diff options
Diffstat (limited to 'src')
64 files changed, 19253 insertions, 19241 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 7fe1b652..648f9414 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,5 +1,55 @@ 2009-05-29 Gabriel Dos Reis <gdr@cs.tamu.edu> + * algebra/algext.spad.pamphlet: Qualify `characteristic'. + * algebra/clifford.spad.pamphlet: Likewise. + * algebra/complet.spad.pamphlet: Likewise. + * algebra/contfrac.spad.pamphlet: Likewise. + * algebra/curve.spad.pamphlet: Likewise. + * algebra/ddfact.spad.pamphlet: Likewise. + * algebra/derham.spad.pamphlet: Likewise. + * algebra/equation2.spad.pamphlet: Likewise. + * algebra/ffcat.spad.pamphlet: Likewise. + * algebra/ffcg.spad.pamphlet: Likewise. + * algebra/fff.spad.pamphlet: Likewise. + * algebra/ffnb.spad.pamphlet: Likewise. + * algebra/ffp.spad.pamphlet: Likewise. + * algebra/ffpoly.spad.pamphlet: Likewise. + * algebra/ffx.spad.pamphlet: Likewise. + * algebra/fmod.spad.pamphlet: Likewise. + * algebra/fortmac.spad.pamphlet: Likewise. + * algebra/fr.spad.pamphlet: Likewise. + * algebra/fraction.spad.pamphlet: Likewise. + * algebra/fspace.spad.pamphlet: Likewise. + * algebra/gaussian.spad.pamphlet: Likewise. + * algebra/gpol.spad.pamphlet: Likewise. + * algebra/intclos.spad.pamphlet: Likewise. + * algebra/interval.spad.pamphlet: Likewise. + * algebra/laurent.spad.pamphlet: Likewise. + * algebra/matrix.spad.pamphlet: Likewise. + * algebra/modring.spad.pamphlet: Likewise. + * algebra/oct.spad.pamphlet: Likewise. + * algebra/opalg.spad.pamphlet: Likewise. + * algebra/padic.spad.pamphlet: Likewise. + * algebra/perman.spad.pamphlet: Likewise. + * algebra/pf.spad.pamphlet: Likewise. + * algebra/pfr.spad.pamphlet: Likewise. + * algebra/poly.spad.pamphlet: Likewise. + * algebra/polycat.spad.pamphlet: Likewise. + * algebra/puiseux.spad.pamphlet: Likewise. + * algebra/quat.spad.pamphlet: Likewise. + * algebra/radix.spad.pamphlet: Likewise. + * algebra/reclos.spad.pamphlet: Likewise. + * algebra/resring.spad.pamphlet: Likewise. + * algebra/sf.spad.pamphlet: Likewise. + * algebra/si.spad.pamphlet: Likewise. + * algebra/solvefor.spad.pamphlet: Likewise. + * algebra/sups.spad.pamphlet: Likewise. + * algebra/taylor.spad.pamphlet: Likewise. + * algebra/vector.spad.pamphlet: Likewise. + * algebra/xpoly.spad.pamphlet: Likewise. + +2009-05-29 Gabriel Dos Reis <gdr@cs.tamu.edu> + Fix SF/2798220 * algebra/fmod.spad.pamphlet (IntegerMod): Define before? * algebra/ffp.spad.pamphlet (FiniteFieldExtensionByPolynomial): diff --git a/src/algebra/algext.spad.pamphlet b/src/algebra/algext.spad.pamphlet index 9a747687..050ccac5 100644 --- a/src/algebra/algext.spad.pamphlet +++ b/src/algebra/algext.spad.pamphlet @@ -75,7 +75,7 @@ SimpleAlgebraicExtension(R:CommutativeRing, coordinates(x) == [coefficient(lift(x),i) for i in 0..d1] represents(vect) == +/[monomial(vect.(i+1),i) for i in 0..d1] definingPolynomial() == M - characteristic() == characteristic()$R + characteristic == characteristic$R rank() == d::PositiveInteger basis() == copy(bsis@Vector(Rep) pretend Vector($)) --!! I inserted 'copy' in the definition of 'basis' -- cjw 7/19/91 diff --git a/src/algebra/clifford.spad.pamphlet b/src/algebra/clifford.spad.pamphlet index ecedf9ac..bbc0f75c 100644 --- a/src/algebra/clifford.spad.pamphlet +++ b/src/algebra/clifford.spad.pamphlet @@ -292,7 +292,7 @@ CliffordAlgebra(n, K, Q): T == Impl where c: K m: Integer - characteristic() == characteristic()$K + characteristic == characteristic$K dimension() == dim::CardinalNumber x = y == diff --git a/src/algebra/complet.spad.pamphlet b/src/algebra/complet.spad.pamphlet index 73cff0fb..d71d3f74 100644 --- a/src/algebra/complet.spad.pamphlet +++ b/src/algebra/complet.spad.pamphlet @@ -100,7 +100,7 @@ OrderedCompletion(R:SetCategory): Exports == Implementation where fininf: (B, R) -> % 1 == [1$R] - characteristic() == characteristic()$R + characteristic == characteristic$R fininf(b, r) == r > 0 => [b] @@ -242,7 +242,7 @@ OnePointCompletion(R:SetCategory): Exports == Implementation where fininf: R -> % 1 == 1$R - characteristic() == characteristic()$R + characteristic == characteristic$R fininf r == zero? r => error "Undefined product" diff --git a/src/algebra/contfrac.spad.pamphlet b/src/algebra/contfrac.spad.pamphlet index e24d5825..615d435a 100644 --- a/src/algebra/contfrac.spad.pamphlet +++ b/src/algebra/contfrac.spad.pamphlet @@ -220,7 +220,7 @@ ContinuedFraction(R): Exports == Implementation where d := qr.remainder [[wh, construct rest reverse_! l], true] - characteristic() == characteristic()$Q + characteristic == characteristic$Q genFromSequence apps == diff --git a/src/algebra/curve.spad.pamphlet b/src/algebra/curve.spad.pamphlet index 37d330ee..7b8e73ff 100644 --- a/src/algebra/curve.spad.pamphlet +++ b/src/algebra/curve.spad.pamphlet @@ -698,8 +698,8 @@ RadicalFunctionField(F, UP, UPUP, radicnd, n): Exports == Impl where startUp b == brandNew?() := b - if zero?(p := characteristic()$F) or p > n then char0StartUp() - else charPStartUp() + if zero?(p := characteristic$F) or p > n then char0StartUp() + else charPStartUp() dsc:RF := ((-1)$Z ** ((n *$N n1) quo 2::N) * (n::Z)**n)$Z * radicnd ** n1 * */[qelt(ibasis, i) ** 2 for i in mini..maxIndex ibasis] diff --git a/src/algebra/ddfact.spad.pamphlet b/src/algebra/ddfact.spad.pamphlet index f160ec23..df499007 100644 --- a/src/algebra/ddfact.spad.pamphlet +++ b/src/algebra/ddfact.spad.pamphlet @@ -82,7 +82,7 @@ DistinctDegreeFactorize(F,FP): C == T ddffact1 : (FP,Boolean) -> List fact ranpol : NNI -> FP - charF : Boolean := characteristic()$F = 2 + charF : Boolean := characteristic$F = 2 --construct a random polynomial of random degree < d ranpol(d:NNI):FP == diff --git a/src/algebra/derham.spad.pamphlet b/src/algebra/derham.spad.pamphlet index 6b77c0e6..404df940 100644 --- a/src/algebra/derham.spad.pamphlet +++ b/src/algebra/derham.spad.pamphlet @@ -266,7 +266,7 @@ AntiSymm(R:Ring, lVar:List Symbol): Export == Implement where m = 0 => 0 [ [Nul(dim), m::R] ] - characteristic() == characteristic()$R + characteristic == characteristic$R generator(j) == -- j < 1 or j > dim => error "your subscript is out of range" diff --git a/src/algebra/equation2.spad.pamphlet b/src/algebra/equation2.spad.pamphlet index e0d3bd30..a621d9f9 100644 --- a/src/algebra/equation2.spad.pamphlet +++ b/src/algebra/equation2.spad.pamphlet @@ -206,7 +206,7 @@ Equation(S: Type): public == private where leftOne eq == 1 = rhs eq * inv rhs eq rightOne eq == lhs eq * inv rhs eq = 1 if S has Ring then - characteristic() == characteristic()$S + characteristic == characteristic$S i:Integer * eq:$ == (i::S) * eq if S has IntegralDomain then factorAndSplit eq == diff --git a/src/algebra/ffcat.spad.pamphlet b/src/algebra/ffcat.spad.pamphlet index 2f3c1ba4..e7ae41ae 100644 --- a/src/algebra/ffcat.spad.pamphlet +++ b/src/algebra/ffcat.spad.pamphlet @@ -57,8 +57,8 @@ FieldOfPrimeCharacteristic:Category == _ ++ primeFrobenius(a,s) returns \spad{a**(p**s)} where p ++ is the characteristic. add - primeFrobenius(a) == a ** characteristic() - primeFrobenius(a,s) == a ** (characteristic()**s) + primeFrobenius(a) == a ** characteristic$% + primeFrobenius(a,s) == a ** (characteristic$%**s) @ \section{category XF ExtensionField} @@ -379,7 +379,7 @@ FiniteAlgebraicExtensionField(F : Field) : Category == _ error "trace: second argument must divide degree of extension" size() == size()$F ** extensionDegree() createNormalElement() == - characteristic() = size() => 1 + characteristic$% = size() => 1 res : $ for i in 1.. repeat res := index(i :: PI) @@ -595,15 +595,15 @@ FiniteFieldCategory() : Category ==_ l:=nullSpace mat empty? l or every?(zero?, first l) => "failed" map(charthRoot,first l) - charthRoot(x:$):$ == x**(size() quo characteristic()) + charthRoot(x:$):$ == x**(size()$% quo characteristic$%) charthRoot(x:%):Union($,"failed") == (charthRoot(x)@$)::Union($,"failed") createPrimitiveElement() == - sm1 : PositiveInteger := (size()$$-1) pretend PositiveInteger + sm1 : PositiveInteger := (size()$%-1) pretend PositiveInteger start : Integer := -- in the polynomial case, index from 1 to characteristic-1 -- gives prime field elements - representationType = "polynomial" => characteristic()::Integer + representationType = "polynomial" => characteristic$% 1 found : Boolean := false e : $ @@ -615,15 +615,14 @@ FiniteFieldCategory() : Category ==_ -- add special implementation for prime field case zero?(a) => false explist := factorsOfCyclicGroupSize() - q:=(size()-1)@Integer + q:=(size()$%-1)@Integer equalone : Boolean := false for exp in explist while not equalone repeat equalone := one?(a**(q quo exp.factor)) not equalone order(e: %): PositiveInteger == e = 0 => error "order(0) is not defined " - ord:Integer:= size()-1 -- order e divides ord - a:Integer:= 0 + ord:Integer:= size()$%-1 -- order e divides ord lof:=factorsOfCyclicGroupSize() for rec in lof repeat -- run through prime divisors a := ord quo (primeDivisor := rec.factor) @@ -649,7 +648,7 @@ FiniteFieldCategory() : Category ==_ b = gen => 1 disclog:Integer:=0 mult:Integer:=1 - groupord := (size() - 1)@Integer + groupord := (size()$% - 1)@Integer exp:Integer:=groupord for f in faclist repeat fac:=f.factor diff --git a/src/algebra/ffcg.spad.pamphlet b/src/algebra/ffcg.spad.pamphlet index 1ed736db..b1ff6b98 100644 --- a/src/algebra/ffcg.spad.pamphlet +++ b/src/algebra/ffcg.spad.pamphlet @@ -264,7 +264,7 @@ FiniteFieldCyclicGroupExtensionByPolynomial(GF,defpol):_ - x:$ == zero? x => 0 - characteristic() =$I 2 => x + characteristic$% =$I 2 => x addmod(x,shift(sizeCG,-1)$SI pretend Rep,sizeCG) generator() == 1$SI @@ -287,7 +287,7 @@ FiniteFieldCyclicGroupExtensionByPolynomial(GF,defpol):_ extensionDegree(): PositiveInteger == extdeg pretend PI - characteristic() == characteristic()$GF + characteristic == characteristic$GF lookup(x:$) == x =$Rep (-$Rep 1$Rep) => sizeFF pretend PI diff --git a/src/algebra/fff.spad.pamphlet b/src/algebra/fff.spad.pamphlet index 3eb3d683..b73ecc98 100644 --- a/src/algebra/fff.spad.pamphlet +++ b/src/algebra/fff.spad.pamphlet @@ -112,7 +112,7 @@ FiniteFieldFunctions(GF): Exports == Implementation where createLowComplexityTable(n) == q:=size()$GF -- this algorithm works only for prime fields - p:=characteristic()$GF + p:=characteristic$GF -- search of a suitable parameter k k:NNI:=0 a:NNI @@ -240,7 +240,7 @@ FiniteFieldFunctions(GF): Exports == Implementation where helparr.(lookup(a -$SAE(GF,SUP,f) 1$SAE(GF,SUP,f)_ )$SAE(GF,SUP,f)):=i::SI a:=a * primElement - characteristic() = 2 => + characteristic$GF = 2 => a:=primElement for i in 1..(qm1 quo 2) repeat zechlog.i:=helparr.lookup(a)$SAE(GF,SUP,f) diff --git a/src/algebra/ffnb.spad.pamphlet b/src/algebra/ffnb.spad.pamphlet index a4441b5a..8b9c7fbd 100644 --- a/src/algebra/ffnb.spad.pamphlet +++ b/src/algebra/ffnb.spad.pamphlet @@ -665,7 +665,7 @@ divisor of the order of the multiplicative group" erg:=concat(erg,v)$Rep erg - characteristic() == characteristic()$GF + characteristic == characteristic$GF random() == random(extdeg)$INBFF diff --git a/src/algebra/ffp.spad.pamphlet b/src/algebra/ffp.spad.pamphlet index c5832f93..02ed358e 100644 --- a/src/algebra/ffp.spad.pamphlet +++ b/src/algebra/ffp.spad.pamphlet @@ -261,7 +261,7 @@ FiniteFieldExtensionByPolynomial(GF:FiniteFieldCategory,_ retractIfCan(x) = "failed" => false true - characteristic() == characteristic()$GF + characteristic == characteristic$GF before?(x,y) == before?(x,y)$Rep @ diff --git a/src/algebra/ffpoly.spad.pamphlet b/src/algebra/ffpoly.spad.pamphlet index ee544ce5..b6f2f767 100644 --- a/src/algebra/ffpoly.spad.pamphlet +++ b/src/algebra/ffpoly.spad.pamphlet @@ -275,7 +275,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where -- qEulerPhiCyclotomic n == -- n = 1 => (sizeGF - 1) pretend PI --- p : PI := characteristic()$GF :: PI +-- p : PI := characteristic$GF :: PI -- (n rem p) = 0 => error -- "cyclotomic polynomial not defined for this argument value" -- q : PI := sizeGF @@ -332,7 +332,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where -- such that d divides q**k - 1 ([LN] p.65, Th. 2.47) n = 1 => (sizeGF - 1) :: NNI :: PI m : PI := n - p : PI := characteristic()$GF :: PI + p : PI := characteristic$GF :: PI q : PI := sizeGF while (m rem p) = 0 repeat -- find m such that m := (m quo p) :: PI -- n = m * p**r and gcd(m,p) = 1 diff --git a/src/algebra/ffx.spad.pamphlet b/src/algebra/ffx.spad.pamphlet index 4e45d712..06546d6b 100644 --- a/src/algebra/ffx.spad.pamphlet +++ b/src/algebra/ffx.spad.pamphlet @@ -36,7 +36,7 @@ IrredPolyOverFiniteField(GF:FiniteFieldCategory): Exports == Impl where getIrredPoly : (Z, N) -> SUP qAdicExpansion: Z -> SUP - p := characteristic()$GF :: N + p := characteristic$GF :: N q := size()$GF :: N qAdicExpansion(z : Z): SUP == diff --git a/src/algebra/fmod.spad.pamphlet b/src/algebra/fmod.spad.pamphlet index 47182caf..62b978fb 100644 --- a/src/algebra/fmod.spad.pamphlet +++ b/src/algebra/fmod.spad.pamphlet @@ -28,7 +28,7 @@ IntegerMod(p:PositiveInteger): Join(CommutativeRing, Finite, ConvertibleTo Integer, StepThrough) == add size() == p - characteristic() == p + characteristic == p lookup x == (zero? x => p; (convert(x)@Integer) :: PositiveInteger) -- Code is duplicated for the optimizer to kick in. diff --git a/src/algebra/fortmac.spad.pamphlet b/src/algebra/fortmac.spad.pamphlet index 07016a41..bc5d62b8 100644 --- a/src/algebra/fortmac.spad.pamphlet +++ b/src/algebra/fortmac.spad.pamphlet @@ -361,7 +361,7 @@ MachineFloat(): Exports == Implementation where sign(m1) = 0 and sign(m2) = -1 => false true - characteristic():NNI == 0 + characteristic:NNI == 0 @ \section{domain MCMPLX MachineComplex} diff --git a/src/algebra/fr.spad.pamphlet b/src/algebra/fr.spad.pamphlet index 082ff876..ebab36e4 100644 --- a/src/algebra/fr.spad.pamphlet +++ b/src/algebra/fr.spad.pamphlet @@ -218,7 +218,7 @@ Factored(R: IntegralDomain): Exports == Implementation where one? u == empty? u.fct and u.unt = 1 mkFF(r, x) == [r, x] coerce(j:Integer):% == (j::R)::% - characteristic() == characteristic()$R + characteristic == characteristic$R i:Integer * u:% == (i :: %) * u r:R * u:% == (r :: %) * u factors u == [[fe.fctr, fe.xpnt] for fe in factorList u] diff --git a/src/algebra/fraction.spad.pamphlet b/src/algebra/fraction.spad.pamphlet index 604771b7..8e0ff164 100644 --- a/src/algebra/fraction.spad.pamphlet +++ b/src/algebra/fraction.spad.pamphlet @@ -105,7 +105,7 @@ LocalAlgebra(A: Algebra R, == Localize(A, R, S) add 1 == 1$A / 1$S x:% * y:% == (numer(x) * numer(y)) / (denom(x) * denom(y)) - characteristic() == characteristic()$A + characteristic == characteristic$A @ \section{category QFCAT QuotientFieldCategory} @@ -180,7 +180,7 @@ QuotientFieldCategory(S: IntegralDomain): Category == map(fn, x) == (fn numer x) / (fn denom x) reducedSystem(m:Matrix %):Matrix S == clearDenominator m - characteristic() == characteristic()$S + characteristic == characteristic$S differentiate(x:%, deriv:S -> S) == n := numer x @@ -560,7 +560,7 @@ Fraction(S: IntegralDomain): QuotientFieldCategory S with -- to find x = p-th root of n/d -- observe that xd is p-th root of n*d**(p-1) ans:=charthRoot(x.num * - (x.den)**(characteristic()$%-1)::NonNegativeInteger) + (x.den)**(characteristic$%-1)::NonNegativeInteger) ans case "failed" => "failed" ans / x.den clear: List % -> List S diff --git a/src/algebra/fspace.spad.pamphlet b/src/algebra/fspace.spad.pamphlet index 5618839b..2a25eb6e 100644 --- a/src/algebra/fspace.spad.pamphlet +++ b/src/algebra/fspace.spad.pamphlet @@ -610,7 +610,7 @@ FunctionSpace(R: SetCategory): Category == Definition where -- cannot use new()$Symbol because of possible re-instantiation gendiff := "%%0"::SY - characteristic() == characteristic()$R + characteristic == characteristic$R coerce(k:K):% == k::MP::% symsub(sy, i) == concat(string sy, convert(i)@String)::SY numerator x == numer(x)::% diff --git a/src/algebra/gaussian.spad.pamphlet b/src/algebra/gaussian.spad.pamphlet index 25836835..2e7bd479 100644 --- a/src/algebra/gaussian.spad.pamphlet +++ b/src/algebra/gaussian.spad.pamphlet @@ -132,7 +132,7 @@ ComplexCategory(R:CommutativeRing): Category == trace x == 2 * real x imaginary() == complex(0, 1) conjugate x == complex(real x, - imag x) - characteristic() == characteristic()$R + characteristic == characteristic$R map(fn, x) == complex(fn real x, fn imag x) x = y == real(x) = real(y) and imag(x) = imag(y) x + y == complex(real x + real y, imag x + imag y) diff --git a/src/algebra/gpol.spad.pamphlet b/src/algebra/gpol.spad.pamphlet index 52918474..4ef5c712 100644 --- a/src/algebra/gpol.spad.pamphlet +++ b/src/algebra/gpol.spad.pamphlet @@ -71,7 +71,7 @@ LaurentPolynomial(R, UP): Exports == Implementation where coerce(p:UP):% == mkgpol(0, p) reductum p == check0(order p, reductum poly p) n:Z * p:% == check0(order p, n * poly p) - characteristic() == characteristic()$R + characteristic == characteristic$R coerce(n:Z):% == n::R::% degree p == degree(poly p)::Z + order p monomial? p == monomial? poly p diff --git a/src/algebra/intclos.spad.pamphlet b/src/algebra/intclos.spad.pamphlet index 5e5a13a5..7507efae 100644 --- a/src/algebra/intclos.spad.pamphlet +++ b/src/algebra/intclos.spad.pamphlet @@ -322,7 +322,7 @@ FunctionFieldIntegralBasis(R,UP,F): Exports == Implementation where tfm := ((rb * tfm0 * transpose rb) exquo (rbden * rbden)) :: Mat integralBasis() == - n := rank()$F; p := characteristic()$F + n := rank()$F; p := characteristic$F (not zero? p) and (n >= p) => error "integralBasis: possible wild ramification" tfm := traceMatrix()$F; disc := determinant tfm @@ -330,7 +330,7 @@ FunctionFieldIntegralBasis(R,UP,F): Exports == Implementation where iIntegralBasis(tfm,disc,sing) localIntegralBasis prime == - n := rank()$F; p := characteristic()$F + n := rank()$F; p := characteristic$F (not zero? p) and (n >= p) => error "integralBasis: possible wild ramification" tfm := traceMatrix()$F; disc := determinant tfm @@ -428,7 +428,7 @@ WildFunctionFieldIntegralBasis(K,R,UP,F): Exports == Implementation where -- 'standardBasis' is the basis for F as a FramedAlgebra; -- usually this is [1,y,y**2,...,y**(n-1)] p2 := prime * prime; sae := SAE(K,R,prime) - p := characteristic()$F; q := size()$sae + p := characteristic$F; q := size()$sae lp := leastPower(q,n) rb := scalarMatrix(n,1); rbinv := scalarMatrix(n,1) -- rb = basis matrix of current order diff --git a/src/algebra/interval.as.pamphlet b/src/algebra/interval.as.pamphlet index 765d7327..5ef14120 100644 --- a/src/algebra/interval.as.pamphlet +++ b/src/algebra/interval.as.pamphlet @@ -261,7 +261,7 @@ Interval(R:FUNCAT): IntervalCategory(R) == add { coerce(u:%):OutputForm == bracket([coerce inf(u), coerce sup(u)]$List(OutputForm)); - characteristic():NonNegativeInteger == 0; + characteristic:NonNegativeInteger == 0; -- Explicit export from TranscendentalFunctionCategory diff --git a/src/algebra/interval.spad.pamphlet b/src/algebra/interval.spad.pamphlet index 04ae4cd9..a15715c9 100644 --- a/src/algebra/interval.spad.pamphlet +++ b/src/algebra/interval.spad.pamphlet @@ -242,7 +242,7 @@ Interval(R:Join(FloatingPointSystem,TranscendentalFunctionCategory)): IntervalCa coerce(u:%):OutputForm == bracket([coerce inf(u), coerce sup(u)]$List(OutputForm)) - characteristic():NonNegativeInteger == 0 + characteristic:NonNegativeInteger == 0 -- Explicit export from TranscendentalFunctionCategory diff --git a/src/algebra/laurent.spad.pamphlet b/src/algebra/laurent.spad.pamphlet index 23d39979..eba51897 100644 --- a/src/algebra/laurent.spad.pamphlet +++ b/src/algebra/laurent.spad.pamphlet @@ -370,7 +370,7 @@ UnivariateLaurentSeriesConstructor(Coef,UTS):_ (s = variable(x)) => differentiate x map(differentiate(#1,s),x) - differentiate(center x,s)*differentiate(x) - characteristic() == characteristic()$Coef + characteristic == characteristic$Coef if Coef has Field then diff --git a/src/algebra/matrix.spad.pamphlet b/src/algebra/matrix.spad.pamphlet index d2b603d8..4a63ccf5 100644 --- a/src/algebra/matrix.spad.pamphlet +++ b/src/algebra/matrix.spad.pamphlet @@ -404,7 +404,7 @@ SquareMatrix(ndim,R): Exports == Implementation where ONE := scalarMatrix 1 1 == ONE - characteristic() == characteristic()$R + characteristic == characteristic$R new c == per new(ndim,ndim,c)$Rep diff --git a/src/algebra/modring.spad.pamphlet b/src/algebra/modring.spad.pamphlet index e4303078..d347318d 100644 --- a/src/algebra/modring.spad.pamphlet +++ b/src/algebra/modring.spad.pamphlet @@ -62,7 +62,7 @@ ModularRing(R,Mod,reduction:(R,Mod) -> R, coerce(x):OutputForm == (x.val)::OutputForm reduce (a:R,m:Mod) == [reduction(a,m),m]$Rep - characteristic():NonNegativeInteger == characteristic()$R + characteristic:NonNegativeInteger == characteristic$R 0 == [0$R,0$Mod]$Rep 1 == [1$R,0$Mod]$Rep zero? x == zero? x.val diff --git a/src/algebra/oct.spad.pamphlet b/src/algebra/oct.spad.pamphlet index b1ed406d..e2b6c52e 100644 --- a/src/algebra/oct.spad.pamphlet +++ b/src/algebra/oct.spad.pamphlet @@ -89,8 +89,8 @@ OctonionCategory(R: CommutativeRing): Category == inv : % -> % ++ inv(o) returns the inverse of o if it exists. add - characteristic() == - characteristic()$R + characteristic == + characteristic$R conjugate x == octon(real x, - imagi x, - imagj x, - imagk x, - imagE x,_ - imagI x, - imagJ x, - imagK x) diff --git a/src/algebra/opalg.spad.pamphlet b/src/algebra/opalg.spad.pamphlet index dc5b5e3f..19a4a9dc 100644 --- a/src/algebra/opalg.spad.pamphlet +++ b/src/algebra/opalg.spad.pamphlet @@ -87,7 +87,7 @@ ModuleOperator(R: Ring, M:LeftModule(R)): Exports == Implementation where elt(x:$, r:M) == +/[t.exp * termeval(t.gen, r) for t in terms x] rmeval(t, r) == t.coef * monomeval(t.monom, r) termcopy t == [[rm.coef, rm.monom] for rm in t] - characteristic() == characteristic()$R + characteristic == characteristic$R mkop(r, fg) == [[r, fg]$RM]$TERM :: $ evaluate(f, g) == nocopy setProperty(retract(f)@OP,OPEVAL,g pretend None) diff --git a/src/algebra/padic.spad.pamphlet b/src/algebra/padic.spad.pamphlet index e17fe7dc..5fc2275c 100644 --- a/src/algebra/padic.spad.pamphlet +++ b/src/algebra/padic.spad.pamphlet @@ -94,7 +94,7 @@ InnerPAdicInteger(p,unBalanced?): Exports == Implementation where Rep := ST I - characteristic() == 0 + characteristic == 0 euclideanSize(x) == order(x) stream(x:%):ST I == x pretend ST(I) diff --git a/src/algebra/perman.spad.pamphlet b/src/algebra/perman.spad.pamphlet index 2fa6e43d..f22aedd1 100644 --- a/src/algebra/perman.spad.pamphlet +++ b/src/algebra/perman.spad.pamphlet @@ -229,7 +229,7 @@ Permanent(n : PositiveInteger, R : Ring with commutative("*")): c : R := 0 sgn : R := 1 if (not (R has IntegralDomain)) - -- or (characteristic()$R = (2:NNI)) + -- or (characteristic$R = (2:NNI)) -- compiler refuses to compile the line above !! or (sgn + sgn = c) then return permanent3(x) diff --git a/src/algebra/pf.spad.pamphlet b/src/algebra/pf.spad.pamphlet index 611fbcff..38c956bb 100644 --- a/src/algebra/pf.spad.pamphlet +++ b/src/algebra/pf.spad.pamphlet @@ -103,7 +103,7 @@ InnerPrimeField(p:PositiveInteger): Exports == Implementation where createNormalElement() == 1 - characteristic() == p + characteristic == p factorsOfCyclicGroupSize() == p=2 => facOfGroupSize -- this fixes an infinite loop of functions diff --git a/src/algebra/pfr.spad.pamphlet b/src/algebra/pfr.spad.pamphlet index eeaa4c2f..21f36929 100644 --- a/src/algebra/pfr.spad.pamphlet +++ b/src/algebra/pfr.spad.pamphlet @@ -231,7 +231,7 @@ PartialFraction(R: EuclideanDomain): Cat == Capsule where 0 == [0$R, nil()$LfTerm] 1 == [1$R, nil()$LfTerm] - characteristic() == characteristic()$R + characteristic == characteristic$R coerce(r): % == [r, nil()$LfTerm] coerce(n): % == [(n :: R), nil()$LfTerm] diff --git a/src/algebra/poly.spad.pamphlet b/src/algebra/poly.spad.pamphlet index 077ba898..c71af1d9 100644 --- a/src/algebra/poly.spad.pamphlet +++ b/src/algebra/poly.spad.pamphlet @@ -438,11 +438,11 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with zero?(cc:=p.first.c ** n) => 0 [[n * p.first.k, cc]] -- not worth doing special trick if characteristic is too small - if characteristic()$R < 3 then return expt(p,n pretend PositiveInteger)$RepeatedSquaring(%) + if characteristic$R < 3 then return expt(p,n pretend PositiveInteger)$RepeatedSquaring(%) y:%:=1 -- break up exponent in qn * characteristic + rn -- exponentiating by the characteristic is fast - rec := divide(n, characteristic()$R) + rec := divide(n, characteristic$R) qn:= rec.quotient rn:= rec.remainder repeat @@ -450,8 +450,8 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with if rn > 1 then y:= y * binomThmExpt([p.first], p.rest, rn) zero? qn => return y -- raise to the characteristic power - p:= [[t.k * characteristic()$R , primeFrobenius(t.c)$R ]$Term for t in p] - rec := divide(qn, characteristic()$R) + p:= [[t.k * characteristic$R , primeFrobenius(t.c)$R ]$Term for t in p] + rec := divide(qn, characteristic$R) qn:= rec.quotient rn:= rec.remainder y diff --git a/src/algebra/polycat.spad.pamphlet b/src/algebra/polycat.spad.pamphlet index 60e29ed0..30d77de8 100644 --- a/src/algebra/polycat.spad.pamphlet +++ b/src/algebra/polycat.spad.pamphlet @@ -501,7 +501,7 @@ PolynomialCategory(R:Ring, E:OrderedAbelianMonoidSup, VarSet:OrderedSet): -- column, i.e. to one variable llR:List List R := [ empty() for z in first ll] monslist:List List % := empty() - ch:=characteristic()$% + ch:=characteristic$% for l in ll repeat mons:= "setUnion"/[primitiveMonomials u for u in l] redmons:List % :=[] @@ -530,7 +530,7 @@ PolynomialCategory(R:Ring, E:OrderedAbelianMonoidSup, VarSet:OrderedSet): ans := charthRoot ground p ans case "failed" => "failed" ans::R::% - ch:=characteristic()$% + ch:=characteristic$% charthRootlv(p,vars,ch) charthRootlv(p,vars,ch) == empty? vars => diff --git a/src/algebra/puiseux.spad.pamphlet b/src/algebra/puiseux.spad.pamphlet index 1bd402aa..ca2a82d7 100644 --- a/src/algebra/puiseux.spad.pamphlet +++ b/src/algebra/puiseux.spad.pamphlet @@ -298,7 +298,7 @@ UnivariatePuiseuxSeriesConstructor(Coef,ULS):_ map(fcn,upxs) == puiseux(getExpon upxs,map(fcn,getULS upxs)) - characteristic() == characteristic()$Coef + characteristic == characteristic$Coef -- multiplyCoefficients(f,upxs) == -- r := getExpon upxs diff --git a/src/algebra/quat.spad.pamphlet b/src/algebra/quat.spad.pamphlet index 709d9331..92ce1e47 100644 --- a/src/algebra/quat.spad.pamphlet +++ b/src/algebra/quat.spad.pamphlet @@ -76,8 +76,8 @@ QuaternionCategory(R: CommutativeRing): Category == add - characteristic() == - characteristic()$R + characteristic == + characteristic$R conjugate x == quatern(real x, - imagI x, - imagJ x, - imagK x) map(fn, x) == diff --git a/src/algebra/radix.spad.pamphlet b/src/algebra/radix.spad.pamphlet index f5ed227e..f67f6a68 100644 --- a/src/algebra/radix.spad.pamphlet +++ b/src/algebra/radix.spad.pamphlet @@ -91,7 +91,7 @@ RadixExpansion(bb): Exports == Implementation where checkRagits: List I -> Boolean -- Arithmetic operations - characteristic() == 0 + characteristic == 0 differentiate a == 0 0 == [1, nil(), nil(), nil()] diff --git a/src/algebra/reclos.spad.pamphlet b/src/algebra/reclos.spad.pamphlet index 3aa33230..23f67912 100644 --- a/src/algebra/reclos.spad.pamphlet +++ b/src/algebra/reclos.spad.pamphlet @@ -380,7 +380,7 @@ RealClosedField : Category == PUB where sqrt(a:Z):$ == sqrt(a::$,2) - characteristic() == 0 + characteristic == 0 rootOf(pol,n,o) == r := rootOf(pol,n) diff --git a/src/algebra/resring.spad.pamphlet b/src/algebra/resring.spad.pamphlet index 5137df07..343c34ca 100644 --- a/src/algebra/resring.spad.pamphlet +++ b/src/algebra/resring.spad.pamphlet @@ -60,7 +60,7 @@ ResidueRing(F,Expon,VarSet,FPol,LFPol) : Dom == Body (n : Integer) * x == n *$Rep x (a : F) * x == a *$Rep x x = y == x =$Rep y - characteristic() == characteristic()$F + characteristic == characteristic$F coerce(x) : OutputForm == coerce(x)$Rep @ diff --git a/src/algebra/sf.spad.pamphlet b/src/algebra/sf.spad.pamphlet index b104b7f5..35c59b87 100644 --- a/src/algebra/sf.spad.pamphlet +++ b/src/algebra/sf.spad.pamphlet @@ -87,7 +87,7 @@ RealNumberSystem(): Category == ++ abs x returns the absolute value of x. add - characteristic() == 0 + characteristic == 0 fractionPart x == x - truncate x truncate x == (negative? x => -floor(-x); floor x) round x == (negative? x => truncate(x-1/2::%); truncate(x+1/2::%)) diff --git a/src/algebra/si.spad.pamphlet b/src/algebra/si.spad.pamphlet index f620c59f..605f78e5 100644 --- a/src/algebra/si.spad.pamphlet +++ b/src/algebra/si.spad.pamphlet @@ -81,7 +81,7 @@ IntegerNumberSystem(): Category == -- commutative("*") -- follows from the above add - characteristic() == 0 + characteristic == 0 differentiate x == 0 even? x == not odd? x positive? x == x > 0 diff --git a/src/algebra/solvefor.spad.pamphlet b/src/algebra/solvefor.spad.pamphlet index faf51c7d..b82f1f35 100644 --- a/src/algebra/solvefor.spad.pamphlet +++ b/src/algebra/solvefor.spad.pamphlet @@ -135,7 +135,7 @@ PolynomialSolveByFormulas(UP, F): PSFcat == PSFdef where error "Leading coefficient must not be 0." needChar0(): Boolean == - characteristic()$F = 0 => true + characteristic$F = 0 => true error "Formula defined only for fields of characteristic 0." linear u == diff --git a/src/algebra/strap/CHAR.lsp b/src/algebra/strap/CHAR.lsp index f16acad3..6e24716c 100644 --- a/src/algebra/strap/CHAR.lsp +++ b/src/algebra/strap/CHAR.lsp @@ -100,8 +100,8 @@ (RETURN (CODE-CHAR (PROG1 (LETT #0# (- |n| 1) |CHAR;index;Pi$;4|) - (|check-subtype| (COND ((< #0# 0) 'NIL) ('T 'T)) - '(|NonNegativeInteger|) #0#)))))) + (|check-subtype| (NOT (< #0# 0)) '(|NonNegativeInteger|) + #0#)))))) (DEFUN |CHAR;lookup;$Pi;5| (|c| $) (PROG (#0=#:G1404) diff --git a/src/algebra/strap/DFLOAT.lsp b/src/algebra/strap/DFLOAT.lsp index f6af98ec..58577fe4 100644 --- a/src/algebra/strap/DFLOAT.lsp +++ b/src/algebra/strap/DFLOAT.lsp @@ -450,8 +450,7 @@ $) (|getShellEntry| $ 35))) |DFLOAT;bits;Pi;10|) - (|check-subtype| - (AND (COND ((< #0# 0) 'NIL) ('T 'T)) (< 0 #0#)) + (|check-subtype| (AND (NOT (< #0# 0)) (< 0 #0#)) '(|PositiveInteger|) #0#))))))) (DEFUN |DFLOAT;max;$;11| ($) @@ -641,8 +640,8 @@ (|DFLOAT;rationalApproximation;$2NniF;84| |x| (PROG1 (LETT #0# (- (FLOAT-DIGITS 0.0) 1) |DFLOAT;retract;$F;77|) - (|check-subtype| (COND ((< #0# 0) 'NIL) ('T 'T)) - '(|NonNegativeInteger|) #0#)) + (|check-subtype| (NOT (< #0# 0)) '(|NonNegativeInteger|) + #0#)) (FLOAT-RADIX 0.0) $)))) (DEFUN |DFLOAT;retractIfCan;$U;78| (|x| $) @@ -652,7 +651,7 @@ (|DFLOAT;rationalApproximation;$2NniF;84| |x| (PROG1 (LETT #0# (- (FLOAT-DIGITS 0.0) 1) |DFLOAT;retractIfCan;$U;78|) - (|check-subtype| (COND ((< #0# 0) 'NIL) ('T 'T)) + (|check-subtype| (NOT (< #0# 0)) '(|NonNegativeInteger|) #0#)) (FLOAT-RADIX 0.0) $))))) @@ -737,9 +736,7 @@ (LETT #0# (- |ex|) |DFLOAT;rationalApproximation;$2NniF;84|) (|check-subtype| - (COND - ((< #0# 0) 'NIL) - ('T 'T)) + (NOT (< #0# 0)) '(|NonNegativeInteger|) #0#))) |DFLOAT;rationalApproximation;$2NniF;84|) (EXIT @@ -834,9 +831,7 @@ (EXPT BASE (PROG1 |ex| (|check-subtype| - (COND - ((< |ex| 0) 'NIL) - ('T 'T)) + (NOT (< |ex| 0)) '(|NonNegativeInteger|) |ex|)))) (|getShellEntry| $ 142))))))) #1# (EXIT #1#))))) diff --git a/src/algebra/strap/FFIELDC-.lsp b/src/algebra/strap/FFIELDC-.lsp index f29249fc..c9d9c3e1 100644 --- a/src/algebra/strap/FFIELDC-.lsp +++ b/src/algebra/strap/FFIELDC-.lsp @@ -82,7 +82,10 @@ (|getShellEntry| $ 34)))))))) (DEFUN |FFIELDC-;charthRoot;2S;6| (|x| $) - (SPADCALL |x| (QUOTIENT2 2 0) (|getShellEntry| $ 43))) + (SPADCALL |x| + (QUOTIENT2 (SPADCALL (|getShellEntry| $ 40)) + (|spadConstant| $ 41)) + (|getShellEntry| $ 43))) (DEFUN |FFIELDC-;charthRoot;SU;7| (|x| $) (CONS 0 (SPADCALL |x| (|getShellEntry| $ 32)))) @@ -90,13 +93,13 @@ (DEFUN |FFIELDC-;createPrimitiveElement;S;8| ($) (PROG (|sm1| |start| |i| |e| |found|) (RETURN - (SEQ (LETT |sm1| (- (SPADCALL (|getShellEntry| $ 46)) 1) + (SEQ (LETT |sm1| (- (SPADCALL (|getShellEntry| $ 40)) 1) |FFIELDC-;createPrimitiveElement;S;8|) (LETT |start| (COND - ((SPADCALL (SPADCALL (|getShellEntry| $ 49)) - (CONS 1 "polynomial") (|getShellEntry| $ 50)) - 0) + ((SPADCALL (SPADCALL (|getShellEntry| $ 48)) + (CONS 1 "polynomial") (|getShellEntry| $ 49)) + (|spadConstant| $ 41)) ('T 1)) |FFIELDC-;createPrimitiveElement;S;8|) (LETT |found| 'NIL |FFIELDC-;createPrimitiveElement;S;8|) @@ -107,9 +110,7 @@ (SPADCALL (PROG1 |i| (|check-subtype| - (AND - (COND ((< |i| 0) 'NIL) ('T 'T)) - (< 0 |i|)) + (AND (NOT (< |i| 0)) (< 0 |i|)) '(|PositiveInteger|) |i|)) (|getShellEntry| $ 14)) |FFIELDC-;createPrimitiveElement;S;8|) @@ -129,9 +130,10 @@ (SEQ (COND ((SPADCALL |a| (|getShellEntry| $ 16)) 'NIL) ('T - (SEQ (LETT |explist| (SPADCALL (|getShellEntry| $ 57)) + (SEQ (LETT |explist| (SPADCALL (|getShellEntry| $ 56)) + |FFIELDC-;primitive?;SB;9|) + (LETT |q| (- (SPADCALL (|getShellEntry| $ 40)) 1) |FFIELDC-;primitive?;SB;9|) - (LETT |q| (- 2 1) |FFIELDC-;primitive?;SB;9|) (LETT |equalone| 'NIL |FFIELDC-;primitive?;SB;9|) (SEQ (LETT |exp| NIL |FFIELDC-;primitive?;SB;9|) (LETT #0# |explist| |FFIELDC-;primitive?;SB;9|) @@ -148,8 +150,8 @@ (SPADCALL (SPADCALL |a| (QUOTIENT2 |q| (QCAR |exp|)) - (|getShellEntry| $ 59)) - (|getShellEntry| $ 60)) + (|getShellEntry| $ 58)) + (|getShellEntry| $ 59)) |FFIELDC-;primitive?;SB;9|))) (LETT #0# (CDR #0#) |FFIELDC-;primitive?;SB;9|) (GO G190) G191 (EXIT NIL)) @@ -161,12 +163,12 @@ (RETURN (SEQ (COND ((SPADCALL |e| (|spadConstant| $ 7) - (|getShellEntry| $ 64)) + (|getShellEntry| $ 63)) (|error| "order(0) is not defined ")) ('T - (SEQ (LETT |ord| (- 2 1) |FFIELDC-;order;SPi;10|) - (LETT |a| 0 |FFIELDC-;order;SPi;10|) - (LETT |lof| (SPADCALL (|getShellEntry| $ 57)) + (SEQ (LETT |ord| (- (SPADCALL (|getShellEntry| $ 40)) 1) + |FFIELDC-;order;SPi;10|) + (LETT |lof| (SPADCALL (|getShellEntry| $ 56)) |FFIELDC-;order;SPi;10|) (SEQ (LETT |rec| NIL |FFIELDC-;order;SPi;10|) (LETT #0# |lof| |FFIELDC-;order;SPi;10|) G190 @@ -185,8 +187,8 @@ (LETT |goon| (SPADCALL (SPADCALL |e| |a| - (|getShellEntry| $ 59)) - (|getShellEntry| $ 60)) + (|getShellEntry| $ 58)) + (|getShellEntry| $ 59)) |FFIELDC-;order;SPi;10|) (SEQ (LETT |j| 0 |FFIELDC-;order;SPi;10|) (LETT #1# (- (QCDR |rec|) 2) @@ -206,8 +208,8 @@ (LETT |goon| (SPADCALL (SPADCALL |e| |a| - (|getShellEntry| $ 59)) - (|getShellEntry| $ 60)) + (|getShellEntry| $ 58)) + (|getShellEntry| $ 59)) |FFIELDC-;order;SPi;10|))) (LETT |j| (QSADD1 |j|) |FFIELDC-;order;SPi;10|) @@ -229,20 +231,24 @@ ((SPADCALL |b| (|getShellEntry| $ 16)) (|error| "discreteLog: logarithm of zero")) ('T - (SEQ (LETT |faclist| (SPADCALL (|getShellEntry| $ 57)) + (SEQ (LETT |faclist| (SPADCALL (|getShellEntry| $ 56)) |FFIELDC-;discreteLog;SNni;11|) (LETT |a| |b| |FFIELDC-;discreteLog;SNni;11|) - (LETT |gen| (SPADCALL (|getShellEntry| $ 68)) + (LETT |gen| (SPADCALL (|getShellEntry| $ 67)) |FFIELDC-;discreteLog;SNni;11|) (EXIT (COND - ((SPADCALL |b| |gen| (|getShellEntry| $ 64)) + ((SPADCALL |b| |gen| (|getShellEntry| $ 63)) 1) ('T (SEQ (LETT |disclog| 0 |FFIELDC-;discreteLog;SNni;11|) (LETT |mult| 1 |FFIELDC-;discreteLog;SNni;11|) - (LETT |groupord| (- 2 1) + (LETT |groupord| + (- + (SPADCALL + (|getShellEntry| $ 40)) + 1) |FFIELDC-;discreteLog;SNni;11|) (LETT |exp| |groupord| |FFIELDC-;discreteLog;SNni;11|) @@ -277,15 +283,15 @@ |FFIELDC-;discreteLog;SNni;11|) (LETT |exptable| (SPADCALL |fac| - (|getShellEntry| $ 70)) + (|getShellEntry| $ 69)) |FFIELDC-;discreteLog;SNni;11|) (LETT |n| (SPADCALL |exptable| - (|getShellEntry| $ 71)) + (|getShellEntry| $ 70)) |FFIELDC-;discreteLog;SNni;11|) (LETT |c| (SPADCALL |a| |exp| - (|getShellEntry| $ 59)) + (|getShellEntry| $ 58)) |FFIELDC-;discreteLog;SNni;11|) (LETT |end| (QUOTIENT2 (- |fac| 1) |n|) @@ -309,7 +315,7 @@ (SPADCALL |c| (|getShellEntry| $ 11)) |exptable| - (|getShellEntry| $ 74)) + (|getShellEntry| $ 73)) |FFIELDC-;discreteLog;SNni;11|) (EXIT (COND @@ -333,9 +339,9 @@ |groupord| |fac|) (- |n|)) (|getShellEntry| $ - 59)) + 58)) (|getShellEntry| $ - 80)) + 79)) |FFIELDC-;discreteLog;SNni;11|))))) (LETT |i| (QSADD1 |i|) |FFIELDC-;discreteLog;SNni;11|) @@ -356,9 +362,9 @@ (SPADCALL |gen| (- |disc1|) (|getShellEntry| $ - 59)) + 58)) (|getShellEntry| $ - 80)) + 79)) |FFIELDC-;discreteLog;SNni;11|)))) ('T (|error| @@ -379,14 +385,14 @@ (SEQ (EXIT (COND ((SPADCALL |b| (|getShellEntry| $ 16)) (SEQ (SPADCALL "discreteLog: logarithm of zero" - (|getShellEntry| $ 86)) + (|getShellEntry| $ 85)) (EXIT (CONS 1 "failed")))) ((SPADCALL |logbase| (|getShellEntry| $ 16)) (SEQ (SPADCALL "discreteLog: logarithm to base zero" - (|getShellEntry| $ 86)) + (|getShellEntry| $ 85)) (EXIT (CONS 1 "failed")))) - ((SPADCALL |b| |logbase| (|getShellEntry| $ 64)) + ((SPADCALL |b| |logbase| (|getShellEntry| $ 63)) (CONS 0 1)) ('T (COND @@ -399,14 +405,14 @@ (|getShellEntry| $ 19))))) (SEQ (SPADCALL "discreteLog: second argument not in cyclic group generated by first argument" - (|getShellEntry| $ 86)) + (|getShellEntry| $ 85)) (EXIT (CONS 1 "failed")))) ('T (SEQ (LETT |faclist| (SPADCALL (SPADCALL |groupord| - (|getShellEntry| $ 90)) - (|getShellEntry| $ 92)) + (|getShellEntry| $ 89)) + (|getShellEntry| $ 91)) |FFIELDC-;discreteLog;2SU;12|) (LETT |a| |b| |FFIELDC-;discreteLog;2SU;12|) @@ -433,7 +439,7 @@ (LETT |primroot| (SPADCALL |logbase| (QUOTIENT2 |groupord| |fac|) - (|getShellEntry| $ 59)) + (|getShellEntry| $ 58)) |FFIELDC-;discreteLog;2SU;12|) (EXIT (SEQ @@ -452,9 +458,9 @@ (LETT |rhoHelp| (SPADCALL |primroot| (SPADCALL |a| |exp| - (|getShellEntry| $ 59)) + (|getShellEntry| $ 58)) |fac| - (|getShellEntry| $ 94)) + (|getShellEntry| $ 93)) |FFIELDC-;discreteLog;2SU;12|) (EXIT (COND @@ -482,8 +488,8 @@ (SPADCALL |logbase| (- |rho|) (|getShellEntry| $ - 59)) - (|getShellEntry| $ 80)) + 58)) + (|getShellEntry| $ 79)) |FFIELDC-;discreteLog;2SU;12|))))))) (LETT |t| (QSADD1 |t|) |FFIELDC-;discreteLog;2SU;12|) @@ -495,25 +501,25 @@ #2# (EXIT #2#))))) (DEFUN |FFIELDC-;squareFreePolynomial| (|f| $) - (SPADCALL |f| (|getShellEntry| $ 99))) + (SPADCALL |f| (|getShellEntry| $ 98))) (DEFUN |FFIELDC-;factorPolynomial| (|f| $) - (SPADCALL |f| (|getShellEntry| $ 101))) + (SPADCALL |f| (|getShellEntry| $ 100))) (DEFUN |FFIELDC-;factorSquareFreePolynomial| (|f| $) (PROG (|flist| |u| #0=#:G1521 #1=#:G1510 #2=#:G1508 #3=#:G1509) (RETURN (SEQ (COND - ((SPADCALL |f| (|spadConstant| $ 102) - (|getShellEntry| $ 103)) - (|spadConstant| $ 104)) + ((SPADCALL |f| (|spadConstant| $ 101) + (|getShellEntry| $ 102)) + (|spadConstant| $ 103)) ('T (SEQ (LETT |flist| - (SPADCALL |f| 'T (|getShellEntry| $ 108)) + (SPADCALL |f| 'T (|getShellEntry| $ 107)) |FFIELDC-;factorSquareFreePolynomial|) (EXIT (SPADCALL (SPADCALL (QCAR |flist|) - (|getShellEntry| $ 109)) + (|getShellEntry| $ 108)) (PROGN (LETT #3# NIL |FFIELDC-;factorSquareFreePolynomial|) @@ -535,13 +541,13 @@ (LETT #1# (SPADCALL (QCAR |u|) (QCDR |u|) - (|getShellEntry| $ 110)) + (|getShellEntry| $ 109)) |FFIELDC-;factorSquareFreePolynomial|) (COND (#3# (LETT #2# (SPADCALL #2# #1# - (|getShellEntry| $ 111)) + (|getShellEntry| $ 110)) |FFIELDC-;factorSquareFreePolynomial|)) ('T (PROGN @@ -554,11 +560,11 @@ (GO G190) G191 (EXIT NIL)) (COND (#3# #2#) - ('T (|spadConstant| $ 112)))) - (|getShellEntry| $ 113)))))))))) + ('T (|spadConstant| $ 111)))) + (|getShellEntry| $ 112)))))))))) (DEFUN |FFIELDC-;gcdPolynomial;3Sup;16| (|f| |g| $) - (SPADCALL |f| |g| (|getShellEntry| $ 115))) + (SPADCALL |f| |g| (|getShellEntry| $ 114))) (DEFUN |FiniteFieldCategory&| (|#1|) (PROG (|dv$1| |dv$| $ |pv$|) @@ -566,7 +572,7 @@ (PROGN (LETT |dv$1| (|devaluate| |#1|) . #0=(|FiniteFieldCategory&|)) (LETT |dv$| (LIST '|FiniteFieldCategory&| |dv$1|) . #0#) - (LETT $ (|newShell| 118) . #0#) + (LETT $ (|newShell| 117) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -590,72 +596,71 @@ (|NonNegativeInteger|) (71 . |size|) (75 . |characteristic|) (79 . |quo|) (85 . **) |FFIELDC-;charthRoot;2S;6| |FFIELDC-;charthRoot;SU;7| - (91 . |size|) (95 . -) + (91 . -) (|Union| '"prime" '"polynomial" '"normal" '"cyclic") - (101 . |representationType|) (105 . =) (111 . |false|) - (115 . |not|) (120 . =) + (97 . |representationType|) (101 . =) (107 . |false|) + (111 . |not|) (116 . =) |FFIELDC-;createPrimitiveElement;S;8| (|Record| (|:| |factor| 20) (|:| |exponent| 20)) - (|List| 55) (126 . |factorsOfCyclicGroupSize|) - (130 . |quo|) (136 . **) (142 . |one?|) - |FFIELDC-;primitive?;SB;9| (147 . |Zero|) (151 . |Zero|) - (155 . =) (|SingleInteger|) (161 . |Zero|) - |FFIELDC-;order;SPi;10| (165 . |primitiveElement|) - (|Table| 10 39) (169 . |tableForDiscreteLogarithm|) - (174 . |#|) (179 . |One|) (|Union| 39 '"failed") - (183 . |search|) (189 . |true|) (193 . *) (199 . +) - (205 . *) (211 . -) (216 . *) (222 . +) + (|List| 54) (122 . |factorsOfCyclicGroupSize|) + (126 . |quo|) (132 . **) (138 . |one?|) + |FFIELDC-;primitive?;SB;9| (143 . |Zero|) (147 . |Zero|) + (151 . =) (|SingleInteger|) (157 . |Zero|) + |FFIELDC-;order;SPi;10| (161 . |primitiveElement|) + (|Table| 10 39) (165 . |tableForDiscreteLogarithm|) + (170 . |#|) (175 . |One|) (|Union| 39 '"failed") + (179 . |search|) (185 . |true|) (189 . *) (195 . +) + (201 . *) (207 . -) (212 . *) (218 . +) |FFIELDC-;discreteLog;SNni;11| (|Void|) (|String|) - (|OutputForm|) (228 . |messagePrint|) (233 . |rem|) - (239 . |zero?|) (|Factored| $) (244 . |factor|) - (|Factored| 20) (249 . |factors|) + (|OutputForm|) (224 . |messagePrint|) (229 . |rem|) + (235 . |zero?|) (|Factored| $) (240 . |factor|) + (|Factored| 20) (245 . |factors|) (|DiscreteLogarithmPackage| 6) - (254 . |shanksDiscLogAlgorithm|) + (250 . |shanksDiscLogAlgorithm|) |FFIELDC-;discreteLog;2SU;12| - (|SparseUnivariatePolynomial| 6) (|Factored| 96) - (|UnivariatePolynomialSquareFree| 6 96) - (261 . |squareFree|) (|DistinctDegreeFactorize| 6 96) - (266 . |factor|) (271 . |Zero|) (275 . =) (281 . |Zero|) - (|Record| (|:| |irr| 96) (|:| |pow| 20)) (|List| 105) - (|Record| (|:| |cont| 6) (|:| |factors| 106)) - (285 . |distdfact|) (291 . |coerce|) (296 . |primeFactor|) - (302 . *) (308 . |One|) (312 . *) (|EuclideanDomain&| 96) - (318 . |gcd|) (|SparseUnivariatePolynomial| $) + (|SparseUnivariatePolynomial| 6) (|Factored| 95) + (|UnivariatePolynomialSquareFree| 6 95) + (257 . |squareFree|) (|DistinctDegreeFactorize| 6 95) + (262 . |factor|) (267 . |Zero|) (271 . =) (277 . |Zero|) + (|Record| (|:| |irr| 95) (|:| |pow| 20)) (|List| 104) + (|Record| (|:| |cont| 6) (|:| |factors| 105)) + (281 . |distdfact|) (287 . |coerce|) (292 . |primeFactor|) + (298 . *) (304 . |One|) (308 . *) (|EuclideanDomain&| 95) + (314 . |gcd|) (|SparseUnivariatePolynomial| $) |FFIELDC-;gcdPolynomial;3Sup;16|) - '#(|primitive?| 324 |order| 329 |nextItem| 339 |init| 344 - |gcdPolynomial| 348 |discreteLog| 354 |differentiate| 365 - |createPrimitiveElement| 370 |conditionP| 374 |charthRoot| - 379) + '#(|primitive?| 320 |order| 325 |nextItem| 335 |init| 340 + |gcdPolynomial| 344 |discreteLog| 350 |differentiate| 361 + |createPrimitiveElement| 366 |conditionP| 370 |charthRoot| + 375) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 117 + (|makeByteWordVec2| 116 '(0 6 0 7 1 6 10 0 11 0 10 0 12 2 10 0 0 0 13 1 6 0 10 14 1 6 15 0 16 1 6 10 0 19 1 21 0 20 22 1 26 25 0 27 1 25 15 0 28 1 25 24 0 29 2 24 15 30 0 31 - 1 6 0 0 32 2 24 0 33 0 34 0 15 39 40 - 0 20 39 41 2 39 0 0 0 42 2 6 0 0 39 - 43 0 6 39 46 2 20 0 0 0 47 0 6 48 49 - 2 48 15 0 0 50 0 15 0 51 1 15 0 0 52 - 2 10 15 0 0 53 0 6 56 57 2 20 0 0 0 - 58 2 6 0 0 20 59 1 6 15 0 60 0 39 0 - 62 0 20 0 63 2 6 15 0 0 64 0 65 0 66 - 0 6 0 68 1 6 69 20 70 1 69 39 0 71 0 - 39 0 72 2 69 73 10 0 74 0 15 0 75 2 - 39 0 39 0 76 2 39 0 0 0 77 2 20 0 20 - 0 78 1 20 0 0 79 2 6 0 0 0 80 2 20 0 - 0 0 81 1 85 83 84 86 2 39 0 0 0 87 1 - 39 15 0 88 1 20 89 0 90 1 91 56 0 92 - 3 93 73 6 6 39 94 1 98 97 96 99 1 100 - 97 96 101 0 96 0 102 2 96 15 0 0 103 - 0 97 0 104 2 100 107 96 15 108 1 96 0 - 6 109 2 97 0 96 20 110 2 97 0 0 0 111 - 0 97 0 112 2 97 0 96 0 113 2 114 0 0 - 0 115 1 0 15 0 61 1 0 10 0 67 1 0 21 - 0 23 1 0 17 0 18 0 0 0 9 2 0 116 116 - 116 117 1 0 39 0 82 2 0 73 0 0 95 1 0 - 0 0 8 0 0 0 54 1 0 36 37 38 1 0 0 0 - 44 1 0 17 0 45))))) + 1 6 0 0 32 2 24 0 33 0 34 0 6 39 40 0 + 6 39 41 2 39 0 0 0 42 2 6 0 0 39 43 2 + 20 0 0 0 46 0 6 47 48 2 47 15 0 0 49 + 0 15 0 50 1 15 0 0 51 2 10 15 0 0 52 + 0 6 55 56 2 20 0 0 0 57 2 6 0 0 20 58 + 1 6 15 0 59 0 39 0 61 0 20 0 62 2 6 + 15 0 0 63 0 64 0 65 0 6 0 67 1 6 68 + 20 69 1 68 39 0 70 0 39 0 71 2 68 72 + 10 0 73 0 15 0 74 2 39 0 39 0 75 2 39 + 0 0 0 76 2 20 0 20 0 77 1 20 0 0 78 2 + 6 0 0 0 79 2 20 0 0 0 80 1 84 82 83 + 85 2 39 0 0 0 86 1 39 15 0 87 1 20 88 + 0 89 1 90 55 0 91 3 92 72 6 6 39 93 1 + 97 96 95 98 1 99 96 95 100 0 95 0 101 + 2 95 15 0 0 102 0 96 0 103 2 99 106 + 95 15 107 1 95 0 6 108 2 96 0 95 20 + 109 2 96 0 0 0 110 0 96 0 111 2 96 0 + 95 0 112 2 113 0 0 0 114 1 0 15 0 60 + 1 0 10 0 66 1 0 21 0 23 1 0 17 0 18 0 + 0 0 9 2 0 115 115 115 116 1 0 39 0 81 + 2 0 72 0 0 94 1 0 0 0 8 0 0 0 53 1 0 + 36 37 38 1 0 0 0 44 1 0 17 0 45))))) '|lookupComplete|)) diff --git a/src/algebra/strap/FPS-.lsp b/src/algebra/strap/FPS-.lsp index c85e10be..20b4f76e 100644 --- a/src/algebra/strap/FPS-.lsp +++ b/src/algebra/strap/FPS-.lsp @@ -22,8 +22,7 @@ (|getShellEntry| $ 16)) 13301)) |FPS-;digits;Pi;2|) - (|check-subtype| - (AND (COND ((< #0# 0) 'NIL) ('T 'T)) (< 0 #0#)) + (|check-subtype| (AND (NOT (< #0# 0)) (< 0 #0#)) '(|PositiveInteger|) #0#))))) (DEFUN |FloatingPointSystem&| (|#1|) diff --git a/src/algebra/strap/ILIST.lsp b/src/algebra/strap/ILIST.lsp index 5f67bbd8..ee920771 100644 --- a/src/algebra/strap/ILIST.lsp +++ b/src/algebra/strap/ILIST.lsp @@ -437,8 +437,7 @@ (|ILIST;rest;$Nni$;19| |p| (PROG1 (LETT #0# (- |n| 1) |ILIST;split!;$I$;29|) - (|check-subtype| - (COND ((< #0# 0) 'NIL) ('T 'T)) + (|check-subtype| (NOT (< #0# 0)) '(|NonNegativeInteger|) #0#)) $) |ILIST;split!;$I$;29|) @@ -460,8 +459,7 @@ (SEQ (LETT |l| (PROG1 (LETT #0# (QUOTIENT2 |n| 2) |ILIST;mergeSort|) - (|check-subtype| - (COND ((< #0# 0) 'NIL) ('T 'T)) + (|check-subtype| (NOT (< #0# 0)) '(|NonNegativeInteger|) #0#)) |ILIST;mergeSort|) (LETT |q| (|ILIST;split!;$I$;29| |p| |l| $) diff --git a/src/algebra/strap/INS-.lsp b/src/algebra/strap/INS-.lsp index ff98f1df..20c9737a 100644 --- a/src/algebra/strap/INS-.lsp +++ b/src/algebra/strap/INS-.lsp @@ -128,13 +128,13 @@ ((SPADCALL |x| (|spadConstant| $ 10) (|getShellEntry| $ 16)) (PROG1 (LETT #0# (- (SPADCALL |x| (|getShellEntry| $ 29))) |INS-;euclideanSize;SNni;9|) - (|check-subtype| (COND ((< #0# 0) 'NIL) ('T 'T)) - '(|NonNegativeInteger|) #0#))) + (|check-subtype| (NOT (< #0# 0)) '(|NonNegativeInteger|) + #0#))) ('T (PROG1 (LETT #1# (SPADCALL |x| (|getShellEntry| $ 29)) |INS-;euclideanSize;SNni;9|) - (|check-subtype| (COND ((< #1# 0) 'NIL) ('T 'T)) - '(|NonNegativeInteger|) #1#))))))) + (|check-subtype| (NOT (< #1# 0)) '(|NonNegativeInteger|) + #1#))))))) (DEFUN |INS-;convert;SF;10| (|x| $) (SPADCALL (SPADCALL |x| (|getShellEntry| $ 29)) diff --git a/src/algebra/strap/ISTRING.lsp b/src/algebra/strap/ISTRING.lsp index 5698408d..f0cba6fe 100644 --- a/src/algebra/strap/ISTRING.lsp +++ b/src/algebra/strap/ISTRING.lsp @@ -206,7 +206,7 @@ (MAKE-FULL-CVEC (PROG1 (LETT #0# (+ (- |m| (+ (- |h| |l|) 1)) |n|) |ISTRING;replace;$Us2$;15|) - (|check-subtype| (COND ((< #0# 0) 'NIL) ('T 'T)) + (|check-subtype| (NOT (< #0# 0)) '(|NonNegativeInteger|) #0#)) (SPADCALL (|getShellEntry| $ 52))) |ISTRING;replace;$Us2$;15|) @@ -750,8 +750,7 @@ |ISTRING;match?;2$CB;34|) $) |ISTRING;match?;2$CB;34|) - (|check-subtype| - (COND ((< #0# 0) 'NIL) ('T 'T)) + (|check-subtype| (NOT (< #0# 0)) '(|NonNegativeInteger|) #0#)) |ISTRING;match?;2$CB;34|) (EXIT (COND @@ -781,10 +780,7 @@ |dontcare| |pattern| (+ |p| 1) $) |ISTRING;match?;2$CB;34|) - (|check-subtype| - (COND - ((< #1# 0) 'NIL) - ('T 'T)) + (|check-subtype| (NOT (< #1# 0)) '(|NonNegativeInteger|) #1#)) |ISTRING;match?;2$CB;34|) (SEQ G190 @@ -807,9 +803,7 @@ |s| |target| |i| $) |ISTRING;match?;2$CB;34|) (|check-subtype| - (COND - ((< #2# 0) 'NIL) - ('T 'T)) + (NOT (< #2# 0)) '(|NonNegativeInteger|) #2#)) |ISTRING;match?;2$CB;34|) (EXIT @@ -835,9 +829,7 @@ (+ |q| 1) $) |ISTRING;match?;2$CB;34|) (|check-subtype| - (COND - ((< #4# 0) 'NIL) - ('T 'T)) + (NOT (< #4# 0)) '(|NonNegativeInteger|) #4#)) |ISTRING;match?;2$CB;34|))))))) diff --git a/src/algebra/strap/LSAGG-.lsp b/src/algebra/strap/LSAGG-.lsp index 09fe53fb..72f15b22 100644 --- a/src/algebra/strap/LSAGG-.lsp +++ b/src/algebra/strap/LSAGG-.lsp @@ -252,8 +252,7 @@ (PROG1 (LETT #0# (- (- |i| 1) |m|) |LSAGG-;insert!;SAIA;7|) - (|check-subtype| - (COND ((< #0# 0) 'NIL) ('T 'T)) + (|check-subtype| (NOT (< #0# 0)) '(|NonNegativeInteger|) #0#)) (|getShellEntry| $ 39)) |LSAGG-;insert!;SAIA;7|) @@ -280,8 +279,7 @@ (PROG1 (LETT #0# (- (- |i| 1) |m|) |LSAGG-;insert!;2AIA;8|) - (|check-subtype| - (COND ((< #0# 0) 'NIL) ('T 'T)) + (|check-subtype| (NOT (< #0# 0)) '(|NonNegativeInteger|) #0#)) (|getShellEntry| $ 39)) |LSAGG-;insert!;2AIA;8|) @@ -360,8 +358,7 @@ (PROG1 (LETT #0# (- (- |i| 1) |m|) |LSAGG-;delete!;AIA;10|) - (|check-subtype| - (COND ((< #0# 0) 'NIL) ('T 'T)) + (|check-subtype| (NOT (< #0# 0)) '(|NonNegativeInteger|) #0#)) (|getShellEntry| $ 39)) |LSAGG-;delete!;AIA;10|) @@ -395,9 +392,7 @@ (LETT #0# (- (+ |h| 1) |m|) |LSAGG-;delete!;AUsA;11|) (|check-subtype| - (COND - ((< #0# 0) 'NIL) - ('T 'T)) + (NOT (< #0# 0)) '(|NonNegativeInteger|) #0#)) (|getShellEntry| $ 39))) ('T @@ -407,9 +402,7 @@ (LETT #1# (- (- |l| 1) |m|) |LSAGG-;delete!;AUsA;11|) (|check-subtype| - (COND - ((< #1# 0) 'NIL) - ('T 'T)) + (NOT (< #1# 0)) '(|NonNegativeInteger|) #1#)) (|getShellEntry| $ 39)) @@ -420,9 +413,7 @@ (LETT #2# (+ (- |h| |l|) 2) |LSAGG-;delete!;AUsA;11|) (|check-subtype| - (COND - ((< #2# 0) 'NIL) - ('T 'T)) + (NOT (< #2# 0)) '(|NonNegativeInteger|) #2#)) (|getShellEntry| $ 39)) @@ -490,8 +481,7 @@ (SEQ (LETT |l| (PROG1 (LETT #0# (QUOTIENT2 |n| 2) |LSAGG-;mergeSort|) - (|check-subtype| - (COND ((< #0# 0) 'NIL) ('T 'T)) + (|check-subtype| (NOT (< #0# 0)) '(|NonNegativeInteger|) #0#)) |LSAGG-;mergeSort|) (LETT |q| @@ -700,8 +690,7 @@ (PROG1 (LETT #0# (- |s| |m|) |LSAGG-;copyInto!;2AIA;22|) - (|check-subtype| - (COND ((< #0# 0) 'NIL) ('T 'T)) + (|check-subtype| (NOT (< #0# 0)) '(|NonNegativeInteger|) #0#)) (|getShellEntry| $ 39)) |LSAGG-;copyInto!;2AIA;22|) @@ -745,8 +734,7 @@ (PROG1 (LETT #0# (- |s| |m|) |LSAGG-;position;SA2I;23|) - (|check-subtype| - (COND ((< #0# 0) 'NIL) ('T 'T)) + (|check-subtype| (NOT (< #0# 0)) '(|NonNegativeInteger|) #0#)) (|getShellEntry| $ 39)) |LSAGG-;position;SA2I;23|) diff --git a/src/algebra/strap/STAGG-.lsp b/src/algebra/strap/STAGG-.lsp index 53a1ca39..d461af4c 100644 --- a/src/algebra/strap/STAGG-.lsp +++ b/src/algebra/strap/STAGG-.lsp @@ -86,8 +86,7 @@ (LETT |x| (SPADCALL |x| (PROG1 |i| - (|check-subtype| - (COND ((< |i| 0) 'NIL) ('T 'T)) + (|check-subtype| (NOT (< |i| 0)) '(|NonNegativeInteger|) |i|)) (|getShellEntry| $ 28)) |STAGG-;elt;AIS;5|) @@ -108,8 +107,7 @@ (SPADCALL (SPADCALL |x| (PROG1 |l| - (|check-subtype| - (COND ((< |l| 0) 'NIL) ('T 'T)) + (|check-subtype| (NOT (< |l| 0)) '(|NonNegativeInteger|) |l|)) (|getShellEntry| $ 28)) (|getShellEntry| $ 33))) @@ -126,18 +124,14 @@ (SPADCALL |x| (PROG1 |l| (|check-subtype| - (COND - ((< |l| 0) 'NIL) - ('T 'T)) + (NOT (< |l| 0)) '(|NonNegativeInteger|) |l|)) (|getShellEntry| $ 28)) (PROG1 (LETT #0# (+ (- |h| |l|) 1) |STAGG-;elt;AUsA;6|) (|check-subtype| - (COND - ((< #0# 0) 'NIL) - ('T 'T)) + (NOT (< #0# 0)) '(|NonNegativeInteger|) #0#)) (|getShellEntry| $ 37))))))))))))) @@ -195,8 +189,7 @@ (LETT |x| (SPADCALL |x| (PROG1 |i| - (|check-subtype| - (COND ((< |i| 0) 'NIL) ('T 'T)) + (|check-subtype| (NOT (< |i| 0)) '(|NonNegativeInteger|) |i|)) (|getShellEntry| $ 28)) |STAGG-;setelt;AI2S;11|) @@ -231,9 +224,7 @@ (SPADCALL |x| (PROG1 |l| (|check-subtype| - (COND - ((< |l| 0) 'NIL) - ('T 'T)) + (NOT (< |l| 0)) '(|NonNegativeInteger|) |l|)) (|getShellEntry| $ 28)) @@ -244,9 +235,7 @@ (LETT #0# (+ (- |h| |l|) 1) |STAGG-;setelt;AUs2S;12|) (|check-subtype| - (COND - ((< #0# 0) 'NIL) - ('T 'T)) + (NOT (< #0# 0)) '(|NonNegativeInteger|) #0#)) (|getShellEntry| $ 28)) diff --git a/src/algebra/strap/URAGG-.lsp b/src/algebra/strap/URAGG-.lsp index 6679030e..5d4e9577 100644 --- a/src/algebra/strap/URAGG-.lsp +++ b/src/algebra/strap/URAGG-.lsp @@ -452,8 +452,7 @@ (SPADCALL |x| (PROG1 (LETT #0# (- |m| |n|) |URAGG-;last;ANniA;22|) - (|check-subtype| - (COND ((< #0# 0) 'NIL) ('T 'T)) + (|check-subtype| (NOT (< #0# 0)) '(|NonNegativeInteger|) #0#)) (|getShellEntry| $ 62)) (|getShellEntry| $ 63))))))))) @@ -590,8 +589,7 @@ (SPADCALL |p| (PROG1 (LETT #0# (- |n| 1) |URAGG-;split!;AIA;32|) - (|check-subtype| - (COND ((< #0# 0) 'NIL) ('T 'T)) + (|check-subtype| (NOT (< #0# 0)) '(|NonNegativeInteger|) #0#)) (|getShellEntry| $ 62)) |URAGG-;split!;AIA;32|) diff --git a/src/algebra/sups.spad.pamphlet b/src/algebra/sups.spad.pamphlet index 100d251e..80d3a02e 100644 --- a/src/algebra/sups.spad.pamphlet +++ b/src/algebra/sups.spad.pamphlet @@ -234,7 +234,7 @@ InnerSparseUnivariatePowerSeries(Coef): Exports == Implementation where --% values - characteristic() == characteristic()$Coef + characteristic == characteristic$Coef 0 == monomial(0,0) 1 == monomial(1,0) diff --git a/src/algebra/taylor.spad.pamphlet b/src/algebra/taylor.spad.pamphlet index 2005597a..a54ec020 100644 --- a/src/algebra/taylor.spad.pamphlet +++ b/src/algebra/taylor.spad.pamphlet @@ -126,7 +126,7 @@ InnerTaylorSeries(Coef): Exports == Implementation where n = 0 => 1 expt(x,n :: PositiveInteger)$RepeatedSquaring(%) - characteristic() == characteristic()$Coef + characteristic == characteristic$Coef pole? x == false iOrder: (ST,NNI,NNI) -> NNI diff --git a/src/algebra/vector.spad.pamphlet b/src/algebra/vector.spad.pamphlet index 1696e4e4..7342a113 100644 --- a/src/algebra/vector.spad.pamphlet +++ b/src/algebra/vector.spad.pamphlet @@ -274,7 +274,7 @@ DirectProductCategory(dim:NonNegativeInteger, R:Type): Category == equation2R: Vector % -> Matrix R coerce(n:Integer):% == n::R::% - characteristic() == characteristic()$R + characteristic == characteristic$R differentiate(z:%, d:R -> R) == map(d, z) equation2R v == diff --git a/src/algebra/xpoly.spad.pamphlet b/src/algebra/xpoly.spad.pamphlet index c80e3e53..ef221d08 100644 --- a/src/algebra/xpoly.spad.pamphlet +++ b/src/algebra/xpoly.spad.pamphlet @@ -1063,7 +1063,7 @@ XRecursivePolynomial(VarSet:OrderedSet,R:Ring): Xcat == Xdef where p case R => 0$% [0$R,p.reg]$VPOLY - characteristic == characteristic()$R + characteristic == characteristic$R recip p == p case R => recip(p::R) "failed" diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index d6e6a459..af67ff62 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2282756 . 3452534663) +(2282756 . 