *3 *4 *4 *4 *6) - (-12 (-5 *4 (-564)) (-5 *5 (-685 (-225))) - (-5 *6 (-3 (|:| |fn| (-388)) (|:| |fp| (-64 -2308)))) (-5 *3 (-225)) - (-5 *2 (-1031)) (-5 *1 (-744))))) -(((*1 *2 *3) - (-12 (-4 *4 (-349)) (-5 *2 (-112)) (-5 *1 (-216 *4 *3)) - (-4 *3 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(-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) + (-4 *7 (-1059 *4 *5 *6)) (-5 *2 (-112)) + (-5 *1 (-1101 *4 *5 *6 *7 *3)) (-4 *3 (-1065 *4 *5 *6 *7))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-979 *2)) (-4 *2 (-1194))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-316 (-564))) (|:| -2308 (-316 (-379))) + (-3 (|:| I (-316 (-564))) (|:| -2306 (-316 (-379))) (|:| CF (-316 (-169 (-379)))) (|:| |switch| (-1169)))) (-5 *1 (-1169))))) -(((*1 *2 *1) - (|partial| -12 (-4 *3 (-1106)) (-4 *3 (-1094)) (-5 *2 (-641 *1)) - (-4 *1 (-430 *3)))) - ((*1 *2 *1) - (|partial| -12 (-5 *2 (-641 (-888 *3))) (-5 *1 (-888 *3)) - (-4 *3 (-1094)))) - ((*1 *2 *1) - (|partial| -12 (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *5 (-846)) - (-5 *2 (-641 *1)) (-4 *1 (-945 *3 *4 *5)))) - ((*1 *2 *3) - (|partial| -12 (-4 *4 (-789)) (-4 *5 (-846)) (-4 *6 (-1045)) - (-4 *7 (-945 *6 *4 *5)) (-5 *2 (-641 *3)) - (-5 *1 (-946 *4 *5 *6 *7 *3)) - (-4 *3 - (-13 (-363) - (-10 -8 (-15 -2423 ($ *7)) (-15 -2324 (*7 $)) - (-15 -2336 (*7 $)))))))) (((*1 *2 *3 *1) (-12 (-4 *1 (-1065 *4 *5 *6 *3)) (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) (-4 *3 (-1059 *4 *5 *6)) (-5 *2 (-112))))) @@ -8330,8 +8188,8 @@ (-12 (-5 *1 (-214 *2)) (-4 *2 (-13 (-846) - (-10 -8 (-15 -4366 ((-1152) $ (-1170))) (-15 -1629 ((-1264) $)) - (-15 -3668 ((-1264) $))))))) + (-10 -8 (-15 -4366 ((-1152) $ (-1170))) (-15 -1630 ((-1264) $)) + (-15 -1757 ((-1264) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-294 *2)) (-4 *2 (-25)) (-4 *2 (-1209)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-294 *2)) (-4 *2 (-25)) (-4 *2 (-1209)))) ((*1 *1 *2 *1) @@ -8354,37 +8212,35 @@ (-12 (-5 *2 (-1150 *3)) (-4 *3 (-1045)) (-5 *1 (-1154 *3)))) ((*1 *2 *2 *2) (-12 (-5 *2 (-939 (-225))) (-5 *1 (-1205)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1257 *2)) (-4 *2 (-1209)) (-4 *2 (-25))))) -(((*1 *1 *2) (-12 (-5 *2 (-564)) (-5 *1 (-858))))) -(((*1 *2 *2 *2) - (|partial| -12 (-4 *3 (-363)) (-5 *1 (-762 *2 *3)) (-4 *2 (-704 *3)))) - ((*1 *1 *1 *1) - (|partial| -12 (-4 *1 (-848 *2)) (-4 *2 (-1045)) (-4 *2 (-363))))) -(((*1 *2 *3) - (-12 (-5 *3 (-641 *4)) (-4 *4 (-363)) (-5 *2 (-685 *4)) - (-5 *1 (-810 *4 *5)) (-4 *5 (-652 *4)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-641 *5)) (-5 *4 (-767)) (-4 *5 (-363)) - (-5 *2 (-685 *5)) (-5 *1 (-810 *5 *6)) (-4 *6 (-652 *5))))) +(((*1 *2 *3 *3 *3) + (-12 (-5 *2 (-641 (-564))) (-5 *1 (-1104)) (-5 *3 (-564))))) +(((*1 *1 *1) (-12 (-4 *1 (-1247 *2)) (-4 *2 (-1209))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-225)) (-5 *4 (-564)) (-5 *2 (-1031)) (-5 *1 (-754))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-641 *7)) (-4 *7 (-846)) (-4 *5 (-905)) (-4 *6 (-789)) + (-4 *8 (-945 *5 *6 *7)) (-5 *2 (-418 (-1166 *8))) + (-5 *1 (-902 *5 *6 *7 *8)) (-5 *4 (-1166 *8)))) + ((*1 *2 *3) + (-12 (-4 *4 (-905)) (-4 *5 (-1235 *4)) (-5 *2 (-418 (-1166 *5))) + (-5 *1 (-903 *4 *5)) (-5 *3 (-1166 *5))))) +(((*1 *2 *3 *3 *4 *3) + (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *2 (-1031)) + (-5 *1 (-751))))) (((*1 *1 *1 *1) (-4 *1 (-657)))) -(((*1 *1 *1) - (-12 (-5 *1 (-594 *2)) (-4 *2 (-38 (-407 (-564)))) (-4 *2 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|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| (-1150 (-225))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -3090 - (-3 (|:| |finite| "The range is finite") - (|:| |lowerInfinite| - "The bottom of range is infinite") - (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| - "Both top and bottom points are infinite") - (|:| |notEvaluated| "Range not yet evaluated")))))))) - (-5 *1 (-559)))) - ((*1 *2 *1) - (-12 (-4 *1 (-602 *3 *4)) (-4 *3 (-1094)) (-4 *4 (-1209)) - (-5 *2 (-641 *4))))) + (-3 (|:| |%series| *8) + (|:| |%problem| (-2 (|:| |func| (-1152)) (|:| |prob| (-1152)))))) + 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(-846)) (-4 *2 (-945 *4 *6 (-860 *3))))) ((*1 *1 *1 *2) @@ -8993,178 +8988,159 @@ (-12 (-4 *1 (-1276 *3 *2)) (-4 *3 (-846)) (-4 *2 (-1045)))) ((*1 *1 *1 *2) (-12 (-5 *1 (-1282 *2 *3)) (-4 *2 (-1045)) (-4 *3 (-842))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1259 (-641 (-2 (|:| -2128 *4) (|:| -2083 (-1114)))))) - (-4 *4 (-349)) (-5 *2 (-1264)) (-5 *1 (-528 *4))))) -(((*1 *2 *1 *1) - (-12 (-4 *1 (-1059 *3 *4 *5)) (-4 *3 (-1045)) (-4 *4 (-789)) - (-4 *5 (-846)) (-5 *2 (-112))))) -(((*1 *2 *3 *4 *5 *3) - (-12 (-5 *4 (-1 *7 *7)) - (-5 *5 - (-1 (-2 (|:| |ans| *6) (|:| -4337 *6) (|:| |sol?