3452610475) (-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 -2371) +(-32 R -2308) ((|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 -2371 UP UPUP -3078) +(-40 -2308 UP UPUP -2130) ((|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))) (-2822 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2822 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2822 (-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)))) (-2822 (|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 -2371) +((|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) ((|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|))))) @@ -111,7 +111,7 @@ NIL (-45 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) ((-4407 . T) (-4408 . T)) -((-2822 (-12 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1982) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3740) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1982) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3740) (|devaluate| |#2|))))))) (-2822 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-2822 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (-2822 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (-2822 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1982) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3740) (|devaluate| |#2|))))))) +((-2807 (-12 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1901) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3813) (|devaluate| |#2|)))))) (-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 (-846))) (|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|)))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (-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|))))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -2371) +(-54 |Base| R -2308) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -167,64 +167,64 @@ NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) ((-4408 . T) (-4407 . T)) -((-2822 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2822 (-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)))) (-2822 (|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|))))) +((-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|))))) (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2822 (-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))))) -(-61 -2620) +((-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))))) +(-61 -2562) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -2620) +(-62 -2562) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-63 -2620) +(-63 -2562) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -2620) +(-64 -2562) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -2620) +(-65 -2562) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}"))) NIL NIL -(-66 -2620) +(-66 -2562) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-67 -2620) +(-67 -2562) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-68 -2620) +(-68 -2562) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-69 -2620) +(-69 -2562) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-70 -2620) +(-70 -2562) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-71 -2620) +(-71 -2562) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-72 -2620) +(-72 -2562) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-73 -2620) +(-73 -2562) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-74 -2620) +(-74 -2562) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -236,55 +236,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-77 -2620) +(-77 -2562) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-78 -2620) +(-78 -2562) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-79 -2620) +(-79 -2562) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -2620) +(-80 -2562) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -2620) +(-81 -2562) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}"))) NIL NIL -(-82 -2620) +(-82 -2562) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -2620) +(-83 -2562) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -2620) +(-84 -2562) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -2620) +(-85 -2562) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -2620) +(-86 -2562) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -2620) +(-87 -2562) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-88 -2620) +(-88 -2562) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-89 -2620) +(-89 -2562) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -295,7 +295,7 @@ NIL (-91 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,{}y,{}...,{}z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2822 (-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))))) +((-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))))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -343,7 +343,7 @@ NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}t1,{}f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t,{} ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2822 (-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))))) +((-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))))) (-104 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,{}q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,{}q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,{}q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL @@ -363,7 +363,7 @@ NIL (-108) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2822 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2822 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2807 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -388,7 +388,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|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 -2371 UP) +(-115 -2308 UP) ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) NIL NIL @@ -399,7 +399,7 @@ NIL (-117 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-905))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1018))) (|HasCategory| (-116 |#1|) (QUOTE (-816))) (-2822 (|HasCategory| (-116 |#1|) (QUOTE (-816))) (|HasCategory| (-116 |#1|) (QUOTE (-846)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-1145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-307))) (|HasCategory| (-116 |#1|) (QUOTE (-545))) (|HasCategory| (-116 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (-2822 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) +((|HasCategory| (-116 |#1|) (QUOTE (-905))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1018))) (|HasCategory| (-116 |#1|) (QUOTE (-816))) (-2807 (|HasCategory| (-116 |#1|) (QUOTE (-816))) (|HasCategory| (-116 |#1|) (QUOTE (-846)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-1145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-307))) (|HasCategory| (-116 |#1|) (QUOTE (-545))) (|HasCategory| (-116 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) (-118 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -415,7 +415,7 @@ NIL (-121 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,{}b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,{}b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2822 (-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))))) +((-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))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL @@ -435,15 +435,15 @@ NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2822 (-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))))) +((-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))))) (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,{}v,{}r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2822 (-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))))) +((-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))))) (-128) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,{}n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) ((-4408 . T) (-4407 . T)) -((-2822 (-12 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-2822 (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-129) (LIST (QUOTE -612) (QUOTE (-536)))) (-2822 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1094)))) (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) +((-2807 (-12 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-2807 (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-129) (LIST (QUOTE -612) (QUOTE (-536)))) (-2807 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1094)))) (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-129) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4409 "*") . T)) NIL -(-135 |minix| -3526 S T$) +(-135 |minix| -3598 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-136 |minix| -3526 R) +(-136 |minix| -3598 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 @@ -495,7 +495,7 @@ NIL (-141) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) ((-4407 . T) (-4397 . T) (-4408 . T)) -((-2822 (-12 (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-2807 (-12 (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-142 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -520,7 +520,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4404 . T)) NIL -(-148 -2371 UP UPUP) +(-148 -2308 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 -2371) +(-158 R -2308) ((|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 @@ -594,7 +594,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-998))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasCategory| |#2| (QUOTE (-1054))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4403)) (|HasAttribute| |#2| (QUOTE -4406)) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556)))) (-166 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4400 -2822 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4403 |has| |#1| (-6 -4403)) (-4406 |has| |#1| (-6 -4406)) (-3581 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4400 -2807 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4403 |has| |#1| (-6 -4403)) (-4406 |has| |#1| (-6 -4406)) (-3654 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-167 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -606,8 +606,8 @@ NIL NIL (-169 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4400 -2822 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4403 |has| |#1| (-6 -4403)) (-4406 |has| |#1| (-6 -4406)) (-3581 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-2822 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-2822 (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-824)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-1018)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-1194)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| 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(|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-2822 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145)))) (-2822 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-349))))) +((-4400 -2807 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4403 |has| |#1| (-6 -4403)) (-4406 |has| |#1| (-6 -4406)) (-3654 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-2807 (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-824)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-1018)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-1194)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-905))))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-905)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-905))))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2807 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-556)))) (-2807 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-824))) (|HasCategory| |#1| (QUOTE (-1054))) (-12 (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasAttribute| |#1| (QUOTE -4403)) (|HasAttribute| |#1| (QUOTE -4406)) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-349))))) (-170 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -680,7 +680,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-188 R -2371) +(-188 R -2308) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -788,23 +788,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -2371 UP UPUP R) +(-215 -2308 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 -2371 FP) +(-216 -2308 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 (-217) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2822 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2822 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2807 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) (-218) ((|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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-219 R -2371) +(-219 R -2308) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -819,18 +819,18 @@ NIL (-222 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2822 (-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))))) +((-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))))) (-223 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,{}df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,{}u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) ((-4404 . T)) NIL -(-224 R -2371) +(-224 R -2308) ((|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 (-225) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-3572 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-3646 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-226) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}"))) @@ -839,7 +839,7 @@ NIL (-227 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,{}Y,{}Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,{}sy,{}sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2822 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4409 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-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| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4409 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-228 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL @@ -876,22 +876,22 @@ 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 -3526 R) +(-237 S -3598 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 -3526 R) +(-238 -3598 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 -3526 A B) +(-239 -3598 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 -3526 R) +(-240 -3598 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)) -((-2822 (-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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(|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -911,7 +911,7 @@ NIL (-245 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) ((-4408 . T) (-4407 . 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(|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL @@ -919,7 +919,7 @@ NIL (-247 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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T)) -((|HasCategory| |#2| (QUOTE (-905))) (-2822 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2822 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2822 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2822 (|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)))) (-2822 (|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)))) (-2822 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|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))))) (-248) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall|)) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall|) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 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(QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1045)))) (-2807 (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1045)))) (|HasCategory| |#3| (QUOTE (-722))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1170)))))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-2807 (|HasCategory| |#3| (QUOTE (-1045))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1094)))) (-2807 (|HasAttribute| |#3| (QUOTE -4404)) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1045)))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -637) (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."))) NIL @@ -987,7 +987,7 @@ NIL (-264 R S V) ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-2822 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2822 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2822 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2822 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#3| (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)))) (-2822 (|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 (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2822 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|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| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#3| (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 (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|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))))) (-265 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -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 -2371) +(-276 R -2308) ((|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 -2371) +(-277 R -2308) ((|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| -3774 -2291 |exactQuo|) +(-289 S R |Mod| -1408 -2063 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL @@ -1106,21 +1106,21 @@ NIL NIL (-294 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1982) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3740) (|devaluate| |#2|)))))) (-2822 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2822 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2822 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) +((-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))))) (-296) ((|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 -2371 S) +(-297 -2308 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 -2371) +(-298 E -2308) ((|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 -2371) +(-310 -2308) ((|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 @@ -1183,7 +1183,7 @@ NIL (-313 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,{}f(var))}."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1018))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (-2822 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-846)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -309) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -286) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-307))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-545))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-846))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))) (-2822 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))))) +((|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1018))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (-2807 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-846)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -309) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -286) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-307))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-545))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-846))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))) (-2807 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))))) (-314 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f,{} e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL @@ -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 -2822 (-2427 (|has| |#1| (-1045)) (|has| |#1| (-637 (-564)))) (-12 (|has| |#1| (-556)) (-2822 (-2427 (|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))) -((-2822 (|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))) (-2822 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2822 (|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)))) (-2822 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2822 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE 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(QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-2822 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2822 (-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 -2371) +((-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)) 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(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) ((|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))) (-2822 (|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))) (-2822 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2822 (|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 -2488) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2822 (-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 -1446) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3762) (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 -3697) (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 @@ -1239,12 +1239,12 @@ NIL (-327 S) ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) ((-4408 . T) (-4407 . T)) -((-2822 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2822 (-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)))) (-2822 (|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 -2371) +((-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) ((|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 -2371) +(-329 -2308) ((|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 -2371 UP UPUP R) +(-334 S -2308 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 -2371 UP UPUP R) +(-335 -2308 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 -2371 UP UPUP R) +(-336 -2308 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 @@ -1292,26 +1292,26 @@ NIL ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{} p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL NIL -(-341 S -2371 UP UPUP) +(-341 S -2308 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 -2371 UP UPUP) +(-342 -2308 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 (-343 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((-2822 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) +((-2807 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) (-344 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((-2822 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2807 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-345 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((-2822 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2807 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-346 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1328,31 +1328,31 @@ NIL ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL -(-350 R UP -2371) +(-350 R UP -2308) ((|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 (-351 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((-2822 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) +((-2807 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) (-352 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((-2822 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2807 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-353 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((-2822 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2807 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-354 |p| |n|) ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((-2822 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) +((-2807 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) (-355 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((-2822 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) -(-356 -2371 GF) +((-2807 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +(-356 -2308 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 @@ -1360,14 +1360,14 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,{}x**q,{}x**(q**2),{}...,{}x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,{}n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-358 -2371 FP FPP) +(-358 -2308 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 (-359 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((-2822 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2807 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-360 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL @@ -1446,7 +1446,7 @@ NIL NIL (-379) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4390 . T) (-4398 . T) (-3572 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4390 . T) (-4398 . T) (-3646 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-380 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf,{} eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,{}lv,{}eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,{}eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,{}eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,{}eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,{}eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -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 -2371 UP UPUP R) +(-392 -2308 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 -2620 |returnType| -2848 |symbols|) +(-398 -2562 |returnType| -2837 |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 -2371 UP) +(-399 -2308 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1546,7 +1546,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4390)) (|HasAttribute| |#1| (QUOTE -4398))) (-404) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-3572 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-3646 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-405 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,{}u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) @@ -1559,7 +1559,7 @@ NIL (-407 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) ((-4394 -12 (|has| |#1| (-6 -4405)) (|has| |#1| (-452)) (|has| |#1| (-6 -4394))) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2822 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-816))) (-2822 (|HasCategory| |#1| (QUOTE (-816))) (|HasCategory| |#1| (QUOTE (-846)))) (-2822 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (-2822 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (-2822 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (-2822 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-545))) (-12 (|HasAttribute| |#1| (QUOTE -4405)) (|HasAttribute| |#1| (QUOTE -4394)) (|HasCategory| |#1| (QUOTE (-452)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2822 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-816))) (-2807 (|HasCategory| |#1| (QUOTE (-816))) (|HasCategory| |#1| (QUOTE (-846)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-545))) (-12 (|HasAttribute| |#1| (QUOTE -4405)) (|HasAttribute| |#1| (QUOTE -4394)) (|HasCategory| |#1| (QUOTE (-452)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-408 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1580,11 +1580,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-413 R -2371 UP A) +(-413 R -2308 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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 -2371 UP A |ibasis|) +(-414 R -2308 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|)))) @@ -1603,7 +1603,7 @@ NIL (-418 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,{}n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,{}n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,{}n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,{}exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,{}listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) ((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -309) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1213))) (-2822 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1213)))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-452)))) +((|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -309) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1213))) (-2807 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1213)))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-452)))) (-419 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,{}v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,{}fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,{}2)} then \\spad{refine(u,{}factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,{}2) * primeFactor(5,{}2)}."))) NIL @@ -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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4407 . T) (-4397 . T) (-4408 . T)) NIL -(-426 R -2371) +(-426 R -2308) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1640,7 +1640,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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 -2371) +(-428 R -2308) ((|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 @@ -1650,17 +1650,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (-430 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4404 -2822 (|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 (|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 -2371) +(-431 R -2308) ((|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 -2371) +(-432 R -2308) ((|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 -2371) +(-433 R -2308) ((|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 -2371 UP) +(-435 R -2308 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 -2371) +(-443 R UP -2308) ((|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 @@ -1747,7 +1747,7 @@ NIL (-454 |vl| R E) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4409 "*") |has| |#2| (-172)) (-4400 |has| |#2| (-556)) (-4405 |has| |#2| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#2| (QUOTE (-905))) (-2822 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2822 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2822 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2822 (|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)))) (-2822 (|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)))) (-2822 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|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))))) (-455 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,{}lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,{}table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,{}prime,{}lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,{}lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,{}prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -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| -2371 R) +(-471 |lv| -2308 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 @@ -1827,11 +1827,11 @@ 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 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2822 (|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))) (-2822 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2822 (|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 -2488) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2822 (-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 -1446) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3762) (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 -3697) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-475 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1982) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3740) (|devaluate| |#2|)))))) (-2822 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2822 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-2822 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094)))) +((-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| |#1| (QUOTE (-846))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#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 -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094)))) (-476 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) ((-4408 . T) (-4407 . T)) @@ -1847,7 +1847,7 @@ NIL (-479 |Key| |Entry| |hashfn|) ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1982) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3740) (|devaluate| |#2|)))))) (-2822 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2822 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2822 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) +((-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))))) (-480) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens,{} maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens,{} leftCandidate,{} rightCandidate,{} left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,{}wt,{}rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,{}n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL @@ -1855,11 +1855,11 @@ NIL (-481 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4409 "*") |has| |#2| (-172)) (-4400 |has| |#2| (-556)) (-4405 |has| |#2| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . 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(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|))))) (-483) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|Identifier|))) "\\spad{headAst(f,{}[x1,{}..,{}xn])} constructs a function definition header."))) NIL @@ -1867,8 +1867,8 @@ NIL (-484 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2822 (-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 -2371 UP UPUP R) +((-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) ((|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 @@ -1879,7 +1879,7 @@ NIL (-487) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2822 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2822 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2807 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) (-488 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1904,7 +1904,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-494 -2371 UP |AlExt| |AlPol|) +(-494 -2308 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 @@ -1915,16 +1915,16 @@ NIL (-496 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4408 . T) (-4407 . T)) -((-2822 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2822 (-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)))) (-2822 (|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|))))) +((-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|))))) (-497 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2822 (-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))))) +((-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))))) (-498 K R UP) ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,{}lr,{}n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,{}q,{}n)} returns the list \\spad{[bas,{}bas^Frob,{}bas^(Frob^2),{}...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,{}n,{}m,{}j)} \\undocumented"))) NIL NIL -(-499 R UP -2371) +(-499 R UP -2308) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1944,7 +1944,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-504 -2371 |Expon| |VarSet| |DPoly|) +(-504 -2308 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-1170))))) @@ -1995,7 +1995,7 @@ NIL (-516 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,{}n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) ((-4408 . T) (-4407 . T)) -((-2822 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2822 (-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)))) (-2822 (|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|))))) +((-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|))))) (-517) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL @@ -2003,15 +2003,15 @@ NIL (-518 |p| |n|) ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((-2822 (|HasCategory| (-581 |#1|) (QUOTE (-145))) (|HasCategory| (-581 |#1|) (QUOTE (-368)))) (|HasCategory| (-581 |#1|) (QUOTE (-147))) (|HasCategory| (-581 |#1|) (QUOTE (-368))) (|HasCategory| (-581 |#1|) (QUOTE (-145)))) +((-2807 (|HasCategory| (-581 |#1|) (QUOTE (-145))) (|HasCategory| (-581 |#1|) (QUOTE (-368)))) (|HasCategory| (-581 |#1|) (QUOTE (-147))) (|HasCategory| (-581 |#1|) (QUOTE (-368))) (|HasCategory| (-581 |#1|) (QUOTE (-145)))) (-519 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2822 (-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))))) +((-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))))) (-520 S |mn|) ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,{}mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) ((-4408 . T) (-4407 . T)) -((-2822 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2822 (-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)))) (-2822 (|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|))))) +((-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|))))) (-521 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL @@ -2023,7 +2023,7 @@ NIL (-523 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2822 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4409 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-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| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4409 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-524) ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) NIL @@ -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 -2371 |Par|) +(-532 K -2308 |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 -2371 |Par|) +(-538 K -2308 |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 @@ -2131,12 +2131,12 @@ NIL (-550 |Key| |Entry| |addDom|) ((|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 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1982) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3740) (|devaluate| |#2|)))))) (-2822 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2822 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2822 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) -(-551 R -2371) +((-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) ((|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 -2371 UP UPUP R) +(-552 R0 -2308 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 @@ -2146,7 +2146,7 @@ NIL NIL (-554 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,{}f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,{}sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,{}sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-3572 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-3646 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-555 S) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) @@ -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 -2371) +(-557 R -2308) ((|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 -2371 L) +(-560 R -2308 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 -2371 UP UPUP R) +(-562 -2308 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 -2371 UP) +(-563 -2308 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 -2371 L) +(-566 R -2308 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 -2371) +(-567 R -2308) ((|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 -2371 UP) +(-568 -2308 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 @@ -2208,27 +2208,27 @@ NIL ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-570 -2371) +(-570 -2308) ((|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 (-571 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) -((-3572 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-3646 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-572) ((|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 -2371) +(-573 R -2308) ((|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 -2371 UP) +(-574 -2308 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 -2371) +(-575 R -2308) ((|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 -2371) +(-583 R -2308) ((|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 -2371) +(-584 E -2308) ((|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 -2371) +(-585 -2308) ((|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))))) @@ -2299,7 +2299,7 @@ NIL (-592 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) ((-4408 . T) (-4407 . T)) -((-2822 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-2822 (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (-2822 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-2807 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-2807 (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (-2807 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-593 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n),{} n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n),{} n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL @@ -2307,7 +2307,7 @@ NIL (-594 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,{}r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,{}r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,{}refer,{}var,{}cen,{}r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,{}g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,{}g,{}taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,{}f)} returns the series \\spad{sum(fn(n) * an * x^n,{}n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,{}n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,{}str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) (((-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))) (-2822 (|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 (-564)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|)))) (|HasCategory| (-564) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2488) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564)))))) +((|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 (-564)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|)))) (|HasCategory| (-564) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2423) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564)))))) (-595 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,{}n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) ((-4402 |has| |#1| (-556)) (-4401 |has| |#1| (-556)) ((-4409 "*") |has| |#1| (-556)) (-4400 |has| |#1| (-556)) (-4404 . T)) @@ -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 -2371 FG) +(-598 R -2308 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 @@ -2331,7 +2331,7 @@ NIL (-600 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4408 . T) (-4407 . T)) -((-2822 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2822 (-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)))) (-2822 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-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| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-601 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2350,12 +2350,12 @@ NIL NIL (-605 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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 -2822 (-2427 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4402 . T) (-4401 . T)) -((-2822 (|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|)))) (-2822 (-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|)))) +((-4404 -2807 (-2359 (|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."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1982) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3740) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-846))) (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 |#1|)) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1901) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3813) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-846))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (LIST (QUOTE -611) (QUOTE (-858))))) (-607 S |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}."))) NIL @@ -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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-613 -2371 UP) +(-613 -2308 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 -2371) +(-620 R -2308) ((|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 @@ -2440,18 +2440,18 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-628 R -2371) +(-628 R -2308) ((|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| -2371) +(-629 |lv| -2308) ((|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 (-630) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) ((-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1982) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3740) (QUOTE (-52))))))) (-2822 (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2822 (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1152) (QUOTE (-846))) (-2822 (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 (-52))) (QUOTE (-1094)))) +((-12 (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1901) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3813) (QUOTE (-52))))))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1152) (QUOTE (-846))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 (-52))) (QUOTE (-1094)))) (-631 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2462,8 +2462,8 @@ NIL NIL (-633 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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 -2822 (-2427 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4402 . T) (-4401 . T)) -((-2822 (|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|)))) (-2822 (-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|)))) +((-4404 -2807 (-2359 (|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))}."))) NIL @@ -2475,7 +2475,7 @@ NIL (-636 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,{}...,{}vn])} returns \\spad{[c1,{}...,{}cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-2416 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) +((-2351 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) (-637 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A,{} v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4404 . T)) @@ -2495,7 +2495,7 @@ NIL (-641 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list."))) ((-4408 . T) (-4407 . T)) -((-2822 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2822 (-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)))) (-2822 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-824))) (|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|))))) +((-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| |#1| (QUOTE (-824))) (|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|))))) (-642 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2503,7 +2503,7 @@ NIL (-643 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2822 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-644 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -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 -2371 L) +(-648 R -2308 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 -2371 UP) +(-653 -2308 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 -1468) +(-654 A -3865) ((|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 -2371) +(-663 -2308) ((|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 -2371 |Row| |Col| M) +(-664 -2308 |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 @@ -2595,7 +2595,7 @@ NIL (-666 |n| R) ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,{}R) b - b *\\$SQMATRIX(n,{}R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) ((-4404 . T) (-4407 . T) (-4401 . T) (-4402 . T)) -((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2822 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|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)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556))) (-2822 (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2807 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|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)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556))) (-2807 (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-667) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL @@ -2615,7 +2615,7 @@ NIL (-671 R) ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,{}x,{}y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,{}i,{}j,{}k,{}s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,{}i,{}j,{}k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,{}y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,{}j,{}k)} create a matrix with all zero terms"))) NIL -((-2822 (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-2822 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2807 (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-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| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-672) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2671,7 +2671,7 @@ NIL (-685 R) ((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal."))) ((-4407 . T) (-4408 . T)) -((-2822 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-2822 (-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)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4409 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2807 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-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 -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4409 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-686 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,{}b,{}c,{}m,{}n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,{}a,{}b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,{}a,{}r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,{}r,{}a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,{}a,{}b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,{}a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,{}a,{}b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,{}a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -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 -2371 FLAF FLAS) +(-688 S -2308 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 @@ -2690,8 +2690,8 @@ NIL NIL (-690) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4400 . T) (-4405 |has| (-695) (-363)) (-4399 |has| (-695) (-363)) (-3581 . T) (-4406 |has| (-695) (-6 -4406)) (-4403 |has| (-695) (-6 -4403)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| (-695) (QUOTE (-147))) (|HasCategory| (-695) (QUOTE (-145))) (|HasCategory| (-695) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-368))) (|HasCategory| (-695) (QUOTE (-363))) (-2822 (|HasCategory| (-695) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-233))) (-2822 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (LIST (QUOTE -286) (QUOTE (-695)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -309) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-695) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (-2822 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-695) (QUOTE (-1018))) (|HasCategory| (-695) (QUOTE (-1194))) (-12 (|HasCategory| (-695) (QUOTE (-998))) (|HasCategory| (-695) (QUOTE (-1194)))) (-2822 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-363))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-905))))) (-2822 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (-12 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-905)))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-905))))) (|HasCategory| (-695) (QUOTE (-545))) (-12 (|HasCategory| (-695) (QUOTE (-1054))) (|HasCategory| (-695) (QUOTE (-1194)))) (|HasCategory| (-695) (QUOTE (-1054))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905))) (-2822 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-363)))) (-2822 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-556)))) (-12 (|HasCategory| (-695) (QUOTE (-233))) (|HasCategory| (-695) (QUOTE (-363)))) (-12 (|HasCategory| (-695) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-556))) (|HasAttribute| (-695) (QUOTE -4406)) (|HasAttribute| (-695) (QUOTE -4403)) (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (-2822 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-145)))) (-2822 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-349))))) +((-4400 . T) (-4405 |has| (-695) (-363)) (-4399 |has| (-695) (-363)) (-3654 . T) (-4406 |has| (-695) (-6 -4406)) (-4403 |has| (-695) (-6 -4403)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| (-695) (QUOTE (-147))) (|HasCategory| (-695) (QUOTE (-145))) (|HasCategory| (-695) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-368))) (|HasCategory| (-695) (QUOTE (-363))) (-2807 (|HasCategory| (-695) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-233))) (-2807 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (LIST (QUOTE -286) (QUOTE (-695)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -309) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-695) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (-2807 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-695) (QUOTE (-1018))) (|HasCategory| (-695) (QUOTE (-1194))) (-12 (|HasCategory| (-695) (QUOTE (-998))) (|HasCategory| (-695) (QUOTE (-1194)))) (-2807 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-363))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-905))))) (-2807 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (-12 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-905)))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-905))))) (|HasCategory| (-695) (QUOTE (-545))) (-12 (|HasCategory| (-695) (QUOTE (-1054))) (|HasCategory| (-695) (QUOTE (-1194)))) (|HasCategory| (-695) (QUOTE (-1054))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905))) (-2807 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-363)))) (-2807 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-556)))) (-12 (|HasCategory| (-695) (QUOTE (-233))) (|HasCategory| (-695) (QUOTE (-363)))) (-12 (|HasCategory| (-695) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-556))) (|HasAttribute| (-695) (QUOTE -4406)) (|HasAttribute| (-695) (QUOTE -4403)) (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-145)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-349))))) (-691 S) ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,{}d,{}n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) ((-4408 . T)) @@ -2704,13 +2704,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,{}b,{}c,{}d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,{}t,{}u,{}f,{}s1,{}l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,{}g,{}s1,{}s2,{}l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,{}f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented"))) NIL NIL -(-694 OV E -2371 PG) +(-694 OV E -2308 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 (-695) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,{}man,{}base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-3572 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-3646 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-696 R) ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m,{} d,{} p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,{}p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m,{} d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) @@ -2736,7 +2736,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,{}b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-702 S -3971 I) +(-702 S -4063 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr,{} x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) NIL NIL @@ -2756,14 +2756,14 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-707 R |Mod| -3774 -2291 |exactQuo|) +(-707 R |Mod| -1408 -2063 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-708 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4403 |has| |#1| (-363)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2822 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (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)))) (-2822 (|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))))) (-2822 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2822 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2822 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2822 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (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))))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-233))) (|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))))) (-709 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2772,7 +2772,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-711 R |Mod| -3774 -2291 |exactQuo|) +(-711 R |Mod| -1408 -2063 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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 -2371) +(-714 -2308) ((|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 -2371 UP) +(-723 -2308 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 @@ -2839,7 +2839,7 @@ NIL (-727 |vl| R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) (((-4409 "*") |has| |#2| (-172)) (-4400 |has| |#2| (-556)) (-4405 |has| |#2| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#2| (QUOTE (-905))) (-2822 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2822 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2822 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2822 (|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)))) (-2822 (|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)))) (-2822 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|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))))) (-728 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,{}var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,{}var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,{}var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -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 -2371) +(-761 -2308) ((|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 -2371) +(-762 P -2308) ((|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 -2371) +(-764 UP -2308) ((|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 -2371) +(-768 R -2308) ((|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 -2371 |ExtF| |SUEx| |ExtP| |n|) +(-773 -2308 |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 @@ -3035,7 +3035,7 @@ NIL (-776 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . 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Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -3043,7 +3043,7 @@ NIL (-778 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4403 |has| |#1| (-363)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . 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(|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL @@ -3104,23 +3104,23 @@ NIL ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4401 . T) (-4402 . T) (-4404 . T)) NIL -(-794 -2822 R OS S) +(-794 -2807 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-795 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-2822 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2822 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-2807 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2807 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (-796) ((|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 -2371 L) +(-797 R -2308 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 -2371) +(-798 R -2308) ((|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 -2371) +(-800 R -2308) ((|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 -2371 UP UPUP R) +(-802 -2308 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 -2371 UP L LQ) +(-803 -2308 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 @@ -3148,38 +3148,38 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|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 -2371 UP L LQ) +(-805 -2308 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 -2371 UP) +(-806 -2308 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 -2371 L UP A LO) +(-807 -2308 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 -2371 UP) +(-808 -2308 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 -2371 LO) +(-809 -2308 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m,{} v)} returns \\spad{[m_0,{} v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,{}v)} returns \\spad{A,{}[[C_1,{}g_1,{}L_1,{}h_1],{}...,{}[C_k,{}g_k,{}L_k,{}h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-810 -2371 LODO) +(-810 -2308 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) 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The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-2822 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2822 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2822 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2822 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-814 (-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)))) (-2822 (|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 (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2822 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|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| (-814 (-1170)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-814 (-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 (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|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))))) (-813 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-4409 "*") |has| |#2| (-363)) (-4400 |has| |#2| (-363)) (-4405 |has| |#2| (-363)) (-4399 |has| |#2| (-363)) (-4404 . T) (-4402 . T) (-4401 . T)) @@ -3247,7 +3247,7 @@ NIL (-829 R) ((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) ((-4404 |has| |#1| (-844))) -((|HasCategory| |#1| (QUOTE (-844))) (-2822 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2822 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-844))) (-2807 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2807 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) (-830 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator `op'.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of `op'."))) NIL @@ -3287,12 +3287,12 @@ NIL (-839 R) ((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4404 |has| |#1| (-844))) -((|HasCategory| |#1| (QUOTE (-844))) (-2822 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2822 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-844))) (-2807 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2807 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) (-840) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-841 -3526 S) +(-841 -3598 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 @@ -3328,11 +3328,11 @@ NIL ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p,{} c,{} m,{} sigma,{} delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p,{} q,{} sigma,{} delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) -(-850 R |sigma| -2928) +(-850 R |sigma| -1924) ((|constructor| (NIL "This is the domain of sparse univariate skew polynomials over an Ore coefficient field. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{} x)} returns the output form of \\spad{p} using \\spad{x} for the otherwise anonymous variable."))) ((-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)))) -(-851 |x| R |sigma| -2928) +(-851 |x| R |sigma| -1924) ((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}."))) ((-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-363)))) @@ -3399,15 +3399,15 @@ NIL (-867 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| (-866 |#1|) (QUOTE (-905))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-147))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-866 |#1|) (QUOTE (-1018))) (|HasCategory| (-866 |#1|) (QUOTE (-816))) (-2822 (|HasCategory| (-866 |#1|) (QUOTE (-816))) (|HasCategory| (-866 |#1|) (QUOTE (-846)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (QUOTE (-1145))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (QUOTE (-233))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -866) (|devaluate| |#1|)) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (QUOTE (-307))) (|HasCategory| (-866 |#1|) (QUOTE (-545))) (|HasCategory| (-866 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (-2822 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))))) +((|HasCategory| (-866 |#1|) (QUOTE (-905))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-147))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-866 |#1|) (QUOTE (-1018))) (|HasCategory| (-866 |#1|) (QUOTE (-816))) (-2807 (|HasCategory| (-866 |#1|) (QUOTE (-816))) (|HasCategory| (-866 |#1|) (QUOTE (-846)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (QUOTE (-1145))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (QUOTE (-233))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -866) (|devaluate| |#1|)) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (QUOTE (-307))) (|HasCategory| (-866 |#1|) (QUOTE (-545))) (|HasCategory| (-866 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))))) (-868 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-816))) (-2822 (|HasCategory| |#2| (QUOTE (-816))) (|HasCategory| |#2| (QUOTE (-846)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2822 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-816))) (-2807 (|HasCategory| |#2| (QUOTE (-816))) (|HasCategory| |#2| (QUOTE (-846)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) (-869 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,{}t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,{}t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2822 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))))) (-870) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL @@ -3463,7 +3463,7 @@ NIL (-883 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,{}...,{}en],{} pat)} matches the pattern pat on the list of expressions \\spad{[e1,{}...,{}en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,{}...,{}en],{} pat)} tests if the list of expressions \\spad{[e1,{}...,{}en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr,{} pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((-12 (-2416 (|HasCategory| |#2| (QUOTE (-1045)))) (-2416 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (-2416 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170))))) +((-12 (-2351 (|HasCategory| |#2| (QUOTE (-1045)))) (-2351 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (-2351 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170))))) (-884 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f,{} [(v1,{}a1),{}...,{}(vn,{}an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL @@ -3472,7 +3472,7 @@ NIL ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-886 R -3971) +(-886 R -4063) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,{}...,{}vn],{} p)} returns \\spad{f(v1,{}...,{}vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v,{} p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p,{} [a1,{}...,{}an],{} f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p,{} [f1,{}...,{}fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p,{} f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -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 -2371) +(-892 UP -2308) ((|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 @@ -3519,7 +3519,7 @@ NIL (-897 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2822 (-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))))) +((-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))))) (-898 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL @@ -3535,7 +3535,7 @@ NIL (-901 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,{}...,{}n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) ((-4404 . T)) -((-2822 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) +((-2807 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) (-902 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL @@ -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 -2371 UP UPUP R) +(-907 R0 -2308 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 -2371) +(-914 -2308) ((|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 -2371 P) +(-918 -2308 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-919 |xx| -2371) +(-919 |xx| -2308) ((|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 -2371) +(-925 R -2308) ((|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 -2371) +(-928 S R -2308) ((|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 @@ -3660,11 +3660,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -882) (|devaluate| |#1|)))) -(-933 R -2371 -3971) +(-933 R -2308 -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 -(-934 -3971) +(-934 -4063) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL @@ -3687,7 +3687,7 @@ NIL (-939 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4408 . T) (-4407 . T)) -((-2822 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2822 (-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)))) (-2822 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-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| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-940 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL @@ -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 -2371) +(-946 E V R P -2308) ((|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 @@ -3723,8 +3723,8 @@ NIL (-948 R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,{}x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-2822 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2822 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2822 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2822 (|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)))) (-2822 (|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)))) (-2822 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-949 E V R P -2371) +((|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) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-452)))) @@ -3747,12 +3747,12 @@ NIL (-954 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4408 . T) (-4407 . T)) -((-2822 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2822 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2822 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2807 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2807 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-955) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -2371) +(-956 -2308) ((|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 @@ -3767,11 +3767,11 @@ NIL (-959 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2822 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2822 (|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| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4405))) +((|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))) (-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| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4405))) (-960 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,{}b)} \\undocumented"))) ((-4404 -12 (|has| |#2| (-473)) (|has| |#1| (-473)))) -((-2822 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-846))))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-2822 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2822 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-2822 (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (-2822 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-846))))) +((-2807 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-846))))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-846))))) (-961) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -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 -2371) +(-981 K R UP -2308) ((|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 @@ -3911,11 +3911,11 @@ NIL (-995 R) ((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) ((-4400 |has| |#1| (-290)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-363))) (-2822 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (-2822 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545)))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-363))) (-2807 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545)))) (-996 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,{}y,{}...,{}z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2822 (-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))))) +((-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))))) (-997 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3924,14 +3924,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-999 -2371 UP UPUP |radicnd| |n|) +(-999 -2308 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))) (-2822 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2822 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2822 (-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)))) (-2822 (|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))))) +((|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))))) (-1000 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,{}cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],{}[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,{}3,{}4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,{}1,{}4,{}2,{}8,{}5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,{}0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2822 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2822 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2807 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) (-1001) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,{}b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL @@ -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 -2371) +(-1009 R -2308) ((|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 -2371) +(-1010 R -2308) ((|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 -2371 UP) +(-1011 -2308 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 -2371 UP) +(-1012 -2308 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 @@ -4011,8 +4011,8 @@ NIL (-1020 |TheField|) ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) ((-4400 . T) (-4405 . T) (-4399 . T) (-4402 . T) (-4401 . T) ((-4409 "*") . T) (-4404 . T)) -((-2822 (|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 -2371 L) +((-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) ((|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 @@ -4048,14 +4048,14 @@ NIL ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-1030 -2371 |Expon| |VarSet| |FPol| |LFPol|) +(-1030 -2308 |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 (-1031) ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -1982 (-1170)) (|:| -3740 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 (-1170)) (|:| -3740 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1982) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3740) (QUOTE (-52))))))) (-2822 (|HasCategory| (-2 (|:| -1982 (-1170)) (|:| -3740 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2822 (|HasCategory| (-2 (|:| -1982 (-1170)) (|:| -3740 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 (-1170)) (|:| -3740 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1982 (-1170)) (|:| -3740 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1982 (-1170)) (|:| -3740 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1094))) (-2822 (|HasCategory| (-2 (|:| -1982 (-1170)) (|:| -3740 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1982 (-1170)) (|:| -3740 (-52))) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1901) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3813) (QUOTE (-52))))))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1094))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (LIST (QUOTE -611) (QUOTE (-858))))) (-1032) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4112,7 +4112,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4404 . T)) NIL -(-1046 |xx| -2371) +(-1046 |xx| -2308) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4127,7 +4127,7 @@ NIL (-1049 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4407 . T) (-4402 . T) (-4401 . T)) -((-2822 (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536)))) (-2822 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (QUOTE (-307))) (|HasCategory| |#3| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-172))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-858))))) +((-2807 (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536)))) (-2807 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (QUOTE (-307))) (|HasCategory| |#3| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-172))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-858))))) (-1050 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL @@ -4159,7 +4159,7 @@ NIL (-1057) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,{}routineName,{}ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,{}s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,{}s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,{}s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,{}s,{}newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,{}s,{}newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,{}y)} merges two tables \\spad{x} and \\spad{y}"))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -1982 (-1170)) (|:| -3740 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 (-1170)) (|:| -3740 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1982) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3740) (QUOTE (-52))))))) (-2822 (|HasCategory| (-2 (|:| -1982 (-1170)) (|:| -3740 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2822 (|HasCategory| (-2 (|:| -1982 (-1170)) (|:| -3740 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 (-1170)) (|:| -3740 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1982 (-1170)) (|:| -3740 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1982 (-1170)) (|:| -3740 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1094))) (-2822 (|HasCategory| (-2 (|:| -1982 (-1170)) (|:| -3740 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1982 (-1170)) (|:| -3740 (-52))) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1901) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3813) (QUOTE (-52))))))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1094))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (LIST (QUOTE -611) (QUOTE (-858))))) (-1058 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL @@ -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 -2371) +(-1070 |Base| R -2308) ((|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 -2371) +(-1071 |Base| R -2308) ((|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 @@ -4227,7 +4227,7 @@ NIL (-1074 R UP M) ((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) ((-4400 |has| |#1| (-363)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-2822 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-2822 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-349)))) (-2822 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-2822 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-349)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))))) (-1075 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4255,7 +4255,7 @@ NIL (-1081 R) ((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential. \\blankline"))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-2822 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2822 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2822 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2822 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1082 (-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)))) (-2822 (|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 (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2822 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|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| (-1082 (-1170)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1082 (-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 (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|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))))) (-1082 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -4315,7 +4315,7 @@ NIL (-1096 S) ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,{}b,{}c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,{}m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{union(s,{}t)},{} \\spad{intersect(s,{}t)},{} \\spad{minus(s,{}t)},{} \\spad{symmetricDifference(s,{}t)} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{member(x,{}t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,{}t)} and \\spad{remove(x,{}t)} is \\spad{O(n)}}"))) ((-4407 . T) (-4397 . T) (-4408 . T)) -((-2822 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2807 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-1097 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL @@ -4359,7 +4359,7 @@ NIL (-1107 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 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(QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-789))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-844))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| (-564) (QUOTE (-846))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1045)))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1170))))) (-2807 (|HasCategory| |#3| (QUOTE (-1045))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564)))))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1094)))) (|HasAttribute| |#3| (QUOTE -4404)) (|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|))))) (-1108 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -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 -2371) +(-1110 R -2308) ((|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 @@ -4407,16 +4407,16 @@ NIL (-1119 R |VarSet|) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-2822 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2822 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2822 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2822 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (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)))) (-2822 (|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)))) (-2822 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|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| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (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))))) (-1120 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,{}b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2822 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) (-1121 R E V P) ((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}"))) ((-4408 . T) (-4407 . T)) NIL -(-1122 UP -2371) +(-1122 UP -2308) ((|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 @@ -4471,11 +4471,11 @@ NIL (-1135 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))) (-2822 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))))) (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))) (-2807 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))))) (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-858))))) (-1136 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) ((-4404 . T) (-4396 |has| |#2| (-6 (-4409 "*"))) (-4407 . T) (-4401 . T) (-4402 . T)) -((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2822 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|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)))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (-2822 (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2807 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|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)))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (-2807 (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-1137 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4495,7 +4495,7 @@ NIL (-1141 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,{}y,{}...,{}z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2822 (-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))))) +((-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))))) (-1142 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL @@ -4507,7 +4507,7 @@ NIL (-1144 |Key| |Ent| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1982) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3740) (|devaluate| |#2|)))))) (-2822 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2822 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-2822 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094)))) +((-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| |#1| (QUOTE (-846))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#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 -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094)))) (-1145) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4531,7 +4531,7 @@ NIL (-1150 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n-1)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,{}x) = [x,{}f(x),{}f(f(x)),{}...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),{}f(),{}f(),{}...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,{}n,{}y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,{}st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,{}s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,{}s) = concat(a,{}s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,{}st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,{}s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) ((-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2822 (-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)))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-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 -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-1151) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) ((-4408 . T) (-4407 . T)) @@ -4539,11 +4539,11 @@ NIL (-1152) NIL ((-4408 . T) (-4407 . T)) -((-2822 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-2807 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-1153 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1982) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3740) (|devaluate| |#1|)))))) (-2822 (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-1094)))) (-2822 (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 |#1|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 |#1|)) (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (-2822 (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 |#1|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1982 (-1152)) (|:| -3740 |#1|)) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1901) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3813) (|devaluate| |#1|)))))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-1094)))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (LIST (QUOTE -611) (QUOTE (-858))))) (-1154 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,{}j=0 to infinity,{}b<i,{}j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b<k> = sum(i+j=k,{}a<i,{}j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,{}b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,{}r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,{}[a0,{}a1,{}a2,{}..])} returns \\spad{[f(0)*a0,{}f(1)*a1,{}f(2)*a2,{}..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,{}a1,{}a2,{}...])} returns \\spad{[a1,{}2 a2,{}3 a3,{}...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0*b0,{}a1*b1,{}..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,{}n+2,{}n+4,{}...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,{}n+1,{}n+2,{}...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,{}coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,{}b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,{}a1,{}...] * r = [a0 * r,{}a1 * r,{}...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,{}a1,{}...] = [r * a0,{}r * a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{ai} * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,{}a1,{}...] = [- a0,{}- a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] - [b0,{}b1,{}..] = [a0 - b0,{}a1 - b1,{}..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] + [b0,{}b1,{}..] = [a0 + b0,{}a1 + b1,{}..]}"))) NIL @@ -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 "*") -2822 (-2427 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-816))) (|has| |#1| (-172)) (-2427 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-905)))) (-4400 -2822 (-2427 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-816))) (|has| |#1| (-556)) (-2427 (|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)} 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 . 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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 . 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(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}.")) 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T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2822 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2822 (|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| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| (-967) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasAttribute| |#1| (QUOTE -4405))) +((|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))) (-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| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| (-967) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasAttribute| |#1| (QUOTE -4405))) (-1173) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,{}tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,{}tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,{}tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,{}tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,{}t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,{}t,{}tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,{}l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,{}l,{}tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,{}t,{}asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,{}t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL @@ -4659,7 +4659,7 @@ NIL (-1182 |Key| |Entry|) ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) ((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1982) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3740) (|devaluate| |#2|)))))) (-2822 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2822 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2822 (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) +((-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))))) (-1183 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a,{} n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a,{} n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,{}...,{}an])} returns \\spad{f(a1,{}...,{}an)} such that if \\spad{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}."))) NIL @@ -4711,7 +4711,7 @@ NIL (-1195 S) ((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1,{} t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4408 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2822 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-1196 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4720,7 +4720,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1198 R -2371) +(-1198 R -2308) ((|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 -2371) +(-1200 R -2308) ((|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|))))) @@ -4743,7 +4743,7 @@ NIL (-1203 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2822 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) (-1204 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,{}ll,{}b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,{}b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL @@ -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 -2371) +(-1207 -2308) ((|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}.")) 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(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 @@ -4859,7 +4859,7 @@ NIL (-1232 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4409 "*") |has| |#2| (-172)) (-4400 |has| |#2| (-556)) (-4403 |has| |#2| (-363)) (-4405 |has| |#2| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2822 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (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)))) (-2822 (|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))))) (-2822 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2822 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2822 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2822 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2807 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (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))))) (-2807 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2807 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2807 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|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))))) (-1233 R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL @@ -4875,7 +4875,7 @@ NIL (-1236 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1106))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2488) (LIST (|devaluate| |#2|) (QUOTE (-1170)))))) +((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1106))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2423) (LIST (|devaluate| |#2|) (QUOTE (-1170)))))) (-1237 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) (((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) @@ -4903,15 +4903,15 @@ 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))) (-2822 (|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))) (-2822 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2822 (|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 -2488) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2822 (-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 -1446) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3762) (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 -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)))))) (-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))) (-2822 (|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))) (-2822 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2822 (|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 -2488) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2822 (-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 -1446) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3762) (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 -3697) (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)) -((|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-172))) (-2822 (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-363))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-452))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-556)))) +((|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-172))) (-2807 (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-363))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-452))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-556)))) (-1246 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -4927,7 +4927,7 @@ NIL (-1249 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 -3762) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1446) (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 -3697) (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))) (-2822 (|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 -2488) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-2822 (-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 -1446) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3762) (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 -3697) (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 -2371 UP L UTS) +(-1253 -2308 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)))) @@ -4967,7 +4967,7 @@ NIL (-1259 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) ((-4408 . T) (-4407 . T)) -((-2822 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2822 (-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)))) (-2822 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-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| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-1260) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -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 -2371) +(-1268 K R UP -2308) ((|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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T)) NIL -(-1277 S -2371) +(-1277 S -2308) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) -(-1278 -2371) +(-1278 -2308) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index cdffe8cb..5436af06 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(161804 . 3452534668) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) #0#) |has| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (-309 (-2 (|:| -1982 |#1|) (|:| -3740 |#2|))))) -((((-564)) . T) (($) -2822 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) (((-407 (-564))) -2822 (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-1034 (-407 (-564))))) ((|#1|) . T)) +(161804 . 3452610480) +(((|#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) (($) -2807 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) (((-407 (-564))) -2807 (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-1034 (-407 (-564))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-564)) . T)) -((($ $) -2822 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) ((|#2| |#2|) . T) ((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564))))) +((($ $) -2807 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) ((|#2| |#2|) . T) ((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564))))) ((($) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#2|) . T)) -((($) -2822 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) ((|#2|) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564))))) +((($) -2807 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) ((|#2|) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564))))) (|has| |#1| (-905)) ((((-858)) . T)) ((((-858)) . T)) @@ -24,19 +24,19 @@ ((((-225)) . T) (((-858)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1|) . T)) -(-2822 (|has| |#1| (-21)) (|has| |#1| (-844))) -((($ $) . T) ((#0=(-407 (-564)) #0#) -2822 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) -(-2822 (|has| |#1| (-816)) (|has| |#1| (-846))) +(-2807 (|has| |#1| (-21)) (|has| |#1| (-844))) +((($ $) . T) ((#0=(-407 (-564)) #0#) -2807 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) +(-2807 (|has| |#1| (-816)) (|has| |#1| (-846))) ((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) |has| |#1| (-1034 (-564))) ((|#1|) . T)) ((((-858)) . T)) ((((-858)) . T)) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-844)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1| |#2| |#3|) . T)) ((((-1175)) . T)) ((((-564)) . T) (((-866 |#1|)) . T) (($) . T) (((-407 (-564))) . T)) -((($) . T) (((-407 (-564))) -2822 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((($) . T) (((-407 (-564))) -2807 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((((-858)) . T)) ((((-1175)) . T)) (((|#4|) . T)) @@ -46,14 +46,14 @@ (((|#1|) . T) ((|#2|) . T)) ((((-1175)) . T)) (((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) |has| |#1| (-1034 (-407 (-564))))) -(-2822 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) -(-2822 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) -(((|#2| (-482 (-2245 |#1|) (-767))) . T)) +(-2807 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2807 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(((|#2| (-482 (-2181 |#1|) (-767))) . T)) (((|#1| (-531 (-1170))) . T)) (((#0=(-866 |#1|) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) ((((-1152)) . T) (((-954 (-129))) . T) (((-858)) . T)) ((((-858)) . T)) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) (|has| |#4| (-368)) (|has| |#3| (-368)) (((|#1|) . T)) @@ -67,13 +67,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-556)) -((((-564)) . T) (((-407 (-564))) -2822 (|has| |#2| (-38 (-407 (-564)))) (|has| |#2| (-1034 (-407 (-564))))) ((|#2|) . T) (($) -2822 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) (((-860 |#1|)) . T)) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-556))) -((((-2 (|:| -2151 |#1|) (|:| -1384 |#2|))) . T)) +((((-564)) . T) (((-407 (-564))) -2807 (|has| |#2| (-38 (-407 (-564)))) (|has| |#2| (-1034 (-407 (-564))))) ((|#2|) . T) (($) -2807 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) (((-860 |#1|)) . T)) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-556))) +((((-2 (|:| -2083 |#1|) (|:| -1410 |#2|))) . T)) ((($) . T)) -((((-564)) . T) (((-407 (-564))) -2822 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) ((|#1|) . T) (($) -2822 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((-1170)) . T)) -((((-858)) -2822 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) +((((-564)) . T) (((-407 (-564))) -2807 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) ((|#1|) . T) (($) -2807 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((-1170)) . T)) +((((-858)) -2807 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) ((((-536)) |has| |#1| (-612 (-536)))) ((((-1170)) . T)) ((((-564)) . T) (($) . T)) @@ -84,66 +84,66 @@ ((((-858)) . T)) ((((-858)) . T)) ((((-407 (-564))) . T) (($) . T)) -((((-407 (-564))) -2822 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) +((((-407 (-564))) -2807 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) ((((-858)) . T)) (((|#1|) . T)) ((((-858)) . T)) ((((-858)) . T)) -(((|#1|) . T) (((-407 (-564))) -2822 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) +(((|#1|) . T) (((-407 (-564))) -2807 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) (((|#1| |#2|) . T)) ((((-858)) . T)) (((|#1|) . T)) -(((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564)))) ((|#2| |#2|) . 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T)) -(-2822 (|has| |#4| (-789)) (|has| |#4| (-844))) -(-2822 (|has| |#4| (-789)) (|has| |#4| (-844))) -(-2822 (|has| |#3| (-789)) (|has| |#3| (-844))) -(-2822 (|has| |#3| (-789)) (|has| |#3| (-844))) +(-2807 (|has| |#4| (-789)) (|has| |#4| (-844))) +(-2807 (|has| |#4| (-789)) (|has| |#4| (-844))) +(-2807 (|has| |#3| (-789)) (|has| |#3| (-844))) +(-2807 (|has| |#3| (-789)) (|has| |#3| (-844))) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-1094)) @@ -157,33 +157,33 @@ ((((-564)) . T)) ((((-564)) . T)) (((|#1|) . T)) -(-2822 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2807 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (((|#1| (-767)) . T)) (|has| |#2| (-789)) -(-2822 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-2807 (|has| |#2| (-789)) (|has| |#2| (-844))) (|has| |#2| (-844)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) ((((-1152) |#1|) . T)) ((((-564) (-129)) . T)) (((|#1|) . 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T)) (|has| |#1| (-556)) (|has| |#1| (-556)) @@ -256,21 +256,21 @@ (((|#2|) . T) (($) . T) (((-407 (-564))) . T)) (-12 (|has| |#1| (-1094)) (|has| |#2| (-1094))) ((($) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T)) -((((-407 (-564))) -2822 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (((-1168 |#1| |#2| |#3|)) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-407 (-564))) -2822 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) +((((-407 (-564))) -2807 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (((-1168 |#1| |#2| |#3|)) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-407 (-564))) -2807 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) (((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) (($) . 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T)) ((((-407 $) (-407 $)) |has| |#2| (-556)) (($ $) . T) ((|#2| |#2|) . T)) -((((-2 (|:| -1982 (-1152)) (|:| -3740 (-52)))) . T)) +((((-2 (|:| -1901 (-1152)) (|:| -3813 (-52)))) . T)) (((|#1|) . T)) (|has| |#2| (-905)) ((((-1152) (-52)) . T)) ((((-564)) |has| #0=(-407 |#2|) (-637 (-564))) ((#0#) . T)) ((((-536)) . T) (((-225)) . T) (((-379)) . T) (((-888 (-379))) . T)) ((((-858)) . T)) -(-2822 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) +(-2807 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) (((|#1|) |has| |#1| (-172))) (((|#1| $) |has| |#1| (-286 |#1| |#1|))) ((((-858)) . T)) @@ -297,15 +297,15 @@ (((|#2|) . T) (((-564)) . T) (((-815 |#1|)) . T)) (|has| |#1| (-1094)) (((|#1|) . 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T)) (((|#1| (-967)) . T)) (((#0=(-866 |#1|) $) |has| #0# (-286 #0# #0#))) @@ -314,7 +314,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1145)) -((((-2 (|:| -1982 (-1152)) (|:| -3740 |#1|))) . T)) +((((-2 (|:| -1901 (-1152)) (|:| -3813 |#1|))) . T)) (|has| (-1245 |#1| |#2| |#3| |#4|) (-145)) (|has| (-1245 |#1| |#2| |#3| |#4|) (-147)) (|has| |#1| (-145)) @@ -326,27 +326,27 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) -((((-1119 |#1| (-1170))) . T) (((-564)) . T) (((-814 (-1170))) . T) (($) -2822 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) -2822 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-1170)) . T)) +((((-1119 |#1| (-1170))) . T) (((-564)) . T) (((-814 (-1170))) . T) (($) -2807 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) -2807 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-1170)) . 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T)) (((|#1|) . T) (((-407 (-564))) . T) (((-564)) . T) (($) . T)) @@ -474,10 +474,10 @@ ((((-564) |#4|) . T)) ((((-564) |#3|) . T)) (((|#1|) . T) (((-564)) |has| |#1| (-637 (-564)))) -(-2822 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2807 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-1245 |#1| |#2| |#3| |#4|)) . T)) ((((-407 (-564))) . T) (((-564)) . T)) -((((-858)) -2822 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2807 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -488,7 +488,7 @@ ((((-564)) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) . T)) (((|#1| |#1|) . T) (($ $) . T) ((#0=(-407 (-564)) #0#) . 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T)) ((((-858)) . T)) ((((-858)) . T)) @@ -731,22 +731,22 @@ (|has| |#1| (-1094)) (((|#2|) . T)) ((((-536)) |has| |#2| (-612 (-536))) (((-888 (-379))) |has| |#2| (-612 (-888 (-379)))) (((-888 (-564))) |has| |#2| (-612 (-888 (-564))))) -(((|#4|) -2822 (|has| |#4| (-172)) (|has| |#4| (-363)))) -(((|#3|) -2822 (|has| |#3| (-172)) (|has| |#3| (-363)))) +(((|#4|) -2807 (|has| |#4| (-172)) (|has| |#4| (-363)))) +(((|#3|) -2807 (|has| |#3| (-172)) (|has| |#3| (-363)))) ((((-858)) . T)) (((|#1|) . T)) -(-2822 (|has| |#2| (-452)) (|has| |#2| (-905))) -(-2822 (|has| |#1| (-452)) (|has| |#1| (-905))) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) +(-2807 (|has| |#2| (-452)) (|has| |#2| (-905))) +(-2807 (|has| |#1| (-452)) (|has| |#1| (-905))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) ((($ $) . T) ((#0=(-1170) $) |has| |#1| (-233)) ((#0# |#1|) |has| |#1| (-233)) ((#1=(-814 (-1170)) |#1|) . T) ((#1# $) . 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T)) (|has| (-407 |#2|) (-147)) (|has| (-407 |#2|) (-145)) @@ -759,15 +759,15 @@ (|has| |#1| (-556)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) ((((-858)) . T)) -((((-2 (|:| -1982 (-1152)) (|:| -3740 |#1|))) . T)) +((((-2 (|:| -1901 (-1152)) (|:| -3813 |#1|))) . T)) (|has| |#1| (-38 (-407 (-564)))) -((((-388) (-2 (|:| -1982 (-1152)) (|:| -3740 |#1|))) . T)) +((((-388) (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|))) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#2| (-1145)) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-556))) ((((-858)) . T) (((-1175)) . T)) ((((-858)) . T) (((-1175)) . T)) ((((-858)) . T) (((-1175)) . T)) @@ -785,7 +785,7 @@ ((((-388) (-1152)) . T)) (|has| |#1| (-556)) ((((-564) |#1|) . T)) -(-2822 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2807 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) (((|#2|) . T)) @@ -801,7 +801,7 @@ ((((-641 |#1|)) . T)) ((((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -(-2822 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(-2807 (|has| |#1| (-846)) (|has| |#1| (-1094))) (((|#2|) |has| |#2| (-309 |#2|))) (((#0=(-564) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -811,7 +811,7 @@ (((#0=(-564) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) . T)) (|has| |#2| (-368)) -(-2822 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(-2807 (|has| |#1| (-846)) (|has| |#1| (-1094))) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) @@ -825,8 +825,8 @@ ((((-858)) . T)) ((((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-858)) -2822 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) -((($) . T) (((-407 (-564))) -2822 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((((-858)) -2807 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((($) . T) (((-407 (-564))) -2807 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((($ $) . T)) ((((-858)) . T)) ((($ $) . T)) @@ -836,12 +836,12 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((($) -2822 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2807 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-407 (-564))) . T) (((-564)) . T)) ((((-564) (-144)) . T)) ((((-144)) . T)) (((|#1|) . T)) -(-2822 (|has| |#1| (-21)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) +(-2807 (|has| |#1| (-21)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) ((((-112)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-112)) . T)) @@ -850,26 +850,26 @@ ((((-858)) . T)) ((((-1175)) . T)) (|has| |#1| (-816)) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (|has| |#1| (-846)) -(-2822 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-2807 (|has| |#1| (-172)) (|has| |#1| (-556))) (|has| |#1| (-556)) ((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) ((|#1|) . T) (((-564)) . T)) (|has| |#1| (-905)) (((|#1|) . T)) (|has| |#1| (-1094)) ((((-858)) . 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T)) -(-2822 (|has| |#2| (-789)) (|has| |#2| (-844))) -(-2822 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-2807 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-2807 (|has| |#2| (-789)) (|has| |#2| (-844))) (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) -(-2822 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) -(-2822 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-722)) (|has| |#2| (-722)))) +(-2807 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2807 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-722)) (|has| |#2| (-722)))) (((|#1|) . T)) (|has| |#2| (-789)) -(-2822 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-2807 (|has| |#2| (-789)) (|has| |#2| (-844))) (((|#1| |#2|) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (|has| |#2| (-844)) @@ -900,8 +900,8 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-407 (-564))) . T) (($) . T)) -((($) |has| |#1| (-556)) ((|#1|) . T) (((-407 (-564))) -2822 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-564)) . T)) -((($) . T) (((-407 (-564))) -2822 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) . T)) +((($) |has| |#1| (-556)) ((|#1|) . T) (((-407 (-564))) -2807 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-564)) . T)) +((($) . T) (((-407 (-564))) -2807 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) . T)) (|has| |#1| (-824)) ((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) |has| |#1| (-1034 (-564))) ((|#1|) . T)) (|has| |#1| (-1094)) @@ -911,29 +911,29 @@ (((|#4|) |has| |#4| (-1094))) (((|#3|) |has| |#3| (-1094))) (|has| |#3| (-368)) -((((-407 (-564))) -2822 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2822 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) +((((-407 (-564))) -2807 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2807 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) ((((-858)) . T)) ((((-858)) . T)) (((|#2|) . T)) (((|#1| |#2|) . 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T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) +((($) -2807 (|has| |#1| (-172)) (|has| |#1| (-556))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) ((((-144)) . T)) (((|#1|) . T)) -((($) -2822 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((|#2|) -2822 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045)))) +((($) -2807 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((|#2|) -2807 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045)))) ((((-144)) . T)) ((((-144)) . T)) ((((-407 (-564))) . #0=(|has| |#2| (-363))) (($) . #0#) ((|#2|) . T) (((-564)) . T)) (((|#1| |#2| |#3|) . T)) -(-2822 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) +(-2807 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) (|has| $ (-147)) (|has| $ (-147)) ((((-1175)) . T)) @@ -941,14 +941,14 @@ ((((-858)) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2822 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1045)) (|has| |#1| (-1106))) +(-2807 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1045)) (|has| |#1| (-1106))) ((($ $) |has| |#1| (-286 $ $)) ((|#1| $) |has| |#1| (-286 |#1| |#1|))) (((|#1| (-407 (-564))) . T)) (((|#1|) . T)) ((((-1170)) . T)) (|has| |#1| (-556)) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-556)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) @@ -959,7 +959,7 @@ (|has| |#1| (-147)) (|has| |#1| (-145)) (|has| |#4| (-844)) -(((|#2| (-240 (-2245 |#1|) (-767)) (-860 |#1|)) . T)) +(((|#2| (-240 (-2181 |#1|) (-767)) (-860 |#1|)) . T)) (|has| |#3| (-844)) (((|#1| (-531 |#3|) |#3|) . T)) (|has| |#1| (-147)) @@ -974,20 +974,20 @@ (|has| |#1| (-145)) ((((-407 (-564))) |has| |#2| (-363)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -(-2822 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) -(-2822 (|has| |#1| (-349)) (|has| |#1| (-368))) +(-2807 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2807 (|has| |#1| (-349)) (|has| |#1| (-368))) ((((-1136 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-172)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-233)) (|has| |#2| (-1045))) -(((|#2|) . T) (((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) -(-2822 (|has| |#3| (-789)) (|has| |#3| (-844))) -(-2822 (|has| |#3| (-789)) (|has| |#3| (-844))) +(((|#2|) . T) (((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) +(-2807 (|has| |#3| (-789)) (|has| |#3| (-844))) +(-2807 (|has| |#3| (-789)) (|has| |#3| (-844))) ((((-858)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) ((((-695)) . T)) -(-2822 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2807 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (|has| |#1| (-556)) (((|#1|) . T)) (((|#1|) . T)) @@ -1011,11 +1011,11 @@ (((|#1| (-407 (-564))) . T)) (((|#3|) . T) (((-610 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) (((|#1|) . 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T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) |has| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (-309 (-2 (|:| -1982 |#1|) (|:| -3740 |#2|))))) -(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -1982 (-1152)) (|:| -3740 |#1|))) |has| (-2 (|:| -1982 (-1152)) (|:| -3740 |#1|)) (-309 (-2 (|:| -1982 (-1152)) (|:| -3740 |#1|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) |has| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (-309 (-2 (|:| -1901 |#1|) (|:| -3813 |#2|))))) +(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -1901 (-1152)) (|:| -3813 |#1|))) |has| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (-309 (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|))))) ((((-858)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1035,10 +1035,10 @@ ((($ $) . T) ((#0=(-860 |#1|) $) . T) ((#0# |#2|) . 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T)) (((|#1|) |has| |#1| (-309 |#1|))) @@ -1126,11 +1126,11 @@ (|has| |#1| (-368)) ((((-1170) $) |has| |#1| (-514 (-1170) $)) (($ $) |has| |#1| (-309 $)) ((|#1| |#1|) |has| |#1| (-309 |#1|)) (((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|))) ((((-1170)) |has| |#1| (-896 (-1170)))) -(-2822 (-12 (|has| |#1| (-233)) (|has| |#1| (-363))) (|has| |#1| (-349))) +(-2807 (-12 (|has| |#1| (-233)) (|has| |#1| (-363))) (|has| |#1| (-349))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-388) |#1|) . T)) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-1094)) (((|#2|) . T) (((-858)) . T)) ((((-858)) . T)) @@ -1138,8 +1138,8 @@ ((((-906 |#1|)) . T)) ((((-858)) . T) (((-1175)) . T)) ((((-1175)) . T)) -((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2822 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) -((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) -2822 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905)))) +((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2807 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) +((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) -2807 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) @@ -1148,16 +1148,16 @@ (((|#1|) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) (((|#1| |#1|) . T)) (((#0=(-866 |#1|)) |has| #0# (-309 #0#))) -((((-564)) . 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T)) (|has| |#1| (-1194)) (((#0=(-564) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) ((((-407 (-564))) . T) (($) . T)) @@ -1168,8 +1168,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-407 (-564)) #0#) . T)) (|has| |#1| (-363)) ((((-564)) . T) (((-407 (-564))) . T) (($) . T)) -((($ $) . T) ((#0=(-407 (-564)) #0#) -2822 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) -((((-858)) -2822 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((($ $) . T) ((#0=(-407 (-564)) #0#) -2807 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) +((((-858)) -2807 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (((|#1|) . T) (($) . T) (((-407 (-564))) . T)) ((((-858)) . T)) ((((-858)) . T)) @@ -1184,22 +1184,22 @@ (((|#1| |#2|) . T)) (|has| |#1| (-844)) (|has| |#1| (-844)) -((($) . T) (((-407 (-564))) -2822 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) -(-2822 (|has| |#1| (-172)) (|has| |#1| (-556))) +((($) . 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T)) +((((-858)) -2807 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-858))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) ((((-1152) (-52)) . T)) ((((-858)) . T)) ((((-564)) |has| #0=(-407 |#2|) (-637 (-564))) ((#0#) . T)) ((($) . T) (((-564)) . T)) ((((-564) (-144)) . T)) -((((-564) (-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T) ((|#1| |#2|) . T)) +((((-564) (-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T) ((|#1| |#2|) . T)) ((((-407 (-564))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) ((((-858)) . T)) ((((-906 |#1|)) . T)) (|has| |#1| (-363)) @@ -1226,21 +1226,21 @@ ((((-858)) . T)) ((($) . T)) (((|#2|) . T) (($) . T)) -((((-564) (-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T) ((|#1| |#2|) . T)) +((((-564) (-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#3|) . T)) (((|#1|) |has| |#1| (-172))) -((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) -2822 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905)))) -((($) -2822 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((($) -2822 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-564)) . T) (((-407 (-564))) -2822 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) +((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) -2807 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905)))) +((($) -2807 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2807 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-564)) . T) (((-407 (-564))) -2807 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (((|#1|) . T)) ((((-536)) |has| |#1| (-612 (-536))) (((-888 (-379))) |has| |#1| (-612 (-888 (-379)))) (((-888 (-564))) |has| |#1| (-612 (-888 (-564))))) ((((-858)) . T)) -(((|#2|) . T) (((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) ((((-506)) . T)) (|has| |#2| (-844)) ((((-506)) . T)) @@ -1248,39 +1248,39 @@ (|has| |#1| (-556)) ((((-1152) |#1|) . T)) (|has| |#1| (-1145)) -(-2822 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2807 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-954 |#1|)) . T)) -(((#0=(-407 (-564)) #0#) -2822 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($ $) -2822 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) ((|#1| |#1|) . T)) +(((#0=(-407 (-564)) #0#) -2807 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($ $) -2807 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) ((|#1| |#1|) . T)) ((((-407 (-564))) |has| |#1| (-1034 (-564))) (((-564)) |has| |#1| (-1034 (-564))) (((-1170)) |has| |#1| (-1034 (-1170))) ((|#1|) . T)) ((((-564) |#2|) . T)) ((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) |has| |#1| (-1034 (-564))) ((|#1|) . 