| (-112))) (-564) - *6)) - (-4 *6 (-363)) (-4 *7 (-1235 *6)) - (-5 *2 - (-3 (-2 (|:| |answer| (-407 *7)) (|:| |a0| *6)) - (-2 (|:| -4354 (-407 *7)) (|:| |coeff| (-407 *7))) "failed")) - (-5 *1 (-574 *6 *7)) (-5 *3 (-407 *7))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-641 (-641 *8))) (-5 *3 (-641 *8)) - (-4 *8 (-1059 *5 *6 *7)) (-4 *5 (-556)) (-4 *6 (-789)) - (-4 *7 (-846)) (-5 *2 (-112)) (-5 *1 (-973 *5 *6 *7 *8))))) 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- (-4 *4 (-945 *6 *7 *8)) (-4 *6 (-452)) (-4 *7 (-789)) (-4 *8 (-846)) - (-5 *2 - (-2 (|:| |lcmfij| *7) (|:| |totdeg| *5) (|:| |poli| *4) - (|:| |polj| *4))) - (-5 *1 (-449 *6 *7 *8 *4))))) -(((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *4 *4)) (-4 *1 (-326 *3 *4)) (-4 *3 (-1045)) - (-4 *4 (-788))))) -(((*1 *2 *1) - (-12 (-5 *2 (-641 (-1195 *3))) (-5 *1 (-1195 *3)) (-4 *3 (-1094))))) -(((*1 *1 *2 *2 *2 *2 *2 *2 *2 *2) - (-12 (-4 *1 (-793 *2)) (-4 *2 (-172)))) - ((*1 *1 *2 *2) - (-12 (-5 *2 (-995 *3)) (-4 *3 (-172)) (-5 *1 (-795 *3))))) +(((*1 *2 *1) (-12 (-4 *1 (-1087 *2)) (-4 *2 (-1209))))) +(((*1 *2 *3 *4 *3 *4 *4 *4) + (-12 (-5 *3 (-685 (-225))) (-5 *4 (-564)) (-5 *2 (-1031)) + (-5 *1 (-752))))) (((*1 *2 *3 *4 *2) (-12 (-5 *4 (-1 *2 *2)) (-4 *2 (-644 *5)) (-4 *5 (-1045)) (-5 *1 (-53 *5 *2 *3)) (-4 *3 (-848 *5)))) @@ -10657,42 +10641,31 @@ ((*1 *2 *3 *2 *2 *4 *5) (-12 (-5 *4 (-99 *2)) (-5 *5 (-1 *2 *2)) (-4 *2 (-1045)) (-5 *1 (-849 *2 *3)) (-4 *3 (-848 *2))))) -(((*1 *2 *3 *4 *4 *4 *5 *6 *7) - (|partial| -12 (-5 *5 (-1170)) - (-5 *6 - (-1 - (-3 - (-2 (|:| |mainpart| *4) - (|:| |limitedlogs| - (-641 (-2 (|:| |coeff| *4) (|:| |logand| *4))))) - "failed") - *4 (-641 *4))) - (-5 *7 - (-1 (-3 (-2 (|:| -4354 *4) (|:| |coeff| *4)) "failed") *4 *4)) - (-4 *4 (-13 (-1194) (-27) (-430 *8))) - (-4 *8 (-13 (-452) (-147) (-1034 *3) (-637 *3))) (-5 *3 (-564)) - (-5 *2 (-641 *4)) (-5 *1 (-1010 *8 *4))))) -(((*1 *1 *2) - (-12 (-5 *2 (-641 (-641 *3))) (-4 *3 (-1094)) (-5 *1 (-901 *3))))) -(((*1 *1 *1 *2 *1) - (-12 (-5 *2 (-564)) (-5 *1 (-1150 *3)) (-4 *3 (-1209)))) - ((*1 *1 *1 *1) - (-12 (|has| *1 (-6 -4408)) (-4 *1 (-1247 *2)) (-4 *2 (-1209))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-641 (-1 (-112) *8))) (-4 *8 (-1059 *5 *6 *7)) - (-4 *5 (-556)) (-4 *6 (-789)) (-4 *7 (-846)) - (-5 *2 (-2 (|:| |goodPols| (-641 *8)) (|:| |badPols| (-641 *8)))) - (-5 *1 (-973 *5 *6 *7 *8)) (-5 *4 (-641 *8))))) +(((*1 *2 *2) + (-12 (-4 *3 (-452)) (-5 *1 (-1200 *3 *2)) + (-4 *2 (-13 (-430 *3) (-1194)))))) +(((*1 *2 *3 *3 *4 *4 *5 *5 *3 *3 *4 *4 *5 *5 *3 *3 *4 *4 *5 *5 *3 *4 *4 + *4 *6 *4) + (-12 (-5 *4 (-564)) (-5 *5 (-685 (-225))) (-5 *6 (-671 (-225))) + (-5 *3 (-225)) (-5 *2 (-1031)) (-5 *1 (-746))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-641 (-858))) (-5 *1 (-858)))) ((*1 *2 *1) (-12 (-5 *2 - (-2 (|:| -4251 (-641 (-858))) (|:| -3190 (-641 (-858))) - (|:| |presup| (-641 (-858))) (|:| -1828 (-641 (-858))) + (-2 (|:| -3718 (-641 (-858))) (|:| -3878 (-641 (-858))) + (|:| |presup| (-641 (-858))) (|:| -3122 (-641 (-858))) (|:| |args| (-641 (-858))))) (-5 *1 (-1170))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-685 *3)) (-4 *3 (-1045)) (-5 *1 (-686 *3))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-1 *7 *7)) + (-5 *5 + (-1 (-2 (|:| |ans| *6) (|:| -4337 *6) (|:| |sol?| (-112))) (-564) + *6)) + (-4 *6 (-363)) (-4 *7 (-1235 *6)) + (-5 *2 (-2 (|:| |answer| (-585 (-407 *7))) (|:| |a0| *6))) + (-5 *1 (-574 *6 *7)) (-5 *3 (-407 *7))))) +(((*1 *2) (-12 (-5 *2 (-1152)) (-5 *1 (-1179))))) +(((*1 *2 *2) (|partial| -12 (-5 *1 (-558 *2)) (-4 *2 (-545))))) (((*1 *1 *2 *1) (-12 (|has| *1 (-6 -4407)) (-4 *1 (-151 *2)) (-4 *2 (-1209)) (-4 *2 (-1094)))) @@ -10709,39 +10682,51 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1134 *3 *4)) (-4 *3 (-13 (-1094) (-34))) (-4 *4 (-13 (-1094) (-34))) (-5 *1 (-1135 *3 *4))))) -(((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-641 (-316 (-225)))) (-5 *3 (-225)) (-5 *2 (-112)) - (-5 *1 (-210))))) -(((*1 *1 *2 *2 *2 *2) (-12 (-5 *1 (-714 *2)) (-4 *2 (-363))))) -(((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-467)))) - ((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-467))))) -(((*1 *2 *3 *3 *3 *4 *4 *5 *5 *5 *3 *5 *5 *3 *6 *3 *3 *3) - (-12 (-5 *5 (-685 (-225))) (-5 *6 (-685 (-564))) (-5 *3 (-564)) - (-5 *4 (-225)) (-5 *2 (-1031)) (-5 *1 (-748))))) +(((*1 *1 *1) (-4 *1 (-1138)))) +(((*1 *2 *1) + (-12 (-5 *2 (-687 (-962 *3))) (-5 *1 (-962 *3)) (-4 *3 (-1094))))) (((*1 *2 *3) - (-12 (-5 *2 (-1 (-939 *3) (-939 *3))) (-5 *1 (-176 *3)) - (-4 *3 (-13 (-363) (-1194) (-998)))))) + (-12 + (-5 *3 + (-2 (|:| |xinit| (-225)) (|:| |xend| (-225)) + (|:| |fn| (-1259 (-316 (-225)))) (|:| |yinit| (-641 (-225))) + (|:| |intvals| (-641 (-225))) (|:| |g| (-316 (-225))) + (|:| |abserr| (-225)) (|:| |relerr| (-225)))) + (-5 *2 + (-2 (|:| |stiffnessFactor| (-379)) (|:| |stabilityFactor| (-379)))) + (-5 *1 (-205))))) +(((*1 *1 *1) (-4 *1 (-1138)))) +(((*1 *2 *3) + (-12 (-4 *4 (-789)) + (-4 *5 (-13 (-846) (-10 -8 (-15 -1311 ((-1170) $))))) (-4 *6 (-556)) + (-5 *2 (-2 (|:| -3878 (-948 *6)) (|:| -2122 (-948 *6)))) + (-5 *1 (-728 *4 *5 *6 *3)) (-4 *3 (-945 (-407 (-948 *6)) *4 *5))))) (((*1 *1 *1 *1) (-12 (-5 *1 (-641 *2)) (-4 *2 (-1094)) (-4 *2 (-1209))))) +(((*1 *2) + (-12 (-5 *2 (-112)) (-5 *1 (-1150 *3)) (-4 *3 (-1094)) + (-4 *3 (-1209))))) (((*1 *2 *1) - (-12 (-5 *2 (-687 (-869 (-962 *3) (-962 *3)))) (-5 *1 (-962 *3)) - (-4 *3 (-1094))))) -(((*1 *2 *3 *4 *5 *6 *7) - (-12 (-5 *3 (-685 *11)) (-5 *4 (-641 (-407 (-948 *8)))) - (-5 *5 (-767)) (-5 *6 (-1152)) (-4 *8 (-13 (-307) (-147))) - (-4 *11 (-945 *8 *10 *9)) (-4 *9 (-13 (-846) (-612 (-1170)))) - (-4 *10 (-789)) + (-12 (-5 *2 - (-2 - (|:| |rgl| - (-641 - (-2 (|:| |eqzro| (-641 *11)) (|:| |neqzro| (-641 *11)) - (|:| |wcond| (-641 (-948 *8))) - (|:| |bsoln| - (-2 (|:| |partsol| (-1259 (-407 (-948 *8)))) - (|:| -1298 (-641 (-1259 (-407 (-948 *8)))))))))) - (|:| |rgsz| (-564)))) - (-5 *1 (-920 *8 *9 *10 *11)) (-5 *7 (-564))))) + (-641 + (-2 (|:| |scalar| (-407 (-564))) (|:| |coeff| (-1166 *3)) + (|:| |logand| (-1166 *3))))) + (-5 *1 (-585 *3)) (-4 *3 (-363))))) +(((*1 *2 *3 *3) + (-12 (-5 *3 (-641 *7)) (-4 *7 (-1059 *4 *5 *6)) (-4 *4 (-452)) + (-4 *5 (-789)) (-4 *6 (-846)) (-5 *2 (-112)) + (-5 *1 (-984 *4 *5 *6 *7 *8)) (-4 *8 (-1065 *4 *5 *6 *7)))) + ((*1 *2 *1 *1) + (-12 (-4 *1 (-1059 *3 *4 *5)) (-4 *3 (-1045)) (-4 *4 (-789)) + (-4 *5 (-846)) (-5 *2 (-112)))) + ((*1 *2 *3 *3) + (-12 (-5 *3 (-641 *7)) (-4 *7 (-1059 *4 *5 *6)) (-4 *4 (-452)) + (-4 *5 (-789)) (-4 *6 (-846)) (-5 *2 (-112)) + (-5 *1 (-1101 *4 *5 *6 *7 *8)) (-4 *8 (-1065 *4 *5 *6 *7)))) + ((*1 *2 *1 *1) + (-12 (-4 *1 (-1202 *3 *4 *5 *6)) (-4 *3 (-556)) (-4 *4 (-789)) + (-4 *5 (-846)) (-4 *6 (-1059 *3 *4 *5)) (-5 *2 (-112))))) (((*1 *2 *3) (-12 (-4 *4 (-1045)) (-4 *2 (-13 (-404) (-1034 *4) (-363) (-1194) (-284))) @@ -10756,23 +10741,59 @@ ((*1 *2 *1) (-12 (-4 *1 (-1257 *2)) (-4 *2 (-1209)) (-4 *2 (-998)) (-4 *2 (-1045))))) -(((*1 *2 *3 *3 *3 *3) - (-12 (-5 *3 (-564)) (-5 *2 (-112)) (-5 *1 (-480))))) -(((*1 *2 *1 *1 *3) - (-12 (-5 *3 (-1 (-112) *5 *5)) (-4 *5 (-13 (-1094) (-34))) - (-5 *2 (-112)) (-5 *1 (-1134 *4 *5)) (-4 *4 (-13 (-1094) (-34)))))) -(((*1 *2 *1 *2) (-12 (-5 *2 (-564)) (-5 *1 (-418 *3)) (-4 *3 (-556))))) -(((*1 *1 *1) (-5 *1 (-1057)))) +(((*1 *1 *2) + (-12 (-5 *2 (-641 (-901 *3))) (-4 *3 (-1094)) (-5 *1 (-900 *3))))) +(((*1 *2) (-12 (-5 *2 (-564)) (-5 *1 (-695)))) + ((*1 *2 *2) (-12 (-5 *2 (-564)) (-5 *1 (-695))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-641 *7)) (-4 *7 (-846)) (-4 *5 (-905)) (-4 *6 (-789)) - (-4 *8 (-945 *5 *6 *7)) (-5 *2 (-418 (-1166 *8))) - (-5 *1 (-902 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(-1023 *5 *6 *7 *8))) (-5 *1 (-1023 *5 *6 *7 *8)))) + ((*1 *2 *3 *4 *4) + (-12 (-5 *3 (-641 (-776 *5 (-860 *6)))) (-5 *4 (-112)) (-4 *5 (-452)) + (-14 *6 (-641 (-1170))) (-5 *2 (-641 (-1042 *5 *6))) + (-5 *1 (-1042 *5 *6)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-641 *8)) (-5 *4 (-112)) (-4 *8 (-1059 *5 *6 *7)) + (-4 *5 (-452)) (-4 *6 (-789)) (-4 *7 (-846)) (-5 *2 (-641 *1)) + (-4 *1 (-1065 *5 *6 *7 *8)))) + ((*1 *2 *3 *4 *4 *4 *4) + (-12 (-5 *3 (-641 *8)) (-5 *4 (-112)) (-4 *8 (-1059 *5 *6 *7)) + (-4 *5 (-452)) (-4 *6 (-789)) (-4 *7 (-846)) + (-5 *2 (-641 (-1140 *5 *6 *7 *8))) (-5 *1 (-1140 *5 *6 *7 *8)))) + ((*1 *2 *3 *4 *4) + (-12 (-5 *3 (-641 *8)) (-5 *4 (-112)) (-4 *8 (-1059 *5 *6 *7)) + (-4 *5 (-452)) (-4 *6 (-789)) (-4 *7 (-846)) + (-5 *2 (-641 (-1140 *5 *6 *7 *8))) (-5 *1 (-1140 *5 *6 *7 *8)))) ((*1 *2 *3) - (-12 (-4 *4 (-905)) (-4 *5 (-1235 *4)) (-5 *2 (-418 (-1166 *5))) - (-5 *1 (-903 *4 *5)) (-5 *3 (-1166 *5))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-112)) (-5 *3 (-641 (-263))) (-5 *1 (-261)))) - ((*1 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-263))))) + (-12 (-5 *3 (-641 *7)) (-4 *7 (-1059 *4 *5 *6)) (-4 *4 (-556)) + (-4 *5 (-789)) (-4 *6 (-846)) (-5 *2 (-641 *1)) + (-4 *1 (-1202 *4 *5 *6 *7))))) +(((*1 *1 *1 *2) + (-12 (-4 *1 (-972 *3 *4 *2 *5)) (-4 *3 (-1045)) (-4 *4 (-789)) + (-4 *2 (-846)) (-4 *5 (-1059 *3 *4 *2))))) +(((*1 *2 *1) + (-12 (-4 *1 (-253 *3 *4 *5 *6)) (-4 *3 (-1045)) (-4 *4 (-846)) + (-4 *5 (-266 *4)) (-4 *6 (-789)) (-5 *2 (-641 *4))))) (((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-31)))) ((*1 *2 *1) (-12 (-5 *2 (-1175)) (-5 *1 (-49)))) ((*1 *2 *1) (-12 (-5 *2 (-641 (-1129))) (-5 *1 (-133)))) @@ -10784,59 +10805,116 @@ ((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-1015)))) ((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-1060)))) ((*1 *2 *1) (-12 (-5 *2 (-641 (-1129))) (-5 *1 (-1090))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-225)) (-5 *1 (-226)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-169 (-225))) (-5 *1 (-226)))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-556)) (-5 *1 (-431 *3 *2)) (-4 *2 (-430 *3)))) - ((*1 *1 *1 *1) (-4 *1 (-1133)))) -(((*1 *1 *2 *3) (-12 (-5 *3 (-564)) (-5 *1 (-418 *2)) (-4 *2 (-556))))) +(((*1 *2 *2 *2) + (-12 + (-5 *2 + (-641 + (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-767)) (|:| |poli| *6) + (|:| |polj| *6)))) + (-4 *4 (-789)) (-4 *6 (-945 *3 *4 *5)) (-4 *3 (-452)) (-4 *5 (-846)) + (-5 *1 (-449 *3 *4 *5 *6))))) +(((*1 *2 *1) + (-12 (-5 *2 (-1150 (-407 *3))) (-5 *1 (-174 *3)) (-4 *3 (-307))))) (((*1 *1 *1 *1) (-12 (-5 *1 (-641 *2)) (-4 *2 (-1094)) (-4 *2 (-1209))))) -(((*1 *2 *3) - (-12 (-5 *3 (-641 (-564))) (-5 *2 (-900 (-564))) (-5 *1 (-913)))) - ((*1 *2) (-12 (-5 *2 (-900 (-564))) (-5 *1 (-913))))) -(((*1 *2 *1 *2) (-12 (-5 *2 (-1114)) (-5 *1 (-529))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1 *4 (-564))) (-5 *5 (-1 (-1150 *4))) (-4 *4 (-363)) - (-4 *4 (-1045)) (-5 *2 (-1150 *4)) (-5 *1 (-1154 *4))))) -(((*1 *2) - (-12 (-4 *1 (-349)) - (-5 *2 (-641 (-2 (|:| -3688 (-564)) (|:| -1410 (-564)))))))) -(((*1 *2 *3) - (-12 (-4 *1 (-796)) - (-5 *3 - (-2 (|:| |xinit| (-225)) (|:| |xend| (-225)) - (|:| |fn| (-1259 (-316 (-225)))) (|:| |yinit| (-641 (-225))) - (|:| |intvals| (-641 (-225))) (|:| |g| (-316 (-225))) - (|:| |abserr| (-225)) (|:| |relerr| (-225)))) - (-5 *2 (-1031))))) -(((*1 *2 *1) (-12 (-4 *1 (-763 *3)) (-4 *3 (-1094)) (-5 *2 (-112))))) -(((*1 *2 *3) +(((*1 *1 *1) + (-12 (-4 *1 (-326 *2 *3)) (-4 *2 (-1045)) (-4 *3 (-788)) + (-4 *2 (-452)))) + ((*1 *1 *1) + (-12 (-4 *1 (-342 *2 *3 *4)) (-4 *2 (-1213)) (-4 *3 (-1235 *2)) + (-4 *4 (-1235 (-407 *3))))) + ((*1 *1 *1) (-12 (-4 *1 (-848 *2)) (-4 *2 (-1045)) (-4 *2 (-452)))) + ((*1 *1 *1 *2) + (-12 (-4 *1 (-945 *3 *4 *2)) (-4 *3 (-1045)) (-4 *4 (-789)) + (-4 *2 (-846)) (-4 *3 (-452)))) + ((*1 *1 *1) + (-12 (-4 *1 (-945 *2 *3 *4)) (-4 *2 (-1045)) (-4 *3 (-789)) + (-4 *4 (-846)) (-4 *2 (-452)))) + ((*1 *2 *2 *3) + (-12 (-4 *3 (-307)) (-4 *3 (-556)) (-5 *1 (-1157 *3 *2)) + (-4 *2 (-1235 *3))))) +(((*1 *2 *2 *1) (-12 (-4 *1 (-991 *2)) (-4 *2 (-1209))))) +(((*1 *2 *1) (-12 (-5 *1 (-1022 *2)) 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- ((*1 *1 *2) (-12 (-5 *2 (-948 *1)) (-4 *1 (-27)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-1170)) (-4 *1 (-29 *3)) (-4 *3 (-556)))) - ((*1 *1 *1) (-12 (-4 *1 (-29 *2)) (-4 *2 (-556)))) + (-5 *2 + (-2 + (|:| -1901 + (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) + (|:| -2141 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) + (|:| |relerr| (-225)))) + (|:| -3813 + (-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| (-1150 (-225))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -2141 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| 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*2) (-12 (-5 *2 (-917)) (-4 *1 (-368)))) @@ -13756,272 +13697,64 @@ ((*1 *2 *1) (-12 (-4 *2 (-846)) (-5 *1 (-709 *2 *3 *4)) (-4 *3 (-1094)) (-14 *4 - (-1 (-112) (-2 (|:| -2083 *2) (|:| -1410 *3)) - (-2 (|:| -2083 *2) (|:| -1410 *3))))))) -(((*1 *1 *2 *3) (-12 (-5 *3 (-564)) (-5 *1 (-418 *2)) (-4 *2 (-556))))) -(((*1 *1 *2 *3 *1 *3) - (-12 (-5 *2 (-888 *4)) (-4 *4 (-1094)) (-5 *1 (-885 *4 *3)) - (-4 *3 (-1094))))) + (-1 (-112) (-2 (|:| -2083 *2) (|:| -1838 *3)) + (-2 (|:| -2083 *2) (|:| -1838 *3))))))) +(((*1 *2 *1) + (-12 (-14 *3 (-641 (-1170))) (-4 *4 (-172)) + (-14 *6 + (-1 (-112) (-2 (|:| -2083 *5) (|:| -1838 *2)) + (-2 (|:| -2083 *5) (|:| -1838 *2)))) + (-4 *2 (-238 (-2181 *3) (-767))) (-5 *1 (-461 *3 *4 *5 *2 *6 *7)) + (-4 *5 (-846)) (-4 *7 (-945 *4 *2 (-860 *3)))))) (((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -3430 (-641 (-225))))) - (-5 *2 (-379)) (-5 *1 (-267)))) + (-12 (-5 *3 (-641 (-564))) (-5 *2 (-900 (-564))) (-5 *1 (-913)))) + ((*1 *2 *3) (-12 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-(((*1 *2 *3 *4) - (-12 (-5 *3 (-641 (-316 (-225)))) (-5 *4 (-767)) - (-5 *2 (-685 (-225))) (-5 *1 (-267))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-564)) (-5 *1 (-480))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-407 *6)) (-4 *5 (-1213)) (-4 *6 (-1235 *5)) - (-5 *2 (-2 (|:| -1410 (-767)) (|:| -4376 *3) (|:| |radicand| *6))) - (-5 *1 (-148 *5 *6 *7)) (-5 *4 (-767)) (-4 *7 (-1235 *3))))) -(((*1 *1 *2 *2) - (-12 - (-5 *2 - (-3 (|:| I (-316 (-564))) (|:| -2308 (-316 (-379))) - (|:| CF (-316 (-169 (-379)))) (|:| |switch| (-1169)))) - (-5 *1 (-1169))))) + (-12 (-5 *3 (-641 (-407 (-948 *4)))) (-4 *4 (-13 (-307) (-147))) + (-5 *2 (-641 (-641 (-294 (-316 *4))))) (-5 *1 (-1123 *4)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-641 (-294 (-407 (-948 *5))))) (-5 *4 (-641 (-1170))) + (-4 *5 (-13 (-307) (-147))) (-5 *2 (-641 (-641 (-294 (-316 *5))))) + (-5 *1 (-1123 *5)))) + ((*1 *2 *3) + (-12 (-5 *3 (-641 (-294 (-407 (-948 *4))))) + (-4 *4 (-13 (-307) (-147))) (-5 *2 (-641 (-641 (-294 (-316 *4))))) + (-5 *1 (-1123 *4))))) 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\ No newline at end of file |