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T)) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) #0#) |has| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (-309 (-2 (|:| -1982 |#1|) (|:| -3740 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) #0#) |has| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (-309 (-2 (|:| -1901 |#1|) (|:| -3813 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) -((((-858)) -2822 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-611 (-858))) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-722)) (|has| |#3| (-789)) (|has| |#3| (-844)) (|has| |#3| (-1045)) (|has| |#3| (-1094))) (((-1259 |#3|)) . T)) +((((-858)) -2807 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-611 (-858))) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-722)) (|has| |#3| (-789)) (|has| |#3| (-844)) (|has| |#3| (-1045)) (|has| |#3| (-1094))) (((-1259 |#3|)) . T)) ((((-564) |#2|) . T)) -(-2822 (|has| |#1| (-846)) (|has| |#1| (-1094))) -(((|#2| |#2|) -2822 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($ $) |has| |#2| (-172))) +(-2807 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(((|#2| |#2|) -2807 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($ $) |has| |#2| (-172))) (((|#2|) . T) (((-564)) . T)) ((((-858)) . T)) ((((-858)) . T)) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T) ((|#2|) . T)) ((((-858)) . T)) ((((-858)) . T)) ((((-1152) (-1170) (-564) (-225) (-858)) . T)) @@ -1315,8 +1315,8 @@ (|has| |#1| (-38 (-407 (-564)))) ((((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-858)) -2822 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) -(((|#2|) -2822 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($) |has| |#2| (-172))) +((((-858)) -2807 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +(((|#2|) -2807 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($) |has| |#2| (-172))) (|has| $ (-147)) ((((-407 |#2|)) . T)) ((((-889 |#1|)) . T) ((|#2|) . T) (((-564)) . T) (((-815 |#1|)) . T)) @@ -1328,11 +1328,11 @@ (((|#3|) |has| |#3| (-172))) (|has| |#1| (-147)) (|has| |#1| (-145)) -(-2822 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2807 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-2822 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2807 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-2822 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2807 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) (((|#1|) . T)) (|has| |#2| (-233)) @@ -1369,7 +1369,7 @@ ((((-995 |#1|)) . T) ((|#1|) . T)) ((((-858)) . T)) ((((-858)) . T)) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) ((((-407 (-564))) . T) (((-407 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1166 |#1|)) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) @@ -1377,9 +1377,9 @@ (|has| |#1| (-846)) (((|#2|) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) -((((-2 (|:| -1982 (-1152)) (|:| -3740 |#1|))) . T)) +((((-2 (|:| -1901 (-1152)) (|:| -3813 |#1|))) . T)) ((((-564) |#2|) . T)) -((((-858)) -2822 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2807 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (((|#2|) . T)) ((((-564) |#3|) . T)) (((|#2|) . T)) @@ -1392,7 +1392,7 @@ (|has| |#1| (-1094)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) #0#) |has| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (-309 (-2 (|:| -1982 |#1|) (|:| -3740 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) #0#) |has| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (-309 (-2 (|:| -1901 |#1|) (|:| -3813 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-38 (-407 (-564)))) (((|#2|) . T)) @@ -1427,19 +1427,19 @@ (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1| |#2|) . T)) ((((-564) (-144)) . T)) -(((#0=(-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) #0#) |has| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (-309 (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) -((($) -2822 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +(((#0=(-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) #0#) |has| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (-309 (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) +((($) -2807 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (|has| |#1| (-846)) (((|#2| (-767) (-1076)) . T)) (((|#1| |#2|) . T)) -(-2822 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-2807 (|has| |#1| (-172)) (|has| |#1| (-556))) (|has| |#1| (-787)) (((|#1|) |has| |#1| (-172))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-2822 (|has| |#1| (-147)) (-12 (|has| |#1| (-363)) (|has| |#2| (-147)))) -(-2822 (|has| |#1| (-145)) (-12 (|has| |#1| (-363)) (|has| |#2| (-145)))) +(-2807 (|has| |#1| (-147)) (-12 (|has| |#1| (-363)) (|has| |#2| (-147)))) +(-2807 (|has| |#1| (-145)) (-12 (|has| |#1| (-363)) (|has| |#2| (-145)))) (((|#4|) . T)) (|has| |#1| (-145)) ((((-1152) |#1|) . T)) @@ -1453,10 +1453,10 @@ (((|#3|) . T)) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-858)) . T)) -(-2822 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(-2807 (|has| |#1| (-846)) (|has| |#1| (-1094))) (((|#1|) . T)) -((((-858)) -2822 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) -((((-858)) -2822 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094))) (((-954 |#1|)) . T)) +((((-858)) -2807 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2807 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094))) (((-954 |#1|)) . T)) (|has| |#1| (-844)) (|has| |#1| (-844)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -1470,8 +1470,8 @@ ((($) . T)) ((((-388) (-1152)) . T)) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((((-858)) -2822 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-858))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -1982 (-1152)) (|:| -3740 #0#))) . T)) +((((-858)) -2807 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-858))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) +(((#0=(-52)) . T) (((-2 (|:| -1901 (-1152)) (|:| -3813 #0#))) . T)) (((|#1|) . T)) ((((-858)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) @@ -1479,7 +1479,7 @@ (|has| |#2| (-145)) (|has| |#2| (-147)) (|has| |#1| (-473)) -(-2822 (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) +(-2807 (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) (|has| |#1| (-363)) ((((-858)) . T)) (|has| |#1| (-38 (-407 (-564)))) @@ -1490,8 +1490,8 @@ (|has| |#1| (-844)) ((((-858)) . T)) (((|#2|) . T)) -((((-407 (-564))) -2822 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2822 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) -(((|#1|) |has| |#1| (-172)) (((-407 (-564))) -2822 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2822 (|has| |#1| (-363)) (|has| |#1| (-556)))) +((((-407 (-564))) -2807 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2807 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) +(((|#1|) |has| |#1| (-172)) (((-407 (-564))) -2807 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2807 (|has| |#1| (-363)) (|has| |#1| (-556)))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#2|) . T) (((-564)) . T) (((-815 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1500,7 +1500,7 @@ ((((-858)) . T)) ((((-858)) . T)) (|has| |#1| (-1094)) -(((|#2| (-482 (-2245 |#1|) (-767)) (-860 |#1|)) . T)) +(((|#2| (-482 (-2181 |#1|) (-767)) (-860 |#1|)) . T)) ((((-407 (-564))) . #0=(|has| |#2| (-363))) (($) . #0#)) (((|#1| (-531 (-1170)) (-1170)) . T)) (((|#1|) . T)) @@ -1520,16 +1520,16 @@ (|has| |#1| (-147)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -1982 (-1152)) (|:| -3740 |#1|))) . T)) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) -((((-2 (|:| -1982 (-1170)) (|:| -3740 (-52)))) . T)) +(((|#1|) . T) (((-2 (|:| -1901 (-1152)) (|:| -3813 |#1|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) +((((-2 (|:| -1901 (-1170)) (|:| -3813 (-52)))) . T)) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) ((((-1170) (-52)) . T)) ((($ $) . T)) (((|#1| (-564)) . T)) ((((-906 |#1|)) . T)) -(((|#1|) -2822 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045))) (($) -2822 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)))) +(((|#1|) -2807 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045))) (($) -2807 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)))) (((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) |has| |#1| (-1034 (-407 (-564))))) (|has| |#1| (-846)) (|has| |#1| (-846)) @@ -1546,11 +1546,11 @@ (((|#4| |#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) (((|#1|) |has| |#1| (-172))) (((|#4| |#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) -(((|#3|) -2822 (|has| |#3| (-172)) (|has| |#3| (-363)))) -(-2822 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-905))) +(((|#3|) -2807 (|has| |#3| (-172)) (|has| |#3| (-363)))) +(-2807 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-905))) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) ((((-564) |#2|) . T)) -(((|#2|) -2822 (|has| |#2| (-172)) (|has| |#2| (-363)))) +(((|#2|) -2807 (|has| |#2| (-172)) (|has| |#2| (-363)))) (|has| |#1| (-349)) (((|#3| |#3|) -12 (|has| |#3| (-309 |#3|)) (|has| |#3| (-1094)))) (((|#2|) . T) (((-564)) . T)) @@ -1559,7 +1559,7 @@ (|has| |#1| (-816)) (|has| |#1| (-816)) (((|#1|) . T)) -(-2822 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2807 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-844)) (|has| |#1| (-844)) (|has| |#1| (-844)) @@ -1568,13 +1568,13 @@ ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) ((((-1170)) |has| |#1| (-896 (-1170))) (((-1076)) . T)) (((|#1|) . T)) (|has| |#1| (-844)) -(((#0=(-2 (|:| -1982 (-1152)) (|:| -3740 (-52))) #0#) |has| (-2 (|:| -1982 (-1152)) (|:| -3740 (-52))) (-309 (-2 (|:| -1982 (-1152)) (|:| -3740 (-52)))))) +(((#0=(-2 (|:| -1901 (-1152)) (|:| -3813 (-52))) #0#) |has| (-2 (|:| -1901 (-1152)) (|:| -3813 (-52))) (-309 (-2 (|:| -1901 (-1152)) (|:| -3813 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (|has| |#1| (-1094)) ((((-858)) . T) (((-1175)) . T)) @@ -1593,11 +1593,11 @@ (((|#1| (-767) (-1076)) . T)) (((|#3|) . T)) ((((-144)) . T)) -((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) -2822 (|has| |#1| (-844)) (|has| |#1| (-1034 (-564)))) ((|#1|) . T)) +((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) -2807 (|has| |#1| (-844)) (|has| |#1| (-1034 (-564)))) ((|#1|) . T)) (((|#1|) . T)) ((((-144)) . T)) (((|#2|) |has| |#2| (-172))) -(-2822 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) +(-2807 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((|#1|) . T)) (|has| |#1| (-145)) (|has| |#1| (-147)) @@ -1620,32 +1620,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1|) . T)) (((|#1| |#2|) . 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T)) +((((-2 (|:| -1901 (-1170)) (|:| -3813 (-52)))) . T)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T)) ((((-668 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1654,7 +1654,7 @@ ((((-858)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-858)) . T)) -((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2822 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) +((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2807 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) ((((-1175)) . T)) ((((-407 (-564))) . T) (($) . T) (((-407 |#1|)) . T) ((|#1|) . T) (((-564)) . T)) (((|#3|) . T) (((-564)) . T) (((-610 $)) . T)) @@ -1662,12 +1662,12 @@ ((((-858)) . T)) ((((-858)) . T)) (((|#2|) . 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T)) (|has| |#1| (-1194)) (|has| |#1| (-1194)) -(-2822 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) +(-2807 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (|has| |#1| (-1194)) (|has| |#1| (-1194)) (((|#3| |#3|) . T)) @@ -1680,16 +1680,16 @@ (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) ((((-1152) (-52)) . T)) (|has| |#1| (-1094)) -(-2822 (|has| |#2| (-816)) (|has| |#2| (-846))) +(-2807 (|has| |#2| (-816)) (|has| |#2| (-846))) (((|#1|) . T)) (((|#1|) |has| |#1| (-172)) (($) . T)) -((($) -2822 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -2822 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((($) -2807 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -2807 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((($) . T)) ((((-1168 |#1| |#2| |#3|)) -12 (|has| (-1168 |#1| |#2| |#3|) (-309 (-1168 |#1| |#2| |#3|))) (|has| |#1| (-363)))) ((((-858)) . T)) ((((-564)) . T) (($) . T)) ((((-767)) . T)) -(-2822 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2807 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-858)) . T)) ((($) . T) (((-564)) . T)) @@ -1697,30 +1697,30 @@ (|has| |#2| (-905)) (|has| |#1| (-363)) (((|#2|) |has| |#2| (-1094))) -(-2822 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) -(-2822 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2807 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2807 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((((-536)) . T) (((-407 (-1166 (-564)))) . T) (((-225)) . T) (((-379)) . T)) ((((-379)) . T) (((-225)) . T) (((-858)) . T)) (|has| |#1| (-905)) (|has| |#1| (-905)) (|has| |#1| (-905)) -(-2822 (|has| |#1| (-452)) (|has| |#1| (-905))) +(-2807 (|has| |#1| (-452)) (|has| |#1| (-905))) ((($) . T) ((|#2|) . T)) -(-2822 (|has| |#1| (-846)) (|has| |#1| (-1094))) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) +(-2807 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) ((((-858)) . T)) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) ((($ $) . T)) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) ((($ $) . T)) ((((-564) (-112)) . T)) ((($) . T)) (((|#1|) . T)) ((((-564)) . T)) ((((-112)) . T)) -(-2822 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2807 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-38 (-407 (-564)))) (((|#1| (-564)) . T)) ((($) . T)) @@ -1742,7 +1742,7 @@ (((|#1| (-1223 |#1| |#2| |#3|)) . T)) (((|#1| (-767)) . T)) (((|#1|) . T)) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) ((((-858)) . T)) (|has| |#1| (-1094)) ((((-1152) |#1|) . T)) @@ -1762,18 +1762,18 @@ (((|#1|) . T)) ((((-564)) . T)) ((((-858)) . T)) -(-2822 (|has| |#1| (-145)) (|has| |#1| (-349))) +(-2807 (|has| |#1| (-145)) (|has| |#1| (-349))) (|has| |#1| (-147)) ((((-858)) . T)) (((|#3|) . T)) -(-2822 (|has| |#3| (-172)) (|has| |#3| (-844)) (|has| |#3| (-1045))) +(-2807 (|has| |#3| (-172)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((((-858)) . T)) ((((-1244 |#2| |#3| |#4|)) . T) (((-1245 |#1| |#2| |#3| |#4|)) . T)) ((((-858)) . T)) -((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (((-610 $)) . T) ((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) -2822 (-12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-407 (-948 |#1|))) |has| |#1| (-556)) (((-948 |#1|)) |has| |#1| (-1045)) (((-1170)) . T)) +((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (((-610 $)) . T) ((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) -2807 (-12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-407 (-948 |#1|))) |has| |#1| (-556)) (((-948 |#1|)) |has| |#1| (-1045)) (((-1170)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-767)) . T)) -((($) -2822 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -2822 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) +((($) -2807 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -2807 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) (((|#1|) |has| |#1| (-309 |#1|))) ((((-1245 |#1| |#2| |#3| |#4|)) . T)) ((((-564)) |has| |#1| (-882 (-564))) (((-379)) |has| |#1| (-882 (-379)))) @@ -1781,7 +1781,7 @@ (|has| |#1| (-556)) (((|#1|) . T)) ((((-858)) . T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) |has| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (-309 (-2 (|:| -1982 |#1|) (|:| -3740 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) |has| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (-309 (-2 (|:| -1901 |#1|) (|:| -3813 |#2|))))) (((|#1|) |has| |#1| (-172))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -1789,7 +1789,7 @@ (((|#1|) . T)) (((|#3|) |has| |#3| (-1094))) ((((-906 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) -(((|#2|) -2822 (|has| |#2| (-172)) (|has| |#2| (-363)))) +(((|#2|) -2807 (|has| |#2| (-172)) (|has| |#2| (-363)))) ((((-1244 |#2| |#3| |#4|)) . T)) ((((-112)) . T)) (|has| |#1| (-816)) @@ -1799,8 +1799,8 @@ (|has| |#1| (-844)) (|has| |#1| (-844)) (((|#1| (-564) (-1076)) . T)) -(-2822 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +(-2807 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) (((|#1| (-407 (-564)) (-1076)) . T)) (((|#1| (-767) (-1076)) . T)) (|has| |#1| (-846)) @@ -1813,33 +1813,33 @@ (|has| |#1| (-1094)) ((((-906 |#1|)) . T) (($) . T) (((-407 (-564))) . T)) (|has| |#1| (-1094)) -((((-564)) -2822 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)))) +((((-564)) -2807 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)))) (((|#1|) . T)) (|has| |#1| (-1094)) ((((-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-637 (-564)))) ((|#2|) |has| |#1| (-363))) -(-2822 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) -((((-685 (-339 (-2501) (-2501 (QUOTE X) (QUOTE HESS)) (-695)))) . T)) +(-2807 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) +((((-685 (-339 (-2435) (-2435 (QUOTE X) (QUOTE HESS)) (-695)))) . T)) (((|#2|) |has| |#2| (-172))) (((|#1|) |has| |#1| (-172))) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) -((((-2 (|:| -1982 (-1152)) (|:| -3740 |#1|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) +((((-2 (|:| -1901 (-1152)) (|:| -3813 |#1|))) . T)) ((((-858)) . T)) (|has| |#3| (-844)) ((((-858)) . T)) ((((-1244 |#2| |#3| |#4|) (-319 |#2| |#3| |#4|)) . T)) ((((-858)) . T)) -(((|#1| |#1|) -2822 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045)))) +(((|#1| |#1|) -2807 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045)))) (((|#1|) . T)) ((((-564)) . T)) ((((-564)) . T)) -(((|#1|) -2822 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045)))) +(((|#1|) -2807 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045)))) (((|#2|) |has| |#2| (-363))) ((($) . T) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-363))) (|has| |#1| (-846)) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -1982 (-1170)) (|:| -3740 (-52)))) |has| (-2 (|:| -1982 (-1170)) (|:| -3740 (-52))) (-309 (-2 (|:| -1982 (-1170)) (|:| -3740 (-52)))))) -(-2822 (|has| |#1| (-452)) (|has| |#1| (-905))) +((((-2 (|:| -1901 (-1170)) (|:| -3813 (-52)))) |has| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (-309 (-2 (|:| -1901 (-1170)) (|:| -3813 (-52)))))) +(-2807 (|has| |#1| (-452)) (|has| |#1| (-905))) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) ((((-858)) . T)) ((((-858)) . T)) @@ -1870,25 +1870,25 @@ (|has| |#1| (-145)) ((((-564)) . T) ((|#1|) . T) (($) . T) (((-407 (-564))) . T) (((-1170)) |has| |#1| (-1034 (-1170)))) (((|#1| |#2|) . T)) -((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) -2822 (|has| |#1| (-844)) (|has| |#1| (-1034 (-564)))) ((|#1|) . T)) +((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) -2807 (|has| |#1| (-844)) (|has| |#1| (-1034 (-564)))) ((|#1|) . T)) ((((-144)) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (((|#1|) . T)) -(-2822 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2807 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) . T) (($ $) . T)) (((|#2|) . T) ((|#1|) . T) (((-564)) . T)) ((((-858)) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((((-858)) -2822 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2807 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (|has| |#1| (-363)) (|has| |#1| (-363)) (|has| (-407 |#2|) (-233)) ((((-641 |#1|)) . T)) (|has| |#1| (-905)) (((|#2|) |has| |#2| (-1045))) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) |has| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (-309 (-2 (|:| -1982 |#1|) (|:| -3740 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) |has| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (-309 (-2 (|:| -1901 |#1|) (|:| -3813 |#2|))))) (|has| |#1| (-363)) (((|#1|) |has| |#1| (-172))) (((|#1| |#1|) . T)) @@ -1913,7 +1913,7 @@ (((|#1|) . T)) (((|#1| (-767) (-1076)) . T)) (((#0=(-407 |#2|) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-564)) -2822 (|has| (-407 (-564)) (-1034 (-564))) (|has| |#1| (-1034 (-564)))) (((-407 (-564))) . T)) +(((|#1|) . T) (((-564)) -2807 (|has| (-407 (-564)) (-1034 (-564))) (|has| |#1| (-1034 (-564)))) (((-407 (-564))) . T)) (((|#1| (-600 |#1| |#3|) (-600 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -1934,25 +1934,25 @@ (((|#2|) |has| |#2| (-172))) (|has| |#2| (-844)) ((((-564)) . T) ((|#2|) . T) (((-407 (-564))) |has| |#2| (-1034 (-407 (-564))))) -((((-112)) |has| |#1| (-1094)) (((-858)) -2822 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)) (|has| |#1| (-1106)) (|has| |#1| (-1094)))) +((((-112)) |has| |#1| (-1094)) (((-858)) -2807 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)) (|has| |#1| (-1106)) (|has| |#1| (-1094)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -1982 (-1152)) (|:| -3740 (-52)))) . T)) +((((-2 (|:| -1901 (-1152)) (|:| -3813 (-52)))) . T)) ((((-858)) . T)) ((((-564) |#1|) . T)) ((((-858)) . T)) ((((-695)) . T) (((-407 (-564))) . T) (((-564)) . T)) (((|#1| |#1|) |has| |#1| (-172))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) |has| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (-309 (-2 (|:| -1982 |#1|) (|:| -3740 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) |has| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (-309 (-2 (|:| -1901 |#1|) (|:| -3813 |#2|))))) ((((-379)) . T)) ((((-695)) . T)) ((((-407 (-564))) . #0=(|has| |#2| (-363))) (($) . #0#)) (((|#1|) |has| |#1| (-172))) ((((-407 (-948 |#1|))) . T)) (((|#2| |#2|) . T)) -(-2822 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) -(-2822 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2807 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2807 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((|#1|) . T)) (((|#2|) . T)) (((|#3|) |has| |#3| (-1045))) @@ -1961,14 +1961,14 @@ (|has| |#1| (-363)) ((((-1170)) |has| |#2| (-896 (-1170)))) ((((-858)) . T)) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) ((((-407 (-564))) . T) (($) . T)) (|has| |#1| (-473)) (|has| |#1| (-368)) (|has| |#1| (-368)) (|has| |#1| (-368)) (|has| |#1| (-363)) -(-2822 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1045)) (|has| |#1| (-1106))) +(-2807 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1045)) (|has| |#1| (-1106))) (|has| |#1| (-38 (-407 (-564)))) ((((-116 |#1|)) . T)) ((((-116 |#1|)) . T)) @@ -1989,11 +1989,11 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-846)) -((((-2 (|:| -1982 (-1152)) (|:| -3740 |#1|))) . T)) +((((-2 (|:| -1901 (-1152)) (|:| -3813 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-147)) (|has| |#1| (-145)) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) |has| (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)) (-309 (-2 (|:| -1982 |#1|) (|:| -3740 |#2|)))) ((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) |has| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (-309 (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)))) ((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) (((|#2|) . T)) (((|#3|) . T)) ((((-116 |#1|)) . T)) @@ -2011,11 +2011,11 @@ ((((-536)) |has| |#1| (-612 (-536))) (((-888 (-564))) |has| |#1| (-612 (-888 (-564)))) (((-888 (-379))) |has| |#1| (-612 (-888 (-379)))) (((-379)) . #0=(|has| |#1| (-1018))) (((-225)) . #0#)) (((|#1|) |has| |#1| (-363))) ((((-858)) . T)) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) ((($ $) . T) (((-610 $) $) . T)) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-556))) ((($) . T) (((-1245 |#1| |#2| |#3| |#4|)) . T) (((-407 (-564))) . T)) -((($) -2822 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-556))) +((($) -2807 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-556))) (|has| |#1| (-363)) (|has| |#1| (-363)) (|has| |#1| (-363)) @@ -2026,9 +2026,9 @@ ((((-379)) . T)) (((|#3|) -12 (|has| |#3| (-309 |#3|)) (|has| |#3| (-1094)))) ((((-858)) . T)) -(-2822 (|has| |#2| (-452)) (|has| |#2| (-905))) +(-2807 (|has| |#2| (-452)) (|has| |#2| (-905))) (((|#1|) . T)) -((((-858)) -2822 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2807 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) ((((-536)) |has| |#1| (-612 (-536)))) (((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) ((((-767)) . T)) @@ -2039,13 +2039,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) ((((-564)) . T)) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-556))) (((#0=(-1244 |#2| |#3| |#4|)) . T) (((-407 (-564))) |has| #0# (-38 (-407 (-564)))) (($) . T)) ((((-564)) . T)) (|has| |#1| (-363)) -(-2822 (-12 (|has| (-1251 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) -(-2822 (-12 (|has| (-1251 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) +(-2807 (-12 (|has| (-1251 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) +(-2807 (-12 (|has| (-1251 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) (|has| |#1| (-363)) (|has| |#1| (-145)) (|has| |#1| (-147)) @@ -2060,23 +2060,23 @@ (((|#2|) . T)) (|has| |#1| (-1094)) (((|#1| |#2|) . T)) -((((-564)) . T) ((|#1|) . T) (((-407 (-564))) -2822 (|has| |#1| (-363)) (|has| |#1| (-1034 (-407 (-564)))))) +((((-564)) . T) ((|#1|) . T) (((-407 (-564))) -2807 (|has| |#1| (-363)) (|has| |#1| (-1034 (-407 (-564)))))) (((|#1|) . T) (((-564)) |has| |#1| (-637 (-564)))) (((|#3|) |has| |#3| (-172))) -(-2822 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) +(-2807 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) ((((-858)) . T)) ((((-564)) . T)) (((|#1| $) |has| |#1| (-286 |#1| |#1|))) ((((-407 (-564))) . T) (($) . T) (((-407 |#1|)) . T) ((|#1|) . T)) ((((-948 |#1|)) . T) (((-858)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -2822 (|has| |#1| (-290)) (|has| |#1| (-363))) ((#0=(-407 (-564)) #0#) |has| |#1| (-363))) -((((-2 (|:| -1982 (-1170)) (|:| -3740 (-52)))) . T)) +(((|#1| |#1|) . T) (($ $) -2807 (|has| |#1| (-290)) (|has| |#1| (-363))) ((#0=(-407 (-564)) #0#) |has| |#1| (-363))) +((((-2 (|:| -1901 (-1170)) (|:| -3813 (-52)))) . T)) ((((-948 |#1|)) . T)) ((($) . T)) ((((-564) |#1|) . T)) ((((-1170)) |has| (-407 |#2|) (-896 (-1170)))) -(((|#1|) . T) (($) -2822 (|has| |#1| (-290)) (|has| |#1| (-363))) (((-407 (-564))) |has| |#1| (-363))) +(((|#1|) . T) (($) -2807 (|has| |#1| (-290)) (|has| |#1| (-363))) (((-407 (-564))) |has| |#1| (-363))) ((((-536)) |has| |#2| (-612 (-536)))) ((((-685 |#2|)) . T) (((-858)) . T)) (((|#1|) . T)) @@ -2084,8 +2084,8 @@ (((|#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) ((((-866 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -(-2822 (|has| |#4| (-789)) (|has| |#4| (-844))) -(-2822 (|has| |#3| (-789)) (|has| |#3| (-844))) +(-2807 (|has| |#4| (-789)) (|has| |#4| (-844))) +(-2807 (|has| |#3| (-789)) (|has| |#3| (-844))) ((((-858)) . T)) ((((-858)) . T)) (((|#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) @@ -2101,17 +2101,17 @@ ((((-407 (-564))) . T) (($) . T)) ((((-407 (-564))) . T) (($) . T)) ((((-407 (-564))) . T) (($) . T)) -(-2822 (|has| |#1| (-452)) (|has| |#1| (-1213))) +(-2807 (|has| |#1| (-452)) (|has| |#1| (-1213))) ((($) . T)) ((((-407 (-564))) |has| #0=(-407 |#2|) (-1034 (-407 (-564)))) (((-564)) |has| #0# (-1034 (-564))) ((#0#) . T)) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) (((|#1| (-767)) . T)) (|has| |#1| (-846)) (((|#1|) . T) (((-564)) |has| |#1| (-637 (-564)))) -((($) -2822 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -2822 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((($) -2807 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -2807 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((((-564)) . T)) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -1982 (-1152)) (|:| -3740 (-52)))) |has| (-2 (|:| -1982 (-1152)) (|:| -3740 (-52))) (-309 (-2 (|:| -1982 (-1152)) (|:| -3740 (-52)))))) +((((-2 (|:| -1901 (-1152)) (|:| -3813 (-52)))) |has| (-2 (|:| -1901 (-1152)) (|:| -3813 (-52))) (-309 (-2 (|:| -1901 (-1152)) (|:| -3813 (-52)))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (|has| |#1| (-844)) (|has| |#1| (-38 (-407 (-564)))) @@ -2135,29 +2135,29 @@ (|has| |#1| (-38 (-407 (-564)))) ((((-1152)) . T) (((-506)) . T) (((-225)) . T) (((-564)) . T)) ((((-858)) . T)) -(((|#2|) . T) (((-564)) . T) (($) -2822 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((-1076)) . T) ((|#1|) . T) (((-407 (-564))) -2822 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564)))))) +(((|#2|) . 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T)) -((($ $) -2822 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) +((($ $) -2807 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) ((((-906 |#1|)) . T)) ((($) . T)) ((((-407 (-948 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -((($) -2822 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2807 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-536)) |has| |#4| (-612 (-536)))) ((((-858)) . T) (((-641 |#4|)) . T)) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-844)) -(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -1982 (-1152)) (|:| -3740 |#1|))) |has| (-2 (|:| -1982 (-1152)) (|:| -3740 |#1|)) (-309 (-2 (|:| -1982 (-1152)) (|:| -3740 |#1|))))) +(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -1901 (-1152)) (|:| -3813 |#1|))) |has| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (-309 (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|))))) (|has| |#1| (-1094)) (|has| |#1| (-363)) (((|#1|) . T)) @@ -2165,16 +2165,16 @@ (((|#1|) . T)) ((((-668 |#1|)) . T)) ((($) . T) (((-407 (-564))) . T)) -((($) -2822 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -2822 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) +((($) -2807 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -2807 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) (|has| |#1| (-145)) (|has| |#1| (-147)) -(-2822 (-12 (|has| (-1168 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) -(-2822 (-12 (|has| (-1168 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) +(-2807 (-12 (|has| (-1168 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) +(-2807 (-12 (|has| (-1168 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-147)) (|has| |#1| (-145)) -((((-858)) -2822 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2807 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) (|has| |#1| (-844)) (((|#1| |#2|) . T)) @@ -2198,9 +2198,9 @@ ((((-858)) . T)) ((((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) ((((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|)) ((|#1| |#1|) |has| |#1| (-309 |#1|))) -(((|#1|) -2822 (|has| |#1| (-172)) (|has| |#1| (-363)))) +(((|#1|) -2807 (|has| |#1| (-172)) (|has| |#1| (-363)))) ((((-316 |#1|)) . T)) (((|#2|) |has| |#2| (-363))) (((|#2|) . T)) @@ -2222,13 +2222,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) ((($ $) . T)) -(-2822 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)) (|has| |#1| (-1106)) (|has| |#1| (-1094))) +(-2807 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)) (|has| |#1| (-1106)) (|has| |#1| (-1094))) (|has| |#1| (-556)) (((|#2|) . T)) ((((-564)) . T)) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) (((|#1|) . T)) -(-2822 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) +(-2807 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) ((((-581 |#1|)) . T)) ((($) . T)) (((|#1| (-59 |#1|) (-59 |#1|)) . T)) @@ -2244,7 +2244,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-1244 |#2| |#3| |#4|)) . T) (((-564)) . T) (((-1245 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-407 (-564))) . T)) -((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (((-564)) -2822 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1034 (-564))) (|has| |#1| (-1045))) ((|#1|) . T) (((-610 $)) . T) (($) |has| |#1| (-556)) (((-407 (-564))) -2822 (|has| |#1| (-556)) (|has| |#1| (-1034 (-407 (-564))))) (((-407 (-948 |#1|))) |has| |#1| (-556)) (((-948 |#1|)) |has| |#1| (-1045)) (((-1170)) . T)) +((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (((-564)) -2807 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1034 (-564))) (|has| |#1| (-1045))) ((|#1|) . T) (((-610 $)) . T) (($) |has| |#1| (-556)) (((-407 (-564))) -2807 (|has| |#1| (-556)) (|has| |#1| (-1034 (-407 (-564))))) (((-407 (-948 |#1|))) |has| |#1| (-556)) (((-948 |#1|)) |has| |#1| (-1045)) (((-1170)) . T)) ((((-407 (-564))) |has| |#2| (-1034 (-407 (-564)))) (((-564)) |has| |#2| (-1034 (-564))) ((|#2|) . T) (((-860 |#1|)) . T)) ((($) . T) (((-116 |#1|)) . T) (((-407 (-564))) . T)) ((((-1119 |#1| |#2|)) . T) ((|#2|) . T) ((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) |has| |#1| (-1034 (-407 (-564))))) @@ -2257,12 +2257,12 @@ (((|#1| |#2|) . T)) ((((-1170) |#1|) . T)) (((|#4|) . T)) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-349))) ((((-1170) (-52)) . T)) ((((-1244 |#2| |#3| |#4|) (-319 |#2| |#3| |#4|)) . T)) ((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) |has| |#1| (-1034 (-564))) ((|#1|) . T)) ((((-858)) . T)) -(-2822 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) +(-2807 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((#0=(-1245 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-172)) ((#0=(-407 (-564)) #0#) |has| |#1| (-556)) (($ $) |has| |#1| (-556))) (((|#1|) . T) (($) . T) (((-407 (-564))) . T)) @@ -2282,14 +2282,14 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) (((|#2| |#3|) . T)) -(-2822 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2807 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) (((|#1| (-531 |#2|)) . T)) (((|#1| (-767)) . T)) (((|#1| (-531 (-1082 (-1170)))) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (|has| |#2| (-905)) -(-2822 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-2807 (|has| |#2| (-789)) (|has| |#2| (-844))) ((((-858)) . T)) ((($ $) . T) ((#0=(-1244 |#2| |#3| |#4|) #0#) . T) ((#1=(-407 (-564)) #1#) |has| #0# (-38 (-407 (-564))))) ((((-906 |#1|)) . T)) @@ -2298,14 +2298,14 @@ ((((-858)) . T)) ((($) . T)) ((($) . T)) -(-2822 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) +(-2807 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) (|has| |#1| (-363)) (|has| |#1| (-363)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1244 |#2| |#3| |#4|)) . T) (((-407 (-564))) |has| #0# (-38 (-407 (-564))))) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -(-2822 (-12 (|has| |#1| (-307)) (|has| |#1| (-905))) (|has| |#1| (-363)) (|has| |#1| (-349))) -(-2822 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) +(-2807 (-12 (|has| |#1| (-307)) (|has| |#1| (-905))) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2807 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) ((((-564)) |has| |#1| (-637 (-564))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-858)) . T)) @@ -2338,26 +2338,26 @@ (((|#1|) |has| |#1| (-172))) ((((-858)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) -(((|#2|) -2822 (|has| |#2| (-6 (-4409 "*"))) (|has| |#2| (-172)))) -(-2822 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) -(-2822 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(((|#2|) -2807 (|has| |#2| (-6 (-4409 "*"))) (|has| |#2| (-172)))) +(-2807 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2807 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (|has| |#2| (-905)) (|has| |#1| (-905)) (((|#2|) |has| |#2| (-172))) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-858)) . T)) ((((-858)) . T)) ((((-536)) . T) (((-564)) . T) (((-888 (-564))) . T) (((-379)) . T) (((-225)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) -((((-2 (|:| -1982 (-1152)) (|:| -3740 (-52)))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) +((((-2 (|:| -1901 (-1152)) (|:| -3813 (-52)))) . T)) (((|#1|) . T)) ((((-858)) . T)) (((|#1| |#2|) . T)) (((|#1| (-407 (-564))) . T)) (((|#1|) . T)) -(-2822 (|has| |#1| (-290)) (|has| |#1| (-363))) +(-2807 (|has| |#1| (-290)) (|has| |#1| (-363))) ((((-144)) . T)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T)) (|has| |#1| (-844)) @@ -2373,7 +2373,7 @@ ((((-858)) . T)) ((((-858)) . T)) ((((-187)) . T) (((-858)) . T)) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-858)) . T)) ((((-858)) . T)) @@ -2386,7 +2386,7 @@ ((((-858)) . T)) ((((-1152)) . T)) ((((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|)) ((|#1| |#1|) |has| |#1| (-309 |#1|))) -((((-2 (|:| -1982 (-1152)) (|:| -3740 |#1|))) . T)) +((((-2 (|:| -1901 (-1152)) (|:| -3813 |#1|))) . T)) (|has| |#1| (-846)) ((((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) @@ -2398,16 +2398,16 @@ (((|#2|) . T)) ((((-906 |#1|)) . T) (((-407 (-564))) . T) (($) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) . T) (((-610 $)) . T)) -(-2822 (|has| |#4| (-172)) (|has| |#4| (-722)) (|has| |#4| (-844)) (|has| |#4| (-1045))) -(-2822 (|has| |#3| (-172)) (|has| |#3| (-722)) (|has| |#3| (-844)) (|has| |#3| (-1045))) +(-2807 (|has| |#4| (-172)) (|has| |#4| (-722)) (|has| |#4| (-844)) (|has| |#4| (-1045))) +(-2807 (|has| |#3| (-172)) (|has| |#3| (-722)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((((-1170) (-52)) . T)) -(-2822 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2807 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2822 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) -(-2822 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2807 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2807 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (|has| |#1| (-905)) ((((-906 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) (|has| |#1| (-905)) @@ -2424,12 +2424,12 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (|has| |#1| (-816)) (((#0=(-906 |#1|) #0#) . T) (($ $) . T) ((#1=(-407 (-564)) #1#) . T)) ((((-407 |#2|)) . T)) (|has| |#1| (-844)) -((((-1195 |#1|)) . T) (((-858)) -2822 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-1195 |#1|)) . T) (((-858)) -2807 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) . T) ((#1=(-564) #1#) . T) (($ $) . T)) ((((-906 |#1|)) . T) (($) . T) (((-407 (-564))) . T)) (((|#2|) |has| |#2| (-1045)) (((-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1045)))) @@ -2440,11 +2440,11 @@ (((|#2|) . T)) ((((-858)) . T)) ((((-407 (-564))) . T) (((-695)) . T) (($) . T) (((-564)) . T)) -(-2822 (|has| |#1| (-145)) (|has| |#1| (-368))) -(-2822 (|has| |#1| (-145)) (|has| |#1| (-368))) -(-2822 (|has| |#1| (-145)) (|has| |#1| (-368))) -((((-2 (|:| -1982 (-1170)) (|:| -3740 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -1982 (-1170)) (|:| -3740 #0#))) . T)) +(-2807 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2807 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2807 (|has| |#1| (-145)) (|has| |#1| (-368))) +((((-2 (|:| -1901 (-1170)) (|:| -3813 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -1901 (-1170)) (|:| -3813 #0#))) . T)) (|has| |#1| (-349)) ((((-564)) . T)) ((((-858)) . T)) @@ -2452,15 +2452,15 @@ (((#0=(-1245 |#1| |#2| |#3| |#4|) $) |has| #0# (-286 #0# #0#))) (|has| |#1| (-363)) (((#0=(-1076) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-349))) (((#0=(-407 (-564)) #0#) . T) ((#1=(-695) #1#) . T) (($ $) . T)) ((((-316 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) |has| |#1| (-363))) ((((-858)) . T)) (|has| |#1| (-1094)) (((|#1|) . T)) -(((|#1|) -2822 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) -(((|#1|) -2822 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) +(((|#1|) -2807 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) +(((|#1|) -2807 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) (((|#2|) . T)) ((((-407 (-564))) . T) (((-695)) . T) (($) . T)) ((((-579)) . T)) @@ -2483,7 +2483,7 @@ (((|#1|) . T)) ((((-564)) . T)) (((|#2|) . T) (((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) ((|#1|) . T) (($) . T) (((-564)) . T)) -(-2822 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2807 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2521,7 +2521,7 @@ (|has| |#2| (-1018)) ((($) . T)) (|has| |#1| (-905)) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2529,9 +2529,9 @@ ((($) . T)) (|has| |#1| (-363)) ((((-906 |#1|)) . T)) -((($) -2822 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2807 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) -(-2822 (|has| |#1| (-368)) (|has| |#1| (-846))) +(-2807 (|has| |#1| (-368)) (|has| |#1| (-846))) (((|#1|) . T)) ((((-767)) . T)) ((((-858)) . T)) @@ -2542,16 +2542,16 @@ ((((-564)) . T) (($) . T)) ((((-564)) . T) (($) . T)) ((((-767) |#1|) . T)) -(((|#2| (-240 (-2245 |#1|) (-767))) . T)) +(((|#2| (-240 (-2181 |#1|) (-767))) . T)) (((|#1| (-531 |#3|)) . T)) ((((-407 (-564))) . T)) -(-2822 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2807 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((((-1152)) . T) (((-858)) . T)) -(((#0=(-2 (|:| -1982 (-1170)) (|:| -3740 (-52))) #0#) |has| (-2 (|:| -1982 (-1170)) (|:| -3740 (-52))) (-309 (-2 (|:| -1982 (-1170)) (|:| -3740 (-52)))))) +(((#0=(-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) #0#) |has| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (-309 (-2 (|:| -1901 (-1170)) (|:| -3813 (-52)))))) ((((-1152)) . T)) (|has| |#1| (-905)) (|has| |#2| (-363)) -(-2822 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2807 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-169 (-379))) . T) (((-225)) . T) (((-379)) . T)) ((((-858)) . T)) (((|#1|) . T)) @@ -2568,11 +2568,11 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2822 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2807 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-38 (-407 (-564)))) (-12 (|has| |#1| (-545)) (|has| |#1| (-824))) ((((-858)) . T)) -((((-1170)) -2822 (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-896 (-1170)))) (-12 (|has| |#1| (-363)) (|has| |#2| (-896 (-1170)))))) +((((-1170)) -2807 (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-896 (-1170)))) (-12 (|has| |#1| (-363)) (|has| |#2| (-896 (-1170)))))) (|has| |#1| (-363)) ((((-1170)) -12 (|has| |#1| (-15 * (|#1| (-407 (-564)) |#1|))) (|has| |#1| (-896 (-1170))))) (|has| |#1| (-363)) @@ -2583,7 +2583,7 @@ (((|#2|) |has| |#1| (-363))) (((|#2|) |has| |#1| (-363))) ((((-564)) . T) (($) . T)) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -2608,9 +2608,9 @@ ((((-379)) -12 (|has| |#1| (-363)) (|has| |#2| (-882 (-379)))) (((-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-882 (-564))))) (|has| |#1| (-363)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-363)) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-363)) (|has| |#1| (-556)) (((|#1|) . T)) @@ -2619,22 +2619,22 @@ ((((-1152)) . T) (((-506)) . T) (((-225)) . T) (((-564)) . T)) (((|#1|) . T)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) -(-2822 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2807 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (((|#2|) . T)) (((|#2|) . T)) -(-2822 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) -((((-2 (|:| -1982 (-1152)) (|:| -3740 |#1|))) . T)) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +(-2807 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) +((((-2 (|:| -1901 (-1152)) (|:| -3813 |#1|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) (|has| |#1| (-38 (-407 (-564)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-407 (-564)))) -(-2822 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2807 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) ((((-1152) |#1|) . T)) -(-2822 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2807 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-2822 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2807 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) ((((-581 |#1|)) . T)) ((($) . T)) @@ -2642,7 +2642,7 @@ (|has| |#1| (-556)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2822 (|has| |#1| (-145)) (|has| |#1| (-349))) +(-2807 (|has| |#1| (-145)) (|has| |#1| (-349))) (|has| |#1| (-147)) ((((-858)) . T)) ((($) . T)) @@ -2670,7 +2670,7 @@ ((((-858)) . T)) ((((-906 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-858)) -2822 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) +((((-858)) -2807 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) ((((-114)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2692,7 +2692,7 @@ ((((-564)) . T)) ((((-858)) . T)) ((((-564)) . T)) -(-2822 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-2807 (|has| |#2| (-789)) (|has| |#2| (-844))) ((((-169 (-379))) . T) (((-225)) . T) (((-379)) . T)) ((((-858)) . T)) ((((-858)) . T)) @@ -2704,9 +2704,9 @@ (((|#1|) . T) (($) . T) (((-407 (-564))) . 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T)) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-556))) ((((-379)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2736,7 +2736,7 @@ (|has| |#1| (-556)) (|has| |#1| (-1094)) ((((-776 |#1| (-860 |#2|))) |has| (-776 |#1| (-860 |#2|)) (-309 (-776 |#1| (-860 |#2|))))) -(-2822 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2807 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -2748,13 +2748,13 @@ (|has| |#2| (-363)) ((((-581 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) ((((-564)) . T) (((-407 (-564))) . T) (($) . T)) -((((-2 (|:| -1982 (-1152)) (|:| -3740 (-52)))) . T)) +((((-2 (|:| -1901 (-1152)) (|:| -3813 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-564)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-858)) . T)) ((((-858)) . 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T)) +((((-1166 |#1|)) . T) (((-564)) . T) (($) -2807 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((-1076)) . T) ((|#1|) . T) (((-407 (-564))) -2807 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564)))))) +(-2807 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) +((((-1119 |#1| (-1170))) . T) (((-564)) . T) (((-1082 (-1170))) . T) (($) -2807 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) -2807 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-1170)) . T)) (((#0=(-581 |#1|) #0#) . T) (($ $) . T) ((#1=(-407 (-564)) #1#) . T)) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) (((|#1|) |has| |#1| (-172))) @@ -2784,7 +2784,7 @@ (((|#1|) . T)) ((((-858)) . T)) ((((-294 |#3|)) . T)) -(((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564)))) ((|#2| |#2|) . T) (($ $) -2822 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) +(((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564)))) ((|#2| |#2|) . T) (($ $) -2807 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) . T)) @@ -2792,21 +2792,21 @@ (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) -((($ $) -2822 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) -((($ $) -2822 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1| |#1|) . 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T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) +((($ $) -2807 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) ((((-858)) . T)) -((($) -2822 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((($) -2822 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2807 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2807 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (|has| |#2| (-905)) (|has| |#1| (-905)) -((($) -2822 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2807 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-858)) . T)) (((|#1|) . T)) -((((-2 (|:| -1982 (-1152)) (|:| -3740 |#1|))) . T)) +((((-2 (|:| -1901 (-1152)) (|:| -3813 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2821,10 +2821,10 @@ (((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) (((#0=(-407 (-564)) #0#) . T)) ((((-407 (-564))) . T)) -(-2822 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2807 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (((|#1|) . T)) (((|#1|) . T)) -(-2822 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2807 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-407 (-564))) . T) (((-564)) . T) (($) . T)) ((((-536)) . T)) ((((-858)) . T)) @@ -2841,12 +2841,12 @@ ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) ((((-1170)) |has| |#1| (-896 (-1170)))) ((((-906 |#1|)) . T) (((-407 (-564))) . T) (($) . T)) -((($) . T) (((-407 (-564))) -2822 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) . T)) -(((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564)))) ((|#1| |#1|) . T) (($ $) -2822 (|has| |#1| (-172)) (|has| |#1| (-556)))) +((($) . T) (((-407 (-564))) -2807 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) . T)) +(((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564)))) ((|#1| |#1|) . T) (($ $) -2807 (|has| |#1| (-172)) (|has| |#1| (-556)))) ((($) . T) (((-407 (-564))) . T)) (((|#1|) . T) (((-407 (-564))) . T) (((-564)) . T) (($) . T)) (((|#2|) |has| |#2| (-1045)) (((-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1045)))) -((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T) (($) -2822 (|has| |#1| (-172)) (|has| |#1| (-556)))) +((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T) (($) -2807 (|has| |#1| (-172)) (|has| |#1| (-556)))) (|has| |#1| (-556)) (((|#1|) |has| |#1| (-363))) ((((-564)) . T)) @@ -2865,8 +2865,8 @@ ((((-858)) . T)) (|has| |#2| (-816)) (|has| |#2| (-816)) -((((-407 (-564))) -2822 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#2|) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-407 (-564))) -2822 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) +((((-407 (-564))) -2807 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#2|) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-407 (-564))) -2807 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) |has| |#1| (-1034 (-407 (-564))))) ((((-564)) |has| |#1| (-882 (-564))) (((-379)) |has| |#1| (-882 (-379)))) @@ -2892,12 +2892,12 @@ (((|#2| (-767)) . T)) ((((-1170)) . T)) ((((-866 |#1|)) . 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T)) (((|#2| |#2|) . T) ((#0=(-407 (-564)) #0#) . T) (($ $) . T)) ((((-564)) . T)) @@ -3241,17 +3241,17 @@ ((((-129)) . T)) ((((-858)) . T)) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) -((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2822 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) +((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2807 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) . T)) (|has| |#1| (-363)) -((($) -2822 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2807 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-1098)) . T)) ((((-858)) . T)) -((($) -2822 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2807 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((($) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T)) ((($) . T)) -((($) -2822 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2807 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-1251 |#1| |#2| |#3|)) . T) (((-1223 |#1| |#2| |#3|)) . T)) ((((-1170)) . T) (((-858)) . T)) (|has| |#2| (-905)) @@ -3261,7 +3261,7 @@ (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-172))) ((((-695)) . T)) -((((-858)) -2822 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2807 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) ((((-1175)) . T)) (((|#1|) |has| |#1| (-172))) ((((-1175)) . T)) @@ -3273,13 +3273,13 @@ ((((-1175)) . T)) ((((-1175)) . T)) ((((-1175)) . T)) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-349))) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-349))) ((((-1175)) . T)) ((((-1175)) . T)) (|has| |#1| (-363)) (|has| |#1| (-363)) -(-2822 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-2807 (|has| |#1| (-172)) (|has| |#1| (-556))) (((|#1| (-564)) . T)) (((|#1| (-407 (-564))) . T)) (((|#1| (-767)) . T)) @@ -3294,16 +3294,16 @@ ((((-888 (-379))) . T) (((-888 (-564))) . T) (((-1170)) . T) (((-536)) . T)) (((|#1|) . T)) ((((-858)) . T)) -(-2822 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) -(-2822 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-789)) (|has| |#2| (-789)))) +(-2807 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2807 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-789)) (|has| |#2| (-789)))) ((((-564)) . T)) ((((-564)) . T)) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-2822 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2807 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-1170)) -12 (|has| |#2| (-896 (-1170))) (|has| |#2| (-1045)))) -(-2822 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-722)) (|has| |#2| (-722)))) +(-2807 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-722)) (|has| |#2| (-722)))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-363)) @@ -3329,7 +3329,7 @@ (((|#1| |#2|) . T)) ((((-564)) . T) ((|#2|) |has| |#2| (-172))) ((((-114)) . T) ((|#1|) . T) (((-564)) . T)) -(-2822 (|has| |#1| (-349)) (|has| |#1| (-368))) +(-2807 (|has| |#1| (-349)) (|has| |#1| (-368))) (((|#1| |#2|) . T)) ((((-225)) . T)) ((((-407 (-564))) . T) (($) . T) (((-564)) . T)) @@ -3341,7 +3341,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-858)) -2822 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) +((((-858)) -2807 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) ((($) . T) (((-407 (-564))) . T)) (|has| |#1| (-905)) (|has| |#1| (-905)) @@ -3352,14 +3352,14 @@ (((|#1| |#1|) |has| |#1| (-172))) (((|#1|) . T) (((-564)) . T)) ((((-1175)) . T)) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2822 (|has| |#1| (-21)) (|has| |#1| (-844))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2807 (|has| |#1| (-21)) (|has| |#1| (-844))) (((|#2|) . T)) -(-2822 (|has| |#1| (-21)) (|has| |#1| (-844))) +(-2807 (|has| |#1| (-21)) (|has| |#1| (-844))) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (((|#1|) . T)) -((((-858)) -2822 (-12 (|has| |#1| (-611 (-858))) (|has| |#2| (-611 (-858)))) (-12 (|has| |#1| (-1094)) (|has| |#2| (-1094))))) +((((-858)) -2807 (-12 (|has| |#1| (-611 (-858))) (|has| |#2| (-611 (-858)))) (-12 (|has| |#1| (-1094)) (|has| |#2| (-1094))))) ((((-407 |#2|) |#3|) . T)) ((((-407 (-564))) . T) (($) . T)) (|has| |#1| (-38 (-407 (-564)))) @@ -3371,19 +3371,19 @@ (((|#1|) . T) (((-407 (-564))) . T) (((-564)) . T) (($) . T)) (((#0=(-564) #0#) . T)) ((($) . T) (((-407 (-564))) . T)) -(-2822 (|has| |#4| (-172)) (|has| |#4| (-722)) (|has| |#4| (-844)) (|has| |#4| (-1045))) -(-2822 (|has| |#3| (-172)) (|has| |#3| (-722)) (|has| |#3| (-844)) (|has| |#3| (-1045))) +(-2807 (|has| |#4| (-172)) (|has| |#4| (-722)) (|has| |#4| (-844)) (|has| |#4| (-1045))) +(-2807 (|has| |#3| (-172)) (|has| |#3| (-722)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((((-858)) . T) (((-1175)) . T)) (|has| |#4| (-789)) -(-2822 (|has| |#4| (-789)) (|has| |#4| (-844))) +(-2807 (|has| |#4| (-789)) (|has| |#4| (-844))) (|has| |#4| (-844)) (|has| |#3| (-789)) ((((-1175)) . T)) -(-2822 (|has| |#3| (-789)) (|has| |#3| (-844))) +(-2807 (|has| |#3| (-789)) (|has| |#3| (-844))) (|has| |#3| (-844)) ((((-564)) . T)) (((|#2|) . T)) -((((-1170)) -2822 (-12 (|has| (-1168 |#1| |#2| |#3|) (-896 (-1170))) (|has| |#1| (-363))) (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-896 (-1170)))))) +((((-1170)) -2807 (-12 (|has| (-1168 |#1| |#2| |#3|) (-896 (-1170))) (|has| |#1| (-363))) (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-896 (-1170)))))) ((((-1170)) -12 (|has| |#1| (-15 * (|#1| (-407 (-564)) |#1|))) (|has| |#1| (-896 (-1170))))) ((((-1170)) -12 (|has| |#1| (-15 * (|#1| (-767) |#1|))) (|has| |#1| (-896 (-1170))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3398,11 +3398,11 @@ ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-1134 |#1| |#2|)) . T)) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -(((|#2|) . T) (((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) -((((-2 (|:| -1982 (-1170)) (|:| -3740 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) +((((-2 (|:| -1901 (-1170)) (|:| -3813 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1018)) -(((|#2|) . T) (((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) ((((-858)) . T)) ((((-536)) |has| |#2| (-612 (-536))) (((-888 (-564))) |has| |#2| (-612 (-888 (-564)))) (((-888 (-379))) |has| |#2| (-612 (-888 (-379)))) (((-379)) . #0=(|has| |#2| (-1018))) (((-225)) . #0#)) ((((-294 |#3|)) . T)) @@ -3418,15 +3418,15 @@ ((((-1168 |#1| |#2| |#3|)) . T)) ((((-1168 |#1| |#2| |#3|)) . T) (((-1161 |#1| |#2| |#3|)) . T)) ((((-858)) . T)) -((((-858)) -2822 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2807 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) ((((-564) |#1|) . 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T)) -((((-858)) -2822 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2807 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) ((((-129)) . T) (((-858)) . T)) ((((-564) |#1|) . T)) ((((-129)) . T)) @@ -3450,13 +3450,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-363)) (|has| |#2| (-286 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-2822 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) -(-2822 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(-2807 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) +(-2807 (|has| |#1| (-846)) (|has| |#1| (-1094))) ((((-858)) . T)) ((((-858)) . T)) ((((-858)) . T)) (((|#1| (-531 |#2|)) . T)) -((((-2 (|:| -1982 (-1170)) (|:| -3740 (-52)))) . T)) +((((-2 (|:| -1901 (-1170)) (|:| -3813 (-52)))) . T)) ((((-564) (-129)) . T)) (((|#1| (-564)) . T)) (((|#1| (-407 (-564))) . T)) @@ -3470,8 +3470,8 @@ ((((-1175)) . T)) ((((-858)) . T) (((-1175)) . T)) ((((-858)) . T) (((-1175)) . T)) -(-2822 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) -(-2822 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2807 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2807 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((($) . T)) (((|#2| (-531 (-860 |#1|))) . T)) ((((-1175)) . T)) @@ -3486,13 +3486,13 @@ ((((-1175)) . T)) ((((-858)) . T) (((-1175)) . T)) ((((-1175)) . T)) -((((-858)) -2822 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2807 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (((|#1|) . T)) (((|#2| (-767)) . T)) (((|#1| |#2|) . T)) ((((-1152) |#1|) . T)) ((((-407 |#2|)) . T)) -((((-2 (|:| -1982 |#1|) (|:| -3740 |#2|))) . T)) +((((-2 (|:| -1901 |#1|) (|:| -3813 |#2|))) . T)) (|has| |#1| (-556)) (|has| |#1| (-556)) ((($) . T) ((|#2|) . T)) @@ -3501,14 +3501,14 @@ ((((-564)) . T) (($) . 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-452) T) ((-359 . -131) T) ((-316 . -400) 141046) ((-313 . -400) 141007) ((-353 . -131) T) ((-345 . -131) T) ((-1175 . -1094) T) ((-1114 . -38) 140994) ((-1088 . -611) 140961) ((-108 . -131) T) ((-950 . -1094) T) ((-917 . -1094) T) ((-767 . -1094) T) ((-668 . -1094) T) ((-697 . -147) T) ((-116 . -147) T) ((-1281 . -21) T) ((-1281 . -25) T) ((-1279 . -21) T) ((-1279 . -25) T) ((-660 . -1051) 140945) ((-531 . -846) T) ((-500 . -846) T) ((-355 . -1051) 140897) ((-352 . -1051) 140849) ((-344 . -1051) 140801) ((-251 . -1209) T) ((-250 . -1209) T) ((-264 . -1051) 140644) ((-247 . -1051) 140487) ((-660 . -111) 140466) ((-547 . -840) T) ((-355 . -111) 140404) ((-352 . -111) 140342) ((-344 . -111) 140280) ((-264 . -111) 140109) ((-247 . -111) 139938) ((-813 . -1213) 139917) ((-621 . -411) 139901) ((-44 . -21) T) ((-44 . -25) T) ((-811 . -637) 139807) ((-813 . -556) 139786) ((-251 . -1034) 139613) ((-250 . -1034) 139440) ((-126 . -119) 139424) ((-906 . -1051) 139389) ((-708 . -102) T) ((-695 . -1052) T) ((-536 . -616) 139292) ((-343 . -172) T) ((-152 . -25) T) ((-88 . -611) 139274) ((-152 . -21) T) ((-906 . -111) 139230) ((-40 . -713) 139175) ((-866 . -1094) T) ((-660 . -614) 139152) ((-642 . -614) 139133) ((-355 . -614) 139070) ((-352 . -614) 139007) ((-547 . -1094) T) ((-344 . -614) 138944) ((-327 . -612) 138905) ((-327 . -611) 138817) ((-264 . -614) 138570) ((-247 . -614) 138355) ((-1222 . -788) 138308) ((-1222 . -791) 138261) ((-251 . -377) 138230) ((-250 . -377) 138199) ((-650 . -38) 138169) ((-606 . -34) T) ((-482 . -1106) 138079) ((-475 . -34) T) ((-1107 . -131) 137949) ((-960 . -25) 137760) ((-906 . -614) 137710) ((-870 . -611) 137692) ((-960 . -21) 137647) ((-811 . -21) 137557) ((-811 . -25) 137408) ((-1215 . -368) T) ((-621 . -1052) T) ((-1172 . -556) 137387) ((-1166 . -47) 137364) ((-355 . -1045) T) ((-352 . -1045) T) ((-482 . -23) 137234) ((-344 . -1045) T) ((-247 . -1045) T) ((-264 . -1045) T) ((-1119 . -47) 137206) ((-117 . -1052) T) ((-1030 . -644) 137180) 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-1094) T) ((-1119 . -882) 136310) ((-129 . -846) T) ((-1166 . -1034) 136190) ((-1119 . -1034) 136073) ((-183 . -611) 136055) ((-850 . -1034) 135951) ((-778 . -286) 135878) ((-813 . -1106) T) ((-1030 . -722) T) ((-600 . -647) 135862) ((-1042 . -972) 135791) ((-995 . -102) T) ((-813 . -23) T) ((-708 . -1145) 135769) ((-690 . -1052) T) ((-600 . -373) 135753) ((-351 . -452) T) ((-343 . -290) T) ((-1260 . -1094) T) ((-248 . -1094) T) ((-399 . -102) T) ((-289 . -21) T) ((-289 . -25) T) ((-361 . -722) T) ((-706 . -1094) T) ((-695 . -1094) T) ((-361 . -473) T) ((-1203 . -611) 135735) ((-1166 . -377) 135719) ((-1119 . -377) 135703) ((-1020 . -411) 135665) ((-141 . -229) 135647) ((-379 . -790) T) ((-379 . -787) T) ((-866 . -172) T) ((-379 . -722) T) ((-707 . -611) 135629) ((-708 . -38) 135458) ((-1259 . -1257) 135442) ((-351 . -402) T) ((-1259 . -1094) 135392) ((-580 . -713) 135379) ((-564 . -713) 135366) ((-495 . -713) 135331) ((-316 . -627) 135310) ((-832 . -722) T) ((-823 . -722) T) ((-641 . -1209) T) ((-1074 . -637) 135258) ((-1166 . -896) 135201) ((-1119 . -896) 135185) ((-658 . -1051) 135169) ((-108 . -637) 135151) ((-482 . -131) 135021) ((-1172 . -1106) T) ((-948 . -47) 134990) ((-621 . -1094) T) ((-658 . -111) 134969) ((-491 . -611) 134935) ((-327 . -288) 134912) ((-481 . -47) 134869) ((-1172 . -23) T) ((-117 . -1094) T) ((-103 . -102) 134847) ((-1271 . -1106) T) ((-548 . -846) T) ((-1049 . -131) T) ((-1020 . -1052) T) ((-815 . -1034) 134831) ((-999 . -720) 134803) ((-1271 . -23) T) ((-695 . -713) 134768) ((-585 . -611) 134750) ((-386 . -1034) 134734) ((-354 . -1052) T) ((-385 . -131) T) ((-324 . -1034) 134718) ((-225 . -882) 134700) ((-1000 . -916) T) ((-91 . -34) T) ((-1000 . -816) T) ((-910 . -916) T) ((-1189 . -611) 134682) ((-1114 . -824) T) ((-487 . -1213) T) ((-1099 . -1094) T) ((-1074 . -21) T) ((-1074 . -25) T) ((-217 . -1213) T) ((-995 . -309) 134647) ((-225 . -1034) 134607) ((-40 . -290) T) ((-710 . -644) 134567) ((-677 . -614) 134548) ((-672 . -614) 134529) ((-487 . -556) T) ((-478 . -614) 134510) ((-359 . -25) T) ((-359 . -21) T) ((-353 . -25) T) ((-217 . -556) T) ((-353 . -21) T) ((-345 . -25) T) ((-345 . -21) T) ((-245 . -614) 134487) ((-138 . -614) 134468) ((-137 . -614) 134449) ((-133 . -614) 134430) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1052) T) ((-580 . -172) T) ((-564 . -172) T) ((-495 . -172) T) ((-654 . -611) 134412) ((-733 . -732) 134396) ((-336 . -611) 134378) ((-68 . -383) T) ((-68 . -395) T) ((-1096 . -107) 134362) ((-1056 . -882) 134344) ((-948 . -882) 134269) ((-649 . -1106) T) ((-621 . -713) 134256) ((-481 . -882) NIL) ((-1140 . -102) T) ((-1088 . -616) 134240) ((-1056 . -1034) 134222) ((-97 . -611) 134204) ((-477 . -147) T) ((-948 . -1034) 134084) ((-117 . -713) 134029) ((-649 . -23) T) ((-481 . -1034) 133905) ((-1081 . -612) NIL) ((-1081 . -611) 133887) ((-778 . -612) NIL) ((-778 . -611) 133848) ((-776 . -612) 133482) ((-776 . -611) 133396) ((-1107 . -637) 133302) ((-461 . -611) 133284) ((-454 . -611) 133266) ((-454 . -612) 133127) ((-1031 . -229) 133073) ((-868 . -905) 133052) ((-126 . -34) T) ((-813 . -131) T) ((-645 . -611) 133034) ((-578 . -102) T) ((-355 . -1278) 133018) ((-352 . -1278) 133002) ((-344 . -1278) 132986) ((-127 . -514) 132919) ((-121 . -514) 132852) ((-511 . -788) T) ((-511 . -791) T) ((-510 . -790) T) ((-103 . -309) 132790) ((-222 . -102) 132768) ((-690 . -1094) T) ((-695 . -172) T) ((-868 . -644) 132720) ((-65 . -384) T) ((-275 . -611) 132702) ((-65 . -395) T) ((-948 . -377) 132686) ((-866 . -290) T) ((-50 . -611) 132668) ((-995 . -38) 132616) ((-581 . -611) 132598) ((-481 . -377) 132582) ((-581 . -612) 132564) ((-518 . -611) 132546) ((-906 . -1278) 132533) ((-867 . -1209) T) ((-697 . -452) T) ((-495 . -514) 132499) ((-487 . -363) T) ((-355 . -368) 132478) ((-352 . -368) 132457) ((-344 . -368) 132436) ((-710 . -722) T) ((-217 . -363) T) ((-116 . -452) T) ((-1282 . -1273) 132420) ((-867 . -880) 132397) ((-867 . -882) NIL) ((-960 . -846) 132296) ((-811 . -846) 132247) ((-1216 . -102) T) ((-650 . -652) 132231) ((-1195 . -34) T) ((-171 . -611) 132213) ((-1107 . -21) 132123) ((-1107 . -25) 131974) ((-867 . -1034) 131951) ((-948 . -896) 131932) ((-1232 . -47) 131909) ((-906 . -368) T) ((-59 . -647) 131893) ((-516 . -647) 131877) ((-481 . -896) 131854) ((-71 . -441) T) ((-71 . -395) T) ((-496 . -647) 131838) ((-59 . -373) 131822) ((-621 . -172) T) ((-516 . -373) 131806) ((-496 . -373) 131790) ((-823 . -704) 131774) ((-1166 . -307) 131753) ((-1172 . -131) T) ((-117 . -172) T) ((-1140 . -309) 131691) ((-169 . -1209) T) ((-633 . -740) 131675) ((-605 . -740) 131659) ((-1271 . -131) T) ((-1244 . -916) 131638) ((-1223 . -916) 131617) ((-1223 . -816) NIL) ((-690 . -713) 131567) ((-1222 . -905) 131520) ((-1020 . -1094) T) ((-867 . -377) 131497) ((-867 . -338) 131474) ((-901 . -1106) T) ((-169 . -880) 131458) ((-169 . -882) 131383) ((-487 . -1106) T) ((-354 . -1094) T) ((-217 . -1106) T) ((-76 . -441) T) ((-76 . -395) T) ((-169 . -1034) 131279) ((-319 . -846) T) ((-1259 . -514) 131212) ((-1243 . -644) 131109) ((-1222 . -644) 130979) ((-868 . -790) 130958) ((-868 . -787) 130937) ((-868 . -722) T) ((-487 . -23) T) ((-223 . -611) 130919) ((-174 . -452) T) ((-222 . -309) 130857) ((-86 . -441) T) ((-86 . -395) T) ((-217 . -23) T) ((-1283 . -1276) 130836) ((-580 . -290) T) ((-564 . -290) T) ((-673 . -1034) 130820) ((-495 . -290) T) ((-136 . -470) 130775) ((-48 . -1094) T) ((-708 . -231) 130759) ((-867 . -896) NIL) ((-1232 . -882) NIL) ((-885 . -102) T) ((-881 . -102) T) ((-388 . -1094) T) ((-169 . -377) 130743) ((-169 . -338) 130727) ((-1232 . -1034) 130607) ((-851 . -1034) 130503) ((-1136 . -102) T) ((-649 . -131) T) ((-117 . -514) 130411) ((-658 . -788) 130390) ((-658 . -791) 130369) ((-571 . -1034) 130351) ((-294 . -1266) 130321) ((-862 . -102) T) ((-959 . -556) 130300) ((-1203 . -1051) 130183) ((-482 . -637) 130089) ((-900 . -1094) T) ((-1020 . -713) 130026) ((-707 . -1051) 129991) ((-615 . -102) T) ((-600 . -34) T) ((-1141 . -1209) T) 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. -1045) T) ((-385 . -21) T) ((-385 . -25) T) ((-690 . -514) NIL) ((-1020 . -172) T) ((-707 . -243) T) ((-1056 . -545) T) ((-506 . -102) T) ((-502 . -102) T) ((-354 . -172) T) ((-343 . -611) 128706) ((-394 . -611) 128688) ((-474 . -722) T) ((-1114 . -844) T) ((-888 . -1034) 128656) ((-108 . -846) T) ((-654 . -1051) 128640) ((-487 . -131) T) ((-1245 . -1052) T) ((-217 . -131) T) ((-1150 . -102) 128618) ((-99 . -1094) T) ((-245 . -662) 128602) ((-245 . -647) 128586) ((-654 . -111) 128565) ((-585 . -614) 128549) ((-316 . -411) 128533) ((-245 . -373) 128517) ((-1153 . -235) 128464) ((-995 . -231) 128448) ((-74 . -1209) T) ((-48 . -172) T) ((-697 . -387) T) ((-697 . -143) T) ((-1282 . -102) T) ((-1189 . -614) 128430) ((-1081 . -1051) 128273) ((-264 . -905) 128252) ((-247 . -905) 128231) ((-778 . -1051) 128054) ((-776 . -1051) 127897) ((-606 . -1209) T) ((-1158 . -611) 127879) ((-1081 . -111) 127708) ((-1042 . -102) T) ((-475 . -1209) T) ((-461 . -1051) 127679) ((-454 . -1051) 127522) ((-660 . -644) 127506) ((-867 . -307) T) ((-778 . -111) 127315) ((-776 . -111) 127144) ((-355 . -644) 127096) ((-352 . -644) 127048) ((-344 . -644) 127000) ((-264 . -644) 126925) ((-247 . -644) 126850) ((-1152 . -846) T) ((-1082 . -1034) 126834) ((-461 . -111) 126795) ((-454 . -111) 126624) ((-1070 . -1034) 126601) ((-996 . -34) T) ((-962 . -611) 126583) ((-954 . -1209) T) ((-126 . -1006) 126567) ((-959 . -1106) T) ((-867 . -1018) NIL) ((-731 . -1106) T) ((-711 . -1106) T) ((-654 . -614) 126485) ((-1259 . -489) 126469) ((-1136 . -38) 126429) ((-959 . -23) T) ((-861 . -1094) T) ((-839 . -102) T) ((-813 . -21) T) ((-813 . -25) T) ((-731 . -23) T) ((-711 . -23) T) ((-110 . -657) T) ((-906 . -644) 126394) ((-581 . -1051) 126359) ((-518 . -1051) 126304) ((-227 . -57) 126262) ((-453 . -23) T) ((-407 . -102) T) ((-263 . -102) T) ((-690 . -290) T) ((-862 . -38) 126232) ((-581 . -111) 126188) ((-518 . -111) 126117) ((-1081 . -614) 125853) ((-418 . -1106) T) ((-316 . -1052) 125743) ((-313 . -1052) T) 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-34) T) ((-519 . -34) T) ((-516 . -34) T) ((-454 . -326) 124196) ((-327 . -373) 124180) ((-497 . -34) T) ((-496 . -34) T) ((-999 . -1145) NIL) ((-727 . -556) 124111) ((-633 . -102) T) ((-605 . -102) T) ((-355 . -722) T) ((-352 . -722) T) ((-344 . -722) T) ((-264 . -722) T) ((-247 . -722) T) ((-1042 . -309) 124019) ((-897 . -1094) 123997) ((-50 . -1045) T) ((-1271 . -21) T) ((-1271 . -25) T) ((-1168 . -556) 123976) ((-1167 . -1213) 123955) ((-581 . -1045) T) ((-518 . -1045) T) ((-1161 . -1213) 123934) ((-361 . -1034) 123918) ((-322 . -1034) 123902) ((-1020 . -290) T) ((-379 . -882) 123884) ((-1167 . -556) 123835) ((-1161 . -556) 123786) ((-999 . -38) 123731) ((-795 . -1106) T) ((-906 . -722) T) ((-581 . -243) T) ((-581 . -233) T) ((-518 . -233) T) ((-518 . -243) T) ((-1120 . -556) 123710) ((-354 . -290) T) ((-643 . -691) 123694) ((-379 . -1034) 123654) ((-1114 . -1052) T) ((-103 . -125) 123638) ((-795 . -23) T) ((-1281 . -1276) 123614) ((-1259 . -286) 123591) ((-407 . -309) 123556) 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-611) 122988) ((-121 . -611) 122920) ((-1287 . -172) T) ((-1167 . -363) 122899) ((-1161 . -363) 122878) ((-316 . -1094) T) ((-418 . -131) T) ((-313 . -1094) T) ((-407 . -38) 122830) ((-1127 . -102) T) ((-1245 . -713) 122722) ((-650 . -1052) T) ((-1129 . -1254) T) ((-319 . -145) 122701) ((-319 . -147) 122680) ((-139 . -1094) T) ((-136 . -1094) T) ((-114 . -1094) T) ((-854 . -102) T) ((-580 . -611) 122662) ((-564 . -612) 122561) ((-564 . -611) 122543) ((-495 . -611) 122525) ((-495 . -612) 122470) ((-485 . -23) T) ((-482 . -846) 122421) ((-487 . -637) 122403) ((-961 . -611) 122385) ((-217 . -637) 122367) ((-225 . -404) T) ((-658 . -644) 122351) ((-55 . -611) 122333) ((-1166 . -916) 122312) ((-727 . -1106) T) ((-351 . -102) T) ((-1208 . -1077) T) ((-1114 . -840) T) ((-814 . -846) T) ((-727 . -23) T) ((-343 . -1051) 122257) ((-1152 . -1151) T) ((-1141 . -107) 122241) ((-1168 . -1106) T) ((-1167 . -1106) T) ((-515 . -1034) 122225) ((-1161 . -1106) T) ((-1120 . -1106) T) ((-343 . -111) 122154) ((-1000 . -1213) T) ((-126 . -1209) T) ((-910 . -1213) T) ((-690 . -286) NIL) ((-1260 . -611) 122136) ((-1168 . -23) T) ((-1167 . -23) T) ((-1161 . -23) T) ((-1000 . -556) T) ((-1136 . -231) 122120) ((-910 . -556) T) ((-1120 . -23) T) ((-248 . -611) 122102) ((-1069 . -1094) T) ((-795 . -131) T) ((-706 . -611) 122084) ((-316 . -713) 121994) ((-313 . -713) 121923) ((-695 . -611) 121905) ((-695 . -612) 121850) ((-407 . -400) 121834) ((-438 . -1094) T) ((-487 . -25) T) ((-487 . -21) T) ((-1114 . -1094) T) ((-217 . -25) T) ((-217 . -21) T) ((-708 . -411) 121818) ((-710 . -1034) 121787) ((-1259 . -611) 121699) ((-1259 . -612) 121660) ((-1245 . -172) T) ((-245 . -34) T) ((-343 . -614) 121590) ((-394 . -614) 121572) ((-922 . -970) T) ((-1195 . -1209) T) ((-658 . -787) 121551) ((-658 . -790) 121530) ((-398 . -395) T) ((-523 . -102) 121508) ((-1031 . -1094) T) ((-222 . -991) 121492) ((-504 . -102) T) ((-621 . -611) 121474) ((-45 . -846) NIL) ((-621 . -612) 121451) ((-1031 . -608) 121426) 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((-1259 . -288) 118146) ((-1203 . -644) 118071) ((-959 . -21) T) ((-959 . -25) T) ((-731 . -21) T) ((-731 . -25) T) ((-711 . -21) T) ((-711 . -25) T) ((-707 . -644) 118036) ((-453 . -21) T) ((-453 . -25) T) ((-339 . -102) T) ((-174 . -102) T) ((-995 . -1052) T) ((-866 . -1045) T) ((-770 . -102) T) ((-1244 . -363) 118015) ((-1243 . -896) 117921) ((-1223 . -363) 117900) ((-1222 . -896) 117751) ((-1020 . -611) 117733) ((-407 . -824) 117686) ((-1168 . -493) 117652) ((-169 . -916) 117583) ((-1167 . -493) 117549) ((-1161 . -493) 117515) ((-708 . -1094) T) ((-1120 . -493) 117481) ((-580 . -1051) 117468) ((-564 . -1051) 117455) ((-495 . -1051) 117420) ((-316 . -290) 117399) ((-313 . -290) T) ((-354 . -611) 117381) ((-418 . -25) T) ((-418 . -21) T) ((-99 . -286) 117360) ((-580 . -111) 117345) ((-564 . -111) 117330) ((-495 . -111) 117286) ((-1170 . -882) 117253) ((-897 . -489) 117237) ((-48 . -611) 117219) ((-48 . -612) 117164) ((-240 . -131) 117034) ((-1232 . -916) 117013) ((-812 . -1213) 116992) ((-388 . -490) 116973) ((-1031 . -514) 116817) ((-388 . -611) 116783) ((-812 . -556) 116714) ((-585 . -644) 116689) ((-264 . -47) 116661) ((-247 . -47) 116618) ((-531 . -509) 116595) ((-580 . -614) 116567) ((-564 . -614) 116539) ((-495 . -614) 116472) ((-1068 . -1209) T) ((-996 . -1209) T) ((-695 . -1051) 116437) ((-1251 . -23) T) ((-1251 . -1106) T) ((-1244 . -1106) T) ((-1223 . -1106) T) ((-999 . -370) 116409) ((-112 . -368) T) ((-474 . -896) 116315) ((-1244 . -23) T) ((-900 . -611) 116297) ((-55 . -614) 116279) ((-91 . -107) 116263) ((-1203 . -722) T) ((-901 . -846) 116214) ((-697 . -1145) T) ((-695 . -111) 116170) ((-1223 . -23) T) ((-595 . -1106) T) ((-594 . -1106) T) ((-708 . -713) 115999) ((-707 . -722) T) ((-1114 . -290) T) ((-1000 . -131) T) ((-487 . -846) T) ((-967 . -131) T) ((-910 . -131) T) ((-795 . -25) T) ((-217 . -846) T) ((-795 . -21) T) ((-580 . -1045) T) ((-564 . -1045) T) ((-495 . -1045) T) ((-595 . -23) T) ((-343 . -1278) 115976) ((-319 . -452) 115955) 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114963) ((-264 . -1034) 114807) ((-247 . -1034) 114683) ((-117 . -111) 114612) ((-59 . -1209) T) ((-519 . -1209) T) ((-516 . -1209) T) ((-497 . -1209) T) ((-496 . -1209) T) ((-437 . -611) 114594) ((-434 . -611) 114576) ((-3 . -102) T) ((-1023 . -1202) 114545) ((-829 . -102) T) ((-685 . -57) 114503) ((-695 . -1045) T) ((-50 . -644) 114477) ((-289 . -452) T) ((-476 . -1202) 114446) ((0 . -102) T) ((-581 . -644) 114411) ((-518 . -644) 114356) ((-49 . -102) T) ((-906 . -1034) 114343) ((-695 . -243) T) ((-1074 . -409) 114322) ((-727 . -637) 114270) ((-995 . -1094) T) ((-708 . -172) 114161) ((-621 . -614) 114056) ((-487 . -988) 114038) ((-264 . -377) 114022) ((-247 . -377) 114006) ((-399 . -1094) T) ((-1022 . -102) 113984) ((-339 . -38) 113968) ((-217 . -988) 113950) ((-117 . -614) 113880) ((-174 . -38) 113812) ((-1243 . -307) 113791) ((-1222 . -307) 113770) ((-654 . -722) T) ((-99 . -611) 113752) ((-1161 . -637) 113704) ((-485 . -25) T) ((-485 . -21) T) ((-1222 . -1018) 113656) ((-621 . -1045) T) ((-379 . -404) T) ((-390 . -102) T) ((-1099 . -616) 113571) ((-264 . -896) 113517) ((-247 . -896) 113494) ((-117 . -1045) T) ((-812 . -1106) T) ((-1081 . -722) T) ((-621 . -233) 113473) ((-619 . -102) T) ((-778 . -722) T) ((-776 . -722) T) ((-413 . -1106) T) ((-117 . -243) T) ((-40 . -368) NIL) ((-117 . -233) NIL) ((-1214 . -846) T) ((-454 . -722) T) ((-812 . -23) T) ((-727 . -25) T) ((-727 . -21) T) ((-1071 . -286) 113452) ((-78 . -396) T) ((-78 . -395) T) ((-533 . -763) 113434) ((-690 . -1051) 113384) ((-1251 . -131) T) ((-1244 . -131) T) ((-1223 . -131) T) ((-1168 . -25) T) ((-1136 . -411) 113368) ((-633 . -367) 113300) ((-605 . -367) 113232) ((-1150 . -1143) 113216) ((-103 . -1094) 113194) ((-1168 . -21) T) ((-1167 . -21) T) ((-861 . -611) 113176) ((-995 . -713) 113124) ((-223 . -644) 113091) ((-690 . -111) 113025) ((-50 . -722) T) ((-1167 . -25) T) ((-351 . -349) T) ((-1161 . -21) T) ((-1074 . -452) 112976) ((-1161 . -25) T) ((-708 . -514) 112923) ((-581 . -722) T) 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((-690 . -233) NIL) ((-839 . -844) 111916) ((-695 . -791) T) ((-695 . -788) T) ((-999 . -411) 111893) ((-354 . -111) 111822) ((-379 . -916) T) ((-407 . -844) 111801) ((-708 . -290) 111712) ((-223 . -722) T) ((-1251 . -493) 111678) ((-1244 . -493) 111644) ((-1223 . -493) 111610) ((-578 . -1094) T) ((-316 . -998) 111589) ((-222 . -1094) 111567) ((-1216 . -840) T) ((-319 . -969) 111529) ((-105 . -102) T) ((-48 . -1051) 111494) ((-1283 . -102) T) ((-381 . -102) T) ((-48 . -111) 111450) ((-1000 . -637) 111432) ((-1245 . -611) 111414) ((-531 . -102) T) ((-500 . -102) T) ((-1127 . -1128) 111398) ((-152 . -1266) 111382) ((-245 . -1209) T) ((-1208 . -102) T) ((-1020 . -614) 111319) ((-1166 . -1213) 111298) ((-354 . -614) 111228) ((-1119 . -1213) 111207) ((-240 . -21) 111117) ((-240 . -25) 110968) ((-127 . -119) 110952) ((-121 . -119) 110936) ((-44 . -740) 110920) ((-1166 . -556) 110831) ((-1119 . -556) 110762) ((-1216 . -1094) T) ((-1031 . -286) 110737) ((-1160 . -1077) T) ((-990 . -1077) T) ((-812 . -131) T) ((-117 . -791) NIL) ((-117 . -788) NIL) ((-355 . -307) T) ((-352 . -307) T) ((-344 . -307) T) ((-251 . -1106) 110647) ((-250 . -1106) 110557) ((-1020 . -1045) T) ((-999 . -1052) T) ((-48 . -614) 110490) ((-343 . -644) 110435) ((-619 . -38) 110419) ((-1272 . -611) 110381) ((-1272 . -612) 110342) ((-1071 . -611) 110324) ((-1020 . -243) T) ((-354 . -1045) T) ((-811 . -1266) 110294) ((-251 . -23) T) ((-250 . -23) T) ((-983 . -611) 110276) ((-733 . -612) 110237) ((-733 . -611) 110219) ((-795 . -846) 110198) ((-1153 . -151) 110145) ((-995 . -514) 110057) ((-354 . -233) T) ((-354 . -243) T) ((-388 . -614) 110038) ((-1000 . -25) T) ((-141 . -611) 110020) ((-141 . -612) 109979) ((-906 . -307) T) ((-1000 . -21) T) ((-967 . -25) T) ((-910 . -21) T) ((-910 . -25) T) ((-427 . -21) T) ((-427 . -25) T) ((-839 . -411) 109963) ((-48 . -1045) T) ((-1281 . -1273) 109947) ((-1279 . -1273) 109931) ((-1031 . -602) 109906) ((-316 . -612) 109767) ((-316 . -611) 109749) ((-313 . -612) NIL) 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-145) NIL) ((-1114 . -612) 108852) ((-438 . -611) 108834) ((-217 . -147) T) ((-217 . -145) NIL) ((-1114 . -611) 108816) ((-129 . -102) T) ((-52 . -102) T) ((-1223 . -637) 108768) ((-479 . -107) 108718) ((-989 . -23) T) ((-1283 . -38) 108688) ((-1166 . -1106) T) ((-1119 . -1106) T) ((-1056 . -1213) T) ((-311 . -102) T) ((-850 . -1106) T) ((-948 . -1213) 108667) ((-481 . -1213) 108646) ((-1056 . -556) T) ((-948 . -556) 108577) ((-1166 . -23) T) ((-1119 . -23) T) ((-850 . -23) T) ((-481 . -556) 108508) ((-1136 . -713) 108440) ((-1140 . -514) 108373) ((-1031 . -612) NIL) ((-1031 . -611) 108355) ((-96 . -1077) T) ((-862 . -713) 108325) ((-1203 . -47) 108294) ((-251 . -131) T) ((-250 . -131) T) ((-1098 . -1094) T) ((-999 . -1094) T) ((-62 . -611) 108276) ((-1161 . -846) NIL) ((-1020 . -788) T) ((-1020 . -791) T) ((-1287 . -1051) 108263) ((-1287 . -111) 108248) ((-866 . -644) 108235) ((-1251 . -25) T) ((-1251 . -21) T) ((-1244 . -21) T) ((-1244 . -25) T) ((-1223 . -21) T) ((-1223 . -25) T) 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-882) NIL) ((-867 . -1106) T) ((-117 . -905) NIL) ((-1281 . -1280) 105089) ((-1279 . -1280) 105068) ((-778 . -882) NIL) ((-776 . -882) 104927) ((-1274 . -25) T) ((-1274 . -21) T) ((-1206 . -102) 104905) ((-1100 . -395) T) ((-621 . -644) 104892) ((-454 . -882) NIL) ((-671 . -102) 104870) ((-1081 . -1034) 104697) ((-867 . -23) T) ((-778 . -1034) 104556) ((-776 . -1034) 104413) ((-117 . -644) 104358) ((-454 . -1034) 104234) ((-316 . -614) 103798) ((-313 . -614) 103681) ((-645 . -1034) 103665) ((-625 . -102) T) ((-222 . -489) 103649) ((-1259 . -34) T) ((-136 . -614) 103633) ((-633 . -713) 103617) ((-605 . -713) 103601) ((-666 . -38) 103561) ((-319 . -102) T) ((-85 . -611) 103543) ((-50 . -1034) 103527) ((-1114 . -1051) 103514) ((-1081 . -377) 103498) ((-778 . -377) 103482) ((-60 . -57) 103444) ((-695 . -790) T) ((-695 . -787) T) ((-581 . -1034) 103431) ((-518 . -1034) 103408) ((-695 . -722) T) ((-324 . -131) T) ((-316 . -1045) 103298) ((-313 . -1045) T) ((-169 . -1106) T) ((-776 . -377) 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101396) ((-1020 . -644) 101333) ((-523 . -1094) 101311) ((-359 . -102) T) ((-353 . -102) T) ((-345 . -102) T) ((-108 . -102) T) ((-504 . -1094) T) ((-354 . -644) 101256) ((-1166 . -637) 101204) ((-1119 . -637) 101152) ((-385 . -509) 101131) ((-829 . -844) 101110) ((-379 . -1213) T) ((-690 . -722) T) ((-339 . -1052) T) ((-1223 . -988) 101062) ((-174 . -1052) T) ((-103 . -611) 100994) ((-1168 . -145) 100973) ((-1168 . -147) 100952) ((-379 . -556) T) ((-1167 . -147) 100931) ((-1167 . -145) 100910) ((-1161 . -145) 100817) ((-407 . -290) T) ((-1161 . -147) 100724) ((-1120 . -147) 100703) ((-1120 . -145) 100682) ((-319 . -38) 100523) ((-169 . -131) T) ((-313 . -791) NIL) ((-313 . -788) NIL) ((-650 . -1045) T) ((-48 . -644) 100488) ((-889 . -614) 100465) ((-1160 . -102) T) ((-990 . -102) T) ((-989 . -21) T) ((-127 . -1006) 100449) ((-121 . -1006) 100433) ((-989 . -25) T) ((-897 . -119) 100417) ((-1152 . -102) T) ((-1232 . -131) T) ((-1166 . -25) T) ((-1166 . -21) T) ((-851 . -131) T) ((-1119 . -25) T) ((-1119 . -21) T) ((-850 . -25) T) ((-850 . -21) T) ((-778 . -307) 100396) ((-643 . -102) 100374) ((-630 . -102) T) ((-1153 . -309) 100169) ((-571 . -131) T) ((-619 . -844) 100148) ((-1150 . -489) 100132) ((-1144 . -151) 100082) ((-1140 . -611) 100044) ((-1140 . -612) 100005) ((-1020 . -787) T) ((-1020 . -790) T) ((-1020 . -722) T) ((-708 . -1051) 99828) ((-484 . -309) 99766) ((-453 . -417) 99736) ((-351 . -172) T) ((-289 . -38) 99723) ((-274 . -102) T) ((-273 . -102) T) ((-272 . -102) T) ((-271 . -102) T) ((-270 . -102) T) ((-269 . -102) T) ((-343 . -1034) 99700) ((-268 . -102) T) ((-212 . -102) T) ((-211 . -102) T) ((-209 . -102) T) ((-208 . -102) T) ((-207 . -102) T) ((-206 . -102) T) ((-203 . -102) T) ((-202 . -102) T) ((-201 . -102) T) ((-200 . -102) T) ((-199 . -102) T) ((-198 . -102) T) ((-197 . -102) T) ((-196 . -102) T) ((-195 . -102) T) ((-194 . -102) T) ((-193 . -102) T) ((-354 . -722) T) ((-708 . -111) 99509) ((-666 . -231) 99493) ((-581 . -307) T) ((-518 . -307) T) ((-294 . -514) 99442) ((-108 . -309) NIL) ((-72 . -395) T) ((-1107 . -102) 99232) ((-829 . -411) 99216) ((-1114 . -791) T) ((-1114 . -788) T) ((-697 . -1094) T) ((-578 . -611) 99198) ((-379 . -363) T) ((-169 . -493) 99176) ((-222 . -611) 99108) ((-134 . -1094) T) ((-116 . -1094) T) ((-48 . -722) T) ((-1042 . -489) 99073) ((-141 . -425) 99055) ((-141 . -368) T) ((-1023 . -102) T) ((-512 . -509) 99034) ((-708 . -614) 98790) ((-476 . -102) T) ((-463 . -102) T) ((-1030 . -1106) T) ((-1216 . -611) 98772) ((-1175 . -1034) 98708) ((-1168 . -35) 98674) ((-1168 . -95) 98640) ((-1168 . -1197) 98606) ((-1168 . -1194) 98572) ((-1152 . -309) NIL) ((-89 . -396) T) ((-89 . -395) T) ((-1074 . -1145) 98551) ((-1167 . -1194) 98517) ((-1167 . -1197) 98483) ((-1030 . -23) T) ((-1167 . -95) 98449) ((-571 . -493) T) ((-1167 . -35) 98415) ((-1161 . -1194) 98381) ((-1161 . -1197) 98347) ((-1161 . -95) 98313) ((-361 . -1106) T) ((-359 . -1145) 98292) ((-353 . -1145) 98271) ((-345 . -1145) 98250) ((-1161 . -35) 98216) ((-1120 . -35) 98182) ((-1120 . -95) 98148) ((-108 . -1145) T) ((-1120 . -1197) 98114) ((-829 . -1052) 98093) ((-643 . -309) 98031) ((-630 . -309) 97882) ((-1120 . -1194) 97848) ((-708 . -1045) T) ((-1056 . -637) 97830) ((-1074 . -38) 97698) ((-948 . -637) 97646) ((-1000 . -147) T) ((-1000 . -145) NIL) ((-379 . -1106) T) ((-324 . -25) T) ((-322 . -23) T) ((-939 . -846) 97625) ((-708 . -326) 97602) ((-481 . -637) 97550) ((-40 . -1034) 97438) ((-708 . -233) T) ((-697 . -713) 97425) ((-339 . -1094) T) ((-174 . -1094) T) ((-331 . -846) T) ((-418 . -452) 97375) ((-379 . -23) T) ((-359 . -38) 97340) ((-353 . -38) 97305) ((-345 . -38) 97270) ((-80 . -441) T) ((-80 . -395) T) ((-225 . -25) T) ((-225 . -21) T) ((-832 . -1106) T) ((-108 . -38) 97220) ((-823 . -1106) T) ((-770 . -1094) T) ((-116 . -713) 97207) ((-668 . -1034) 97191) ((-610 . -102) T) ((-832 . -23) T) ((-823 . -23) T) ((-1150 . -286) 97168) ((-1107 . -309) 97106) ((-1096 . -235) 97090) ((-64 . -396) T) ((-64 . -395) T) 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T) ((-116 . -172) T) ((-1107 . -38) 95694) ((-169 . -637) 95642) ((-1049 . -102) T) ((-995 . -614) 95532) ((-867 . -25) T) ((-811 . -238) 95511) ((-867 . -21) T) ((-814 . -102) T) ((-414 . -102) T) ((-385 . -102) T) ((-110 . -309) NIL) ((-227 . -102) 95489) ((-127 . -1209) T) ((-121 . -1209) T) ((-1030 . -131) T) ((-666 . -367) 95473) ((-995 . -1045) T) ((-1232 . -637) 95421) ((-1098 . -611) 95403) ((-999 . -611) 95385) ((-515 . -23) T) ((-510 . -23) T) ((-343 . -307) T) ((-508 . -23) T) ((-322 . -131) T) ((-3 . -1094) T) ((-999 . -612) 95369) ((-995 . -243) 95348) ((-995 . -233) 95327) ((-1287 . -722) T) ((-1251 . -145) 95306) ((-829 . -1094) T) ((-1251 . -147) 95285) ((-1244 . -147) 95264) ((-1244 . -145) 95243) ((-1243 . -1213) 95222) ((-1223 . -145) 95129) ((-1223 . -147) 95036) ((-1222 . -1213) 95015) ((-379 . -131) T) ((-564 . -882) 94997) ((0 . -1094) T) ((-174 . -172) T) ((-169 . -21) T) ((-169 . -25) T) ((-49 . -1094) T) ((-1245 . -644) 94902) ((-1243 . -556) 94853) ((-710 . 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-905) NIL) ((-1217 . -840) T) ((-695 . -1034) 94031) ((-707 . -916) T) ((-474 . -1213) 94010) ((-1167 . -452) 93989) ((-1161 . -452) 93968) ((-330 . -102) T) ((-868 . -1106) T) ((-316 . -644) 93789) ((-313 . -644) 93718) ((-474 . -556) 93669) ((-339 . -514) 93635) ((-550 . -151) 93585) ((-40 . -307) T) ((-839 . -611) 93567) ((-697 . -290) T) ((-868 . -23) T) ((-379 . -493) T) ((-1074 . -231) 93537) ((-512 . -102) T) ((-407 . -612) 93344) ((-407 . -611) 93326) ((-263 . -611) 93308) ((-116 . -290) T) ((-1245 . -722) T) ((-1243 . -363) 93287) ((-1222 . -363) 93266) ((-1272 . -34) T) ((-1217 . -1094) T) ((-117 . -1209) T) ((-108 . -231) 93248) ((-1172 . -102) T) ((-477 . -1094) T) ((-523 . -489) 93232) ((-733 . -34) T) ((-482 . -38) 93202) ((-141 . -34) T) ((-117 . -880) 93179) ((-117 . -882) NIL) ((-621 . -1034) 93062) ((-641 . -846) 93041) ((-1271 . -102) T) ((-295 . -102) T) ((-708 . -368) 93020) ((-117 . -1034) 92997) ((-390 . -713) 92981) ((-619 . -713) 92965) ((-45 . -309) 92769) 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((-45 . -282) 91723) ((-105 . -1094) T) ((-68 . -611) 91705) ((-966 . -102) T) ((-860 . -102) T) ((-621 . -896) 91664) ((-1283 . -1094) T) ((-381 . -1094) T) ((-82 . -1209) T) ((-1208 . -1094) T) ((-1056 . -846) T) ((-117 . -896) NIL) ((-778 . -916) 91643) ((-709 . -846) T) ((-531 . -1094) T) ((-500 . -1094) T) ((-355 . -1213) T) ((-352 . -1213) T) ((-344 . -1213) T) ((-264 . -1213) 91622) ((-247 . -1213) 91601) ((-533 . -856) T) ((-1107 . -231) 91570) ((-1152 . -824) T) ((-1136 . -1051) 91554) ((-390 . -757) T) ((-690 . -1209) T) ((-687 . -1034) 91538) ((-355 . -556) T) ((-352 . -556) T) ((-344 . -556) T) ((-264 . -556) 91469) ((-247 . -556) 91400) ((-525 . -1077) T) ((-1136 . -111) 91379) ((-453 . -740) 91349) ((-862 . -1051) 91319) ((-813 . -38) 91261) ((-690 . -880) 91243) ((-690 . -882) 91225) ((-295 . -309) 91029) ((-906 . -1213) T) ((-666 . -411) 91013) ((-862 . -111) 90978) ((-690 . -1034) 90923) ((-1000 . -452) T) ((-906 . -556) T) ((-533 . -611) 90905) ((-581 . -916) T) ((-474 . -1106) T) ((-518 . -916) T) ((-1150 . -288) 90882) ((-910 . -452) T) ((-65 . -611) 90864) ((-630 . -229) 90810) ((-474 . -23) T) ((-1114 . -790) T) ((-868 . -131) T) ((-1114 . -787) T) ((-1274 . -1276) 90789) ((-1114 . -722) T) ((-650 . -644) 90763) ((-294 . -611) 90504) ((-1136 . -614) 90422) ((-1031 . -34) T) ((-811 . -844) 90401) ((-580 . -307) T) ((-564 . -307) T) ((-495 . -307) T) ((-1283 . -713) 90371) ((-690 . -377) 90353) ((-690 . -338) 90335) ((-477 . -172) T) ((-381 . -713) 90305) ((-862 . -614) 90240) ((-867 . -846) NIL) ((-564 . -1018) T) ((-495 . -1018) T) ((-1127 . -611) 90222) ((-1107 . -238) 90201) ((-214 . -102) T) ((-1144 . -102) T) ((-71 . -611) 90183) ((-1136 . -1045) T) ((-1172 . -38) 90080) ((-854 . -611) 90062) ((-564 . -545) T) ((-666 . -1052) T) ((-727 . -945) 90015) ((-1136 . -233) 89994) ((-1076 . -1094) T) ((-1030 . -25) T) ((-1030 . -21) T) ((-999 . -1051) 89939) ((-901 . -102) T) ((-862 . -1045) T) ((-690 . -896) NIL) ((-355 . -329) 89923) ((-355 . -363) T) ((-352 . -329) 89907) ((-352 . -363) T) ((-344 . -329) 89891) ((-344 . -363) T) ((-487 . -102) T) ((-1271 . -38) 89861) ((-546 . -846) T) ((-523 . -683) 89811) ((-217 . -102) T) ((-1020 . -1034) 89691) ((-999 . -111) 89620) ((-1168 . -969) 89589) ((-520 . -151) 89573) ((-1074 . -370) 89552) ((-351 . -611) 89534) ((-322 . -21) T) ((-354 . -1034) 89511) ((-322 . -25) T) ((-1167 . -969) 89473) ((-1161 . -969) 89442) ((-76 . -611) 89424) ((-1120 . -969) 89391) ((-695 . -307) T) ((-129 . -840) T) ((-906 . -363) T) ((-379 . -25) T) ((-379 . -21) T) ((-906 . -329) 89378) ((-86 . -611) 89360) ((-695 . -1018) T) ((-673 . -846) T) ((-1243 . -131) T) ((-1222 . -131) T) ((-897 . -1006) 89344) ((-832 . -21) T) ((-48 . -1034) 89287) ((-832 . -25) T) ((-823 . -25) T) ((-823 . -21) T) ((-1281 . -1052) T) ((-549 . -102) T) ((-1279 . -1052) T) ((-650 . -722) T) ((-1098 . -616) 89190) ((-999 . -614) 89120) ((-1282 . -1051) 89104) ((-811 . -411) 89073) ((-103 . -119) 89057) ((-129 . -1094) T) ((-52 . -1094) T) ((-922 . -611) 89039) ((-867 . -988) 89016) ((-819 . -102) T) ((-1282 . -111) 88995) ((-649 . -38) 88965) ((-571 . -846) T) ((-355 . -1106) T) ((-352 . -1106) T) ((-344 . -1106) T) ((-264 . -1106) T) ((-247 . -1106) T) ((-621 . -307) 88944) ((-1144 . -309) 88748) ((-524 . -1077) T) ((-311 . -1094) T) ((-660 . -23) T) ((-482 . -231) 88717) ((-152 . -1052) T) ((-355 . -23) T) ((-352 . -23) T) ((-344 . -23) T) ((-117 . -307) T) ((-264 . -23) T) ((-247 . -23) T) ((-999 . -1045) T) ((-708 . -905) 88696) ((-1150 . -614) 88673) ((-999 . -233) 88645) ((-999 . -243) T) ((-117 . -1018) NIL) ((-906 . -1106) T) ((-1244 . -452) 88624) ((-1223 . -452) 88603) ((-523 . -611) 88535) ((-708 . -644) 88460) ((-407 . -1051) 88412) ((-504 . -611) 88394) ((-906 . -23) T) ((-487 . -309) NIL) ((-1282 . -614) 88350) ((-474 . -131) T) ((-217 . -309) NIL) ((-407 . -111) 88288) ((-811 . -1052) 88218) ((-733 . -1092) 88202) ((-1243 . -493) 88168) ((-1222 . -493) 88134) ((-548 . -840) T) ((-141 . -1092) 88116) ((-477 . -290) T) ((-1282 . -1045) T) ((-1214 . -102) T) ((-1057 . -102) T) ((-839 . -614) 87984) ((-500 . -514) NIL) ((-482 . -238) 87963) ((-407 . -614) 87861) ((-1166 . -145) 87840) ((-1166 . -147) 87819) ((-1119 . -147) 87798) ((-1119 . -145) 87777) ((-633 . -1051) 87761) ((-605 . -1051) 87745) ((-1168 . -1250) 87729) ((-666 . -1094) T) ((-666 . -1048) 87669) ((-1168 . -1237) 87646) ((-548 . -1094) T) ((-487 . -1145) T) ((-1167 . -1242) 87607) ((-1167 . -1237) 87577) ((-1167 . -1240) 87561) ((-217 . -1145) T) ((-343 . -916) T) ((-814 . -266) 87545) ((-633 . -111) 87524) ((-605 . -111) 87503) ((-1161 . -1221) 87464) ((-839 . -1045) 87443) ((-1161 . -1237) 87420) ((-515 . -25) T) ((-495 . -302) T) ((-511 . -23) T) ((-510 . -25) T) ((-508 . -25) T) ((-507 . -23) T) ((-1161 . -1219) 87404) ((-407 . -1045) T) ((-319 . -1052) T) ((-690 . -307) T) ((-108 . -844) T) ((-708 . -722) T) ((-407 . -243) T) ((-407 . -233) 87383) ((-487 . -38) 87333) ((-217 . -38) 87283) ((-474 . -493) 87249) ((-1216 . -368) T) ((-1152 . -1138) T) ((-1095 . -102) T) ((-697 . -611) 87231) ((-697 . -612) 87146) ((-710 . -21) T) ((-710 . -25) T) ((-1129 . -102) T) ((-134 . -611) 87128) ((-116 . -611) 87110) ((-157 . -25) T) ((-1281 . -1094) T) ((-868 . -637) 87058) ((-1279 . -1094) T) ((-959 . -102) T) ((-731 . -102) T) ((-711 . -102) T) ((-453 . -102) T) ((-812 . -452) 87009) ((-44 . -1094) T) ((-1082 . -846) T) ((-660 . -131) T) ((-1057 . -309) 86860) ((-666 . -713) 86844) ((-289 . -1052) T) ((-355 . -131) T) ((-352 . -131) T) ((-344 . -131) T) ((-264 . -131) T) ((-247 . -131) T) ((-418 . -102) T) ((-152 . -1094) T) ((-45 . -229) 86794) ((-954 . -846) 86773) ((-995 . -644) 86711) ((-240 . -1266) 86681) ((-1020 . -307) T) ((-294 . -1051) 86602) ((-906 . -131) T) ((-40 . -916) T) ((-487 . -400) 86584) ((-354 . -307) T) ((-217 . -400) 86566) ((-1074 . -411) 86550) ((-294 . -111) 86466) ((-1177 . -846) T) ((-1176 . -846) T) ((-868 . -25) T) ((-868 . -21) T) ((-339 . -611) 86448) ((-1245 . -47) 86392) ((-225 . -147) T) ((-174 . -611) 86374) ((-1107 . -844) 86353) ((-770 . -611) 86335) ((-128 . -846) T) ((-606 . -235) 86282) ((-475 . -235) 86232) ((-1281 . -713) 86202) ((-48 . -307) T) ((-1279 . -713) 86172) ((-65 . -614) 86101) ((-960 . -1094) T) ((-811 . -1094) 85891) ((-312 . -102) T) ((-897 . -1209) T) ((-48 . -1018) T) ((-1222 . -637) 85799) ((-685 . -102) 85777) ((-44 . -713) 85761) ((-550 . -102) T) ((-294 . -614) 85692) ((-67 . -383) T) ((-67 . -395) T) ((-658 . -23) T) ((-666 . -757) T) ((-1206 . -1094) 85670) ((-351 . -1051) 85615) ((-671 . -1094) 85593) ((-1056 . -147) T) ((-948 . -147) 85572) ((-948 . -145) 85551) ((-795 . -102) T) ((-152 . -713) 85535) ((-481 . -147) 85514) ((-481 . -145) 85493) ((-351 . -111) 85422) ((-1074 . -1052) T) ((-322 . -846) 85401) ((-1251 . -969) 85370) ((-625 . -1094) T) ((-1244 . -969) 85332) ((-511 . -131) T) ((-507 . -131) T) ((-295 . -229) 85282) ((-359 . -1052) T) ((-353 . -1052) T) ((-345 . -1052) T) ((-294 . -1045) 85224) ((-1223 . -969) 85193) ((-379 . -846) T) ((-108 . -1052) T) ((-995 . -722) T) ((-866 . -916) T) ((-839 . -791) 85172) ((-839 . -788) 85151) ((-418 . -309) 85090) ((-468 . -102) T) ((-594 . -969) 85059) ((-319 . -1094) T) ((-407 . -791) 85038) ((-407 . -788) 85017) ((-500 . -489) 84999) ((-1245 . -1034) 84965) ((-1243 . -21) T) ((-1243 . -25) T) ((-1222 . -21) T) ((-1222 . -25) T) ((-811 . -713) 84907) ((-351 . -614) 84837) ((-695 . -404) T) ((-1272 . -1209) T) ((-604 . -102) T) ((-1107 . -411) 84806) ((-999 . -368) NIL) ((-667 . -102) T) ((-180 . -102) T) ((-161 . -102) T) ((-156 . -102) T) ((-154 . -102) T) ((-103 . -34) T) ((-733 . -1209) T) ((-44 . -757) T) ((-592 . -102) T) ((-77 . -396) T) ((-77 . -395) T) ((-649 . -652) 84790) ((-141 . -1209) T) ((-867 . -147) T) ((-867 . -145) NIL) ((-1208 . -93) T) ((-351 . -1045) T) ((-70 . -383) T) ((-70 . -395) T) ((-1159 . -102) T) ((-666 . -514) 84723) ((-685 . -309) 84661) ((-959 . -38) 84558) ((-731 . -38) 84528) ((-550 . -309) 84332) ((-316 . -1209) T) ((-351 . -233) T) ((-351 . -243) T) ((-313 . -1209) T) ((-289 . -1094) T) ((-1174 . -611) 84314) ((-707 . -1213) T) ((-1150 . -647) 84298) ((-1203 . -556) 84277) ((-707 . -556) T) ((-316 . -880) 84261) ((-316 . -882) 84186) ((-313 . -880) 84147) ((-313 . -882) NIL) ((-795 . -309) 84112) ((-319 . -713) 83953) ((-324 . -323) 83930) ((-485 . -102) T) ((-474 . -25) T) ((-474 . -21) T) ((-418 . -38) 83904) ((-316 . -1034) 83567) ((-225 . -1194) T) ((-225 . -1197) T) ((-3 . -611) 83549) ((-313 . -1034) 83479) ((-2 . -1094) T) ((-2 . |RecordCategory|) T) ((-829 . -611) 83461) ((-1107 . -1052) 83391) ((-580 . -916) T) ((-564 . -816) T) ((-564 . -916) T) ((-495 . -916) T) ((-136 . -1034) 83375) ((-225 . -95) T) ((-75 . -441) T) ((-75 . -395) T) ((0 . -611) 83357) ((-169 . -147) 83336) ((-169 . -145) 83287) ((-225 . -35) T) ((-49 . -611) 83269) ((-477 . -1052) T) ((-487 . -231) 83251) ((-484 . -964) 83235) ((-482 . -844) 83214) ((-217 . -231) 83196) ((-81 . -441) T) ((-81 . -395) T) ((-1140 . -34) T) ((-811 . -172) 83175) ((-727 . -102) T) ((-1022 . -611) 83142) ((-500 . -286) 83117) ((-316 . -377) 83086) ((-313 . -377) 83047) ((-313 . -338) 83008) ((-1079 . -611) 82990) ((-812 . -945) 82937) ((-658 . -131) T) ((-1232 . -145) 82916) ((-1232 . -147) 82895) ((-1168 . -102) T) ((-1167 . -102) T) ((-1161 . -102) T) ((-1153 . -1094) T) ((-1120 . -102) T) ((-222 . -34) T) ((-289 . -713) 82882) ((-1153 . -608) 82858) ((-592 . -309) NIL) ((-484 . -1094) 82836) ((-390 . -611) 82818) ((-510 . -846) T) ((-1144 . -229) 82768) ((-1251 . -1250) 82752) ((-1251 . -1237) 82729) ((-1244 . -1242) 82690) ((-1244 . -1237) 82660) ((-1244 . -1240) 82644) ((-1223 . -1221) 82605) ((-1223 . -1237) 82582) ((-619 . -611) 82564) ((-1223 . -1219) 82548) ((-695 . -916) T) ((-1168 . -284) 82514) ((-1167 . -284) 82480) ((-1161 . -284) 82446) ((-1074 . -1094) T) ((-1055 . -1094) T) ((-48 . -302) T) ((-316 . -896) 82412) ((-313 . -896) NIL) ((-1055 . -1062) 82391) ((-1114 . -882) 82373) ((-795 . -38) 82357) ((-264 . -637) 82305) ((-247 . -637) 82253) ((-697 . -1051) 82240) ((-594 . -1237) 82217) ((-1120 . -284) 82183) ((-319 . -172) 82114) ((-359 . -1094) T) ((-353 . -1094) T) ((-345 . -1094) T) ((-500 . -19) 82096) ((-1114 . -1034) 82078) ((-1096 . -151) 82062) ((-108 . -1094) T) ((-116 . -1051) 82049) ((-707 . -363) T) ((-500 . -602) 82024) ((-697 . -111) 82009) ((-436 . -102) T) ((-45 . -1143) 81959) ((-116 . -111) 81944) ((-633 . -716) T) ((-605 . -716) T) ((-811 . -514) 81877) ((-1031 . -1209) T) ((-939 . -151) 81861) ((-1217 . -611) 81843) ((-1166 . -452) 81774) ((-1160 . -1094) T) ((-1152 . -1094) T) ((-525 . -102) T) ((-520 . -102) 81724) ((-1136 . -644) 81698) ((-1119 . -452) 81649) ((-1081 . -1213) 81628) ((-778 . -1213) 81607) ((-776 . -1213) 81586) ((-62 . -1209) T) ((-477 . -611) 81538) ((-477 . -612) 81460) ((-1081 . -556) 81391) ((-990 . -1094) T) ((-778 . -556) 81302) ((-776 . -556) 81233) ((-482 . -411) 81202) ((-621 . -916) 81181) ((-454 . -1213) 81160) ((-727 . -309) 81147) ((-697 . -614) 81119) ((-398 . -611) 81101) ((-671 . -514) 81034) ((-660 . -25) T) ((-660 . -21) T) ((-454 . -556) 80965) ((-355 . -25) T) ((-355 . -21) T) ((-117 . -916) T) ((-117 . -816) NIL) ((-352 . -25) T) ((-352 . -21) T) ((-344 . -25) T) ((-344 . -21) T) ((-264 . -25) T) ((-264 . -21) T) ((-247 . -25) T) ((-247 . -21) T) ((-83 . -384) T) ((-83 . -395) T) ((-134 . -614) 80947) ((-116 . -614) 80919) ((-1261 . -611) 80901) ((-1215 . -846) T) ((-1203 . -1106) T) ((-1203 . -23) T) ((-1161 . -309) 80786) ((-1120 . -309) 80773) ((-1074 . -713) 80641) ((-862 . -644) 80601) ((-939 . -976) 80585) ((-906 . -21) T) ((-289 . -172) T) ((-906 . -25) T) ((-311 . -93) T) ((-868 . -846) 80536) ((-707 . -1106) T) ((-707 . -23) T) ((-697 . -1045) T) ((-643 . -1094) 80514) ((-630 . -1094) T) ((-581 . -1213) T) ((-518 . -1213) T) ((-697 . -233) T) ((-630 . -608) 80489) ((-581 . -556) T) ((-518 . -556) T) ((-359 . -713) 80441) ((-339 . -1051) 80425) ((-353 . -713) 80377) ((-345 . -713) 80329) ((-174 . -1051) 80261) ((-174 . -111) 80172) ((-108 . -713) 80122) ((-339 . -111) 80101) ((-274 . -1094) T) ((-273 . -1094) T) ((-272 . -1094) T) ((-271 . -1094) T) ((-270 . -1094) T) ((-269 . -1094) T) ((-268 . -1094) T) ((-212 . -1094) T) ((-211 . -1094) T) ((-169 . -1197) 80079) ((-169 . -1194) 80057) ((-209 . -1094) T) ((-208 . -1094) T) ((-116 . -1045) T) ((-207 . -1094) T) ((-206 . -1094) T) ((-203 . -1094) T) ((-202 . -1094) T) ((-201 . -1094) T) ((-200 . -1094) T) ((-199 . -1094) T) ((-198 . -1094) T) ((-197 . -1094) T) ((-196 . -1094) T) ((-195 . -1094) T) ((-194 . -1094) T) ((-193 . -1094) T) ((-240 . -102) 79847) ((-169 . -35) 79825) ((-169 . -95) 79803) ((-650 . -1034) 79699) ((-482 . -1052) 79629) ((-1107 . -1094) 79419) ((-1136 . -34) T) ((-666 . -489) 79403) ((-73 . -1209) T) ((-105 . -611) 79385) ((-1283 . -611) 79367) ((-381 . -611) 79349) ((-339 . -614) 79301) ((-174 . -614) 79218) ((-1208 . -490) 79199) ((-727 . -38) 79048) ((-571 . -1197) T) ((-571 . -1194) T) ((-531 . -611) 79030) ((-520 . -309) 78968) ((-500 . -611) 78950) ((-500 . -612) 78932) ((-1208 . -611) 78898) ((-1161 . -1145) NIL) ((-1023 . -1065) 78867) ((-1023 . -1094) T) ((-1000 . -102) T) ((-967 . -102) T) ((-910 . -102) T) ((-889 . -1034) 78844) ((-1136 . -722) T) ((-999 . -644) 78789) ((-476 . -1094) T) ((-463 . -1094) T) ((-585 . -23) T) ((-571 . -35) T) ((-571 . -95) T) ((-427 . -102) T) ((-1057 . -229) 78735) ((-1168 . -38) 78632) ((-862 . -722) T) ((-690 . -916) T) ((-511 . -25) T) ((-507 . -21) T) ((-507 . -25) T) ((-1167 . -38) 78473) ((-339 . -1045) T) ((-1161 . -38) 78269) ((-1074 . -172) T) ((-174 . -1045) T) ((-1120 . -38) 78166) ((-708 . -47) 78143) ((-359 . -172) T) ((-353 . -172) T) ((-519 . -57) 78117) ((-497 . -57) 78067) ((-351 . -1278) 78044) ((-225 . -452) T) ((-319 . -290) 77995) ((-345 . -172) T) ((-174 . -243) T) ((-1222 . -846) 77894) ((-108 . -172) T) ((-868 . -988) 77878) ((-654 . -1106) T) ((-581 . -363) T) ((-581 . -329) 77865) ((-518 . -329) 77842) ((-518 . -363) T) ((-316 . -307) 77821) ((-313 . -307) T) ((-600 . -846) 77800) ((-1107 . -713) 77742) ((-520 . -282) 77726) ((-654 . -23) T) ((-418 . -231) 77710) ((-313 . -1018) NIL) ((-336 . -23) T) ((-103 . -1006) 77694) ((-45 . -36) 77673) ((-610 . -1094) T) ((-351 . -368) T) ((-524 . -102) T) ((-495 . -27) T) ((-240 . -309) 77611) ((-1081 . -1106) T) ((-1282 . -644) 77585) ((-778 . -1106) T) ((-776 . -1106) T) ((-454 . -1106) T) ((-1056 . -452) T) ((-948 . -452) 77536) ((-1109 . -1077) T) ((-110 . -1094) T) ((-1081 . -23) T) ((-813 . -1052) T) ((-778 . -23) T) ((-776 . -23) T) ((-481 . -452) 77487) ((-1153 . -514) 77270) ((-381 . -382) 77249) ((-1172 . -411) 77233) ((-461 . -23) T) ((-454 . -23) T) ((-96 . -1094) T) ((-484 . -514) 77166) ((-289 . -290) T) ((-1076 . -611) 77148) ((-1076 . -612) 77129) ((-407 . -905) 77108) ((-50 . -1106) T) ((-1020 . -916) T) ((-999 . -722) T) ((-708 . -882) NIL) ((-581 . -1106) T) ((-518 . -1106) T) ((-839 . -644) 77081) ((-1203 . -131) T) ((-1161 . -400) 77033) ((-1000 . -309) NIL) ((-811 . -489) 77017) ((-354 . -916) T) ((-1150 . -34) T) ((-407 . -644) 76969) ((-50 . -23) T) ((-707 . -131) T) ((-708 . -1034) 76849) ((-581 . -23) T) ((-108 . -514) NIL) ((-518 . -23) T) ((-169 . -409) 76820) ((-1134 . -1094) T) ((-1274 . -1273) 76804) ((-697 . -791) T) ((-697 . -788) T) ((-1114 . -307) T) ((-379 . -147) T) ((-280 . -611) 76786) ((-1222 . -988) 76756) ((-48 . -916) T) ((-671 . -489) 76740) ((-251 . -1266) 76710) ((-250 . -1266) 76680) ((-1170 . -846) T) ((-1107 . -172) 76659) ((-1114 . -1018) T) ((-1042 . -34) T) ((-832 . -147) 76638) ((-832 . -145) 76617) ((-733 . -107) 76601) ((-610 . -132) T) ((-482 . -1094) 76391) ((-1172 . -1052) T) ((-867 . -452) T) ((-85 . -1209) T) ((-240 . -38) 76361) ((-141 . -107) 76343) ((-708 . -377) 76327) ((-829 . -614) 76195) ((-1114 . -545) T) ((-579 . -102) T) ((-129 . -490) 76177) ((-390 . -1051) 76161) ((-1282 . -722) T) ((-1166 . -945) 76130) ((-129 . -611) 76097) ((-52 . -611) 76079) ((-1119 . -945) 76046) ((-649 . -411) 76030) ((-1271 . -1052) T) ((-619 . -1051) 76014) ((-658 . -25) T) ((-658 . -21) T) ((-1152 . -514) NIL) ((-1251 . -102) T) ((-1244 . -102) T) ((-390 . -111) 75993) ((-222 . -254) 75977) ((-1223 . -102) T) ((-1049 . -1094) T) ((-1000 . -1145) T) ((-1049 . -1048) 75917) ((-814 . -1094) T) ((-343 . -1213) T) ((-633 . -644) 75901) ((-619 . -111) 75880) ((-605 . -644) 75864) ((-595 . -102) T) ((-311 . -490) 75845) ((-585 . -131) T) ((-594 . -102) T) ((-414 . -1094) T) ((-385 . -1094) T) ((-311 . -611) 75811) ((-227 . -1094) 75789) ((-643 . -514) 75722) ((-630 . -514) 75566) ((-829 . -1045) 75545) ((-641 . -151) 75529) ((-343 . -556) T) ((-708 . -896) 75472) ((-550 . -229) 75422) ((-1251 . -284) 75388) ((-1074 . -290) 75339) ((-487 . -844) T) ((-223 . -1106) T) ((-1244 . -284) 75305) ((-1223 . -284) 75271) ((-1000 . -38) 75221) ((-217 . -844) T) ((-1203 . -493) 75187) ((-910 . -38) 75139) ((-839 . -790) 75118) ((-839 . -787) 75097) ((-839 . -722) 75076) ((-359 . -290) T) ((-353 . -290) T) ((-345 . -290) T) ((-169 . -452) 75007) ((-427 . -38) 74991) ((-108 . -290) T) ((-223 . -23) T) ((-407 . -790) 74970) ((-407 . -787) 74949) ((-407 . -722) T) ((-500 . -288) 74924) ((-477 . -1051) 74889) ((-654 . -131) T) ((-619 . -614) 74858) ((-1107 . -514) 74791) ((-336 . -131) T) ((-169 . -402) 74770) ((-482 . -713) 74712) ((-811 . -286) 74689) ((-477 . -111) 74645) ((-649 . -1052) T) ((-1232 . -452) 74576) ((-1270 . -1077) T) ((-1269 . -1077) T) ((-1081 . -131) T) ((-1049 . -713) 74518) ((-778 . -131) T) ((-776 . -131) T) ((-571 . -452) T) ((-1023 . -514) 74451) ((-619 . -1045) T) ((-591 . -1094) T) ((-533 . -173) T) ((-461 . -131) T) ((-454 . -131) T) ((-45 . -1094) T) ((-385 . -713) 74421) ((-813 . -1094) T) ((-476 . -514) 74354) ((-463 . -514) 74287) ((-453 . -367) 74257) ((-45 . -608) 74236) ((-316 . -302) T) ((-477 . -614) 74186) ((-666 . -611) 74148) ((-59 . -846) 74127) ((-1223 . -309) 74012) ((-548 . -611) 73994) ((-1000 . -400) 73976) ((-811 . -602) 73953) ((-516 . -846) 73932) ((-496 . -846) 73911) ((-40 . -1213) T) ((-995 . -1034) 73807) ((-50 . -131) T) ((-581 . -131) T) ((-518 . -131) T) ((-294 . -644) 73667) ((-343 . -329) 73644) ((-343 . -363) T) ((-322 . -323) 73621) ((-319 . -286) 73606) ((-40 . -556) T) ((-379 . -1194) T) ((-379 . -1197) T) ((-1031 . -1185) 73581) ((-1182 . -235) 73531) ((-1161 . -231) 73483) ((-330 . -1094) T) ((-379 . -95) T) ((-379 . -35) T) ((-1031 . -107) 73429) ((-477 . -1045) T) ((-479 . -235) 73379) ((-1153 . -489) 73313) ((-1283 . -1051) 73297) ((-381 . -1051) 73281) ((-477 . -243) T) ((-812 . -102) T) ((-710 . -147) 73260) ((-710 . -145) 73239) ((-484 . -489) 73223) ((-485 . -335) 73192) ((-1283 . -111) 73171) ((-512 . -1094) T) ((-482 . -172) 73150) ((-995 . -377) 73134) ((-413 . -102) T) ((-381 . -111) 73113) ((-995 . -338) 73097) ((-279 . -979) 73081) ((-278 . -979) 73065) ((-1281 . -611) 73047) ((-1279 . -611) 73029) ((-110 . -514) NIL) ((-1166 . -1235) 73013) ((-850 . -848) 72997) ((-1172 . -1094) T) ((-103 . -1209) T) ((-948 . -945) 72958) ((-813 . -713) 72900) ((-1223 . -1145) NIL) ((-481 . -945) 72845) ((-1056 . -143) T) ((-60 . -102) 72823) ((-44 . -611) 72805) ((-78 . -611) 72787) ((-351 . -644) 72732) ((-1271 . -1094) T) ((-511 . -846) T) ((-343 . -1106) T) ((-295 . -1094) T) ((-995 . -896) 72691) ((-295 . -608) 72670) ((-1283 . -614) 72619) ((-1251 . -38) 72516) ((-1244 . -38) 72357) ((-1223 . -38) 72153) ((-487 . -1052) T) ((-381 . -614) 72137) ((-217 . -1052) T) ((-343 . -23) T) ((-152 . -611) 72119) ((-829 . -791) 72098) ((-829 . -788) 72077) ((-1208 . -614) 72058) ((-595 . -38) 72031) ((-594 . -38) 71928) ((-866 . -556) T) ((-223 . -131) T) ((-319 . -998) 71894) ((-79 . -611) 71876) ((-708 . -307) 71855) ((-294 . -722) 71757) ((-820 . -102) T) ((-860 . -840) T) ((-294 . -473) 71736) ((-1274 . -102) T) ((-40 . -363) T) ((-868 . -147) 71715) ((-868 . -145) 71694) ((-1152 . -489) 71676) ((-1283 . -1045) T) ((-482 . 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-611) 69165) ((-901 . -1094) T) ((-695 . -556) T) ((-129 . -614) 69147) ((-866 . -1106) T) ((-454 . -637) 69095) ((-901 . -899) 69079) ((-379 . -452) T) ((-487 . -1094) T) ((-939 . -309) 69017) ((-697 . -644) 69004) ((-549 . -840) T) ((-217 . -1094) T) ((-316 . -916) 68983) ((-313 . -916) T) ((-313 . -816) NIL) ((-390 . -716) T) ((-866 . -23) T) ((-116 . -644) 68970) ((-474 . -145) 68949) ((-418 . -411) 68933) ((-474 . -147) 68912) ((-110 . -489) 68894) ((-311 . -614) 68875) ((-2 . -611) 68857) ((-186 . -102) T) ((-1152 . -19) 68839) ((-1152 . -602) 68814) ((-654 . -21) T) ((-654 . -25) T) ((-592 . -1138) T) ((-1107 . -286) 68791) ((-336 . -25) T) ((-336 . -21) T) ((-495 . -363) T) ((-1274 . -38) 68761) ((-1136 . -1209) T) ((-630 . -602) 68736) ((-549 . -1094) T) ((-1081 . -25) T) ((-1081 . -21) T) ((-531 . -788) T) ((-531 . -791) T) ((-117 . -1213) T) ((-959 . -1052) T) ((-621 . -556) T) ((-778 . -25) T) ((-778 . -21) T) ((-776 . -21) T) ((-776 . -25) T) ((-731 . -1052) T) ((-711 . -1052) T) ((-666 . -1051) 68720) ((-517 . -1077) T) ((-461 . -25) T) ((-117 . -556) T) ((-461 . -21) T) ((-454 . -25) T) ((-454 . -21) T) ((-1281 . -1051) 68704) ((-1136 . -1034) 68600) ((-813 . -290) 68579) ((-1279 . -1051) 68563) ((-819 . -1094) T) ((-1243 . -1194) 68529) ((-962 . -963) T) ((-666 . -111) 68508) ((-295 . -514) 68300) ((-1243 . -1197) 68266) ((-1243 . -95) 68232) ((-1226 . -102) 68210) ((-251 . -309) 68148) ((-250 . -309) 68086) ((-1223 . -231) 68038) ((-1153 . -612) NIL) ((-1153 . -611) 68020) ((-1222 . -1194) 67986) ((-1222 . -1197) 67952) ((-1217 . -368) T) ((-96 . -93) T) ((-1214 . -840) T) ((-1136 . -377) 67936) ((-1114 . -816) T) ((-1114 . -916) T) ((-1107 . -602) 67913) ((-1074 . -612) 67897) ((-484 . -611) 67829) ((-811 . -288) 67806) ((-606 . -151) 67753) ((-418 . -1052) T) ((-487 . -713) 67703) ((-482 . -489) 67687) ((-327 . -846) 67666) ((-339 . -644) 67640) ((-50 . -21) T) ((-50 . -25) T) ((-217 . -713) 67590) ((-169 . -720) 67561) ((-174 . -644) 67493) 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-1051) 65783) ((-690 . -556) T) ((-695 . -23) T) ((-643 . -611) 65715) ((-643 . -612) 65676) ((-630 . -612) NIL) ((-630 . -611) 65658) ((-487 . -172) T) ((-223 . -21) T) ((-217 . -172) T) ((-223 . -25) T) ((-474 . -1197) 65624) ((-474 . -1194) 65590) ((-274 . -611) 65572) ((-273 . -611) 65554) ((-272 . -611) 65536) ((-271 . -611) 65518) ((-270 . -611) 65500) ((-500 . -647) 65482) ((-269 . -611) 65464) ((-339 . -722) T) ((-268 . -611) 65446) ((-110 . -19) 65428) ((-174 . -722) T) ((-500 . -373) 65410) ((-212 . -611) 65392) ((-520 . -1143) 65376) ((-500 . -123) T) ((-110 . -602) 65351) ((-211 . -611) 65333) ((-474 . -35) 65299) ((-474 . -95) 65265) ((-209 . -611) 65247) ((-208 . -611) 65229) ((-207 . -611) 65211) ((-206 . -611) 65193) ((-203 . -611) 65175) ((-202 . -611) 65157) ((-201 . -611) 65139) ((-200 . -611) 65121) ((-199 . -611) 65103) ((-198 . -611) 65085) ((-197 . -611) 65067) ((-536 . -1097) 65019) ((-196 . -611) 65001) ((-195 . -611) 64983) ((-45 . -489) 64920) ((-194 . -611) 64902) ((-193 . -611) 64884) ((-152 . -614) 64853) ((-1109 . -102) T) ((-811 . -111) 64743) ((-641 . -102) 64693) ((-482 . -286) 64670) ((-1107 . -611) 64401) ((-1095 . -1094) T) ((-1042 . -1209) T) ((-1282 . -1034) 64385) ((-621 . -1106) T) ((-1166 . -309) 64372) ((-1129 . -1094) T) ((-1119 . -309) 64359) ((-1090 . -1077) T) ((-1084 . -1077) T) ((-1067 . -1077) T) ((-1060 . -1077) T) ((-1032 . -1077) T) ((-1015 . -1077) T) ((-117 . -1106) T) ((-815 . -102) T) ((-624 . -1077) T) ((-621 . -23) T) ((-1144 . -514) 64151) ((-483 . -1077) T) ((-386 . -102) T) ((-324 . -102) T) ((-218 . -1077) T) ((-959 . -1094) T) ((-152 . -1045) T) ((-727 . -411) 64135) ((-117 . -23) T) ((-999 . -896) 64087) ((-731 . -1094) T) ((-711 . -1094) T) ((-453 . -1094) T) ((-407 . -1209) T) ((-316 . -430) 64071) ((-591 . -93) T) ((-1023 . -612) 64032) ((-1020 . -1213) T) ((-225 . -102) T) ((-1023 . -611) 63994) ((-812 . -231) 63978) ((-811 . -614) 63708) ((-1020 . -556) T) ((-829 . -644) 63681) ((-354 . -1213) T) 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. -38) 46268) ((-354 . -25) T) ((-354 . -21) T) ((-187 . -102) T) ((-162 . -102) T) ((-249 . -102) T) ((-157 . -102) T) ((-355 . -1266) 46252) ((-352 . -1266) 46236) ((-344 . -1266) 46220) ((-169 . -349) 46199) ((-564 . -846) T) ((-1114 . -23) T) ((-87 . -611) 46181) ((-697 . -307) T) ((-832 . -38) 46151) ((-823 . -38) 46121) ((-1271 . -614) 46063) ((-1245 . -131) T) ((-1144 . -288) 46042) ((-960 . -789) 45995) ((-960 . -790) 45948) ((-811 . -787) 45927) ((-116 . -307) T) ((-91 . -309) 45865) ((-671 . -34) T) ((-550 . -602) 45844) ((-48 . -25) T) ((-48 . -21) T) ((-811 . -790) 45795) ((-811 . -789) 45774) ((-697 . -1018) T) ((-649 . -1051) 45758) ((-960 . -722) 45657) ((-811 . -722) 45567) ((-960 . -473) 45520) ((-482 . -791) 45471) ((-482 . -788) 45422) ((-906 . -1266) 45409) ((-1172 . -1045) T) ((-649 . -111) 45388) ((-1172 . -326) 45365) ((-1195 . -102) 45343) ((-1095 . -611) 45325) ((-697 . -545) T) ((-812 . -1094) T) ((-1271 . -1045) T) ((-1129 . -490) 45306) ((-1215 . -102) T) 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. -286) 26276) ((-487 . -905) NIL) ((-316 . -29) 26246) ((-108 . -1209) T) ((-999 . -1106) T) ((-217 . -905) NIL) ((-910 . -1051) 26198) ((-1074 . -1034) 26094) ((-1000 . -111) 26028) ((-999 . -23) T) ((-733 . -691) 26012) ((-264 . -231) 25996) ((-427 . -1051) 25980) ((-379 . -1052) T) ((-240 . -614) 25710) ((-910 . -111) 25648) ((-690 . -1197) NIL) ((-487 . -644) 25598) ((-108 . -880) 25580) ((-108 . -882) 25562) ((-690 . -1194) NIL) ((-217 . -644) 25512) ((-359 . -1034) 25496) ((-353 . -1034) 25480) ((-327 . -309) 25418) ((-345 . -1034) 25402) ((-225 . -290) T) ((-427 . -111) 25381) ((-60 . -611) 25313) ((-169 . -172) T) ((-1114 . -846) T) ((-108 . -1034) 25273) ((-888 . -1094) T) ((-832 . -1052) T) ((-823 . -1052) T) ((-690 . -35) NIL) ((-690 . -95) NIL) ((-313 . -988) 25234) ((-183 . -102) T) ((-580 . -452) T) ((-564 . -452) T) ((-495 . -452) T) ((-407 . -363) T) ((-240 . -1045) 25164) ((-1144 . -34) T) ((-477 . -916) T) ((-995 . -637) 25112) ((-251 . -602) 25089) ((-250 . -602) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 62efa594..35ac95fd 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3452534661) +(30 . 3452610474) (4410 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -477,660 +477,659 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |height| |appendPoint| |setAdaptive3D| |coHeight| - |revert| |safetyMargin| |monicCompleteDecompose| |integralAtInfinity?| - |perfectSquare?| |someBasis| |resultantnaif| |setMaxPoints3D| - |infRittWu?| |lift| |splitNodeOf!| |lagrange| |removeZeroes| - |deleteProperty!| |dominantTerm| |numFunEvals| |chiSquare| |showAll?| - |convert| |unknownEndian| |identification| |halfExtendedResultant1| - |euclideanGroebner| |reduce| |pointLists| |compBound| |box| - |expintfldpoly| |cPower| |leftTrace| |torsion?| |upperCase!| - |viewport3D| |e01daf| |dmpToP| |atoms| |palginfieldint| |hspace| - |defineProperty| |hasoln| |constant?| |recolor| |OMconnOutDevice| - |cycleRagits| |invmultisect| |trigs| |digit| |root?| |conical| - |primintegrate| |symbol| |sample| |numeric| |internalSubPolSet?| - |modifyPointData| |cylindrical| |numberOfNormalPoly| |clipSurface| - |basisOfRightAnnihilator| |mightHaveRoots| |zeroDimPrime?| - |permutationGroup| |OMputAttr| |expression| |radical| |variable?| - |rightScalarTimes!| |numberOfOperations| |showTheFTable| |normalise| - |nextNormalPoly| |localIntegralBasis| |pmComplexintegrate| |jacobian| - |indicialEquations| |integer| |OMgetEndAttr| |cycleEntry| |decrease| - |antisymmetric?| |removeSinhSq| |precision| |real?| - |internalIntegrate0| |safeFloor| |rk4a| |fixedDivisor| |pol| - |exponent| |ocf2ocdf| |d01gbf| |redPol| |clip| |maximumExponent| - |isAnd| |anfactor| |clearTheSymbolTable| |c06gbf| |errorKind| |vark| - |middle| |normalizedAssociate| |nonQsign| |e02ahf| |getGoodPrime| - |beauzamyBound| |f04maf| |laguerre| |updateStatus!| |OMgetAttr| - |reduced?| |declare| |s18dcf| |pushuconst| |torsionIfCan| - |algebraicOf| |mapUp!| |copies| |createNormalPoly| |relationsIdeal| - |numberOfMonomials| |f02abf| |s19adf| |tail| |pdf2df| |truncate| - |dequeue!| |pointSizeDefault| |port| |scripted?| |complexNormalize| - |OMUnknownCD?| |usingTable?| |slash| |rootPoly| |principalIdeal| - |normal01| ** |key?| |bubbleSort!| |inrootof| |byte| - |differentialVariables| |ricDsolve| |setEpilogue!| |lllip| |c06gsf| - |fullDisplay| |before?| |linearDependence| |integrate| |t| - |outputList| |leviCivitaSymbol| |tanAn| |label| |rules| - |associatorDependence| |oddInfiniteProduct| |sparsityIF| |error| - |getOperator| |tubeRadius| |stFunc1| |iibinom| |extractSplittingLeaf| - |c06ekf| |imagk| |realElementary| |rombergo| |assert| |unknown| |diff| - |intensity| |summation| |f04qaf| |rootsOf| |lambert| - |conditionsForIdempotents| |rationalIfCan| |int| |leader| - |primitivePart| |fortranCharacter| |splitLinear| |ramifiedAtInfinity?| - |clearTheFTable| |outputAsScript| |ignore?| |numberOfFactors| - |constantIfCan| |fractRagits| |identity| |nullSpace| |every?| - |makeFloatFunction| |binarySearchTree| |createGenericMatrix| - |nextIrreduciblePoly| |aspFilename| |chvar| |listexp| |pr2dmp| |row| - |chineseRemainder| |commaSeparate| |iiacos| |orthonormalBasis| - |mainVariables| |generalInfiniteProduct| |Beta| |cardinality| - |algebraicCoefficients?| |addPoint| |range| |sturmSequence| |tRange| - |showArrayValues| |graeffe| |readable?| |any| |iiatan| |readInt32!| - |definingPolynomial| |jacobi| |li| |constructor| |simplifyPower| - |addBadValue| |finiteBound| |superscript| |simpleBounds?| |minPol| - |max| |nthr| |showRegion| |component| |wordInGenerators| |bytes| - |possiblyInfinite?| |points| |product| |option| |Frobenius| - |insertRoot!| |mapBivariate| |unmakeSUP| |extractTop!| - |reduceByQuasiMonic| |useNagFunctions| |factorOfDegree| - |OMUnknownSymbol?| |secIfCan| |ellipticCylindrical| |d01akf| - |physicalLength| |fortranLinkerArgs| |d01ajf| |extend| |alternative?| - |univariatePolynomials| |zeroVector| |power| |sumOfKthPowerDivisors| - |ratDsolve| |irreducibleRepresentation| |zCoord| |critpOrder| - |particularSolution| |checkPrecision| |repeatUntilLoop| |nullary| - |deepExpand| |OMlistSymbols| |rowEchelon| |systemSizeIF| |ran| - |e04naf| |rightTrim| |bezoutMatrix| |curry| |discreteLog| |evaluate| - |genericRightMinimalPolynomial| |makeSin| |leadingSupport| |setref| - |polynomialZeros| |collect| |leftTrim| |mapGen| |orbit| |ODESolve| - |subNode?| |copy!| |coleman| |SFunction| |fortranTypeOf| |leftUnits| - |laurentIfCan| |thenBranch| |coth2tanh| |rootPower| |minrank| |rotate| - |iicoth| |scopes| |parametersOf| |lfextlimint| |algebraicSort| - |f04arf| |isAbsolutelyIrreducible?| |printInfo| |changeName| - |compdegd| |calcRanges| |cAsech| |expandLog| |complete| |bumprow| - |basisOfLeftAnnihilator| |test| |mainForm| |clearFortranOutputStack| - 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|createMultiplicationTable| |characteristicSet| |option?| |OMread| - |relerror| |queue| |getButtonValue| |OMgetError| |internal?| |qelt| - |topPredicate| |sizeMultiplication| |invertibleSet| |edf2ef| - |solveLinearPolynomialEquation| |mainPrimitivePart| |cyclic?| - |shuffle| |isExpt| |outerProduct| |transcendenceDegree| |qsetelt| - |ratDenom| |createMultiplicationMatrix| |decreasePrecision| |btwFact| - |cons| |addPointLast| |finiteBasis| |ffactor| |readUInt32!| - |outputArgs| |makeRecord| |set| |subTriSet?| |xRange| |create3Space| - |find| |roughSubIdeal?| |morphism| |realEigenvalues| - |generalizedEigenvector| |karatsuba| |rowEchelonLocal| |bernoulli| - |largest| |yRange| |sumOfSquares| |pointColorPalette| - |selectSumOfSquaresRoutines| |exponents| |cRationalPower| |overset?| - |mirror| |alphabetic| |e01bef| |prinshINFO| |zRange| |aQuadratic| - |writable?| |minGbasis| |d01alf| |lighting| |showTypeInOutput| - |initiallyReduce| |exprex| |s15adf| |mathieu12| |map!| |pushdown| - |perfectNthRoot| |LowTriBddDenomInv| |processTemplate| |e04mbf| - 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|cAtanh| |resetNew| |complexForm| |index?| |next| |rquo| BY |smith| - |compose| |character?| |s13adf| |mkIntegral| |wholePart| |setfirst!| - |f07fdf| |OMgetEndObject| |leaves| |flexible?| |e04ucf| |ord| - |basicSet| |s13aaf| |combineFeatureCompatibility| |zeroSetSplit| - |even?| |replaceKthElement| |factor1| |rk4qc| |zero?| |ef2edf| - |printStats!| |rightFactorCandidate| |applyQuote| |sup| - |quasiComponent| |putGraph| |gensym| |getOperands| |readBytes!| - |restorePrecision| |initiallyReduced?| |mainKernel| |less?| - |trailingCoefficient| |indiceSubResultant| |parabolic| |viewDefaults| - |removeRedundantFactorsInPols| |makeCos| |explicitEntries?| - |rightTraceMatrix| |rightExtendedGcd| |exponential1| |getExplanations| - |extractIndex| |tableForDiscreteLogarithm| |OMgetBVar| - |primitiveElement| |shallowExpand| |unitNormal| |cCsch| |s19abf| - |ruleset| |mesh| |bitCoef| |subscript| |coercePreimagesImages| - |polyRDE| |binomThmExpt| |routines| NOT |mainMonomial| |cLog| |pquo| - |OMgetInteger| |integer?| |distFact| |radix| |weights| |redmat| - 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|lazyPrem| |integralLastSubResultant| |modularFactor| - |genericLeftTraceForm| |leftLcm| |\\/| |sincos| + |gethi| GT - |makeGraphImage| |withPredicates| |mat| |coerceImages| |f02xef| - |readUInt16!| |d01anf| |algintegrate| - |curveColor| LE - |listConjugateBases| |f02aef| |c05pbf| |resize| - |pushFortranOutputStack| |fTable| |iiacsc| |leftExtendedGcd| - |removeIrreducibleRedundantFactors| / |cSech| LT |modularGcdPrimitive| - |companionBlocks| |genericRightTrace| |modulus| - |popFortranOutputStack| |initials| |halfExtendedResultant2| - |symmetricGroup| |tanNa| |mkcomm| |infinityNorm| |asinIfCan| - |jordanAdmissible?| |denomLODE| |outputAsFortran| |normalElement| - |compile| |internalIntegrate| |boundOfCauchy| |f01rcf| - |constantKernel| |traverse| |abelianGroup| |univariate?| |sub| - |retract| |laplacian| |iicot| |generalizedEigenvectors| |clikeUniv| - |virtualDegree| |fglmIfCan| |acoshIfCan| |vertConcat| - |factorByRecursion| |e01baf| |associates?| |totalLex| |adaptive| - |branchPoint?| |cAcsch| |rroot| |rewriteIdealWithRemainder| |property| - |rewriteSetWithReduction| |subSet| |meshPar1Var| |subResultantChain| - |trivialIdeal?| |rischDE| |factorials| |leftScalarTimes!| |style| - |horizConcat| |mergeDifference| |alternating| |makeMulti| - |bipolarCylindrical| |lSpaceBasis| |f01rdf| |roughEqualIdeals?| |nlde| - |nativeModuleExtension| |d01fcf| |s17aff| |resultantEuclidean| - |homogeneous?| |primaryDecomp| |tubePointsDefault| |bounds| |maxrow| - |quoByVar| |units| |functionIsFracPolynomial?| |iiasec| |back| - |makeViewport2D| |OMputEndApp| |genericLeftDiscriminant| - |resetVariableOrder| |partialFraction| |curve| |cAsinh| |bringDown| - |lieAdmissible?| |leftDiscriminant| |listOfMonoms| |monomials| - |allRootsOf| |mindegTerm| |s21bdf| |divide| |crest| |determinant| - |mappingAst| |infix| |c06eaf| |reverse| |plus| |clearCache| - |cosSinInfo| |returnTypeOf| |quasiRegular| |OMgetType| |quasiMonic?| - |optpair| |var1Steps| |cyclicParents| |iiasin| |OMsupportsCD?| - |polCase| |irreducibleFactors| |curveColorPalette| - |internalLastSubResultant| |gderiv| |maxIndex| |cycleLength| - |generalizedInverse| |code| |Hausdorff| |rur| |subPolSet?| - |scaleRoots| |listBranches| |upperCase?| |exteriorDifferential| - |shiftRoots| |shellSort| |alphanumeric?| |gcdPrimitive| |numerator| - |setImagSteps| |stoseInvertible?reg| |vector| |bright| |comp| |tanSum| - |normalForm| |stoseSquareFreePart| |symmetric?| |times| |subspace| - |innerint| |open?| |goto| |showClipRegion| |differentiate| |initial| - |collectUpper| |wronskianMatrix| |OMputString| |innerSolve| |roman| - |limitedint| |inR?| |any?| |predicates| |splitDenominator| - |semicolonSeparate| |startTableGcd!| |edf2df| |function| |findCycle| - |moduleSum| |removeSuperfluousCases| |powerAssociative?| |hitherPlane| - |modifyPoint| |palglimint0| |stoseInvertible?| |makeUnit| - |sylvesterMatrix| |elliptic| |writeUInt8!| |makeFR| - |complexEigenvectors| |bitTruth| |failed| |factorAndSplit| - |createNormalElement| |birth| |dom| |computePowers| |monom| |eval| - |escape| |d01apf| |signAround| |getRef| |OMencodingUnknown| |updatF| - |extendedResultant| |s14abf| |leftTraceMatrix| |rule| |bandedJacobian| - |quotientByP| |lflimitedint| |trigs2explogs| |opeval| - |innerEigenvectors| |badValues| |mainContent| |isOpen?| |e01bhf| - |semiIndiceSubResultantEuclidean| |OMputEndBind| |cycleSplit!| - |localUnquote| |parametric?| |string?| |prinb| |common| |solid?| - |mpsode| |firstUncouplingMatrix| |tanh2coth| |cycles| |eulerPhi| - |lazyIntegrate| |iiGamma| |linearPart| |seriesSolve| |concat!| - |linearDependenceOverZ| |rewriteIdealWithHeadRemainder| |mainValue| - |sinhcosh| |lazyGintegrate| |inHallBasis?| |selectAndPolynomials| - |coefficient| |e02gaf| |title| |droot| |nthFlag| |nthFractionalTerm| - |brillhartTrials| |expr| |setRow!| |qualifier| |monomialIntPoly| - |replace| |discriminantEuclidean| |halfExtendedSubResultantGcd2| - |OMconnectTCP| |stiffnessAndStabilityFactor| |pole?| - |useSingleFactorBound?| |aromberg| |computeInt| |probablyZeroDim?| - |getGraph| |equiv| |e| |swap| |nextsubResultant2| |subMatrix| - |OMputBind| |pseudoRemainder| |minPoly| |lineColorDefault| - |separateFactors| |mapUnivariate| |OMputSymbol| |e01bgf| |f04atf| |sn| - |testDim| |OMgetFloat| |iiacot| |variable| |true| |f04faf| |hcrf| - |dimensionOfIrreducibleRepresentation| |binary| |abs| |s14aaf| - |iterators| |ipow| |internalSubQuasiComponent?| |nothing| |changeVar| - |conjugates| |outlineRender| |palgextint0| |setelt!| - |prolateSpheroidal| |part?| |writeLine!| |convergents| - |recoverAfterFail| |cartesian| |rootProduct| |e04dgf| |repeating| - |duplicates?| |setStatus| |init| |divisors| |cyclicGroup| - |totalDifferential| |linearMatrix| |hessian| |wholeRadix| |colorDef| - |useEisensteinCriterion| |changeMeasure| |headAst| - |squareFreePolynomial| |dihedral| |swap!| |iisqrt2| |imaginary| - |compiledFunction| |keys| |digamma| |mainExpression| |subHeight| - |leftMinimalPolynomial| |hostPlatform| |degreeSubResultantEuclidean| - |divisor| |fortranInteger| |solve1| |satisfy?| |properties| - |raisePolynomial| |rightNorm| |polyPart| |width| |prime?| - |rowEchLocal| |diagonal?| |genericRightTraceForm| |translate| |module| - |mapUnivariateIfCan| |cycleTail| |gcdprim| |s17ajf| - |singleFactorBound| |rewriteSetByReducingWithParticularGenerators| - |coefChoose| |newReduc| |HermiteIntegrate| |bezoutResultant| |basis| - |lex| |surface| |leftFactor| |squareFreePrim| |lazyPseudoQuotient| - |exprHasAlgebraicWeight| |rightTrace| |partialQuotients| - |littleEndian| |Nul| |charpol| |readInt16!| |rank| |roughUnitIdeal?| - |eigenMatrix| |trueEqual| |doubleDisc| |sorted?| |tubeRadiusDefault| - |unparse| |scanOneDimSubspaces| |nary?| |quadraticNorm| |normal?| - |leftRemainder| |inconsistent?| |gramschmidt| |exptMod| |chiSquare1| - |iisin| |packageCall| |rootDirectory| |laurentRep| - |resetAttributeButtons| |nullity| |infieldint| |s17ahf| - |purelyAlgebraic?| |insertBottom!| |weierstrass| |outputSpacing| - |optional| |subst| |OMputEndObject| |shufflein| |choosemon| - |medialSet| |LazardQuotient| |iiasech| |rotate!| |nthExpon| - |rootKerSimp| |endOfFile?| |binaryTree| |dmp2rfi| |screenResolution3D| - |interpret| |bothWays| |subResultantGcdEuclidean| |s20adf| |stack| - |bindings| |makeVariable| |sPol| |rightDiscriminant| |in?| - |semiResultantReduitEuclidean| |minimalPolynomial| - |factorGroebnerBasis| |vectorise| |contract| |antiCommutative?| - |messagePrint| |sts2stst| |numericIfCan| |lists| |splitSquarefree| - |FormatRoman| |anticoord| |scale| |cAcos| |tower| |df2ef| |Lazard2| - |stoseInvertible?sqfreg| |unitsColorDefault| |formula| |lifting1| - |pointColor| |safeCeiling| |gradient| |has?| |s13acf| |writeInt8!| - |generalTwoFactor| |se2rfi| |useEisensteinCriterion?| |extractPoint| - |prime| |rowEch| |objects| |startStats!| |dim| |sayLength| - |fixedPoints| |countable?| |optAttributes| - |removeRoughlyRedundantFactorsInPols| |leftZero| |base| - |strongGenerators| |BumInSepFFE| |knownInfBasis| |iiacosh| SEGMENT - |groebner| |hMonic| |readIfCan!| |nil| |omError| |number?| - |univariateSolve| |integerIfCan| |s18adf| |odd?| |nrows| |cAtan| - |kovacic| |tube| |sortConstraints| |exprToGenUPS| |complexNumeric| - |parseString| |rightLcm| |neglist| |ncols| |permutationRepresentation| - |oddlambert| |quickSort| |inverseIntegralMatrixAtInfinity| - |computeBasis| |center| |linearPolynomials| |ReduceOrder| |polygon?| - |d02kef| |discriminant| |complexSolve| |approximate| |kernels| - |symmetricProduct| |numberOfImproperPartitions| |s21bcf| |push!| - |OMgetEndApp| |minimize| |trapezoidal| |complex| |getMatch| |log| - |alphanumeric| |antiCommutator| |hdmpToP| |univariate| |qroot| - |lazyPquo| |datalist| |argumentListOf| |cAsin| |outputForm| - |changeNameToObjf| |node| |subscriptedVariables| |linear?| |hue| - |mainMonomials| |unexpand| |lowerCase?| |f02bbf| |OMputEndAttr| - |primPartElseUnitCanonical!| |setright!| |sizeLess?| |erf| - |extendedEuclidean| |imagE| |high| |changeThreshhold| |compound?| - |measure2Result| |c06fqf| |doubleFloatFormat| |factor| |c06frf| - |factorSFBRlcUnit| |clipPointsDefault| |mapExponents| - |leftRegularRepresentation| |swapColumns!| |concat| |rename| |sqrt| - |evenlambert| |unaryFunction| |rdHack1| |genericLeftTrace| - |makeViewport3D| |createIrreduciblePoly| |whatInfinity| |eigenvalues| - |subtractIfCan| |dilog| |e02bbf| |stoseInvertibleSetsqfreg| |real| - |mainVariable?| |point| |exponentialOrder| |nextSublist| |capacity| - |expint| |setMaxPoints| |previous| |iisinh| |quasiMonicPolynomials| - |sin| |imag| |realRoots| |fortranCompilerName| |setFormula!| - |mantissa| |elRow2!| |supRittWu?| |uniform01| |elementary| - |directProduct| |double?| |cos| |setScreenResolution3D| |llprop| - |setProperty| |f01bsf| |cyclotomic| |palgintegrate| - |genericRightDiscriminant| |cCosh| |const| |tan| - |resultantReduitEuclidean| |series| |jacobiIdentity?| |setEmpty!| - |returns| |nextPartition| |definingEquations| |palglimint| |sqfree| - |brace| |cot| |mapDown!| |monomRDEsys| |LiePoly| |nodes| |airyBi| - |setStatus!| |OMcloseConn| |qfactor| |destruct| |sec| |ode2| - |inputBinaryFile| |transcendent?| |stirling1| |powmod| |cAcosh| - |source| |setButtonValue| |push| |f02wef| |patternMatch| |csc| - |OMputBVar| |getCurve| |expenseOfEvaluation| |acothIfCan| |child?| - |specialTrigs| |eq?| |leftRankPolynomial| |leadingCoefficientRicDE| - |positiveRemainder| |asin| |min| |loopPoints| |category| |credPol| - |degreePartition| |genericLeftMinimalPolynomial| |duplicates| |twist| - |equation| |c02agf| |acos| |drawToScale| |wordInStrongGenerators| - |setAttributeButtonStep| |domain| |mkPrim| |LiePolyIfCan| |mesh?| - |iitanh| |monomial| |quadraticForm| |atan| |simpson| |clearTheIFTable| - |entry| |implies| |package| |cyclicEqual?| |permutation| |Ei| - |graphState| |idealiserMatrix| |show| |multivariate| |infiniteProduct| - |acot| |oneDimensionalArray| |stoseInternalLastSubResultant| - |objectOf| |cyclic| |rotatez| |target| |scalarMatrix| - |continuedFraction| |s17dcf| |orbits| |variables| |asec| |powerSum| - |repSq| |symmetricPower| |solveLinearPolynomialEquationByFractions| - |cyclicSubmodule| |axes| |trace| |monicLeftDivide| |postfix| |acsc| - |reduction| |remove!| |moduloP| |ScanFloatIgnoreSpacesIfCan| - |multiple?| |zeroMatrix| |associatedEquations| |equality| |e01saf| - |sinh| |parents| |expenseOfEvaluationIF| |removeCosSq| |expPot| - |shade| |iFTable| |cn| |insertionSort!| |cosh| |viewWriteAvailable| - |expandTrigProducts| |realSolve| |integralBasis| |maxrank| |minordet| - |ravel| |LagrangeInterpolation| |c05adf| |f01maf| |tanh| - |computeCycleEntry| |iiabs| |shallowCopy| |internalDecompose| - |cyclicCopy| |integral?| |reshape| |block| |coth| |taylor| |sh| - |exprToXXP| |e02dff| |hyperelliptic| |log2| |e01sef| - |OMsupportsSymbol?| |callForm?| |rootBound| |f01qcf| |sech| |laurent| - |squareFreeFactors| |setelt| |outputMeasure| - |halfExtendedSubResultantGcd1| |diagonals| - |semiLastSubResultantEuclidean| |coord| |s21baf| |csch| |puiseux| - |inspect| |infieldIntegrate| |palgLODE| |nor| |areEquivalent?| - |solveRetract| |pleskenSplit| |d03faf| |lexGroebner| |asinh| - |mainSquareFreePart| |copy| |setvalue!| |complement| |green| |ldf2vmf| - |e02zaf| |inv| |SturmHabichtSequence| |acosh| |rischNormalize| - |lazyPseudoRemainder| |linearlyDependent?| |screenResolution| |e02baf| - |collectQuasiMonic| |factors| |update| |ground?| |commutativeEquality| - |atanh| |drawCurves| |freeOf?| |constantRight| |parts| |iisech| - |e02bdf| |OMunhandledSymbol| |bitLength| |conjugate| |cup| - |insertTop!| |ground| |acoth| |bat| |cTan| |autoCoerce| - |completeEchelonBasis| |startTable!| |universe| |derivative| |f02aff| - |leadingMonomial| |asech| |bivariateSLPEBR| |monic?| |acosIfCan| - |pushdterm| |lexico| |null?| |froot| |leadingCoefficient| |upperCase| - |setLength!| |changeBase| |closed?| |certainlySubVariety?| |airyAi| - |iipow| |removeConstantTerm| |c06gqf| |multiple| |primitiveMonomials| - |iiexp| |csch2sinh| |deref| |rootSplit| |completeHensel| - |doubleResultant| |position| |pmintegrate| |leaf?| |writeBytes!| |say| - |complementaryBasis| |lintgcd| |rightCharacteristicPolynomial| - |acschIfCan| |rename!| |ip4Address| |rectangularMatrix| - |relativeApprox| |flexibleArray| |match?| |argscript| |pomopo!| - |iiatanh| |outputBinaryFile| |iiacsch| |variationOfParameters| - |integralRepresents| |ratPoly| |unit?| |enumerate| - |nextLatticePermutation| |zeroSetSplitIntoTriangularSystems| - |charthRoot| |polygon| |nthRootIfCan| |s17akf| |leastAffineMultiple| - |c02aff| |outputAsTex| |c05nbf| |leftDivide| |digits| - |basisOfRightNucleus| |meatAxe| |plotPolar| - |functionIsContinuousAtEndPoints| |removeSinSq| |viewThetaDefault| - |findConstructor| |measure| |debug| |hash| |norm| |sinh2csch| |fmecg| - |xn| |mathieu11| |bsolve| |rischDEsys| |count| |constantLeft| D - |composites| |double| |unrankImproperPartitions1| |extendedIntegrate| - |OMencodingXML| |deriv| |linkToFortran| |unary?| |shiftRight| - |whileLoop| |s17adf| |realZeros| |setchildren!| |epilogue| |iiacoth| - |contours| |eisensteinIrreducible?| |factorset| |just| |musserTrials| - |setClosed| |csc2sin| |graphImage| |reciprocalPolynomial| - |FormatArabic| |e01bff| |f02awf| |f01brf| |numFunEvals3D| |mapmult| - |cap| |fillPascalTriangle| |leftMult| |point?| |aCubic| |empty| - |showTheRoutinesTable| |bumptab| |irreducible?| |totalGroebner| - |extension| |palgRDE0| |power!| |generalLambert| |addPoint2| - |limitPlus| |bottom!| |setAdaptive| |belong?| |d02gbf| |overlabel| - |coth2trigh| |normalDeriv| |pade| |f02adf| |symmetricTensors| |fi2df| - |s20acf| |prefixRagits| |factorSquareFreeByRecursion| |zero| - |rightGcd| |ode| |doubleComplex?| |perfectSqrt| |thetaCoord| |column| - |declare!| |dn| |operators| |identitySquareMatrix| - |selectODEIVPRoutines| |oddintegers| |OMputEndBVar| |kroneckerDelta| - |df2mf| |polygamma| |uniform| |predicate| |constantOperator| - |hexDigit?| |dualSignature| |upDateBranches| |And| |complexZeros| - |dfRange| |mainVariable| |minRowIndex| |unravel| |monomRDE| - |palgextint| |arbitrary| |extractBottom!| |intPatternMatch| - |factorPolynomial| |Or| |getCode| |pair?| |imagJ| |listLoops| - |setnext!| |readLine!| |rightRecip| |byteBuffer| |rotatey| |leftPower| - |chainSubResultants| |Not| |var2Steps| |diophantineSystem| |OMgetAtp| - |simplify| |primitivePart!| |enterInCache| |e04ycf| |df2fi| - |zeroDimensional?| |innerSolve1| |floor| |d02gaf| |blankSeparate| - |critMonD1| |indiceSubResultantEuclidean| |critB| |prevPrime| - |expIfCan| |reindex| |chebyshevU| |triangularSystems| - |nextsousResultant2| LODO2FUN |graphStates| |univcase| |seed| |e04gcf| - |distance| |createZechTable| |explimitedint| |LyndonWordsList1| - |mapExpon| |signatureAst| |trim| |viewWriteDefault| |clipWithRanges| - |linearAssociatedOrder| |exprToUPS| |laplace| - |cyclotomicFactorization| |segment| |basisOfLeftNucloid| - |numberOfComponents| |f02bjf| |lastSubResultant| |iisec| |composite| - |genericLeftNorm| |coordinate| |getMeasure| |mindeg| |dioSolve| - |c06gcf| |argumentList!| |hconcat| |dark| |node?| |lazyVariations| - |parameters| |logIfCan| |pushup| |hclf| |tab1| |iicsch| |alphabetic?| - |iifact| |setprevious!| |mkAnswer| |setMinPoints3D| |id| |split!| - |setTex!| |extendIfCan| |removeRedundantFactorsInContents| - |squareFree| |gcdcofact| |hostByteOrder| |build| |cycle| |fractRadix| - |quartic| |directSum| |printInfo!| |cyclotomicDecomposition| - |countRealRoots| |heapSort| |readInt8!| |groebgen| |interactiveEnv| - |euclideanSize| |exists?| |noKaratsuba| |logical?| |e04jaf| - |rubiksGroup| |table| |operator| |pseudoDivide| |rightPower| - |OMreadFile| |s19aaf| |nand| |generic| |weighted| |meshPar2Var| |new| - |removeCoshSq| |besselY| |readLineIfCan!| |groebner?| |mdeg| - |distdfact| |showScalarValues| |rootOfIrreduciblePoly| - |partialNumerators| |reducedContinuedFraction| |primlimintfrac| - |insert| |remainder| |loadNativeModule| |binaryFunction| |e02akf| - |leftNorm| |approxNthRoot| |overlap| |padicFraction| |maxPoints3D| - |f04adf| |createLowComplexityNormalBasis| |bit?| |setPoly| |yCoord| - |OMgetEndBVar| |prepareSubResAlgo| |clipBoolean| |iitan| - |radicalEigenvalues| |d02bhf| |create| |representationType| - |generalizedContinuumHypothesisAssumed| |primitive?| |unitNormalize| - |rightQuotient| |options| |check| |OMputObject| |linear| |goodPoint| - |mergeFactors| |conjug| |startTableInvSet!| |solve| |approxSqrt| - |wreath| |decompose| |pi| |d02ejf| |polyred| |lfextendedint| |f07fef| - |reverse!| |normalized?| |nsqfree| |psolve| |plot| |eigenvector| - |LyndonWordsList| |whitePoint| |infinity| |numberOfComputedEntries| - |transcendentalDecompose| |retractIfCan| |qqq| |polynomial| - |normalizeIfCan| |getOrder| |isTerm| |drawStyle| |deepCopy| - |applyRules| |consnewpol| |getBadValues| |string| |makeSUP| - |isConnected?| |selectIntegrationRoutines| |central?| |iisqrt3| - |exprHasLogarithmicWeights| |subNodeOf?| |unvectorise| |cSec| - |OMconnInDevice| |leftQuotient| |degreeSubResultant| |rarrow| - |maxPoints| |setLabelValue| F2FG |c06fpf| |sum| |ptree| |refine| - |characteristicSerie| |close!| |recip| |kernel| |internalZeroSetSplit| - |gbasis| |sec2cos| |semiSubResultantGcdEuclidean1| |enqueue!| - |prindINFO| |curve?| |rightRank| |e02dcf| |trapezoidalo| |draw| - |setFieldInfo| |getIdentifier| |eigenvectors| |iprint| - |mainCharacterization| |updatD| |idealSimplify| |fprindINFO| - |partition| |hypergeometric0F1| |rightRegularRepresentation| - |leftExactQuotient| |setleft!| |tracePowMod| |resultantEuclideannaif| - |mapSolve| |radicalEigenvectors| |left| |transform| |pdct| |nthCoef| - |rightMult| |generators| |operation| |Aleph| |zeroDim?| |isImplies| - |symFunc| |localAbs| |right| |isQuotient| |skewSFunction| - |denominator| |f04jgf| |generic?| |primPartElseUnitCanonical| - |getZechTable| |limitedIntegrate| |HenselLift| |lp| |firstSubsetGray| - |rk4| |iidprod| |taylorRep| |selectfirst| |setOrder| |sqfrFactor| - |makeObject| |highCommonTerms| |errorInfo| |completeSmith| |addiag| - |clearTable!| |move| |map| |genericRightNorm| |internalAugment| - |separateDegrees| |linGenPos| |minimumExponent| |curryLeft| - |LazardQuotient2| |positiveSolve| |quote| |elt| |euler| |empty?| - |currentEnv| |merge!| |squareMatrix| |increment| |generalSqFr| - |countRealRootsMultiple| |euclideanNormalForm| |coef| |schwerpunkt| - |permanent| |mapCoef| |frst| |integralCoordinates| |sort!| |f2df| - |outputFloating| |bfEntry| |extractIfCan| |basisOfNucleus| |d01amf| - |useSingleFactorBound| |KrullNumber| |nil| |infinite| - |arbitraryExponent| |approximate| |complex| |shallowMutable| - |canonical| |noetherian| |central| |partiallyOrderedSet| - |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| - |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| - |canonicalUnitNormal| |multiplicativeValuation| |finiteAggregate| - |shallowlyMutable| |commutative|)
\ No newline at end of file + |Record| |Union| |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| + |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| + |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| + |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| + |finiteAggregate| |shallowlyMutable| |commutative|)
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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) . 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T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -2822 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2822 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -2822 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-614 #0=(-407 (-564))) -12 (|has| |#2| (-1034 (-407 (-564)))) (|has| |#2| (-1094))) ((-614 (-564)) -2822 (|has| |#2| (-1045)) (-12 (|has| |#2| (-1034 (-564))) (|has| |#2| (-1094))) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-614 |#2|) -2822 (|has| |#2| (-1094)) (|has| |#2| (-172))) ((-611 (-858)) -2822 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-611 (-858))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-611 (-1259 |#2|)) . 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|) . T) ((-514 |#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-644 |#2|) -2822 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-644 $) -2822 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-637 (-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1045))) ((-637 |#2|) |has| |#2| (-1045)) ((-713 |#2|) -2822 (|has| |#2| (-363)) (|has| |#2| (-172))) ((-722) -2822 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-722)) (|has| |#2| (-172))) ((-787) |has| |#2| (-844)) ((-788) -2822 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-789) |has| |#2| (-789)) ((-790) -2822 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-791) -2822 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-844) |has| |#2| (-844)) ((-846) -2822 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-896 (-1170)) -12 (|has| |#2| (-896 (-1170))) (|has| |#2| (-1045))) ((-1034 #0#) -12 (|has| |#2| (-1034 (-407 (-564)))) (|has| |#2| (-1094))) ((-1034 (-564)) -12 (|has| |#2| (-1034 (-564))) (|has| |#2| (-1094))) ((-1034 |#2|) |has| |#2| (-1094)) ((-1051 |#2|) -2822 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-1051 $) |has| |#2| (-172)) ((-1045) -2822 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-1052) -2822 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-1106) -2822 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-722)) (|has| |#2| (-172))) ((-1094) -2822 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1209) . T) ((-1266 |#2|) |has| |#2| (-363))) -((-1907 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-1319 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-4353 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) -(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -1907 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -1319 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -4353 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-767) (-1209) (-1209)) (T -239)) -((-4353 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-767)) (-4 *6 (-1209)) (-4 *7 (-1209)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-1319 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-767)) (-4 *6 (-1209)) (-4 *2 (-1209)) (-5 *1 (-239 *5 *6 *2)))) (-1907 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-767)) (-4 *7 (-1209)) (-4 *5 (-1209)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) -(-10 -7 (-15 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|%noBranch|) (IF (|has| |t#2| (-131)) (-6 (-131)) |%noBranch|) (IF (|has| |t#2| (-722)) (PROGN (-6 (-722)) (-15 * ($ |t#2| $)) (-15 * ($ $ |t#2|))) |%noBranch|) (IF (|has| |t#2| (-368)) (-6 (-368)) |%noBranch|) (IF (|has| |t#2| (-172)) (PROGN (-6 (-38 |t#2|)) (-6 (-172))) |%noBranch|) (IF (|has| |t#2| (-6 -4404)) (-6 -4404) |%noBranch|) (IF (|has| |t#2| (-844)) (-6 (-844)) |%noBranch|) (IF (|has| |t#2| (-789)) (-6 (-789)) |%noBranch|) (IF (|has| |t#2| (-363)) (-6 (-1266 |t#2|)) |%noBranch|))) +(((-21) -2807 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-23) -2807 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-25) -2807 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -2807 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2807 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -2807 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-614 #0=(-407 (-564))) -12 (|has| |#2| (-1034 (-407 (-564)))) (|has| |#2| (-1094))) ((-614 (-564)) -2807 (|has| |#2| (-1045)) (-12 (|has| |#2| (-1034 (-564))) (|has| |#2| (-1094))) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-614 |#2|) -2807 (|has| |#2| (-1094)) (|has| |#2| (-172))) ((-611 (-858)) -2807 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-611 (-858))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-611 (-1259 |#2|)) . 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|) . T) ((-514 |#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-644 |#2|) -2807 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-644 $) -2807 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-637 (-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1045))) ((-637 |#2|) |has| |#2| (-1045)) ((-713 |#2|) -2807 (|has| |#2| (-363)) (|has| |#2| (-172))) ((-722) -2807 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-722)) (|has| |#2| (-172))) ((-787) |has| |#2| (-844)) ((-788) -2807 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-789) |has| |#2| (-789)) ((-790) -2807 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-791) -2807 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-844) |has| |#2| (-844)) ((-846) -2807 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-896 (-1170)) -12 (|has| |#2| (-896 (-1170))) (|has| |#2| (-1045))) ((-1034 #0#) -12 (|has| |#2| (-1034 (-407 (-564)))) (|has| |#2| (-1094))) ((-1034 (-564)) -12 (|has| |#2| (-1034 (-564))) (|has| |#2| (-1094))) ((-1034 |#2|) |has| |#2| (-1094)) ((-1051 |#2|) -2807 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-1051 $) |has| |#2| (-172)) ((-1045) -2807 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-1052) -2807 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-1106) -2807 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-722)) (|has| |#2| (-172))) ((-1094) -2807 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1209) . 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2807 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-407 (-564)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2807 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-614 #0#) -2807 (|has| |#1| (-1034 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564))))) ((-614 (-564)) . T) ((-614 |#1|) . T) ((-614 |#2|) . T) ((-614 |#3|) . T) ((-614 $) -2807 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-611 (-858)) . 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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 $) -2822 (|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) -2822 (|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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T) ((-644 |#2|) |has| |#1| (-363)) ((-644 $) . T) ((-637 (-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-637 (-564)))) ((-637 |#2|) |has| |#1| (-363)) ((-713 #1#) -2822 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-713 |#1|) |has| |#1| (-172)) ((-713 |#2|) |has| |#1| (-363)) ((-713 $) -2822 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-722) . 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T) ((-23) . T) ((-47 |#1| #0=(-564)) . T) ((-25) . T) ((-38 #1=(-407 (-564))) -2807 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-38 |#1|) |has| |#1| (-172)) ((-38 |#2|) |has| |#1| (-363)) ((-38 $) -2807 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-35) |has| |#1| (-38 (-407 (-564)))) ((-95) |has| |#1| (-38 (-407 (-564)))) ((-102) . T) ((-111 #1# #1#) -2807 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-363)) ((-111 $ $) -2807 (|has| |#1| (-556)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-131) . T) ((-145) -2807 (-12 (|has| |#1| (-363)) (|has| |#2| (-145))) (|has| |#1| (-145))) ((-147) -2807 (-12 (|has| |#1| (-363)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-614 #1#) -2807 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-614 (-564)) . T) ((-614 #2=(-1170)) -12 (|has| |#1| (-363)) (|has| |#2| (-1034 (-1170)))) ((-614 |#1|) |has| |#1| (-172)) ((-614 |#2|) . T) ((-614 $) -2807 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-611 (-858)) . T) ((-172) -2807 (|has| |#1| (-556)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-612 (-225)) -12 (|has| |#1| (-363)) (|has| |#2| (-1018))) ((-612 (-379)) -12 (|has| |#1| (-363)) (|has| |#2| (-1018))) ((-612 (-536)) -12 (|has| |#1| (-363)) (|has| |#2| (-612 (-536)))) ((-612 (-888 (-379))) -12 (|has| |#1| (-363)) (|has| |#2| (-612 (-888 (-379))))) ((-612 (-888 (-564))) -12 (|has| |#1| (-363)) (|has| |#2| (-612 (-888 (-564))))) ((-231 |#2|) |has| |#1| (-363)) ((-233) -2807 (-12 (|has| |#1| (-363)) (|has| |#2| (-233))) (|has| |#1| (-15 * (|#1| (-564) |#1|)))) ((-243) |has| |#1| (-363)) ((-284) |has| |#1| (-38 (-407 (-564)))) ((-286 |#2| $) -12 (|has| |#1| (-363)) (|has| |#2| (-286 |#2| |#2|))) ((-286 $ $) |has| (-564) (-1106)) ((-290) -2807 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-307) |has| |#1| (-363)) ((-309 |#2|) -12 (|has| |#1| (-363)) (|has| |#2| (-309 |#2|))) ((-363) |has| |#1| (-363)) ((-338 |#2|) |has| |#1| (-363)) ((-377 |#2|) |has| |#1| (-363)) ((-400 |#2|) |has| |#1| (-363)) ((-452) |has| |#1| (-363)) ((-493) |has| |#1| (-38 (-407 (-564)))) ((-514 (-1170) |#2|) -12 (|has| |#1| (-363)) (|has| |#2| (-514 (-1170) |#2|))) ((-514 |#2| |#2|) -12 (|has| |#1| (-363)) (|has| |#2| (-309 |#2|))) ((-556) -2807 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-644 #1#) -2807 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-644 |#1|) . T) ((-644 |#2|) |has| |#1| (-363)) ((-644 $) . T) ((-637 (-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-637 (-564)))) ((-637 |#2|) |has| |#1| (-363)) ((-713 #1#) -2807 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-713 |#1|) |has| |#1| (-172)) ((-713 |#2|) |has| |#1| (-363)) ((-713 $) -2807 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-722) . T) ((-787) -12 (|has| |#1| (-363)) (|has| |#2| (-816))) ((-788) -12 (|has| |#1| (-363)) (|has| |#2| (-816))) ((-790) -12 (|has| |#1| (-363)) (|has| |#2| (-816))) ((-791) -12 (|has| |#1| (-363)) (|has| |#2| (-816))) ((-816) -12 (|has| |#1| (-363)) (|has| |#2| (-816))) ((-844) -12 (|has| |#1| (-363)) (|has| |#2| (-816))) ((-846) -2807 (-12 (|has| |#1| (-363)) (|has| |#2| (-846))) (-12 (|has| |#1| (-363)) (|has| |#2| (-816)))) ((-896 (-1170)) -2807 (-12 (|has| |#1| (-363)) (|has| |#2| (-896 (-1170)))) (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-896 (-1170))))) ((-882 (-379)) -12 (|has| |#1| (-363)) (|has| |#2| (-882 (-379)))) ((-882 (-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-882 (-564)))) ((-880 |#2|) |has| |#1| (-363)) ((-905) -12 (|has| |#1| (-363)) (|has| |#2| (-905))) ((-969 |#1| #0# (-1076)) . T) ((-916) |has| |#1| (-363)) ((-988 |#2|) |has| |#1| (-363)) ((-998) |has| |#1| (-38 (-407 (-564)))) ((-1018) -12 (|has| |#1| (-363)) (|has| |#2| (-1018))) ((-1034 (-407 (-564))) -12 (|has| |#1| (-363)) (|has| |#2| (-1034 (-564)))) ((-1034 (-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-1034 (-564)))) ((-1034 #2#) -12 (|has| |#1| (-363)) (|has| |#2| (-1034 (-1170)))) ((-1034 |#2|) . T) ((-1051 #1#) -2807 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-1051 |#1|) . T) ((-1051 |#2|) |has| |#1| (-363)) ((-1051 $) -2807 (|has| |#1| (-556)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-1045) . T) ((-1052) . T) ((-1106) . T) ((-1094) . T) ((-1145) -12 (|has| |#1| (-363)) (|has| |#2| (-1145))) ((-1194) |has| |#1| (-38 (-407 (-564)))) ((-1197) |has| |#1| (-38 (-407 (-564)))) ((-1209) |has| |#1| (-363)) ((-1213) |has| |#1| (-363)) ((-1219 |#1|) . T) ((-1237 |#1| #0#) . 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-8 NIL NIL NIL) (-1270 3156552 3156772 3156842 "WHILEAST" 3156902 T WHILEAST (NIL) -8 NIL NIL NIL) (-1269 3156024 3156269 3156363 "WHEREAST" 3156480 T WHEREAST (NIL) -8 NIL NIL NIL) (-1268 3154910 3155108 3155403 "WFFINTBS" 3155821 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1267 3152814 3153241 3153703 "WEIER" 3154482 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1266 3151935 3152385 3152427 "VSPACE" 3152563 NIL VSPACE (NIL T) -9 NIL 3152637 NIL) (-1265 3151773 3151800 3151891 "VSPACE-" 3151896 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1264 3151581 3151624 3151692 "VOID" 3151727 T VOID (NIL) -8 NIL NIL NIL) (-1263 3149717 3150076 3150482 "VIEW" 3151197 T VIEW (NIL) -7 NIL NIL NIL) (-1262 3146141 3146780 3147517 "VIEWDEF" 3149002 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1261 3135445 3137689 3139862 "VIEW3D" 3143990 T VIEW3D (NIL) -8 NIL NIL NIL) (-1260 3127696 3129356 3130935 "VIEW2D" 3133888 T VIEW2D (NIL) -8 NIL NIL NIL) (-1259 3123050 3127466 3127558 "VECTOR" 3127639 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1258 3121627 3121886 3122204 "VECTOR2" 3122780 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1257 3115106 3119411 3119454 "VECTCAT" 3120447 NIL VECTCAT (NIL T) -9 NIL 3121033 NIL) (-1256 3114120 3114374 3114764 "VECTCAT-" 3114769 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1255 3113574 3113771 3113891 "VARIABLE" 3114035 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1254 3113507 3113512 3113542 "UTYPE" 3113547 T UTYPE (NIL) -9 NIL NIL NIL) (-1253 3112337 3112491 3112753 "UTSODETL" 3113333 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1252 3109777 3110237 3110761 "UTSODE" 3111878 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1251 3101614 3107403 3107892 "UTS" 3109346 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1250 3092822 3098181 3098224 "UTSCAT" 3099336 NIL UTSCAT (NIL T) -9 NIL 3100093 NIL) (-1249 3090170 3090892 3091881 "UTSCAT-" 3091886 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1248 3089797 3089840 3089973 "UTS2" 3090121 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1247 3084023 3086635 3086678 "URAGG" 3088748 NIL URAGG (NIL T) -9 NIL 3089471 NIL) (-1246 3080962 3081825 3082948 "URAGG-" 3082953 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1245 3076672 3079597 3080062 "UPXSSING" 3080626 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1244 3068738 3075919 3076192 "UPXS" 3076457 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1243 3061811 3068642 3068714 "UPXSCONS" 3068719 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1242 3052021 3058806 3058868 "UPXSCCA" 3059442 NIL UPXSCCA (NIL T T) -9 NIL 3059675 NIL) (-1241 3051659 3051744 3051918 "UPXSCCA-" 3051923 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1240 3041722 3048280 3048323 "UPXSCAT" 3048971 NIL UPXSCAT (NIL T) -9 NIL 3049579 NIL) (-1239 3041152 3041231 3041410 "UPXS2" 3041637 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1238 3039806 3040059 3040410 "UPSQFREE" 3040895 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1237 3033559 3036608 3036663 "UPSCAT" 3037824 NIL UPSCAT (NIL T T) -9 NIL 3038598 NIL) (-1236 3032763 3032970 3033297 "UPSCAT-" 3033302 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1235 3018878 3026638 3026681 "UPOLYC" 3028782 NIL UPOLYC (NIL T) -9 NIL 3030003 NIL) (-1234 3010206 3012632 3015779 "UPOLYC-" 3015784 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1233 3009833 3009876 3010009 "UPOLYC2" 3010157 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1232 3001644 3009516 3009645 "UP" 3009752 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1231 3000983 3001090 3001254 "UPMP" 3001533 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1230 3000536 3000617 3000756 "UPDIVP" 3000896 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1229 2999104 2999353 2999669 "UPDECOMP" 3000285 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1228 2998339 2998451 2998636 "UPCDEN" 2998988 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1227 2997858 2997927 2998076 "UP2" 2998264 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1226 2996325 2997062 2997339 "UNISEG" 2997616 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1225 2995540 2995667 2995872 "UNISEG2" 2996168 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1224 2994600 2994780 2995006 "UNIFACT" 2995356 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1223 2978532 2993777 2994028 "ULS" 2994407 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1222 2966531 2978436 2978508 "ULSCONS" 2978513 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1221 2949112 2961089 2961151 "ULSCCAT" 2961789 NIL ULSCCAT (NIL T T) -9 NIL 2962077 NIL) (-1220 2948162 2948407 2948795 "ULSCCAT-" 2948800 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1219 2938002 2944474 2944517 "ULSCAT" 2945380 NIL ULSCAT (NIL T) -9 NIL 2946110 NIL) (-1218 2937432 2937511 2937690 "ULS2" 2937917 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1217 2936522 2937032 2937139 "UINT8" 2937250 T UINT8 (NIL) -8 NIL NIL 2937335) (-1216 2935611 2936121 2936228 "UINT64" 2936339 T UINT64 (NIL) -8 NIL NIL 2936424) (-1215 2934700 2935210 2935317 "UINT32" 2935428 T UINT32 (NIL) -8 NIL NIL 2935513) (-1214 2933789 2934299 2934406 "UINT16" 2934517 T UINT16 (NIL) -8 NIL NIL 2934602) (-1213 2932158 2933115 2933145 "UFD" 2933357 T UFD (NIL) -9 NIL 2933471 NIL) (-1212 2931952 2931998 2932093 "UFD-" 2932098 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1211 2931034 2931217 2931433 "UDVO" 2931758 T UDVO (NIL) -7 NIL NIL NIL) (-1210 2928850 2929259 2929730 "UDPO" 2930598 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1209 2928783 2928788 2928818 "TYPE" 2928823 T TYPE (NIL) -9 NIL NIL NIL) (-1208 2928543 2928738 2928769 "TYPEAST" 2928774 T TYPEAST (NIL) -8 NIL NIL NIL) (-1207 2927514 2927716 2927956 "TWOFACT" 2928337 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1206 2926537 2926923 2927158 "TUPLE" 2927314 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1205 2924228 2924747 2925286 "TUBETOOL" 2926020 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1204 2923077 2923282 2923523 "TUBE" 2924021 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1203 2917806 2922049 2922332 "TS" 2922829 NIL TS (NIL T) -8 NIL NIL NIL) (-1202 2906446 2910565 2910662 "TSETCAT" 2915931 NIL TSETCAT (NIL T T T T) -9 NIL 2917462 NIL) (-1201 2901178 2902778 2904669 "TSETCAT-" 2904674 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1200 2895817 2896664 2897593 "TRMANIP" 2900314 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1199 2895258 2895321 2895484 "TRIMAT" 2895749 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1198 2893124 2893361 2893718 "TRIGMNIP" 2895007 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1197 2892644 2892757 2892787 "TRIGCAT" 2893000 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1196 2892313 2892392 2892533 "TRIGCAT-" 2892538 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1195 2889158 2891171 2891452 "TREE" 2892067 NIL TREE (NIL T) -8 NIL NIL NIL) (-1194 2888432 2888960 2888990 "TRANFUN" 2889025 T TRANFUN (NIL) -9 NIL 2889091 NIL) (-1193 2887711 2887902 2888182 "TRANFUN-" 2888187 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1192 2887515 2887547 2887608 "TOPSP" 2887672 T TOPSP (NIL) -7 NIL NIL NIL) (-1191 2886863 2886978 2887132 "TOOLSIGN" 2887396 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1190 2885497 2886040 2886279 "TEXTFILE" 2886646 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1189 2883409 2883950 2884379 "TEX" 2885090 T TEX (NIL) -8 NIL NIL NIL) (-1188 2883190 2883221 2883293 "TEX1" 2883372 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1187 2882838 2882901 2882991 "TEMUTL" 2883122 T TEMUTL (NIL) -7 NIL NIL NIL) (-1186 2880992 2881272 2881597 "TBCMPPK" 2882561 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1185 2872769 2879152 2879208 "TBAGG" 2879608 NIL TBAGG (NIL T T) -9 NIL 2879819 NIL) (-1184 2867839 2869327 2871081 "TBAGG-" 2871086 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1183 2867223 2867330 2867475 "TANEXP" 2867728 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1182 2860613 2867080 2867173 "TABLE" 2867178 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1181 2860025 2860124 2860262 "TABLEAU" 2860510 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1180 2854633 2855853 2857101 "TABLBUMP" 2858811 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1179 2853855 2854002 2854183 "SYSTEM" 2854474 T SYSTEM (NIL) -8 NIL NIL NIL) (-1178 2850314 2851013 2851796 "SYSSOLP" 2853106 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1177 2849321 2849826 2849945 "SYSNNI" 2850131 NIL SYSNNI (NIL NIL) -8 NIL NIL 2850216) (-1176 2848591 2849050 2849129 "SYSINT" 2849189 NIL SYSINT (NIL NIL) -8 NIL NIL 2849234) (-1175 2844923 2845869 2846579 "SYNTAX" 2847903 T SYNTAX (NIL) -8 NIL NIL NIL) (-1174 2842081 2842683 2843315 "SYMTAB" 2844313 T SYMTAB (NIL) -8 NIL NIL NIL) (-1173 2837330 2838232 2839215 "SYMS" 2841120 T SYMS (NIL) -8 NIL NIL NIL) (-1172 2834565 2836788 2837018 "SYMPOLY" 2837135 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1171 2834082 2834157 2834280 "SYMFUNC" 2834477 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1170 2830101 2831394 2832207 "SYMBOL" 2833291 T SYMBOL (NIL) -8 NIL NIL NIL) (-1169 2823640 2825329 2827049 "SWITCH" 2828403 T SWITCH (NIL) -8 NIL NIL NIL) (-1168 2816874 2822461 2822764 "SUTS" 2823395 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1167 2808940 2816121 2816394 "SUPXS" 2816659 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2800700 2808558 2808684 "SUP" 2808849 NIL SUP (NIL T) -8 NIL NIL NIL) (-1165 2799859 2799986 2800203 "SUPFRACF" 2800568 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1164 2799480 2799539 2799652 "SUP2" 2799794 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1163 2797928 2798202 2798558 "SUMRF" 2799179 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1162 2797263 2797329 2797521 "SUMFS" 2797849 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1161 2781230 2796440 2796691 "SULS" 2797070 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2780832 2781052 2781122 "SUCHTAST" 2781182 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1159 2780127 2780357 2780497 "SUCH" 2780740 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1158 2773994 2775033 2775992 "SUBSPACE" 2779215 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1157 2773424 2773514 2773678 "SUBRESP" 2773882 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1156 2766789 2768089 2769400 "STTF" 2772160 NIL STTF (NIL T) -7 NIL NIL NIL) (-1155 2760962 2762082 2763229 "STTFNC" 2765689 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1154 2752273 2754144 2755938 "STTAYLOR" 2759203 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1153 2745403 2752137 2752220 "STRTBL" 2752225 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1152 2740767 2745358 2745389 "STRING" 2745394 T STRING (NIL) -8 NIL NIL NIL) (-1151 2735628 2740140 2740170 "STRICAT" 2740229 T STRICAT (NIL) -9 NIL 2740291 NIL) (-1150 2728383 2733247 2733858 "STREAM" 2735052 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1149 2727893 2727970 2728114 "STREAM3" 2728300 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1148 2726875 2727058 2727293 "STREAM2" 2727706 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1147 2726563 2726615 2726708 "STREAM1" 2726817 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1146 2725579 2725760 2725991 "STINPROD" 2726379 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1145 2725131 2725341 2725371 "STEP" 2725451 T STEP (NIL) -9 NIL 2725529 NIL) (-1144 2718563 2725030 2725107 "STBL" 2725112 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1143 2713689 2717784 2717827 "STAGG" 2717980 NIL STAGG (NIL T) -9 NIL 2718069 NIL) (-1142 2711391 2711993 2712865 "STAGG-" 2712870 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1141 2709538 2711161 2711253 "STACK" 2711334 NIL STACK (NIL T) -8 NIL NIL NIL) (-1140 2702234 2707679 2708135 "SREGSET" 2709168 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1139 2694659 2696028 2697541 "SRDCMPK" 2700840 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2687576 2692099 2692129 "SRAGG" 2693432 T SRAGG (NIL) -9 NIL 2694040 NIL) (-1137 2686593 2686848 2687227 "SRAGG-" 2687232 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1136 2681053 2685540 2685961 "SQMATRIX" 2686219 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1135 2674739 2677771 2678498 "SPLTREE" 2680398 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1134 2670702 2671395 2672041 "SPLNODE" 2674165 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1133 2669749 2669982 2670012 "SPFCAT" 2670456 T SPFCAT (NIL) -9 NIL NIL NIL) (-1132 2668486 2668696 2668960 "SPECOUT" 2669507 T SPECOUT (NIL) -7 NIL NIL NIL) (-1131 2660112 2661882 2661912 "SPADXPT" 2666304 T SPADXPT (NIL) -9 NIL 2668338 NIL) (-1130 2659873 2659913 2659982 "SPADPRSR" 2660065 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1129 2658028 2659828 2659859 "SPADAST" 2659864 T SPADAST (NIL) -8 NIL NIL NIL) (-1128 2649973 2651746 2651789 "SPACEC" 2656162 NIL SPACEC (NIL T) -9 NIL 2657978 NIL) (-1127 2648103 2649905 2649954 "SPACE3" 2649959 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1126 2646855 2647026 2647317 "SORTPAK" 2647908 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1125 2644947 2645250 2645662 "SOLVETRA" 2646519 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1124 2643997 2644219 2644480 "SOLVESER" 2644720 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1123 2639299 2640189 2641184 "SOLVERAD" 2643049 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1122 2635114 2635723 2636452 "SOLVEFOR" 2638666 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1121 2629384 2634463 2634560 "SNTSCAT" 2634565 NIL SNTSCAT (NIL T T T T) -9 NIL 2634635 NIL) (-1120 2623490 2627707 2628098 "SMTS" 2629074 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1119 2618175 2623378 2623455 "SMP" 2623460 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1118 2616334 2616635 2617033 "SMITH" 2617872 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1117 2609194 2613385 2613488 "SMATCAT" 2614839 NIL SMATCAT (NIL NIL T T T) -9 NIL 2615389 NIL) (-1116 2606134 2606957 2608135 "SMATCAT-" 2608140 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1115 2603800 2605370 2605413 "SKAGG" 2605674 NIL SKAGG (NIL T) -9 NIL 2605809 NIL) (-1114 2600108 2603216 2603411 "SINT" 2603598 T SINT (NIL) -8 NIL NIL 2603771) (-1113 2599880 2599918 2599984 "SIMPAN" 2600064 T SIMPAN (NIL) -7 NIL NIL NIL) (-1112 2599159 2599415 2599555 "SIG" 2599762 T SIG (NIL) -8 NIL NIL NIL) (-1111 2597997 2598218 2598493 "SIGNRF" 2598918 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1110 2596830 2596981 2597265 "SIGNEF" 2597826 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1109 2596136 2596413 2596537 "SIGAST" 2596728 T SIGAST (NIL) -8 NIL NIL NIL) (-1108 2593826 2594280 2594786 "SHP" 2595677 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1107 2587678 2593727 2593803 "SHDP" 2593808 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1106 2587251 2587443 2587473 "SGROUP" 2587566 T SGROUP (NIL) -9 NIL 2587628 NIL) (-1105 2587109 2587135 2587208 "SGROUP-" 2587213 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1104 2583944 2584642 2585365 "SGCF" 2586408 T SGCF (NIL) -7 NIL NIL NIL) (-1103 2578312 2583391 2583488 "SFRTCAT" 2583493 NIL SFRTCAT (NIL T T T T) -9 NIL 2583532 NIL) (-1102 2571733 2572751 2573887 "SFRGCD" 2577295 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1101 2564860 2565932 2567118 "SFQCMPK" 2570666 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2564480 2564569 2564680 "SFORT" 2564801 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1099 2563598 2564320 2564441 "SEXOF" 2564446 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1098 2562705 2563479 2563547 "SEX" 2563552 T SEX (NIL) -8 NIL NIL NIL) (-1097 2558218 2558933 2559028 "SEXCAT" 2561965 NIL SEXCAT (NIL T T T T T) -9 NIL 2562543 NIL) (-1096 2555371 2558152 2558200 "SET" 2558205 NIL SET (NIL T) -8 NIL NIL NIL) (-1095 2553595 2554084 2554389 "SETMN" 2555112 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1094 2553091 2553243 2553273 "SETCAT" 2553449 T SETCAT (NIL) -9 NIL 2553559 NIL) (-1093 2552871 2552923 2553022 "SETCAT-" 2553027 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1092 2549232 2551332 2551375 "SETAGG" 2552245 NIL SETAGG (NIL T) -9 NIL 2552585 NIL) (-1091 2548690 2548806 2549043 "SETAGG-" 2549048 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1090 2548133 2548386 2548487 "SEQAST" 2548611 T SEQAST (NIL) -8 NIL NIL NIL) (-1089 2547332 2547626 2547687 "SEGXCAT" 2547973 NIL SEGXCAT (NIL T T) -9 NIL 2548093 NIL) (-1088 2546338 2546998 2547180 "SEG" 2547185 NIL SEG (NIL T) -8 NIL NIL NIL) (-1087 2545317 2545531 2545574 "SEGCAT" 2546096 NIL SEGCAT (NIL T) -9 NIL 2546317 NIL) (-1086 2544318 2544696 2544896 "SEGBIND" 2545152 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1085 2543939 2543998 2544111 "SEGBIND2" 2544253 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1084 2543512 2543740 2543817 "SEGAST" 2543884 T SEGAST (NIL) -8 NIL NIL NIL) (-1083 2542731 2542857 2543061 "SEG2" 2543356 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1082 2542141 2542666 2542713 "SDVAR" 2542718 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1081 2534668 2541911 2542041 "SDPOL" 2542046 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1080 2533261 2533527 2533846 "SCPKG" 2534383 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1079 2532425 2532597 2532789 "SCOPE" 2533091 T SCOPE (NIL) -8 NIL NIL NIL) (-1078 2531645 2531779 2531958 "SCACHE" 2532280 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1077 2531291 2531477 2531507 "SASTCAT" 2531512 T SASTCAT (NIL) -9 NIL 2531525 NIL) (-1076 2530778 2531126 2531202 "SAOS" 2531237 T SAOS (NIL) -8 NIL NIL NIL) (-1075 2530343 2530378 2530551 "SAERFFC" 2530737 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1074 2524282 2530240 2530320 "SAE" 2530325 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1073 2523875 2523910 2524069 "SAEFACT" 2524241 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1072 2522196 2522510 2522911 "RURPK" 2523541 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1071 2520833 2521139 2521444 "RULESET" 2522030 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1070 2518056 2518586 2519044 "RULE" 2520514 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1069 2517668 2517850 2517933 "RULECOLD" 2518008 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1068 2517458 2517486 2517557 "RTVALUE" 2517619 T RTVALUE (NIL) -8 NIL NIL NIL) (-1067 2516929 2517175 2517269 "RSTRCAST" 2517386 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1066 2511777 2512572 2513492 "RSETGCD" 2516128 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1065 2501007 2506086 2506183 "RSETCAT" 2510302 NIL RSETCAT (NIL T T T T) -9 NIL 2511399 NIL) (-1064 2498934 2499473 2500297 "RSETCAT-" 2500302 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1063 2491319 2492696 2494216 "RSDCMPK" 2497533 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1062 2489298 2489765 2489839 "RRCC" 2490925 NIL RRCC (NIL T T) -9 NIL 2491269 NIL) (-1061 2488649 2488823 2489102 "RRCC-" 2489107 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1060 2488092 2488345 2488446 "RPTAST" 2488570 T RPTAST (NIL) -8 NIL NIL NIL) (-1059 2462363 2471712 2471779 "RPOLCAT" 2482443 NIL RPOLCAT (NIL T T T) -9 NIL 2485602 NIL) (-1058 2453861 2456201 2459323 "RPOLCAT-" 2459328 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1057 2444792 2452072 2452554 "ROUTINE" 2453401 T ROUTINE (NIL) -8 NIL NIL NIL) (-1056 2441590 2444418 2444558 "ROMAN" 2444674 T ROMAN (NIL) -8 NIL NIL NIL) (-1055 2439834 2440450 2440710 "ROIRC" 2441395 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1054 2436192 2438470 2438500 "RNS" 2438804 T RNS (NIL) -9 NIL 2439077 NIL) (-1053 2434701 2435084 2435618 "RNS-" 2435693 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1052 2434124 2434532 2434562 "RNG" 2434567 T RNG (NIL) -9 NIL 2434588 NIL) (-1051 2433490 2433878 2433921 "RMODULE" 2433983 NIL RMODULE (NIL T) -9 NIL 2434025 NIL) (-1050 2432326 2432420 2432756 "RMCAT2" 2433391 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1049 2429176 2431672 2431969 "RMATRIX" 2432088 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1048 2422092 2424352 2424467 "RMATCAT" 2427826 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2428808 NIL) (-1047 2421467 2421614 2421921 "RMATCAT-" 2421926 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1046 2421034 2421109 2421237 "RINTERP" 2421386 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1045 2420127 2420681 2420711 "RING" 2420767 T RING (NIL) -9 NIL 2420859 NIL) (-1044 2419919 2419963 2420060 "RING-" 2420065 NIL RING- (NIL T) -8 NIL NIL NIL) (-1043 2418760 2418997 2419255 "RIDIST" 2419683 T RIDIST (NIL) -7 NIL NIL NIL) (-1042 2410049 2418228 2418434 "RGCHAIN" 2418608 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1041 2409399 2409805 2409846 "RGBCSPC" 2409904 NIL RGBCSPC (NIL T) -9 NIL 2409956 NIL) (-1040 2408557 2408938 2408979 "RGBCMDL" 2409211 NIL RGBCMDL (NIL T) -9 NIL 2409325 NIL) (-1039 2405551 2406165 2406835 "RF" 2407921 NIL RF (NIL T) -7 NIL NIL NIL) (-1038 2405197 2405260 2405363 "RFFACTOR" 2405482 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1037 2404922 2404957 2405054 "RFFACT" 2405156 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1036 2403039 2403403 2403785 "RFDIST" 2404562 T RFDIST (NIL) -7 NIL NIL NIL) (-1035 2402492 2402584 2402747 "RETSOL" 2402941 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1034 2402128 2402208 2402251 "RETRACT" 2402384 NIL RETRACT (NIL T) -9 NIL 2402471 NIL) (-1033 2401977 2402002 2402089 "RETRACT-" 2402094 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1032 2401579 2401799 2401869 "RETAST" 2401929 T RETAST (NIL) -8 NIL NIL NIL) (-1031 2394317 2401232 2401359 "RESULT" 2401474 T RESULT (NIL) -8 NIL NIL NIL) (-1030 2392908 2393586 2393785 "RESRING" 2394220 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1029 2392544 2392593 2392691 "RESLATC" 2392845 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1028 2392249 2392284 2392391 "REPSQ" 2392503 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1027 2389671 2390251 2390853 "REP" 2391669 T REP (NIL) -7 NIL NIL NIL) (-1026 2389368 2389403 2389514 "REPDB" 2389630 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1025 2383268 2384657 2385880 "REP2" 2388180 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1024 2379645 2380326 2381134 "REP1" 2382495 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1023 2372341 2377786 2378242 "REGSET" 2379275 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1022 2371106 2371489 2371739 "REF" 2372126 NIL REF (NIL T) -8 NIL NIL NIL) (-1021 2370483 2370586 2370753 "REDORDER" 2370990 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1020 2366451 2369696 2369923 "RECLOS" 2370311 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1019 2365503 2365684 2365899 "REALSOLV" 2366258 T REALSOLV (NIL) -7 NIL NIL NIL) (-1018 2365349 2365390 2365420 "REAL" 2365425 T REAL (NIL) -9 NIL 2365460 NIL) (-1017 2361832 2362634 2363518 "REAL0Q" 2364514 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1016 2357433 2358421 2359482 "REAL0" 2360813 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1015 2356904 2357150 2357244 "RDUCEAST" 2357361 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1014 2356309 2356381 2356588 "RDIV" 2356826 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1013 2355377 2355551 2355764 "RDIST" 2356131 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1012 2353974 2354261 2354633 "RDETRS" 2355085 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1011 2351786 2352240 2352778 "RDETR" 2353516 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1010 2350411 2350689 2351086 "RDEEFS" 2351502 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1009 2348920 2349226 2349651 "RDEEF" 2350099 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1008 2343146 2346056 2346086 "RCFIELD" 2347381 T RCFIELD (NIL) -9 NIL 2348111 NIL) (-1007 2341210 2341714 2342410 "RCFIELD-" 2342485 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1006 2337479 2339311 2339354 "RCAGG" 2340438 NIL RCAGG (NIL T) -9 NIL 2340903 NIL) (-1005 2337107 2337201 2337364 "RCAGG-" 2337369 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1004 2336442 2336554 2336719 "RATRET" 2336991 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1003 2335995 2336062 2336183 "RATFACT" 2336370 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1002 2335303 2335423 2335575 "RANDSRC" 2335865 T RANDSRC (NIL) -7 NIL NIL NIL) (-1001 2335037 2335081 2335154 "RADUTIL" 2335252 T RADUTIL (NIL) -7 NIL NIL NIL) (-1000 2328153 2333870 2334180 "RADIX" 2334761 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-999 2319774 2327997 2328125 "RADFF" 2328130 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-998 2319426 2319501 2319529 "RADCAT" 2319686 T RADCAT (NIL) -9 NIL NIL NIL) (-997 2319211 2319259 2319356 "RADCAT-" 2319361 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-996 2317314 2318986 2319075 "QUEUE" 2319155 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-995 2313855 2317251 2317296 "QUAT" 2317301 NIL QUAT (NIL T) -8 NIL NIL NIL) (-994 2313493 2313536 2313663 "QUATCT2" 2313806 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-993 2307205 2310542 2310582 "QUATCAT" 2311362 NIL QUATCAT (NIL T) -9 NIL 2312128 NIL) (-992 2303349 2304386 2305773 "QUATCAT-" 2305867 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-991 2300822 2302433 2302474 "QUAGG" 2302849 NIL QUAGG (NIL T) -9 NIL 2303024 NIL) (-990 2300427 2300647 2300715 "QQUTAST" 2300774 T QQUTAST (NIL) -8 NIL NIL NIL) (-989 2299325 2299825 2299997 "QFORM" 2300299 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-988 2290503 2295742 2295782 "QFCAT" 2296440 NIL QFCAT (NIL T) -9 NIL 2297441 NIL) (-987 2286075 2287276 2288867 "QFCAT-" 2288961 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-986 2285713 2285756 2285883 "QFCAT2" 2286026 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-985 2285173 2285283 2285413 "QEQUAT" 2285603 T QEQUAT (NIL) -8 NIL NIL NIL) (-984 2278320 2279392 2280576 "QCMPACK" 2284106 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-983 2275869 2276317 2276745 "QALGSET" 2277975 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-982 2275114 2275288 2275520 "QALGSET2" 2275689 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-981 2273804 2274028 2274345 "PWFFINTB" 2274887 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-980 2271986 2272154 2272508 "PUSHVAR" 2273618 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-979 2267904 2268958 2268999 "PTRANFN" 2270883 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-978 2266306 2266597 2266919 "PTPACK" 2267615 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-977 2265938 2265995 2266104 "PTFUNC2" 2266243 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-976 2260417 2264810 2264851 "PTCAT" 2265147 NIL PTCAT (NIL T) -9 NIL 2265300 NIL) (-975 2260075 2260110 2260234 "PSQFR" 2260376 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-974 2258670 2258968 2259302 "PSEUDLIN" 2259773 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-973 2245433 2247804 2250128 "PSETPK" 2256430 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-972 2238451 2241191 2241287 "PSETCAT" 2244308 NIL PSETCAT (NIL T T T T) -9 NIL 2245122 NIL) (-971 2236287 2236921 2237742 "PSETCAT-" 2237747 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-970 2235636 2235801 2235829 "PSCURVE" 2236097 T PSCURVE (NIL) -9 NIL 2236264 NIL) (-969 2231958 2233474 2233539 "PSCAT" 2234383 NIL PSCAT (NIL T T T) -9 NIL 2234623 NIL) (-968 2231021 2231237 2231637 "PSCAT-" 2231642 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-967 2229726 2230386 2230591 "PRTITION" 2230836 T PRTITION (NIL) -8 NIL NIL NIL) (-966 2229201 2229447 2229539 "PRTDAST" 2229654 T PRTDAST (NIL) -8 NIL NIL NIL) (-965 2218291 2220505 2222693 "PRS" 2227063 NIL PRS (NIL T T) -7 NIL NIL NIL) (-964 2216102 2217641 2217681 "PRQAGG" 2217864 NIL PRQAGG (NIL T) -9 NIL 2217966 NIL) (-963 2215306 2215611 2215639 "PROPLOG" 2215886 T PROPLOG (NIL) -9 NIL 2216052 NIL) (-962 2213736 2214257 2214514 "PROPFRML" 2215082 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-961 2213205 2213312 2213440 "PROPERTY" 2213628 T PROPERTY (NIL) -8 NIL NIL NIL) (-960 2207263 2211371 2212191 "PRODUCT" 2212431 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-959 2204541 2206721 2206955 "PR" 2207074 NIL PR (NIL T T) -8 NIL NIL NIL) (-958 2204337 2204369 2204428 "PRINT" 2204502 T PRINT (NIL) -7 NIL NIL NIL) (-957 2203677 2203794 2203946 "PRIMES" 2204217 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-956 2201742 2202143 2202609 "PRIMELT" 2203256 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-955 2201471 2201520 2201548 "PRIMCAT" 2201672 T PRIMCAT (NIL) -9 NIL NIL NIL) (-954 2197586 2201409 2201454 "PRIMARR" 2201459 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-953 2196593 2196771 2196999 "PRIMARR2" 2197404 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-952 2196236 2196292 2196403 "PREASSOC" 2196531 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-951 2195711 2195844 2195872 "PPCURVE" 2196077 T PPCURVE (NIL) -9 NIL 2196213 NIL) (-950 2195306 2195506 2195589 "PORTNUM" 2195648 T PORTNUM (NIL) -8 NIL NIL NIL) (-949 2192665 2193064 2193656 "POLYROOT" 2194887 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-948 2186847 2192269 2192429 "POLY" 2192538 NIL POLY (NIL T) -8 NIL NIL NIL) (-947 2186230 2186288 2186522 "POLYLIFT" 2186783 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-946 2182505 2182954 2183583 "POLYCATQ" 2185775 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-945 2169637 2174757 2174822 "POLYCAT" 2178336 NIL POLYCAT (NIL T T T) -9 NIL 2180214 NIL) (-944 2163086 2164948 2167332 "POLYCAT-" 2167337 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-943 2162673 2162741 2162861 "POLY2UP" 2163012 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-942 2162305 2162362 2162471 "POLY2" 2162610 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-941 2160990 2161229 2161505 "POLUTIL" 2162079 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-940 2159345 2159622 2159953 "POLTOPOL" 2160712 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-939 2154812 2159281 2159327 "POINT" 2159332 NIL POINT (NIL T) -8 NIL NIL NIL) (-938 2152999 2153356 2153731 "PNTHEORY" 2154457 T PNTHEORY (NIL) -7 NIL NIL NIL) (-937 2151457 2151754 2152153 "PMTOOLS" 2152697 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-936 2151050 2151128 2151245 "PMSYM" 2151373 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-935 2150560 2150629 2150803 "PMQFCAT" 2150975 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-934 2149915 2150025 2150181 "PMPRED" 2150437 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-933 2149308 2149394 2149556 "PMPREDFS" 2149816 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-932 2147972 2148180 2148558 "PMPLCAT" 2149070 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-931 2147504 2147583 2147735 "PMLSAGG" 2147887 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-930 2146977 2147053 2147235 "PMKERNEL" 2147422 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-929 2146594 2146669 2146782 "PMINS" 2146896 NIL PMINS (NIL T) -7 NIL NIL NIL) (-928 2146036 2146105 2146314 "PMFS" 2146519 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-927 2145264 2145382 2145587 "PMDOWN" 2145913 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-926 2144431 2144589 2144770 "PMASS" 2145103 T PMASS (NIL) -7 NIL NIL NIL) (-925 2143704 2143814 2143977 "PMASSFS" 2144318 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-924 2143359 2143427 2143521 "PLOTTOOL" 2143630 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-923 2137966 2139170 2140318 "PLOT" 2142231 T PLOT (NIL) -8 NIL NIL NIL) (-922 2133770 2134814 2135735 "PLOT3D" 2137065 T PLOT3D (NIL) -8 NIL NIL NIL) (-921 2132682 2132859 2133094 "PLOT1" 2133574 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-920 2108071 2112748 2117599 "PLEQN" 2127948 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-919 2107389 2107511 2107691 "PINTERP" 2107936 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-918 2107082 2107129 2107232 "PINTERPA" 2107336 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-917 2106303 2106851 2106938 "PI" 2106978 T PI (NIL) -8 NIL NIL 2107045) (-916 2104666 2105641 2105669 "PID" 2105851 T PID (NIL) -9 NIL 2105985 NIL) (-915 2104417 2104454 2104529 "PICOERCE" 2104623 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-914 2103737 2103876 2104052 "PGROEB" 2104273 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-913 2099324 2100138 2101043 "PGE" 2102852 T PGE (NIL) -7 NIL NIL NIL) (-912 2097447 2097694 2098060 "PGCD" 2099041 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-911 2096785 2096888 2097049 "PFRPAC" 2097331 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-910 2093426 2095333 2095686 "PFR" 2096464 NIL PFR (NIL T) -8 NIL NIL NIL) (-909 2091815 2092059 2092384 "PFOTOOLS" 2093173 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-908 2090348 2090587 2090938 "PFOQ" 2091572 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-907 2088849 2089061 2089417 "PFO" 2090132 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-906 2085402 2088738 2088807 "PF" 2088812 NIL PF (NIL NIL) -8 NIL NIL NIL) (-905 2082802 2084073 2084101 "PFECAT" 2084686 T PFECAT (NIL) -9 NIL 2085070 NIL) (-904 2082247 2082401 2082615 "PFECAT-" 2082620 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-903 2080850 2081102 2081403 "PFBRU" 2081996 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-902 2078715 2079068 2079500 "PFBR" 2080501 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-901 2074597 2076091 2076767 "PERM" 2078072 NIL PERM (NIL T) -8 NIL NIL NIL) (-900 2069831 2070804 2071674 "PERMGRP" 2073760 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-899 2067937 2068894 2068935 "PERMCAT" 2069381 NIL PERMCAT (NIL T) -9 NIL 2069686 NIL) (-898 2067590 2067631 2067755 "PERMAN" 2067890 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-897 2065078 2067255 2067377 "PENDTREE" 2067501 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-896 2063137 2063905 2063946 "PDRING" 2064603 NIL PDRING (NIL T) -9 NIL 2064889 NIL) (-895 2062240 2062458 2062820 "PDRING-" 2062825 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-894 2059455 2060233 2060901 "PDEPROB" 2061592 T PDEPROB (NIL) -8 NIL NIL NIL) (-893 2057000 2057504 2058059 "PDEPACK" 2058920 T PDEPACK (NIL) -7 NIL NIL NIL) (-892 2055912 2056102 2056353 "PDECOMP" 2056799 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-891 2053491 2054334 2054362 "PDECAT" 2055149 T PDECAT (NIL) -9 NIL 2055862 NIL) (-890 2053242 2053275 2053365 "PCOMP" 2053452 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-889 2051420 2052043 2052340 "PBWLB" 2052971 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-888 2043893 2045493 2046831 "PATTERN" 2050103 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-887 2043525 2043582 2043691 "PATTERN2" 2043830 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-886 2041282 2041670 2042127 "PATTERN1" 2043114 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-885 2038650 2039231 2039712 "PATRES" 2040847 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-884 2038214 2038281 2038413 "PATRES2" 2038577 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-883 2036097 2036502 2036909 "PATMATCH" 2037881 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-882 2035607 2035816 2035857 "PATMAB" 2035964 NIL PATMAB (NIL T) -9 NIL 2036047 NIL) (-881 2034125 2034461 2034719 "PATLRES" 2035412 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-880 2033671 2033794 2033835 "PATAB" 2033840 NIL PATAB (NIL T) -9 NIL 2034012 NIL) (-879 2031152 2031684 2032257 "PARTPERM" 2033118 T PARTPERM (NIL) -7 NIL NIL NIL) (-878 2030773 2030836 2030938 "PARSURF" 2031083 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-877 2030405 2030462 2030571 "PARSU2" 2030710 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-876 2030169 2030209 2030276 "PARSER" 2030358 T PARSER (NIL) -7 NIL NIL NIL) (-875 2029790 2029853 2029955 "PARSCURV" 2030100 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-874 2029422 2029479 2029588 "PARSC2" 2029727 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-873 2029061 2029119 2029216 "PARPCURV" 2029358 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-872 2028693 2028750 2028859 "PARPC2" 2028998 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-871 2028213 2028299 2028418 "PAN2EXPR" 2028594 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-870 2026990 2027334 2027562 "PALETTE" 2028005 T PALETTE (NIL) -8 NIL NIL NIL) (-869 2025383 2025995 2026355 "PAIR" 2026676 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-868 2019253 2024642 2024836 "PADICRC" 2025238 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-867 2012482 2018599 2018783 "PADICRAT" 2019101 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-866 2010797 2012419 2012464 "PADIC" 2012469 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-865 2007973 2009537 2009577 "PADICCT" 2010158 NIL PADICCT (NIL NIL) -9 NIL 2010440 NIL) (-864 2006930 2007130 2007398 "PADEPAC" 2007760 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-863 2006142 2006275 2006481 "PADE" 2006792 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-862 2004529 2005350 2005630 "OWP" 2005946 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-861 2004022 2004235 2004332 "OVERSET" 2004452 T OVERSET (NIL) -8 NIL NIL NIL) (-860 2003068 2003627 2003799 "OVAR" 2003890 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-859 2002332 2002453 2002614 "OUT" 2002927 T OUT (NIL) -7 NIL NIL NIL) (-858 1991203 1993441 1995641 "OUTFORM" 2000152 T OUTFORM (NIL) -8 NIL NIL NIL) (-857 1990539 1990800 1990927 "OUTBFILE" 1991096 T OUTBFILE (NIL) -8 NIL NIL NIL) (-856 1989846 1990011 1990039 "OUTBCON" 1990357 T OUTBCON (NIL) -9 NIL 1990523 NIL) (-855 1989447 1989559 1989716 "OUTBCON-" 1989721 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-854 1988827 1989176 1989265 "OSI" 1989378 T OSI (NIL) -8 NIL NIL NIL) (-853 1988357 1988695 1988723 "OSGROUP" 1988728 T OSGROUP (NIL) -9 NIL 1988750 NIL) (-852 1987102 1987329 1987614 "ORTHPOL" 1988104 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-851 1984653 1986937 1987058 "OREUP" 1987063 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-850 1982056 1984344 1984471 "ORESUP" 1984595 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-849 1979584 1980084 1980645 "OREPCTO" 1981545 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-848 1973374 1975575 1975616 "OREPCAT" 1977964 NIL OREPCAT (NIL T) -9 NIL 1979068 NIL) (-847 1970521 1971303 1972361 "OREPCAT-" 1972366 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-846 1969672 1969970 1969998 "ORDSET" 1970307 T ORDSET (NIL) -9 NIL 1970471 NIL) (-845 1969103 1969251 1969475 "ORDSET-" 1969480 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-844 1967703 1968494 1968522 "ORDRING" 1968724 T ORDRING (NIL) -9 NIL 1968849 NIL) (-843 1967348 1967442 1967586 "ORDRING-" 1967591 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-842 1966728 1967191 1967219 "ORDMON" 1967224 T ORDMON (NIL) -9 NIL 1967245 NIL) (-841 1965890 1966037 1966232 "ORDFUNS" 1966577 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-840 1965228 1965647 1965675 "ORDFIN" 1965740 T ORDFIN (NIL) -9 NIL 1965814 NIL) (-839 1961787 1963814 1964223 "ORDCOMP" 1964852 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-838 1961053 1961180 1961366 "ORDCOMP2" 1961647 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1957634 1958544 1959358 "OPTPROB" 1960259 T OPTPROB (NIL) -8 NIL NIL NIL) (-836 1954436 1955075 1955779 "OPTPACK" 1956950 T OPTPACK (NIL) -7 NIL NIL NIL) (-835 1952123 1952889 1952917 "OPTCAT" 1953736 T OPTCAT (NIL) -9 NIL 1954386 NIL) (-834 1951539 1951800 1951905 "OPSIG" 1952038 T OPSIG (NIL) -8 NIL NIL NIL) (-833 1951307 1951346 1951412 "OPQUERY" 1951493 T OPQUERY (NIL) -7 NIL NIL NIL) (-832 1948438 1949618 1950122 "OP" 1950836 NIL OP (NIL T) -8 NIL NIL NIL) (-831 1947947 1948144 1948185 "OPERCAT" 1948320 NIL OPERCAT (NIL T) -9 NIL 1948388 NIL) (-830 1947793 1947820 1947906 "OPERCAT-" 1947911 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-829 1944605 1946590 1946959 "ONECOMP" 1947457 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-828 1943910 1944025 1944199 "ONECOMP2" 1944477 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-827 1943329 1943435 1943565 "OMSERVER" 1943800 T OMSERVER (NIL) -7 NIL NIL NIL) (-826 1940191 1942769 1942809 "OMSAGG" 1942870 NIL OMSAGG (NIL T) -9 NIL 1942934 NIL) (-825 1938814 1939077 1939359 "OMPKG" 1939929 T OMPKG (NIL) -7 NIL NIL NIL) (-824 1938244 1938347 1938375 "OM" 1938674 T OM (NIL) -9 NIL NIL NIL) (-823 1936791 1937793 1937962 "OMLO" 1938125 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-822 1935751 1935898 1936118 "OMEXPR" 1936617 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-821 1935042 1935297 1935433 "OMERR" 1935635 T OMERR (NIL) -8 NIL NIL NIL) (-820 1934193 1934463 1934623 "OMERRK" 1934902 T OMERRK (NIL) -8 NIL NIL NIL) (-819 1933644 1933870 1933978 "OMENC" 1934105 T OMENC (NIL) -8 NIL NIL NIL) (-818 1927539 1928724 1929895 "OMDEV" 1932493 T OMDEV (NIL) -8 NIL NIL NIL) (-817 1926608 1926779 1926973 "OMCONN" 1927365 T OMCONN (NIL) -8 NIL NIL NIL) (-816 1925195 1926171 1926199 "OINTDOM" 1926204 T OINTDOM (NIL) -9 NIL 1926225 NIL) (-815 1920974 1922185 1922901 "OFMONOID" 1924511 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-814 1920385 1920911 1920956 "ODVAR" 1920961 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-813 1917808 1920130 1920285 "ODR" 1920290 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-812 1910389 1917584 1917710 "ODPOL" 1917715 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-811 1904211 1910261 1910366 "ODP" 1910371 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-810 1902977 1903192 1903467 "ODETOOLS" 1903985 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-809 1899944 1900602 1901318 "ODESYS" 1902310 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-808 1894826 1895734 1896759 "ODERTRIC" 1899019 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-807 1894252 1894334 1894528 "ODERED" 1894738 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-806 1891140 1891688 1892365 "ODERAT" 1893675 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-805 1888097 1888564 1889161 "ODEPRRIC" 1890669 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-804 1886040 1886636 1887122 "ODEPROB" 1887631 T ODEPROB (NIL) -8 NIL NIL NIL) (-803 1882560 1883045 1883692 "ODEPRIM" 1885519 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-802 1881809 1881911 1882171 "ODEPAL" 1882452 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-801 1877971 1878762 1879626 "ODEPACK" 1880965 T ODEPACK (NIL) -7 NIL NIL NIL) (-800 1877032 1877139 1877361 "ODEINT" 1877860 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-799 1871133 1872558 1874005 "ODEIFTBL" 1875605 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-798 1866531 1867317 1868269 "ODEEF" 1870292 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-797 1865880 1865969 1866192 "ODECONST" 1866436 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-796 1864005 1864666 1864694 "ODECAT" 1865299 T ODECAT (NIL) -9 NIL 1865830 NIL) (-795 1860877 1863717 1863836 "OCT" 1863918 NIL OCT (NIL T) -8 NIL NIL NIL) (-794 1860515 1860558 1860685 "OCTCT2" 1860828 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-793 1855255 1857689 1857729 "OC" 1858826 NIL OC (NIL T) -9 NIL 1859684 NIL) (-792 1852482 1853230 1854220 "OC-" 1854314 NIL OC- (NIL T T) -8 NIL NIL NIL) (-791 1851834 1852302 1852330 "OCAMON" 1852335 T OCAMON (NIL) -9 NIL 1852356 NIL) (-790 1851365 1851706 1851734 "OASGP" 1851739 T OASGP (NIL) -9 NIL 1851759 NIL) (-789 1850626 1851115 1851143 "OAMONS" 1851183 T OAMONS (NIL) -9 NIL 1851226 NIL) (-788 1850040 1850473 1850501 "OAMON" 1850506 T OAMON (NIL) -9 NIL 1850526 NIL) (-787 1849318 1849836 1849864 "OAGROUP" 1849869 T OAGROUP (NIL) -9 NIL 1849889 NIL) (-786 1849008 1849058 1849146 "NUMTUBE" 1849262 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-785 1842581 1844099 1845635 "NUMQUAD" 1847492 T NUMQUAD (NIL) -7 NIL NIL NIL) (-784 1838337 1839325 1840350 "NUMODE" 1841576 T NUMODE (NIL) -7 NIL NIL NIL) (-783 1835692 1836572 1836600 "NUMINT" 1837523 T NUMINT (NIL) -9 NIL 1838287 NIL) (-782 1834640 1834837 1835055 "NUMFMT" 1835494 T NUMFMT (NIL) -7 NIL NIL NIL) (-781 1820999 1823944 1826476 "NUMERIC" 1832147 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-780 1815369 1820448 1820543 "NTSCAT" 1820548 NIL NTSCAT (NIL T T T T) -9 NIL 1820587 NIL) (-779 1814563 1814728 1814921 "NTPOLFN" 1815208 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-778 1802640 1811388 1812200 "NSUP" 1813784 NIL NSUP (NIL T) -8 NIL NIL NIL) (-777 1802272 1802329 1802438 "NSUP2" 1802577 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-776 1792500 1802046 1802179 "NSMP" 1802184 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-775 1790932 1791233 1791590 "NREP" 1792188 NIL NREP (NIL T) -7 NIL NIL NIL) (-774 1789523 1789775 1790133 "NPCOEF" 1790675 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-773 1788589 1788704 1788920 "NORMRETR" 1789404 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-772 1786630 1786920 1787329 "NORMPK" 1788297 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-771 1786315 1786343 1786467 "NORMMA" 1786596 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-770 1786115 1786272 1786301 "NONE" 1786306 T NONE (NIL) -8 NIL NIL NIL) (-769 1785904 1785933 1786002 "NONE1" 1786079 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-768 1785401 1785463 1785642 "NODE1" 1785836 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-767 1783644 1784495 1784750 "NNI" 1785097 T NNI (NIL) -8 NIL NIL 1785332) (-766 1782064 1782377 1782741 "NLINSOL" 1783312 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-765 1778305 1779300 1780199 "NIPROB" 1781185 T NIPROB (NIL) -8 NIL NIL NIL) (-764 1777062 1777296 1777598 "NFINTBAS" 1778067 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-763 1776236 1776712 1776753 "NETCLT" 1776925 NIL NETCLT (NIL T) -9 NIL 1777007 NIL) (-762 1774944 1775175 1775456 "NCODIV" 1776004 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-761 1774706 1774743 1774818 "NCNTFRAC" 1774901 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-760 1772886 1773250 1773670 "NCEP" 1774331 NIL NCEP (NIL T) -7 NIL NIL NIL) (-759 1771757 1772530 1772558 "NASRING" 1772668 T NASRING (NIL) -9 NIL 1772748 NIL) (-758 1771552 1771596 1771690 "NASRING-" 1771695 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-757 1770679 1771204 1771232 "NARNG" 1771349 T NARNG (NIL) -9 NIL 1771440 NIL) (-756 1770371 1770438 1770572 "NARNG-" 1770577 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-755 1769250 1769457 1769692 "NAGSP" 1770156 T NAGSP (NIL) -7 NIL NIL NIL) (-754 1760522 1762206 1763879 "NAGS" 1767597 T NAGS (NIL) -7 NIL NIL NIL) (-753 1759070 1759378 1759709 "NAGF07" 1760211 T NAGF07 (NIL) -7 NIL NIL NIL) (-752 1753608 1754899 1756206 "NAGF04" 1757783 T NAGF04 (NIL) -7 NIL NIL NIL) (-751 1746576 1748190 1749823 "NAGF02" 1751995 T NAGF02 (NIL) -7 NIL NIL NIL) (-750 1741800 1742900 1744017 "NAGF01" 1745479 T NAGF01 (NIL) -7 NIL NIL NIL) (-749 1735428 1736994 1738579 "NAGE04" 1740235 T NAGE04 (NIL) -7 NIL NIL NIL) (-748 1726597 1728718 1730848 "NAGE02" 1733318 T NAGE02 (NIL) -7 NIL NIL NIL) (-747 1722550 1723497 1724461 "NAGE01" 1725653 T NAGE01 (NIL) -7 NIL NIL NIL) (-746 1720345 1720879 1721437 "NAGD03" 1722012 T NAGD03 (NIL) -7 NIL NIL NIL) (-745 1712095 1714023 1715977 "NAGD02" 1718411 T NAGD02 (NIL) -7 NIL NIL NIL) (-744 1705906 1707331 1708771 "NAGD01" 1710675 T NAGD01 (NIL) -7 NIL NIL NIL) (-743 1702115 1702937 1703774 "NAGC06" 1705089 T NAGC06 (NIL) -7 NIL NIL NIL) (-742 1700580 1700912 1701268 "NAGC05" 1701779 T NAGC05 (NIL) -7 NIL NIL NIL) (-741 1699956 1700075 1700219 "NAGC02" 1700456 T NAGC02 (NIL) -7 NIL NIL NIL) (-740 1698990 1699573 1699613 "NAALG" 1699692 NIL NAALG (NIL T) -9 NIL 1699753 NIL) (-739 1698825 1698854 1698944 "NAALG-" 1698949 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-738 1692775 1693883 1695070 "MULTSQFR" 1697721 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-737 1692094 1692169 1692353 "MULTFACT" 1692687 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-736 1685152 1689057 1689110 "MTSCAT" 1690180 NIL MTSCAT (NIL T T) -9 NIL 1690694 NIL) (-735 1684864 1684918 1685010 "MTHING" 1685092 NIL MTHING (NIL T) -7 NIL NIL NIL) (-734 1684656 1684689 1684749 "MSYSCMD" 1684824 T MSYSCMD (NIL) -7 NIL NIL NIL) (-733 1680738 1683411 1683731 "MSET" 1684369 NIL MSET (NIL T) -8 NIL NIL NIL) (-732 1677807 1680299 1680340 "MSETAGG" 1680345 NIL MSETAGG (NIL T) -9 NIL 1680379 NIL) (-731 1673648 1675186 1675931 "MRING" 1677107 NIL MRING (NIL T T) -8 NIL NIL NIL) (-730 1673214 1673281 1673412 "MRF2" 1673575 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-729 1672832 1672867 1673011 "MRATFAC" 1673173 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-728 1670444 1670739 1671170 "MPRFF" 1672537 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-727 1664741 1670298 1670395 "MPOLY" 1670400 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-726 1664231 1664266 1664474 "MPCPF" 1664700 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-725 1663745 1663788 1663972 "MPC3" 1664182 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1662940 1663021 1663242 "MPC2" 1663660 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-723 1661241 1661578 1661968 "MONOTOOL" 1662600 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-722 1660466 1660783 1660811 "MONOID" 1661030 T MONOID (NIL) -9 NIL 1661177 NIL) (-721 1660012 1660131 1660312 "MONOID-" 1660317 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-720 1650836 1656779 1656838 "MONOGEN" 1657512 NIL MONOGEN (NIL T T) -9 NIL 1657968 NIL) (-719 1648054 1648789 1649789 "MONOGEN-" 1649908 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-718 1646887 1647333 1647361 "MONADWU" 1647753 T MONADWU (NIL) -9 NIL 1647991 NIL) (-717 1646259 1646418 1646666 "MONADWU-" 1646671 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-716 1645618 1645862 1645890 "MONAD" 1646097 T MONAD (NIL) -9 NIL 1646209 NIL) (-715 1645303 1645381 1645513 "MONAD-" 1645518 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-714 1643592 1644216 1644495 "MOEBIUS" 1645056 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-713 1642958 1643362 1643402 "MODULE" 1643407 NIL MODULE (NIL T) -9 NIL 1643433 NIL) (-712 1642526 1642622 1642812 "MODULE-" 1642817 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-711 1640206 1640890 1641217 "MODRING" 1642350 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1637150 1638311 1638832 "MODOP" 1639735 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-709 1635738 1636217 1636494 "MODMONOM" 1637013 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-708 1625780 1634029 1634443 "MODMON" 1635375 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-707 1622936 1624624 1624900 "MODFIELD" 1625655 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-706 1621913 1622217 1622407 "MMLFORM" 1622766 T MMLFORM (NIL) -8 NIL NIL NIL) (-705 1621439 1621482 1621661 "MMAP" 1621864 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-704 1619622 1620389 1620430 "MLO" 1620853 NIL MLO (NIL T) -9 NIL 1621095 NIL) (-703 1616988 1617504 1618106 "MLIFT" 1619103 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-702 1616379 1616463 1616617 "MKUCFUNC" 1616899 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-701 1615978 1616048 1616171 "MKRECORD" 1616302 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-700 1615025 1615187 1615415 "MKFUNC" 1615789 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-699 1614413 1614517 1614673 "MKFLCFN" 1614908 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-698 1613690 1613792 1613977 "MKBCFUNC" 1614306 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-697 1610397 1613244 1613380 "MINT" 1613574 T MINT (NIL) -8 NIL NIL NIL) (-696 1609209 1609452 1609729 "MHROWRED" 1610152 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-695 1604589 1607744 1608149 "MFLOAT" 1608824 T MFLOAT (NIL) -8 NIL NIL NIL) (-694 1603946 1604022 1604193 "MFINFACT" 1604501 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-693 1600261 1601109 1601993 "MESH" 1603082 T MESH (NIL) -7 NIL NIL NIL) (-692 1598651 1598963 1599316 "MDDFACT" 1599948 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-691 1595446 1597810 1597851 "MDAGG" 1598106 NIL MDAGG (NIL T) -9 NIL 1598249 NIL) (-690 1585189 1594739 1594946 "MCMPLX" 1595259 T MCMPLX (NIL) -8 NIL NIL NIL) (-689 1584330 1584476 1584676 "MCDEN" 1585038 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-688 1582220 1582490 1582870 "MCALCFN" 1584060 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-687 1581145 1581385 1581618 "MAYBE" 1582026 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-686 1578757 1579280 1579842 "MATSTOR" 1580616 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-685 1574714 1578129 1578377 "MATRIX" 1578542 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-684 1570478 1571187 1571923 "MATLIN" 1574071 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-683 1560584 1563770 1563847 "MATCAT" 1568727 NIL MATCAT (NIL T T T) -9 NIL 1570144 NIL) (-682 1556940 1557961 1559317 "MATCAT-" 1559322 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-681 1555534 1555687 1556020 "MATCAT2" 1556775 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-680 1553646 1553970 1554354 "MAPPKG3" 1555209 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-679 1552627 1552800 1553022 "MAPPKG2" 1553470 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-678 1551126 1551410 1551737 "MAPPKG1" 1552333 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-677 1550205 1550532 1550709 "MAPPAST" 1550969 T MAPPAST (NIL) -8 NIL NIL NIL) (-676 1549816 1549874 1549997 "MAPHACK3" 1550141 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-675 1549408 1549469 1549583 "MAPHACK2" 1549748 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-674 1548845 1548949 1549091 "MAPHACK1" 1549299 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-673 1546924 1547545 1547849 "MAGMA" 1548573 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-672 1546403 1546648 1546739 "MACROAST" 1546853 T MACROAST (NIL) -8 NIL NIL NIL) (-671 1542821 1544642 1545103 "M3D" 1545975 NIL M3D (NIL T) -8 NIL NIL NIL) (-670 1536927 1541190 1541231 "LZSTAGG" 1542013 NIL LZSTAGG (NIL T) -9 NIL 1542308 NIL) (-669 1532884 1534058 1535515 "LZSTAGG-" 1535520 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-668 1529971 1530775 1531262 "LWORD" 1532429 NIL LWORD (NIL T) -8 NIL NIL NIL) (-667 1529547 1529775 1529850 "LSTAST" 1529916 T LSTAST (NIL) -8 NIL NIL NIL) (-666 1522713 1529318 1529452 "LSQM" 1529457 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-665 1521937 1522076 1522304 "LSPP" 1522568 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-664 1519749 1520050 1520506 "LSMP" 1521626 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-663 1516528 1517202 1517932 "LSMP1" 1519051 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-662 1510405 1515695 1515736 "LSAGG" 1515798 NIL LSAGG (NIL T) -9 NIL 1515876 NIL) (-661 1507100 1508024 1509237 "LSAGG-" 1509242 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-660 1504699 1506244 1506493 "LPOLY" 1506895 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-659 1504281 1504366 1504489 "LPEFRAC" 1504608 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-658 1502602 1503375 1503628 "LO" 1504113 NIL LO (NIL T T T) -8 NIL NIL NIL) (-657 1502254 1502366 1502394 "LOGIC" 1502505 T LOGIC (NIL) -9 NIL 1502586 NIL) (-656 1502116 1502139 1502210 "LOGIC-" 1502215 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-655 1501309 1501449 1501642 "LODOOPS" 1501972 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-654 1498732 1501225 1501291 "LODO" 1501296 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-653 1497270 1497505 1497858 "LODOF" 1498479 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-652 1493592 1496023 1496064 "LODOCAT" 1496502 NIL LODOCAT (NIL T) -9 NIL 1496713 NIL) (-651 1493325 1493383 1493510 "LODOCAT-" 1493515 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-650 1490645 1493166 1493284 "LODO2" 1493289 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-649 1488080 1490582 1490627 "LODO1" 1490632 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-648 1486961 1487126 1487431 "LODEEF" 1487903 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-647 1482200 1485091 1485132 "LNAGG" 1486079 NIL LNAGG (NIL T) -9 NIL 1486523 NIL) (-646 1481347 1481561 1481903 "LNAGG-" 1481908 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-645 1477483 1478272 1478911 "LMOPS" 1480762 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-644 1476852 1477240 1477281 "LMODULE" 1477342 NIL LMODULE (NIL T) -9 NIL 1477384 NIL) (-643 1474050 1476497 1476620 "LMDICT" 1476762 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-642 1473749 1473958 1474018 "LITERAL" 1474023 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-641 1466932 1472695 1472993 "LIST" 1473484 NIL LIST (NIL T) -8 NIL NIL NIL) (-640 1466457 1466531 1466670 "LIST3" 1466852 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-639 1465464 1465642 1465870 "LIST2" 1466275 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-638 1463598 1463910 1464309 "LIST2MAP" 1465111 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-637 1462294 1462964 1463005 "LINEXP" 1463260 NIL LINEXP (NIL T) -9 NIL 1463409 NIL) (-636 1460941 1461201 1461498 "LINDEP" 1462046 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-635 1457708 1458427 1459204 "LIMITRF" 1460196 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-634 1456011 1456307 1456716 "LIMITPS" 1457403 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-633 1450439 1455522 1455750 "LIE" 1455832 NIL LIE (NIL T T) -8 NIL NIL NIL) (-632 1449462 1449931 1449971 "LIECAT" 1450111 NIL LIECAT (NIL T) -9 NIL 1450262 NIL) (-631 1449303 1449330 1449418 "LIECAT-" 1449423 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-630 1441799 1448752 1448917 "LIB" 1449158 T LIB (NIL) -8 NIL NIL NIL) (-629 1437434 1438317 1439252 "LGROBP" 1440916 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-628 1435443 1435717 1436066 "LF" 1437155 NIL LF (NIL T T) -7 NIL NIL NIL) (-627 1434283 1434975 1435003 "LFCAT" 1435210 T LFCAT (NIL) -9 NIL 1435349 NIL) (-626 1431185 1431815 1432503 "LEXTRIPK" 1433647 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-625 1427929 1428755 1429258 "LEXP" 1430765 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-624 1427405 1427650 1427742 "LETAST" 1427857 T LETAST (NIL) -8 NIL NIL NIL) (-623 1425803 1426116 1426517 "LEADCDET" 1427087 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-622 1424993 1425067 1425296 "LAZM3PK" 1425724 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-621 1419910 1423070 1423608 "LAUPOL" 1424505 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-620 1419489 1419533 1419694 "LAPLACE" 1419860 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-619 1417428 1418590 1418841 "LA" 1419322 NIL LA (NIL T T T) -8 NIL NIL NIL) (-618 1416475 1417059 1417100 "LALG" 1417162 NIL LALG (NIL T) -9 NIL 1417221 NIL) (-617 1416189 1416248 1416384 "LALG-" 1416389 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-616 1416024 1416048 1416089 "KVTFROM" 1416151 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-615 1414947 1415391 1415576 "KTVLOGIC" 1415859 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-614 1414782 1414806 1414847 "KRCFROM" 1414909 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-613 1413686 1413873 1414172 "KOVACIC" 1414582 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-612 1413521 1413545 1413586 "KONVERT" 1413648 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-611 1413356 1413380 1413421 "KOERCE" 1413483 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-610 1411038 1411826 1412227 "KERNEL" 1412988 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-609 1410534 1410615 1410747 "KERNEL2" 1410952 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-608 1404304 1409073 1409127 "KDAGG" 1409504 NIL KDAGG (NIL T T) -9 NIL 1409710 NIL) (-607 1403833 1403957 1404162 "KDAGG-" 1404167 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-606 1396981 1403494 1403649 "KAFILE" 1403711 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-605 1391409 1396492 1396720 "JORDAN" 1396802 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-604 1390788 1391058 1391179 "JOINAST" 1391308 T JOINAST (NIL) -8 NIL NIL NIL) (-603 1390634 1390693 1390748 "JAVACODE" 1390753 T JAVACODE (NIL) -8 NIL NIL NIL) (-602 1386886 1388839 1388893 "IXAGG" 1389822 NIL IXAGG (NIL T T) -9 NIL 1390281 NIL) (-601 1385805 1386111 1386530 "IXAGG-" 1386535 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1381337 1385727 1385786 "IVECTOR" 1385791 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-599 1380103 1380340 1380606 "ITUPLE" 1381104 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-598 1378617 1378794 1379087 "ITRIGMNP" 1379925 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-597 1377362 1377566 1377849 "ITFUN3" 1378393 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-596 1376994 1377051 1377160 "ITFUN2" 1377299 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-595 1374796 1375856 1376155 "ITAYLOR" 1376728 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-594 1363741 1368933 1370096 "ISUPS" 1373666 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-593 1362845 1362985 1363221 "ISUMP" 1363588 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-592 1358059 1362646 1362725 "ISTRING" 1362798 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-591 1357535 1357780 1357872 "ISAST" 1357987 T ISAST (NIL) -8 NIL NIL NIL) (-590 1356745 1356826 1357042 "IRURPK" 1357449 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-589 1355681 1355882 1356122 "IRSN" 1356525 T IRSN (NIL) -7 NIL NIL NIL) (-588 1353752 1354107 1354536 "IRRF2F" 1355319 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-587 1353499 1353537 1353613 "IRREDFFX" 1353708 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-586 1352114 1352373 1352672 "IROOT" 1353232 NIL IROOT (NIL T) -7 NIL NIL NIL) (-585 1348718 1349798 1350490 "IR" 1351454 NIL IR (NIL T) -8 NIL NIL NIL) (-584 1346331 1346826 1347392 "IR2" 1348196 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-583 1345431 1345544 1345758 "IR2F" 1346214 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-582 1345222 1345256 1345316 "IPRNTPK" 1345391 T IPRNTPK (NIL) -7 NIL NIL NIL) (-581 1341802 1345111 1345180 "IPF" 1345185 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-580 1340129 1341727 1341784 "IPADIC" 1341789 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-579 1339441 1339689 1339819 "IP4ADDR" 1340019 T IP4ADDR (NIL) -8 NIL NIL NIL) (-578 1338914 1339145 1339255 "IOMODE" 1339351 T IOMODE (NIL) -8 NIL NIL NIL) (-577 1337987 1338511 1338638 "IOBFILE" 1338807 T IOBFILE (NIL) -8 NIL NIL NIL) (-576 1337475 1337891 1337919 "IOBCON" 1337924 T IOBCON (NIL) -9 NIL 1337945 NIL) (-575 1336986 1337044 1337227 "INVLAPLA" 1337411 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-574 1326634 1328988 1331374 "INTTR" 1334650 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-573 1322969 1323711 1324576 "INTTOOLS" 1325819 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-572 1322555 1322646 1322763 "INTSLPE" 1322872 T INTSLPE (NIL) -7 NIL NIL NIL) (-571 1320509 1322478 1322537 "INTRVL" 1322542 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-570 1318111 1318623 1319198 "INTRF" 1319994 NIL INTRF (NIL T) -7 NIL NIL NIL) (-569 1317522 1317619 1317761 "INTRET" 1318009 NIL INTRET (NIL T) -7 NIL NIL NIL) (-568 1315519 1315908 1316378 "INTRAT" 1317130 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-567 1312782 1313365 1313984 "INTPM" 1315004 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-566 1309526 1310126 1310864 "INTPAF" 1312168 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-565 1304705 1305667 1306718 "INTPACK" 1308495 T INTPACK (NIL) -7 NIL NIL NIL) (-564 1301582 1304434 1304561 "INT" 1304598 T INT (NIL) -8 NIL NIL NIL) (-563 1300834 1300986 1301194 "INTHERTR" 1301424 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-562 1300273 1300353 1300541 "INTHERAL" 1300748 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-561 1298119 1298562 1299019 "INTHEORY" 1299836 T INTHEORY (NIL) -7 NIL NIL NIL) (-560 1289525 1291146 1292918 "INTG0" 1296471 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-559 1270098 1274888 1279698 "INTFTBL" 1284735 T INTFTBL (NIL) -8 NIL NIL NIL) (-558 1269347 1269485 1269658 "INTFACT" 1269957 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-557 1266774 1267220 1267777 "INTEF" 1268901 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-556 1265207 1265946 1265974 "INTDOM" 1266275 T INTDOM (NIL) -9 NIL 1266482 NIL) (-555 1264576 1264750 1264992 "INTDOM-" 1264997 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-554 1261036 1262960 1263014 "INTCAT" 1263813 NIL INTCAT (NIL T) -9 NIL 1264133 NIL) (-553 1260508 1260611 1260739 "INTBIT" 1260928 T INTBIT (NIL) -7 NIL NIL NIL) (-552 1259207 1259361 1259668 "INTALG" 1260353 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-551 1258690 1258780 1258937 "INTAF" 1259111 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-550 1252033 1258500 1258640 "INTABL" 1258645 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-549 1251337 1251803 1251868 "INT8" 1251902 T INT8 (NIL) -8 NIL NIL 1251947) (-548 1250640 1251106 1251171 "INT64" 1251205 T INT64 (NIL) -8 NIL NIL 1251250) (-547 1249943 1250409 1250474 "INT32" 1250508 T INT32 (NIL) -8 NIL NIL 1250553) (-546 1249246 1249712 1249777 "INT16" 1249811 T INT16 (NIL) -8 NIL NIL 1249856) (-545 1244226 1246935 1246963 "INS" 1247897 T INS (NIL) -9 NIL 1248562 NIL) (-544 1241466 1242237 1243211 "INS-" 1243284 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1240241 1240468 1240766 "INPSIGN" 1241219 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1239359 1239476 1239673 "INPRODPF" 1240121 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1238253 1238370 1238607 "INPRODFF" 1239239 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1237253 1237405 1237665 "INNMFACT" 1238089 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1236450 1236547 1236735 "INMODGCD" 1237152 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1234958 1235203 1235527 "INFSP" 1236195 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1234142 1234259 1234442 "INFPROD0" 1234838 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1230997 1232207 1232722 "INFORM" 1233635 T INFORM (NIL) -8 NIL NIL NIL) (-535 1230607 1230667 1230765 "INFORM1" 1230932 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1230130 1230219 1230333 "INFINITY" 1230513 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1229306 1229850 1229951 "INETCLTS" 1230049 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1227922 1228172 1228493 "INEP" 1229054 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1227171 1227819 1227884 "INDE" 1227889 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1226735 1226803 1226920 "INCRMAPS" 1227098 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1225553 1226004 1226210 "INBFILE" 1226549 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1220853 1221789 1222733 "INBFF" 1224641 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1219761 1220030 1220058 "INBCON" 1220571 T INBCON (NIL) -9 NIL 1220837 NIL) (-526 1219013 1219236 1219512 "INBCON-" 1219517 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1218492 1218737 1218828 "INAST" 1218942 T INAST (NIL) -8 NIL NIL NIL) (-524 1217919 1218171 1218277 "IMPTAST" 1218406 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1214365 1217763 1217867 "IMATRIX" 1217872 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1213077 1213200 1213515 "IMATQF" 1214221 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1211297 1211524 1211861 "IMATLIN" 1212833 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1205875 1211221 1211279 "ILIST" 1211284 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1203780 1205735 1205848 "IIARRAY2" 1205853 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1199178 1203691 1203755 "IFF" 1203760 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1198525 1198795 1198911 "IFAST" 1199082 T IFAST (NIL) -8 NIL NIL NIL) (-516 1193520 1197817 1198005 "IFARRAY" 1198382 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1192700 1193424 1193497 "IFAMON" 1193502 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1192284 1192349 1192403 "IEVALAB" 1192610 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1191959 1192027 1192187 "IEVALAB-" 1192192 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1191590 1191873 1191936 "IDPO" 1191941 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1190840 1191479 1191554 "IDPOAMS" 1191559 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1190147 1190729 1190804 "IDPOAM" 1190809 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1189206 1189482 1189535 "IDPC" 1189948 NIL IDPC (NIL T T) -9 NIL 1190097 NIL) (-508 1188675 1189098 1189171 "IDPAM" 1189176 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1188051 1188567 1188640 "IDPAG" 1188645 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1187696 1187887 1187962 "IDENT" 1187996 T IDENT (NIL) -8 NIL NIL NIL) (-505 1183951 1184799 1185694 "IDECOMP" 1186853 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1176788 1177874 1178921 "IDEAL" 1182987 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1175952 1176064 1176263 "ICDEN" 1176672 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1175023 1175432 1175579 "ICARD" 1175825 T ICARD (NIL) -8 NIL NIL NIL) (-501 1173083 1173396 1173801 "IBPTOOLS" 1174700 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1168690 1172703 1172816 "IBITS" 1173002 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1165413 1165989 1166684 "IBATOOL" 1168107 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1163192 1163654 1164187 "IBACHIN" 1164948 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1161021 1163038 1163141 "IARRAY2" 1163146 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1157127 1160947 1161004 "IARRAY1" 1161009 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1151236 1155539 1156020 "IAN" 1156666 T IAN (NIL) -8 NIL NIL NIL) (-494 1150747 1150804 1150977 "IALGFACT" 1151173 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1150275 1150388 1150416 "HYPCAT" 1150623 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1149813 1149930 1150116 "HYPCAT-" 1150121 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1149408 1149608 1149691 "HOSTNAME" 1149750 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1149253 1149290 1149331 "HOMOTOP" 1149336 NIL HOMOTOP (NIL T) -9 NIL 1149369 NIL) (-489 1145885 1147263 1147304 "HOAGG" 1148285 NIL HOAGG (NIL T) -9 NIL 1148964 NIL) (-488 1144479 1144878 1145404 "HOAGG-" 1145409 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1138483 1144074 1144223 "HEXADEC" 1144350 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1137231 1137453 1137716 "HEUGCD" 1138260 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1136307 1137068 1137198 "HELLFDIV" 1137203 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1134486 1136084 1136172 "HEAP" 1136251 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1133749 1134038 1134172 "HEADAST" 1134372 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1127615 1133664 1133726 "HDP" 1133731 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1121603 1127250 1127402 "HDMP" 1127516 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1120927 1121067 1121231 "HB" 1121459 T HB (NIL) -7 NIL NIL NIL) (-479 1114313 1120773 1120877 "HASHTBL" 1120882 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1113789 1114034 1114126 "HASAST" 1114241 T HASAST (NIL) -8 NIL NIL NIL) (-477 1111567 1113411 1113593 "HACKPI" 1113627 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1107235 1111420 1111533 "GTSET" 1111538 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1100650 1107113 1107211 "GSTBL" 1107216 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1092928 1099681 1099946 "GSERIES" 1100441 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1092069 1092486 1092514 "GROUP" 1092717 T GROUP (NIL) -9 NIL 1092851 NIL) (-472 1091435 1091594 1091845 "GROUP-" 1091850 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1089802 1090123 1090510 "GROEBSOL" 1091112 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1088716 1089004 1089055 "GRMOD" 1089584 NIL GRMOD (NIL T T) -9 NIL 1089752 NIL) (-469 1088484 1088520 1088648 "GRMOD-" 1088653 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1083774 1084838 1085838 "GRIMAGE" 1087504 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1082240 1082501 1082825 "GRDEF" 1083470 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1081684 1081800 1081941 "GRAY" 1082119 T GRAY (NIL) -7 NIL NIL NIL) (-465 1080871 1081277 1081328 "GRALG" 1081481 NIL GRALG (NIL T T) -9 NIL 1081574 NIL) (-464 1080532 1080605 1080768 "GRALG-" 1080773 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1077309 1080117 1080295 "GPOLSET" 1080439 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1076663 1076720 1076978 "GOSPER" 1077246 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1072395 1073101 1073627 "GMODPOL" 1076362 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1071400 1071584 1071822 "GHENSEL" 1072207 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1065556 1066399 1067419 "GENUPS" 1070484 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1065253 1065304 1065393 "GENUFACT" 1065499 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1064665 1064742 1064907 "GENPGCD" 1065171 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1064139 1064174 1064387 "GENMFACT" 1064624 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1062705 1062962 1063269 "GENEEZ" 1063882 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1056851 1062316 1062478 "GDMP" 1062628 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1046193 1050622 1051728 "GCNAALG" 1055834 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1044586 1045448 1045476 "GCDDOM" 1045731 T GCDDOM (NIL) -9 NIL 1045888 NIL) (-451 1044056 1044183 1044398 "GCDDOM-" 1044403 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1042728 1042913 1043217 "GB" 1043835 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1031344 1033674 1036066 "GBINTERN" 1040419 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1029181 1029473 1029894 "GBF" 1031019 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1027962 1028127 1028394 "GBEUCLID" 1028997 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1027311 1027436 1027585 "GAUSSFAC" 1027833 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1025678 1025980 1026294 "GALUTIL" 1027030 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1023986 1024260 1024584 "GALPOLYU" 1025405 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1021351 1021641 1022048 "GALFACTU" 1023683 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1013157 1014656 1016264 "GALFACT" 1019783 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1010545 1011203 1011231 "FVFUN" 1012387 T FVFUN (NIL) -9 NIL 1013107 NIL) (-440 1009811 1009993 1010021 "FVC" 1010312 T FVC (NIL) -9 NIL 1010495 NIL) (-439 1009454 1009636 1009704 "FUNDESC" 1009763 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1009069 1009251 1009332 "FUNCTION" 1009406 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1006813 1007391 1007857 "FT" 1008623 T FT (NIL) -8 NIL NIL NIL) (-436 1005604 1006114 1006317 "FTEM" 1006630 T FTEM (NIL) -8 NIL NIL NIL) (-435 1003895 1004184 1004581 "FSUPFACT" 1005295 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1002292 1002581 1002913 "FST" 1003583 T FST (NIL) -8 NIL NIL NIL) (-433 1001491 1001597 1001785 "FSRED" 1002174 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 1000190 1000446 1000793 "FSPRMELT" 1001206 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 997496 997934 998420 "FSPECF" 999753 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 979651 987975 988016 "FS" 991900 NIL FS (NIL T) -9 NIL 994189 NIL) (-429 968294 971287 975344 "FS-" 975644 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 967822 967876 968046 "FSINT" 968235 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 966114 966815 967118 "FSERIES" 967601 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 965156 965272 965496 "FSCINT" 965994 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 961364 964100 964141 "FSAGG" 964511 NIL FSAGG (NIL T) -9 NIL 964770 NIL) (-424 959126 959727 960523 "FSAGG-" 960618 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 958168 958311 958538 "FSAGG2" 958979 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 955850 956130 956677 "FS2UPS" 957886 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 955484 955527 955656 "FS2" 955801 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 954362 954533 954835 "FS2EXPXP" 955309 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 953788 953903 954055 "FRUTIL" 954242 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 945202 949283 950641 "FR" 952462 NIL FR (NIL T) -8 NIL NIL NIL) (-417 940250 942920 942960 "FRNAALG" 944356 NIL FRNAALG (NIL T) -9 NIL 944963 NIL) (-416 935923 936999 938274 "FRNAALG-" 939024 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 935561 935604 935731 "FRNAAF2" 935874 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 933941 934415 934710 "FRMOD" 935373 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 931692 932324 932641 "FRIDEAL" 933732 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 930887 930974 931263 "FRIDEAL2" 931599 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 930020 930434 930475 "FRETRCT" 930480 NIL FRETRCT (NIL T) -9 NIL 930656 NIL) (-410 929132 929363 929714 "FRETRCT-" 929719 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 926310 927520 927579 "FRAMALG" 928461 NIL FRAMALG (NIL T T) -9 NIL 928753 NIL) (-408 924444 924899 925529 "FRAMALG-" 925752 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 918365 923919 924195 "FRAC" 924200 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 918001 918058 918165 "FRAC2" 918302 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 917637 917694 917801 "FR2" 917938 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 912275 915162 915190 "FPS" 916309 T FPS (NIL) -9 NIL 916866 NIL) (-403 911724 911833 911997 "FPS-" 912143 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 909144 910813 910841 "FPC" 911066 T FPC (NIL) -9 NIL 911208 NIL) (-401 908937 908977 909074 "FPC-" 909079 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 907727 908425 908466 "FPATMAB" 908471 NIL FPATMAB (NIL T) -9 NIL 908623 NIL) (-399 905400 905903 906329 "FPARFRAC" 907364 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 900793 901292 901974 "FORTRAN" 904832 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 898509 899009 899548 "FORT" 900274 T FORT (NIL) -7 NIL NIL NIL) (-396 896185 896747 896775 "FORTFN" 897835 T FORTFN (NIL) -9 NIL 898459 NIL) (-395 895949 895999 896027 "FORTCAT" 896086 T FORTCAT (NIL) -9 NIL 896148 NIL) (-394 894055 894565 894955 "FORMULA" 895579 T FORMULA (NIL) -8 NIL NIL NIL) (-393 893843 893873 893942 "FORMULA1" 894019 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 893366 893418 893591 "FORDER" 893785 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 892462 892626 892819 "FOP" 893193 T FOP (NIL) -7 NIL NIL NIL) (-390 891043 891742 891916 "FNLA" 892344 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 889772 890187 890215 "FNCAT" 890675 T FNCAT (NIL) -9 NIL 890935 NIL) (-388 889311 889731 889759 "FNAME" 889764 T FNAME (NIL) -8 NIL NIL NIL) (-387 887940 888903 888931 "FMTC" 888936 T FMTC (NIL) -9 NIL 888972 NIL) (-386 884273 885463 886092 "FMONOID" 887344 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 883465 884015 884164 "FM" 884169 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 880889 881535 881563 "FMFUN" 882707 T FMFUN (NIL) -9 NIL 883415 NIL) (-383 880158 880339 880367 "FMC" 880657 T FMC (NIL) -9 NIL 880839 NIL) (-382 877326 878186 878240 "FMCAT" 879435 NIL FMCAT (NIL T T) -9 NIL 879930 NIL) (-381 876192 877092 877192 "FM1" 877271 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 873966 874382 874876 "FLOATRP" 875743 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 867540 871695 872316 "FLOAT" 873365 T FLOAT (NIL) -8 NIL NIL NIL) (-378 864978 865478 866056 "FLOATCP" 867007 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 863753 864591 864632 "FLINEXP" 864637 NIL FLINEXP (NIL T) -9 NIL 864730 NIL) (-376 862907 863142 863470 "FLINEXP-" 863475 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 861983 862127 862351 "FLASORT" 862759 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 859174 860042 860094 "FLALG" 861321 NIL FLALG (NIL T T) -9 NIL 861788 NIL) (-373 852910 856660 856701 "FLAGG" 857963 NIL FLAGG (NIL T) -9 NIL 858615 NIL) (-372 851636 851975 852465 "FLAGG-" 852470 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 850678 850821 851048 "FLAGG2" 851489 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 847619 848627 848686 "FINRALG" 849814 NIL FINRALG (NIL T T) -9 NIL 850322 NIL) (-369 846779 847008 847347 "FINRALG-" 847352 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 846159 846398 846426 "FINITE" 846622 T FINITE (NIL) -9 NIL 846729 NIL) (-367 838591 840778 840818 "FINAALG" 844485 NIL FINAALG (NIL T) -9 NIL 845938 NIL) (-366 833923 834973 836117 "FINAALG-" 837496 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 833291 833678 833781 "FILE" 833853 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 831949 832287 832341 "FILECAT" 833025 NIL FILECAT (NIL T T) -9 NIL 833241 NIL) (-363 829783 831311 831339 "FIELD" 831379 T FIELD (NIL) -9 NIL 831459 NIL) (-362 828403 828788 829299 "FIELD-" 829304 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 826253 827038 827385 "FGROUP" 828089 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 825343 825507 825727 "FGLMICPK" 826085 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 821175 825268 825325 "FFX" 825330 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 820776 820837 820972 "FFSLPE" 821108 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 816765 817548 818344 "FFPOLY" 820012 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 816269 816305 816514 "FFPOLY2" 816723 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 812112 816188 816251 "FFP" 816256 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 807510 812023 812087 "FF" 812092 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 802636 806853 807043 "FFNBX" 807364 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 797565 801771 802029 "FFNBP" 802490 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 792198 796849 797060 "FFNB" 797398 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 791030 791228 791543 "FFINTBAS" 791995 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 787223 789437 789465 "FFIELDC" 790085 T FFIELDC (NIL) -9 NIL 790461 NIL) (-348 785885 786256 786753 "FFIELDC-" 786758 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 785454 785500 785624 "FFHOM" 785827 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 783149 783636 784153 "FFF" 784969 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 778767 782891 782992 "FFCGX" 783092 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 774388 778499 778606 "FFCGP" 778710 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 769571 774115 774223 "FFCG" 774324 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 751369 760442 760528 "FFCAT" 765693 NIL FFCAT (NIL T T T) -9 NIL 767144 NIL) (-341 746567 747614 748928 "FFCAT-" 750158 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 745978 746021 746256 "FFCAT2" 746518 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 735300 738950 740170 "FEXPR" 744830 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 734300 734735 734776 "FEVALAB" 734860 NIL FEVALAB (NIL T) -9 NIL 735121 NIL) (-337 733459 733669 734007 "FEVALAB-" 734012 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 732025 732842 733045 "FDIV" 733358 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 729065 729806 729921 "FDIVCAT" 731489 NIL FDIVCAT (NIL T T T T) -9 NIL 731926 NIL) (-334 728827 728854 729024 "FDIVCAT-" 729029 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 728047 728134 728411 "FDIV2" 728734 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 726733 726992 727281 "FCPAK1" 727778 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 725832 726233 726374 "FCOMP" 726624 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 709534 712982 716520 "FC" 722314 T FC (NIL) -8 NIL NIL NIL) (-329 702078 706098 706138 "FAXF" 707940 NIL FAXF (NIL T) -9 NIL 708632 NIL) (-328 699354 700012 700837 "FAXF-" 701302 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 694406 698730 698906 "FARRAY" 699211 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 689625 691691 691744 "FAMR" 692767 NIL FAMR (NIL T T) -9 NIL 693227 NIL) (-325 688515 688817 689252 "FAMR-" 689257 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 687684 688437 688490 "FAMONOID" 688495 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 685470 686180 686233 "FAMONC" 687174 NIL FAMONC (NIL T T) -9 NIL 687560 NIL) (-322 684135 685224 685361 "FAGROUP" 685366 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 681930 682249 682652 "FACUTIL" 683816 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 681029 681214 681436 "FACTFUNC" 681740 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 673451 680332 680531 "EXPUPXS" 680885 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 670934 671474 672060 "EXPRTUBE" 672885 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 667205 667797 668527 "EXPRODE" 670273 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 652690 665854 666283 "EXPR" 666809 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 647244 647831 648637 "EXPR2UPS" 651988 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 646876 646933 647042 "EXPR2" 647181 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 638267 646029 646319 "EXPEXPAN" 646713 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 638067 638224 638253 "EXIT" 638258 T EXIT (NIL) -8 NIL NIL NIL) (-311 637547 637791 637882 "EXITAST" 637996 T EXITAST (NIL) -8 NIL NIL NIL) (-310 637174 637236 637349 "EVALCYC" 637479 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 636715 636833 636874 "EVALAB" 637044 NIL EVALAB (NIL T) -9 NIL 637148 NIL) (-308 636196 636318 636539 "EVALAB-" 636544 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 633630 634932 634960 "EUCDOM" 635515 T EUCDOM (NIL) -9 NIL 635865 NIL) (-306 632035 632477 633067 "EUCDOM-" 633072 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 619573 622333 625083 "ESTOOLS" 629305 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 619205 619262 619371 "ESTOOLS2" 619510 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 618956 618998 619078 "ESTOOLS1" 619157 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 612993 614601 614629 "ES" 617397 T ES (NIL) -9 NIL 618807 NIL) (-301 607940 609227 611044 "ES-" 611208 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 604314 605075 605855 "ESCONT" 607180 T ESCONT (NIL) -7 NIL NIL NIL) (-299 604059 604091 604173 "ESCONT1" 604276 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 603734 603784 603884 "ES2" 604003 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 603364 603422 603531 "ES1" 603670 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 602580 602709 602885 "ERROR" 603208 T ERROR (NIL) -7 NIL NIL NIL) (-295 595972 602439 602530 "EQTBL" 602535 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 588475 591286 592735 "EQ" 594556 NIL -2111 (NIL T) -8 NIL NIL NIL) (-293 588107 588164 588273 "EQ2" 588412 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 583396 584445 585538 "EP" 587046 NIL EP (NIL T) -7 NIL NIL NIL) (-291 581996 582287 582593 "ENV" 583110 T ENV (NIL) -8 NIL NIL NIL) (-290 581141 581695 581723 "ENTIRER" 581728 T ENTIRER (NIL) -9 NIL 581774 NIL) (-289 577608 579096 579466 "EMR" 580940 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 576752 576937 576991 "ELTAGG" 577371 NIL ELTAGG (NIL T T) -9 NIL 577582 NIL) (-287 576471 576533 576674 "ELTAGG-" 576679 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 576260 576289 576343 "ELTAB" 576427 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 575386 575532 575731 "ELFUTS" 576111 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 575128 575184 575212 "ELEMFUN" 575317 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 574998 575019 575087 "ELEMFUN-" 575092 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 569842 573098 573139 "ELAGG" 574079 NIL ELAGG (NIL T) -9 NIL 574542 NIL) (-281 568127 568561 569224 "ELAGG-" 569229 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 566792 567070 567363 "ELABEXPR" 567854 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 559656 561459 562286 "EFUPXS" 566068 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 553106 554907 555717 "EFULS" 558932 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 550591 550949 551421 "EFSTRUC" 552738 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 540442 542008 543555 "EF" 549106 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 539516 539927 540076 "EAB" 540313 T EAB (NIL) -8 NIL NIL NIL) (-274 538698 539475 539503 "E04UCFA" 539508 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 537880 538657 538685 "E04NAFA" 538690 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 537062 537839 537867 "E04MBFA" 537872 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 536244 537021 537049 "E04JAFA" 537054 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 535428 536203 536231 "E04GCFA" 536236 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 534612 535387 535415 "E04FDFA" 535420 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 533794 534571 534599 "E04DGFA" 534604 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 527967 529319 530683 "E04AGNT" 532450 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 526647 527153 527193 "DVARCAT" 527668 NIL DVARCAT (NIL T) -9 NIL 527867 NIL) (-265 525851 526063 526377 "DVARCAT-" 526382 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 518988 525650 525779 "DSMP" 525784 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 513770 514933 516001 "DROPT" 517940 T DROPT (NIL) -8 NIL NIL NIL) (-262 513435 513494 513592 "DROPT1" 513705 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 508550 509676 510813 "DROPT0" 512318 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 506895 507220 507606 "DRAWPT" 508184 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 501482 502405 503484 "DRAW" 505869 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 501115 501168 501286 "DRAWHACK" 501423 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 499846 500115 500406 "DRAWCX" 500844 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 499361 499430 499581 "DRAWCURV" 499772 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 489829 491791 493906 "DRAWCFUN" 497266 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 486595 488524 488565 "DQAGG" 489194 NIL DQAGG (NIL T) -9 NIL 489467 NIL) (-253 475139 481600 481683 "DPOLCAT" 483535 NIL DPOLCAT (NIL T T T T) -9 NIL 484080 NIL) (-252 469975 471324 473282 "DPOLCAT-" 473287 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 463097 469836 469934 "DPMO" 469939 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 456122 462877 463044 "DPMM" 463049 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 455727 456041 456089 "DOMCTOR" 456094 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 454995 455249 455386 "DOMAIN" 455610 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 448983 454630 454782 "DMP" 454896 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 448583 448639 448783 "DLP" 448921 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 442405 447910 448100 "DLIST" 448425 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 439202 441258 441299 "DLAGG" 441849 NIL DLAGG (NIL T) -9 NIL 442079 NIL) (-243 437981 438645 438673 "DIVRING" 438765 T DIVRING (NIL) -9 NIL 438848 NIL) (-242 437218 437408 437708 "DIVRING-" 437713 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 435320 435677 436083 "DISPLAY" 436832 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 429208 435234 435297 "DIRPROD" 435302 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 428056 428259 428524 "DIRPROD2" 429001 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 417265 423271 423324 "DIRPCAT" 423734 NIL DIRPCAT (NIL NIL T) -9 NIL 424574 NIL) (-237 414591 415233 416114 "DIRPCAT-" 416451 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 413878 414038 414224 "DIOSP" 414425 T DIOSP (NIL) -7 NIL NIL NIL) (-235 410533 412790 412831 "DIOPS" 413265 NIL DIOPS (NIL T) -9 NIL 413494 NIL) (-234 410082 410196 410387 "DIOPS-" 410392 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 408940 409568 409596 "DIFRING" 409783 T DIFRING (NIL) -9 NIL 409893 NIL) (-232 408586 408663 408815 "DIFRING-" 408820 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 406357 407629 407670 "DIFEXT" 408033 NIL DIFEXT (NIL T) -9 NIL 408327 NIL) (-230 404642 405070 405736 "DIFEXT-" 405741 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 401917 404174 404215 "DIAGG" 404220 NIL DIAGG (NIL T) -9 NIL 404240 NIL) (-228 401301 401458 401710 "DIAGG-" 401715 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 396718 400260 400537 "DHMATRIX" 401070 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 392330 393239 394249 "DFSFUN" 395728 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 387408 391261 391573 "DFLOAT" 392038 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 385671 385952 386341 "DFINTTLS" 387116 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 382700 383692 384092 "DERHAM" 385337 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 380501 382475 382564 "DEQUEUE" 382644 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 379755 379888 380071 "DEGRED" 380363 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 376185 376930 377776 "DEFINTRF" 378983 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 373740 374209 374801 "DEFINTEF" 375704 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 373090 373360 373475 "DEFAST" 373645 T DEFAST (NIL) -8 NIL NIL NIL) (-217 367094 372685 372834 "DECIMAL" 372961 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 364606 365064 365570 "DDFACT" 366638 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 364202 364245 364396 "DBLRESP" 364557 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 362074 362435 362795 "DBASE" 363969 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 361316 361554 361700 "DATAARY" 361973 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 360422 361275 361303 "D03FAFA" 361308 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 359529 360381 360409 "D03EEFA" 360414 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 357479 357945 358434 "D03AGNT" 359060 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 356768 357438 357466 "D02EJFA" 357471 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 356057 356727 356755 "D02CJFA" 356760 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 355346 356016 356044 "D02BHFA" 356049 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 354635 355305 355333 "D02BBFA" 355338 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 347832 349421 351027 "D02AGNT" 353049 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 345600 346123 346669 "D01WGTS" 347306 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 344667 345559 345587 "D01TRNS" 345592 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 343735 344626 344654 "D01GBFA" 344659 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 342803 343694 343722 "D01FCFA" 343727 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 341871 342762 342790 "D01ASFA" 342795 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 340939 341830 341858 "D01AQFA" 341863 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 340007 340898 340926 "D01APFA" 340931 T D01APFA (NIL) -8 NIL NIL NIL) (-197 339075 339966 339994 "D01ANFA" 339999 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 338143 339034 339062 "D01AMFA" 339067 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 337211 338102 338130 "D01ALFA" 338135 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 336279 337170 337198 "D01AKFA" 337203 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 335347 336238 336266 "D01AJFA" 336271 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 328642 330195 331756 "D01AGNT" 333806 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 327979 328107 328259 "CYCLOTOM" 328510 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 324714 325427 326154 "CYCLES" 327272 T CYCLES (NIL) -7 NIL NIL NIL) (-189 324026 324160 324331 "CVMP" 324575 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 321867 322125 322494 "CTRIGMNP" 323754 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 321335 321661 321734 "CTOR" 321814 T CTOR (NIL) -8 NIL NIL NIL) (-186 320844 321066 321167 "CTORKIND" 321254 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 320166 320451 320479 "CTORCAT" 320661 T CTORCAT (NIL) -9 NIL 320774 NIL) (-184 319764 319875 320034 "CTORCAT-" 320039 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 319253 319467 319565 "CTORCALL" 319686 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 318627 318726 318879 "CSTTOOLS" 319150 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 314426 315083 315841 "CRFP" 317939 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 313901 314147 314239 "CRCEAST" 314354 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 312948 313133 313361 "CRAPACK" 313705 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 312332 312433 312637 "CPMATCH" 312824 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 312057 312085 312191 "CPIMA" 312298 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 308421 309093 309811 "COORDSYS" 311392 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 307833 307954 308096 "CONTOUR" 308299 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 303724 305836 306328 "CONTFRAC" 307373 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 303604 303625 303653 "CONDUIT" 303690 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 302743 303297 303325 "COMRING" 303330 T COMRING (NIL) -9 NIL 303382 NIL) (-171 301797 302101 302285 "COMPPROP" 302579 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 301458 301493 301621 "COMPLPAT" 301756 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 291752 301267 301376 "COMPLEX" 301381 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 291388 291445 291552 "COMPLEX2" 291689 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 291106 291141 291239 "COMPFACT" 291347 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 275582 285565 285605 "COMPCAT" 286609 NIL COMPCAT (NIL T) -9 NIL 287955 NIL) (-165 265093 268021 271648 "COMPCAT-" 272004 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 264822 264850 264953 "COMMUPC" 265059 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 264616 264650 264709 "COMMONOP" 264783 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 264172 264367 264454 "COMM" 264549 T COMM (NIL) -8 NIL NIL NIL) (-161 263748 263976 264051 "COMMAAST" 264117 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 262997 263191 263219 "COMBOPC" 263557 T COMBOPC (NIL) -9 NIL 263732 NIL) (-159 261893 262103 262345 "COMBINAT" 262787 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258350 258924 259551 "COMBF" 261315 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 257108 257466 257701 "COLOR" 258135 T COLOR (NIL) -8 NIL NIL NIL) (-156 256584 256829 256921 "COLONAST" 257036 T COLONAST (NIL) -8 NIL NIL NIL) (-155 256224 256271 256396 "CMPLXRT" 256531 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 255672 255924 256023 "CLLCTAST" 256145 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 251172 252202 253282 "CLIP" 254612 T CLIP (NIL) -7 NIL NIL NIL) (-152 249518 250278 250517 "CLIF" 250999 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 245693 247664 247705 "CLAGG" 248634 NIL CLAGG (NIL T) -9 NIL 249170 NIL) (-150 244115 244572 245155 "CLAGG-" 245160 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 243659 243744 243884 "CINTSLPE" 244024 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 241160 241631 242179 "CHVAR" 243187 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240369 240923 240951 "CHARZ" 240956 T CHARZ (NIL) -9 NIL 240971 NIL) (-146 240123 240163 240241 "CHARPOL" 240323 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 239216 239803 239831 "CHARNZ" 239878 T CHARNZ (NIL) -9 NIL 239934 NIL) (-144 237178 237906 238241 "CHAR" 238901 T CHAR (NIL) -8 NIL NIL NIL) (-143 236904 236965 236993 "CFCAT" 237104 T CFCAT (NIL) -9 NIL NIL NIL) (-142 236149 236260 236442 "CDEN" 236788 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 232114 235302 235582 "CCLASS" 235889 T CCLASS (NIL) -8 NIL NIL NIL) (-140 231421 231564 231727 "CATEGORY" 231971 T -10 (NIL) -8 NIL NIL NIL) (-139 231026 231340 231388 "CATCTOR" 231393 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 230477 230729 230827 "CATAST" 230948 T CATAST (NIL) -8 NIL NIL NIL) (-137 229953 230198 230290 "CASEAST" 230405 T CASEAST (NIL) -8 NIL NIL NIL) (-136 224962 225982 226735 "CARTEN" 229256 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 224070 224218 224439 "CARTEN2" 224809 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 222385 223220 223477 "CARD" 223833 T CARD (NIL) -8 NIL NIL NIL) (-133 221961 222189 222264 "CAPSLAST" 222330 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 221465 221673 221701 "CACHSET" 221833 T CACHSET (NIL) -9 NIL 221911 NIL) (-131 220935 221257 221285 "CABMON" 221335 T CABMON (NIL) -9 NIL 221391 NIL) (-130 220408 220639 220749 "BYTEORD" 220845 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 219384 219942 220084 "BYTE" 220247 T BYTE (NIL) -8 NIL NIL 220369) (-128 214734 218889 219061 "BYTEBUF" 219232 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 212243 214426 214533 "BTREE" 214660 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209692 211891 212013 "BTOURN" 212153 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 207062 209162 209203 "BTCAT" 209271 NIL BTCAT (NIL T) -9 NIL 209348 NIL) (-124 206729 206809 206958 "BTCAT-" 206963 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 201994 205872 205900 "BTAGG" 206122 T BTAGG (NIL) -9 NIL 206283 NIL) (-122 201484 201609 201815 "BTAGG-" 201820 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 198479 200762 200977 "BSTREE" 201301 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 197617 197743 197927 "BRILL" 198335 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 194269 196343 196384 "BRAGG" 197033 NIL BRAGG (NIL T) -9 NIL 197291 NIL) (-118 192798 193204 193759 "BRAGG-" 193764 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 186027 192144 192328 "BPADICRT" 192646 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184342 185964 186009 "BPADIC" 186014 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 184040 184070 184184 "BOUNDZRO" 184306 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 179132 180330 181273 "BOP" 183117 T BOP (NIL) -8 NIL NIL NIL) (-113 176913 177317 177792 "BOP1" 178690 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 175738 176487 176636 "BOOLEAN" 176784 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175074 175478 175532 "BMODULE" 175537 NIL BMODULE (NIL T T) -9 NIL 175602 NIL) (-110 170875 174872 174945 "BITS" 175021 T BITS (NIL) -8 NIL NIL NIL) (-109 170296 170415 170555 "BINDING" 170755 T BINDING (NIL) -8 NIL NIL NIL) (-108 164303 169893 170041 "BINARY" 170168 T BINARY (NIL) -8 NIL NIL NIL) (-107 162083 163558 163599 "BGAGG" 163859 NIL BGAGG (NIL T) -9 NIL 163996 NIL) (-106 161914 161946 162037 "BGAGG-" 162042 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160985 161298 161503 "BFUNCT" 161729 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159675 159853 160141 "BEZOUT" 160809 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156144 158527 158857 "BBTREE" 159378 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155878 155931 155959 "BASTYPE" 156078 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155731 155759 155832 "BASTYPE-" 155837 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155165 155241 155393 "BALFACT" 155642 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154021 154580 154766 "AUTOMOR" 155010 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153747 153752 153778 "ATTREG" 153783 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151999 152444 152796 "ATTRBUT" 153413 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151607 151827 151893 "ATTRAST" 151951 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151143 151256 151282 "ATRIG" 151483 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150952 150993 151080 "ATRIG-" 151085 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150597 150783 150809 "ASTCAT" 150814 T ASTCAT (NIL) -9 NIL 150844 NIL) (-92 150324 150383 150502 "ASTCAT-" 150507 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148473 150100 150188 "ASTACK" 150267 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146978 147275 147640 "ASSOCEQ" 148155 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146010 146637 146761 "ASP9" 146885 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145773 145958 145997 "ASP8" 146002 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144641 145378 145520 "ASP80" 145662 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143539 144276 144408 "ASP7" 144540 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142493 143216 143334 "ASP78" 143452 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141462 142173 142290 "ASP77" 142407 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140374 141100 141231 "ASP74" 141362 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139274 140009 140141 "ASP73" 140273 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138378 139100 139200 "ASP6" 139205 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137322 138055 138173 "ASP55" 138291 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136271 136996 137115 "ASP50" 137234 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135359 135972 136082 "ASP4" 136192 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134447 135060 135170 "ASP49" 135280 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133231 133986 134154 "ASP42" 134336 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132007 132764 132934 "ASP41" 133118 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130957 131684 131802 "ASP35" 131920 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130722 130905 130944 "ASP34" 130949 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130459 130526 130602 "ASP33" 130677 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129352 130094 130226 "ASP31" 130358 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129117 129300 129339 "ASP30" 129344 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128852 128921 128997 "ASP29" 129072 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128617 128800 128839 "ASP28" 128844 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128382 128565 128604 "ASP27" 128609 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127466 128080 128191 "ASP24" 128302 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126542 127268 127380 "ASP20" 127385 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125630 126243 126353 "ASP1" 126463 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124572 125304 125423 "ASP19" 125542 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124309 124376 124452 "ASP12" 124527 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123161 123908 124052 "ASP10" 124196 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121012 123005 123096 "ARRAY2" 123101 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116777 120660 120774 "ARRAY1" 120929 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 115809 115982 116203 "ARRAY12" 116600 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110121 112039 112114 "ARR2CAT" 114744 NIL ARR2CAT (NIL T T T) -9 NIL 115502 NIL) (-56 107555 108299 109253 "ARR2CAT-" 109258 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106872 107182 107307 "ARITY" 107448 T ARITY (NIL) -8 NIL NIL NIL) (-54 105648 105800 106099 "APPRULE" 106708 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105299 105347 105466 "APPLYORE" 105594 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104246 104564 104759 "ANY" 105122 T ANY (NIL) -8 NIL NIL NIL) (-51 103524 103647 103804 "ANY1" 104120 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101054 101961 102288 "ANTISYM" 103248 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 100546 100761 100857 "ANON" 100976 T ANON (NIL) -8 NIL NIL NIL) (-48 94795 99085 99539 "AN" 100110 T AN (NIL) -8 NIL NIL NIL) (-47 91017 92405 92456 "AMR" 93204 NIL AMR (NIL T T) -9 NIL 93804 NIL) (-46 90129 90350 90713 "AMR-" 90718 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74568 90046 90107 "ALIST" 90112 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71370 74162 74331 "ALGSC" 74486 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 67925 68480 69087 "ALGPKG" 70810 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67202 67303 67487 "ALGMFACT" 67811 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63154 63760 64378 "ALGMANIP" 66762 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 3205276 3205281 3205286 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3205261 3205266 3205271 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3205246 3205251 3205256 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3205231 3205236 3205241 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1287 3204374 3205106 3205183 "ZMOD" 3205188 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1286 3203484 3203648 3203857 "ZLINDEP" 3204206 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1285 3192784 3194552 3196524 "ZDSOLVE" 3201614 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1284 3192030 3192171 3192360 "YSTREAM" 3192630 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1283 3189804 3191331 3191535 "XRPOLY" 3191873 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1282 3186357 3187675 3188250 "XPR" 3189276 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1281 3184078 3185688 3185892 "XPOLY" 3186188 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1280 3181835 3183203 3183258 "XPOLYC" 3183546 NIL XPOLYC (NIL T T) -9 NIL 3183659 NIL) (-1279 3178210 3180352 3180740 "XPBWPOLY" 3181493 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1278 3174086 3176373 3176415 "XF" 3177036 NIL XF (NIL T) -9 NIL 3177436 NIL) (-1277 3173707 3173795 3173964 "XF-" 3173969 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1276 3169007 3170296 3170351 "XFALG" 3172523 NIL XFALG (NIL T T) -9 NIL 3173312 NIL) (-1275 3168140 3168244 3168449 "XEXPPKG" 3168899 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1274 3166249 3167990 3168086 "XDPOLY" 3168091 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1273 3165160 3165760 3165803 "XALG" 3165808 NIL XALG (NIL T) -9 NIL 3165919 NIL) (-1272 3158602 3163137 3163631 "WUTSET" 3164752 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1271 3156858 3157654 3157977 "WP" 3158413 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1270 3156460 3156680 3156750 "WHILEAST" 3156810 T WHILEAST (NIL) -8 NIL NIL NIL) (-1269 3155932 3156177 3156271 "WHEREAST" 3156388 T WHEREAST (NIL) -8 NIL NIL NIL) (-1268 3154818 3155016 3155311 "WFFINTBS" 3155729 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1267 3152722 3153149 3153611 "WEIER" 3154390 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1266 3151843 3152293 3152335 "VSPACE" 3152471 NIL VSPACE (NIL T) -9 NIL 3152545 NIL) (-1265 3151681 3151708 3151799 "VSPACE-" 3151804 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1264 3151489 3151532 3151600 "VOID" 3151635 T VOID (NIL) -8 NIL NIL NIL) (-1263 3149625 3149984 3150390 "VIEW" 3151105 T VIEW (NIL) -7 NIL NIL NIL) (-1262 3146049 3146688 3147425 "VIEWDEF" 3148910 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1261 3135353 3137597 3139770 "VIEW3D" 3143898 T VIEW3D (NIL) -8 NIL NIL NIL) (-1260 3127604 3129264 3130843 "VIEW2D" 3133796 T VIEW2D (NIL) -8 NIL NIL NIL) (-1259 3122958 3127374 3127466 "VECTOR" 3127547 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1258 3121535 3121794 3122112 "VECTOR2" 3122688 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1257 3115014 3119319 3119362 "VECTCAT" 3120355 NIL VECTCAT (NIL T) -9 NIL 3120941 NIL) (-1256 3114028 3114282 3114672 "VECTCAT-" 3114677 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1255 3113482 3113679 3113799 "VARIABLE" 3113943 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1254 3113415 3113420 3113450 "UTYPE" 3113455 T UTYPE (NIL) -9 NIL NIL NIL) (-1253 3112245 3112399 3112661 "UTSODETL" 3113241 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1252 3109685 3110145 3110669 "UTSODE" 3111786 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1251 3101522 3107311 3107800 "UTS" 3109254 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1250 3092730 3098089 3098132 "UTSCAT" 3099244 NIL UTSCAT (NIL T) -9 NIL 3100001 NIL) (-1249 3090077 3090800 3091789 "UTSCAT-" 3091794 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1248 3089704 3089747 3089880 "UTS2" 3090028 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1247 3083930 3086542 3086585 "URAGG" 3088655 NIL URAGG (NIL T) -9 NIL 3089378 NIL) (-1246 3080869 3081732 3082855 "URAGG-" 3082860 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1245 3076579 3079504 3079969 "UPXSSING" 3080533 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1244 3068645 3075826 3076099 "UPXS" 3076364 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1243 3061718 3068549 3068621 "UPXSCONS" 3068626 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1242 3051928 3058713 3058775 "UPXSCCA" 3059349 NIL UPXSCCA (NIL T T) -9 NIL 3059582 NIL) (-1241 3051566 3051651 3051825 "UPXSCCA-" 3051830 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1240 3041629 3048187 3048230 "UPXSCAT" 3048878 NIL UPXSCAT (NIL T) -9 NIL 3049486 NIL) (-1239 3041059 3041138 3041317 "UPXS2" 3041544 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1238 3039713 3039966 3040317 "UPSQFREE" 3040802 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1237 3033466 3036515 3036570 "UPSCAT" 3037731 NIL UPSCAT (NIL T T) -9 NIL 3038505 NIL) (-1236 3032670 3032877 3033204 "UPSCAT-" 3033209 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1235 3018785 3026545 3026588 "UPOLYC" 3028689 NIL UPOLYC (NIL T) -9 NIL 3029910 NIL) (-1234 3010113 3012539 3015686 "UPOLYC-" 3015691 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1233 3009740 3009783 3009916 "UPOLYC2" 3010064 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1232 3001551 3009423 3009552 "UP" 3009659 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1231 3000890 3000997 3001161 "UPMP" 3001440 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1230 3000443 3000524 3000663 "UPDIVP" 3000803 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1229 2999011 2999260 2999576 "UPDECOMP" 3000192 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1228 2998246 2998358 2998543 "UPCDEN" 2998895 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1227 2997765 2997834 2997983 "UP2" 2998171 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1226 2996232 2996969 2997246 "UNISEG" 2997523 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1225 2995447 2995574 2995779 "UNISEG2" 2996075 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1224 2994507 2994687 2994913 "UNIFACT" 2995263 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1223 2978439 2993684 2993935 "ULS" 2994314 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1222 2966438 2978343 2978415 "ULSCONS" 2978420 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1221 2949019 2960996 2961058 "ULSCCAT" 2961696 NIL ULSCCAT (NIL T T) -9 NIL 2961984 NIL) (-1220 2948069 2948314 2948702 "ULSCCAT-" 2948707 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1219 2937909 2944381 2944424 "ULSCAT" 2945287 NIL ULSCAT (NIL T) -9 NIL 2946017 NIL) (-1218 2937339 2937418 2937597 "ULS2" 2937824 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1217 2936429 2936939 2937046 "UINT8" 2937157 T UINT8 (NIL) -8 NIL NIL 2937242) (-1216 2935518 2936028 2936135 "UINT64" 2936246 T UINT64 (NIL) -8 NIL NIL 2936331) (-1215 2934607 2935117 2935224 "UINT32" 2935335 T UINT32 (NIL) -8 NIL NIL 2935420) (-1214 2933696 2934206 2934313 "UINT16" 2934424 T UINT16 (NIL) -8 NIL NIL 2934509) (-1213 2932065 2933022 2933052 "UFD" 2933264 T UFD (NIL) -9 NIL 2933378 NIL) (-1212 2931859 2931905 2932000 "UFD-" 2932005 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1211 2930941 2931124 2931340 "UDVO" 2931665 T UDVO (NIL) -7 NIL NIL NIL) (-1210 2928757 2929166 2929637 "UDPO" 2930505 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1209 2928690 2928695 2928725 "TYPE" 2928730 T TYPE (NIL) -9 NIL NIL NIL) (-1208 2928450 2928645 2928676 "TYPEAST" 2928681 T TYPEAST (NIL) -8 NIL NIL NIL) (-1207 2927421 2927623 2927863 "TWOFACT" 2928244 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1206 2926444 2926830 2927065 "TUPLE" 2927221 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1205 2924135 2924654 2925193 "TUBETOOL" 2925927 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1204 2922984 2923189 2923430 "TUBE" 2923928 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1203 2917713 2921956 2922239 "TS" 2922736 NIL TS (NIL T) -8 NIL NIL NIL) (-1202 2906353 2910472 2910569 "TSETCAT" 2915838 NIL TSETCAT (NIL T T T T) -9 NIL 2917369 NIL) (-1201 2901085 2902685 2904576 "TSETCAT-" 2904581 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1200 2895724 2896571 2897500 "TRMANIP" 2900221 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1199 2895165 2895228 2895391 "TRIMAT" 2895656 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1198 2893031 2893268 2893625 "TRIGMNIP" 2894914 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1197 2892551 2892664 2892694 "TRIGCAT" 2892907 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1196 2892220 2892299 2892440 "TRIGCAT-" 2892445 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1195 2889065 2891078 2891359 "TREE" 2891974 NIL TREE (NIL T) -8 NIL NIL NIL) (-1194 2888339 2888867 2888897 "TRANFUN" 2888932 T TRANFUN (NIL) -9 NIL 2888998 NIL) (-1193 2887618 2887809 2888089 "TRANFUN-" 2888094 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1192 2887422 2887454 2887515 "TOPSP" 2887579 T TOPSP (NIL) -7 NIL NIL NIL) (-1191 2886770 2886885 2887039 "TOOLSIGN" 2887303 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1190 2885404 2885947 2886186 "TEXTFILE" 2886553 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1189 2883316 2883857 2884286 "TEX" 2884997 T TEX (NIL) -8 NIL NIL NIL) (-1188 2883097 2883128 2883200 "TEX1" 2883279 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1187 2882745 2882808 2882898 "TEMUTL" 2883029 T TEMUTL (NIL) -7 NIL NIL NIL) (-1186 2880899 2881179 2881504 "TBCMPPK" 2882468 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1185 2872676 2879059 2879115 "TBAGG" 2879515 NIL TBAGG (NIL T T) -9 NIL 2879726 NIL) (-1184 2867746 2869234 2870988 "TBAGG-" 2870993 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1183 2867130 2867237 2867382 "TANEXP" 2867635 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1182 2860520 2866987 2867080 "TABLE" 2867085 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1181 2859932 2860031 2860169 "TABLEAU" 2860417 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1180 2854540 2855760 2857008 "TABLBUMP" 2858718 NIL TABLBUMP (NIL T) -7 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 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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 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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 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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))
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*3)) (-4 *4 (-1235 *3))))) +(((*1 *1 *2) (-12 (-5 *1 (-227 *2)) (-4 *2 (-13 (-363) (-1194)))))) (((*1 *2 *3) - (-12 (-5 *3 (-1136 *4 *2)) (-14 *4 (-917)) - (-4 *2 (-13 (-1045) (-10 -7 (-6 (-4409 "*"))))) - (-5 *1 (-898 *4 *2))))) + (-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 (-5 *2 (-169 *4)) (-5 *1 (-181 *4 *3)) - (-4 *4 (-13 (-363) (-844))) (-4 *3 (-1235 *2))))) + (-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))))) (((*1 *2 *3 *1) (-12 (-5 *3 (-1283 *4 *2)) (-4 *1 (-374 *4 *2)) (-4 *4 (-846)) (-4 *2 (-172)))) @@ -59,35 +57,57 @@ (-4 *2 (-1045)))) ((*1 *2 *1 *3) (-12 (-4 *2 (-1045)) (-5 *1 (-1282 *2 *3)) (-4 *3 (-842))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-641 *2)) (-4 *2 (-945 *4 *5 *6)) (-4 *4 (-307)) - (-4 *5 (-789)) (-4 *6 (-846)) (-5 *1 (-447 *4 *5 *6 *2))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1232 *5 *4)) (-4 *4 (-452)) (-4 *4 (-816)) - (-14 *5 (-1170)) (-5 *2 (-564)) (-5 *1 (-1108 *4 *5))))) -(((*1 *2 *3) - (-12 (-4 *4 (-349)) (-5 *2 (-418 (-1166 (-1166 *4)))) - (-5 *1 (-1207 *4)) (-5 *3 (-1166 (-1166 *4)))))) -(((*1 *2) - (-12 (-5 *2 (-1 *3 *3)) (-5 *1 (-530 *3)) (-4 *3 (-13 (-722) (-25)))))) -(((*1 *1 *2) - (-12 (-5 *2 (-685 *4)) (-4 *4 (-1045)) (-5 *1 (-1136 *3 *4)) - (-14 *3 (-767))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-282 *2)) (-4 *2 (-1209)) (-4 *2 (-846)))) - ((*1 *1 *2 *1 *1) - (-12 (-5 *2 (-1 (-112) *3 *3)) (-4 *1 (-282 *3)) (-4 *3 (-1209)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-964 *2)) (-4 *2 (-846))))) +(((*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 *1) (-12 (-4 *1 (-34)) (-5 *2 (-112)))) - ((*1 *2 *1) - (-12 (-4 *3 (-452)) (-4 *4 (-846)) (-4 *5 (-789)) (-5 *2 (-112)) - (-5 *1 (-983 *3 *4 *5 *6)) (-4 *6 (-945 *3 *5 *4)))) - ((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-1134 *3 *4)) (-4 *3 (-13 (-1094) (-34))) - (-4 *4 (-13 (-1094) (-34)))))) -(((*1 *2 *2) (-12 (-5 *2 (-564)) (-5 *1 (-561)))) - ((*1 *2 *3) - (-12 (-5 *2 (-1166 (-407 (-564)))) (-5 *1 (-938)) (-5 *3 (-564))))) +(((*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 *3) + (-12 (-5 *2 (-1172 (-407 (-564)))) (-5 *1 (-190)) (-5 *3 (-564))))) (((*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)))) @@ -119,14 +139,14 @@ (-12 (-5 *3 (-1170)) (-5 *2 (-245 (-1152))) (-5 *1 (-214 *4)) (-4 *4 (-13 (-846) - (-10 -8 (-15 -4363 ((-1152) $ *3)) (-15 -1679 ((-1264) $)) - (-15 -1443 ((-1264) $))))))) + (-10 -8 (-15 -4366 ((-1152) $ *3)) (-15 -1629 ((-1264) $)) + (-15 -3668 ((-1264) $))))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-985)) (-5 *1 (-214 *3)) (-4 *3 (-13 (-846) - (-10 -8 (-15 -4363 ((-1152) $ (-1170))) (-15 -1679 ((-1264) $)) - (-15 -1443 ((-1264) $))))))) + (-10 -8 (-15 -4366 ((-1152) $ (-1170))) (-15 -1629 ((-1264) $)) + (-15 -3668 ((-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)))) @@ -212,63 +232,25 @@ (-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 *1) (-5 *1 (-144))) ((*1 *1 *1) (-5 *1 (-858)))) -(((*1 *2 *3) - (-12 (-5 *3 (-1042 *4 *5)) (-4 *4 (-13 (-844) (-307) (-147) (-1018))) - (-14 *5 (-641 (-1170))) (-5 *2 (-641 (-641 (-1020 (-407 *4))))) - (-5 *1 (-1285 *4 *5 *6)) (-14 *6 (-641 (-1170))))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-641 (-948 *5))) (-5 *4 (-112)) - (-4 *5 (-13 (-844) (-307) (-147) (-1018))) - (-5 *2 (-641 (-641 (-1020 (-407 *5))))) (-5 *1 (-1285 *5 *6 *7)) - (-14 *6 (-641 (-1170))) (-14 *7 (-641 (-1170))))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-641 (-948 *5))) (-5 *4 (-112)) - (-4 *5 (-13 (-844) (-307) (-147) (-1018))) - (-5 *2 (-641 (-641 (-1020 (-407 *5))))) (-5 *1 (-1285 *5 *6 *7)) - (-14 *6 (-641 (-1170))) (-14 *7 (-641 (-1170))))) - ((*1 *2 *3) - (-12 (-5 *3 (-641 (-948 *4))) - (-4 *4 (-13 (-844) (-307) (-147) (-1018))) - (-5 *2 (-641 (-641 (-1020 (-407 *4))))) (-5 *1 (-1285 *4 *5 *6)) - (-14 *5 (-641 (-1170))) (-14 *6 (-641 (-1170)))))) -(((*1 *1 *1 *1 *1 *2) - (-12 (-5 *2 (-767)) (-4 *1 (-1059 *3 *4 *5)) (-4 *3 (-1045)) - (-4 *4 (-789)) (-4 *5 (-846)) (-4 *3 (-556))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1094)) (-4 *5 (-1094)) - (-4 *6 (-1094)) (-5 *2 (-1 *6 *5)) (-5 *1 (-680 *4 *5 *6))))) -(((*1 *2) (-12 (-5 *2 (-564)) (-5 *1 (-695)))) - ((*1 *2 *2) (-12 (-5 *2 (-564)) (-5 *1 (-695))))) -(((*1 *2 *3) - (-12 (-5 *3 (-641 (-481 *4 *5))) (-14 *4 (-641 (-1170))) - (-4 *5 (-452)) - (-5 *2 - (-2 (|:| |gblist| (-641 (-247 *4 *5))) - (|:| |gvlist| (-641 (-564))))) - (-5 *1 (-629 *4 *5))))) -(((*1 *2 *3) - (-12 (-4 *4 (-349)) - (-5 *2 (-641 (-2 (|:| |deg| (-767)) (|:| -2475 *3)))) - (-5 *1 (-216 *4 *3)) (-4 *3 (-1235 *4))))) -(((*1 *2 *3 *1 *4 *4 *4 *4 *4) - (-12 (-5 *4 (-112)) (-4 *5 (-452)) (-4 *6 (-789)) (-4 *7 (-846)) - (-5 *2 (-641 (-1023 *5 *6 *7 *3))) (-5 *1 (-1023 *5 *6 *7 *3)) - (-4 *3 (-1059 *5 *6 *7)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-641 *6)) (-4 *1 (-1065 *3 *4 *5 *6)) (-4 *3 (-452)) - (-4 *4 (-789)) (-4 *5 (-846)) (-4 *6 (-1059 *3 *4 *5)))) - ((*1 *1 *2 *1) - (-12 (-4 *1 (-1065 *3 *4 *5 *2)) (-4 *3 (-452)) (-4 *4 (-789)) - (-4 *5 (-846)) (-4 *2 (-1059 *3 *4 *5)))) - ((*1 *2 *3 *1 *4 *4 *4 *4 *4) - (-12 (-5 *4 (-112)) (-4 *5 (-452)) (-4 *6 (-789)) (-4 *7 (-846)) - (-5 *2 (-641 (-1140 *5 *6 *7 *3))) (-5 *1 (-1140 *5 *6 *7 *3)) - (-4 *3 (-1059 *5 *6 *7))))) +(((*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 (-407 (-948 *3))) (-5 *1 (-453 *3 *4 *5 *6)) - (-4 *3 (-556)) (-4 *3 (-172)) (-14 *4 (-917)) - (-14 *5 (-641 (-1170))) (-14 *6 (-1259 (-685 *3)))))) + (-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 *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))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-47 *3 *4)) (-4 *3 (-1045)) (-4 *4 (-788)))) @@ -375,9 +357,9 @@ (-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 (|:| -2329 *5) (|:| |coeff| *5)) "failed")) + (-5 *4 (-3 (-2 (|:| -4354 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-363)) (-4 *6 (-363)) - (-5 *2 (-2 (|:| -2329 *6) (|:| |coeff| *6))) + (-5 *2 (-2 (|:| -4354 *6) (|:| |coeff| *6))) (-5 *1 (-584 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) @@ -496,7 +478,7 @@ (-4 *8 (-1045)) (-4 *6 (-789)) (-4 *2 (-13 (-1094) - (-10 -8 (-15 -3049 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-767)))))) + (-10 -8 (-15 -3069 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-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)) @@ -509,8 +491,8 @@ (-4 *2 (-945 (-948 *4) *5 *6)) (-4 *5 (-789)) (-4 *6 (-13 (-846) - (-10 -8 (-15 -1314 ((-1170) $)) - (-15 -3346 ((-3 $ "failed") (-1170)))))) + (-10 -8 (-15 -1311 ((-1170) $)) + (-15 -3395 ((-3 $ "failed") (-1170)))))) (-5 *1 (-980 *4 *5 *6 *2)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-556)) (-4 *6 (-556)) @@ -597,25 +579,22 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1045)) (-5 *1 (-1282 *3 *4)) (-4 *4 (-842))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-767)) (-5 *2 (-1264)) (-5 *1 (-1260)))) - ((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-767)) (-5 *2 (-1264)) (-5 *1 (-1261))))) -(((*1 *2) - (-12 (-5 *2 (-1264)) (-5 *1 (-1186 *3 *4)) (-4 *3 (-1094)) - (-4 *4 (-1094))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1150 (-1150 *4))) (-5 *2 (-1150 *4)) (-5 *1 (-1154 *4)) - (-4 *4 (-1045))))) -(((*1 *2 *3) - (-12 (-4 *4 (-307)) (-4 *5 (-373 *4)) (-4 *6 (-373 *4)) +(((*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 - (-2 (|:| |Smith| *3) (|:| |leftEqMat| *3) (|:| |rightEqMat| *3))) - (-5 *1 (-1118 *4 *5 *6 *3)) (-4 *3 (-683 *4 *5 *6))))) -(((*1 *2 *1) (-12 (-5 *2 (-641 (-1170))) (-5 *1 (-821))))) -(((*1 *1 *1 *1) - (-12 (-4 *1 (-323 *2 *3)) (-4 *2 (-1094)) (-4 *3 (-131)) - (-4 *3 (-788))))) + (-641 + (-641 + (-3 (|:| -2562 (-1170)) + (|:| -1557 (-641 (-3 (|:| S (-1170)) (|:| P (-948 (-564)))))))))) + (-5 *1 (-1174))))) (((*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)))) @@ -669,71 +648,78 @@ (-12 (-5 *3 (-878 *5)) (-5 *4 (-1086 (-379))) (-4 *5 (-13 (-612 (-536)) (-1094))) (-5 *2 (-1127 (-225))) (-5 *1 (-259 *5))))) -(((*1 *1 *2 *3) (-12 (-5 *3 (-564)) (-5 *1 (-418 *2)) (-4 *2 (-556))))) -(((*1 *2 *3) - (-12 (-5 *3 (-641 *4)) (-4 *4 (-1094)) (-5 *2 (-1264)) - (-5 *1 (-1210 *4)))) - ((*1 *2 *3 *3) - (-12 (-5 *3 (-641 *4)) (-4 *4 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(-1059 *4 *5 *6)) (-4 *4 (-556)) + (-4 *5 (-789)) (-4 *6 (-846)) (-5 *1 (-973 *4 *5 *6 *2))))) +(((*1 *1 *1) (-12 (-4 *1 (-425 *2)) (-4 *2 (-1094)) (-4 *2 (-368))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-976 *2)) (-4 *2 (-1045)))) + ((*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 (-1045))))) +(((*1 *2 *1) (-12 (-4 *1 (-1247 *3)) (-4 *3 (-1209)) (-5 *2 (-767))))) +(((*1 *2) (-12 (-5 *2 (-1264)) (-5 *1 (-559))))) (((*1 *2 *1) (-12 (-4 *1 (-132)) (-5 *2 (-767)))) ((*1 *2 *3 *1 *2) (-12 (-5 *2 (-564)) (-4 *1 (-373 *3)) (-4 *3 (-1209)) @@ -3258,27 +2305,32 @@ ((*1 *2 *1) (-12 (-5 *2 (-1114)) (-5 *1 (-529)))) ((*1 *2 *3 *1 *2) (-12 (-4 *1 (-1138)) (-5 *2 (-564)) (-5 *3 (-141)))) ((*1 *2 *1 *1 *2) (-12 (-4 *1 (-1138)) (-5 *2 (-564))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1 *2 *2)) (-4 *5 (-363)) (-4 *6 (-1235 (-407 *2))) - (-4 *2 (-1235 *5)) (-5 *1 (-215 *5 *2 *6 *3)) - (-4 *3 (-342 *5 *2 *6))))) -(((*1 *2 *3 *2 *4 *5) - (-12 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*3 (-407 (-948 *4))) (-4 *4 (-556)) + (-4 *4 (-612 *2)) (-5 *2 (-379)) (-5 *1 (-781 *4)))) + ((*1 *2 *3 *4) + (|partial| -12 (-5 *3 (-407 (-948 *5))) (-5 *4 (-917)) (-4 *5 (-556)) + (-4 *5 (-612 *2)) (-5 *2 (-379)) (-5 *1 (-781 *5)))) + ((*1 *2 *3) + (|partial| -12 (-5 *3 (-316 *4)) (-4 *4 (-556)) (-4 *4 (-846)) + (-4 *4 (-612 *2)) (-5 *2 (-379)) (-5 *1 (-781 *4)))) + ((*1 *2 *3 *4) + (|partial| -12 (-5 *3 (-316 *5)) (-5 *4 (-917)) (-4 *5 (-556)) + (-4 *5 (-846)) (-4 *5 (-612 *2)) (-5 *2 (-379)) + (-5 *1 (-781 *5))))) +(((*1 *2 *3) + (-12 (-4 *4 (-13 (-556) (-1034 (-564)))) (-4 *5 (-430 *4)) + (-5 *2 (-418 *3)) (-5 *1 (-435 *4 *5 *3)) (-4 *3 (-1235 *5))))) (((*1 *2 *1) (-12 (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *5 (-846)) (-5 *2 (-641 *1)) (-4 *1 (-945 *3 *4 *5))))) @@ -3286,33 +2338,36 @@ (-12 (-4 *3 (-1094)) (-5 *1 (-925 *3 *2)) (-4 *2 (-430 *3)))) ((*1 *2 *3) (-12 (-5 *3 (-1170)) (-5 *2 (-316 (-564))) (-5 *1 (-926))))) -(((*1 *2 *3 *3 *4 *3) - (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) 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-(((*1 *1) (-5 *1 (-141))) ((*1 *1 *1) (-5 *1 (-144))) - ((*1 *1 *1) (-4 *1 (-1138)))) +(((*1 *2 *1 *2) + (-12 (|has| *1 (-6 -4408)) (-4 *1 (-1006 *2)) (-4 *2 (-1209))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-685 (-407 (-564)))) + (-5 *2 + (-641 + (-2 (|:| |outval| *4) (|:| |outmult| (-564)) + (|:| |outvect| (-641 (-685 *4)))))) + (-5 *1 (-775 *4)) (-4 *4 (-13 (-363) (-844)))))) +(((*1 *2 *1) + (-12 (-4 *1 (-602 *2 *3)) (-4 *3 (-1209)) (-4 *2 (-1094)) + (-4 *2 (-846))))) +(((*1 *1 *2) (-12 (-5 *2 (-641 (-379))) (-5 *1 (-263)))) + ((*1 *1) + (|partial| -12 (-4 *1 (-367 *2)) (-4 *2 (-556)) (-4 *2 (-172)))) + ((*1 *2 *1) (-12 (-5 *1 (-418 *2)) (-4 *2 (-556))))) +(((*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 *2 *2) + (-12 (-5 *2 (-641 *3)) (-4 *3 (-1235 (-564))) (-5 *1 (-486 *3))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1170)) (-4 *5 (-363)) (-5 *2 (-1150 (-1150 (-948 *5)))) + (-5 *1 (-1267 *5)) (-5 *4 (-1150 (-948 *5)))))) +(((*1 *1 *2 *3) + (-12 (-5 *1 (-960 *2 *3)) (-4 *2 (-1094)) (-4 *3 (-1094))))) +(((*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 (-4 *1 (-47 *2 *3)) (-4 *3 (-788)) (-4 *2 (-1045)))) ((*1 *2 *1) (-12 (-4 *2 (-1045)) (-5 *1 (-50 *2 *3)) (-14 *3 (-641 (-1170))))) @@ -3322,10 +2377,10 @@ ((*1 *2 *1) (-12 (-4 *1 (-382 *2 *3)) (-4 *3 (-1094)) (-4 *2 (-1045)))) ((*1 *2 *1) - (-12 (-14 *3 (-641 (-1170))) (-4 *5 (-238 (-2245 *3) (-767))) + (-12 (-14 *3 (-641 (-1170))) (-4 *5 (-238 (-2181 *3) (-767))) (-14 *6 - (-1 (-112) (-2 (|:| -2151 *4) (|:| -1384 *5)) - (-2 (|:| -2151 *4) (|:| -1384 *5)))) + (-1 (-112) (-2 (|:| -2083 *4) (|:| -1410 *5)) + (-2 (|:| -2083 *4) (|:| -1410 *5)))) (-4 *2 (-172)) (-5 *1 (-461 *3 *2 *4 *5 *6 *7)) (-4 *4 (-846)) (-4 *7 (-945 *2 *5 (-860 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-509 *2 *3)) (-4 *3 (-846)) (-4 *2 (-1094)))) @@ -3342,36 +2397,51 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-1059 *3 *4 *2)) (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *2 (-846))))) -(((*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 (|:| -1384 (-767)) (|:| -4373 *3) (|:| |radicand| *3))) - (-5 *1 (-949 *5 *6 *7 *8 *3)) (-5 *4 (-767)) - (-4 *3 - (-13 (-363) - (-10 -8 (-15 -2488 ($ *8)) (-15 -2388 (*8 $)) (-15 -2402 (*8 $)))))))) -(((*1 *2 *1) - (-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 *2 *1 *1) (-12 (-5 *2 (-112)) (-5 *1 (-668 *3)) (-4 *3 (-846)))) - ((*1 *2 *1 *1) (-12 (-5 *2 (-112)) (-5 *1 (-673 *3)) (-4 *3 (-846)))) - ((*1 *2 *1 *1) (-12 (-5 *2 (-112)) (-5 *1 (-815 *3)) (-4 *3 (-846))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1166 *2)) (-4 *2 (-945 (-407 (-948 *6)) *5 *4)) - (-5 *1 (-728 *5 *4 *6 *2)) (-4 *5 (-789)) - (-4 *4 (-13 (-846) (-10 -8 (-15 -1314 ((-1170) $))))) - (-4 *6 (-556))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-979 *2)) (-4 *2 (-1194))))) -(((*1 *2 *3) - (-12 (-4 *4 (-1045)) (-5 *2 (-112)) (-5 *1 (-444 *4 *3)) - (-4 *3 (-1235 *4)))) +(((*1 *1 *1) + (-12 (-4 *1 (-1059 *2 *3 *4)) (-4 *2 (-1045)) (-4 *3 (-789)) + (-4 *4 (-846)) (-4 *2 (-452))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-1150 *4)) (-5 *3 (-1 *4 (-564))) (-4 *4 (-1045)) + (-5 *1 (-1154 *4))))) +(((*1 *1 *2) (-12 (-5 *2 (-564)) (-5 *1 (-858))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-1166 *6)) (-5 *3 (-564)) (-4 *6 (-307)) (-4 *4 (-789)) + (-4 *5 (-846)) (-5 *1 (-738 *4 *5 *6 *7)) (-4 *7 (-945 *6 *4 *5))))) +(((*1 *2 *2) (-12 (-5 *2 (-316 (-225))) (-5 *1 (-267))))) +(((*1 *2 *3) (-12 (-5 *2 (-418 *3)) (-5 *1 (-558 *3)) (-4 *3 (-545)))) + ((*1 *2 *3) + (-12 (-4 *4 (-789)) (-4 *5 (-846)) (-4 *6 (-307)) (-5 *2 (-418 *3)) + (-5 *1 (-738 *4 *5 *6 *3)) (-4 *3 (-945 *6 *4 *5)))) + ((*1 *2 *3) + (-12 (-4 *4 (-789)) (-4 *5 (-846)) (-4 *6 (-307)) + (-4 *7 (-945 *6 *4 *5)) (-5 *2 (-418 (-1166 *7))) + (-5 *1 (-738 *4 *5 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(-4 *4 (-13 (-844) (-307) (-147) (-1018))) + (-14 *5 (-641 (-1170))) + (-5 *2 + (-641 (-1140 *4 (-531 (-860 *6)) (-860 *6) (-776 *4 (-860 *6))))) + (-5 *1 (-1285 *4 *5 *6)) (-14 *6 (-641 (-1170)))))) +(((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-917)) (-5 *4 (-1152)) (-5 *2 (-1264)) (-5 *1 (-1260))))) +(((*1 *2 *3) (-12 (-5 *3 (-1152)) (-5 *2 (-1264)) (-5 *1 (-858))))) +(((*1 *1 *1 *1 *2 *3) + (-12 (-5 *2 (-939 *5)) (-5 *3 (-767)) (-4 *5 (-1045)) + (-5 *1 (-1158 *4 *5)) (-14 *4 (-917))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) @@ -3393,10 +2463,10 @@ (-12 (-4 *1 (-382 *3 *2)) (-4 *3 (-1045)) (-4 *2 (-1094)))) ((*1 *2 *1) (-12 (-14 *3 (-641 (-1170))) (-4 *4 (-172)) - (-4 *6 (-238 (-2245 *3) (-767))) + (-4 *6 (-238 (-2181 *3) (-767))) (-14 *7 - (-1 (-112) (-2 (|:| -2151 *5) (|:| -1384 *6)) - (-2 (|:| -2151 *5) (|:| -1384 *6)))) + (-1 (-112) (-2 (|:| -2083 *5) (|:| -1410 *6)) + (-2 (|:| -2083 *5) (|:| -1410 *6)))) (-5 *2 (-709 *5 *6 *7)) (-5 *1 (-461 *3 *4 *5 *6 *7 *8)) (-4 *5 (-846)) (-4 *8 (-945 *4 *6 (-860 *3))))) ((*1 *2 *1) @@ -3405,30 +2475,52 @@ ((*1 *1 *1) (-12 (-4 *1 (-969 *2 *3 *4)) (-4 *2 (-1045)) (-4 *3 (-788)) (-4 *4 (-846))))) -(((*1 *2 *3 *3 *4 *3) - (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *2 (-1031)) - (-5 *1 (-751))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-114)) (-5 *3 (-641 (-1 *4 (-641 *4)))) (-4 *4 (-1094)) - (-5 *1 (-113 *4)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-114)) (-5 *3 (-1 *4 *4)) (-4 *4 (-1094)) - (-5 *1 (-113 *4)))) - ((*1 *2 *3) - (|partial| -12 (-5 *3 (-114)) (-5 *2 (-641 (-1 *4 (-641 *4)))) - (-5 *1 (-113 *4)) (-4 *4 (-1094))))) -(((*1 *1) (-12 (-4 *1 (-425 *2)) (-4 *2 (-368)) (-4 *2 (-1094))))) (((*1 *2 *3 *3 *3) - (-12 (-5 *3 (-1152)) (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) - (-4 *7 (-1059 *4 *5 *6)) (-5 *2 (-1264)) - (-5 *1 (-984 *4 *5 *6 *7 *8)) (-4 *8 (-1065 *4 *5 *6 *7)))) - ((*1 *2 *3 *3 *3) - (-12 (-5 *3 (-1152)) (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) - (-4 *7 (-1059 *4 *5 *6)) (-5 *2 (-1264)) - (-5 *1 (-1101 *4 *5 *6 *7 *8)) (-4 *8 (-1065 *4 *5 *6 *7))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1259 (-1259 *4))) (-4 *4 (-1045)) (-5 *2 (-685 *4)) - (-5 *1 (-1025 *4))))) + (-12 (-5 *2 (-641 (-564))) (-5 *1 (-1104)) (-5 *3 (-564))))) +(((*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 (-1066 *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)))) + (-5 *1 (-1066 *6 *7 *4 *8 *9))))) +(((*1 *1 *1) + (-12 (-4 *1 (-945 *2 *3 *4)) (-4 *2 (-1045)) (-4 *3 (-789)) + (-4 *4 (-846)) (-4 *2 (-452)))) + ((*1 *2 *3 *1) + (-12 (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) + (-4 *3 (-1059 *4 *5 *6)) + (-5 *2 (-641 (-2 (|:| |val| *3) (|:| -3577 *1)))) + (-4 *1 (-1065 *4 *5 *6 *3)))) + ((*1 *1 *1) (-4 *1 (-1213))) + ((*1 *2 *2) + (-12 (-4 *3 (-556)) (-5 *1 (-1238 *3 *2)) + (-4 *2 (-13 (-1235 *3) (-556) (-10 -8 (-15 -2123 ($ $ $)))))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-641 (-948 *4))) (-5 *3 (-641 (-1170))) (-4 *4 (-452)) + (-5 *1 (-914 *4))))) +(((*1 *1) (-5 *1 (-437)))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-641 *6)) (-4 *6 (-1059 *3 *4 *5)) (-4 *3 (-452)) + (-4 *3 (-556)) (-4 *4 (-789)) (-4 *5 (-846)) + (-5 *1 (-973 *3 *4 *5 *6))))) +(((*1 *2 *3 *4 *3 *5) + (-12 (-5 *3 (-1152)) (-5 *4 (-169 (-225))) (-5 *5 (-564)) + (-5 *2 (-1031)) (-5 *1 (-754))))) +(((*1 *2) + (-12 (-4 *4 (-172)) (-5 *2 (-112)) (-5 *1 (-366 *3 *4)) + (-4 *3 (-367 *4)))) + ((*1 *2) (-12 (-4 *1 (-367 *3)) (-4 *3 (-172)) (-5 *2 (-112))))) +(((*1 *2 *3 *4 *5 *6) + (-12 (-5 *4 (-112)) (-5 *5 (-1096 (-767))) (-5 *6 (-767)) + (-5 *2 + (-2 (|:| |contp| (-564)) + (|:| -4109 (-641 (-2 (|:| |irr| *3) (|:| -1987 (-564))))))) + (-5 *1 (-442 *3)) (-4 *3 (-1235 (-564)))))) (((*1 *2 *1) (-12 (-5 *1 (-687 *2)) (-4 *2 (-611 (-858))))) ((*1 *2 *1) (-12 (-4 *1 (-1131)) (-5 *2 (-564)))) ((*1 *2 *1) (-12 (-4 *1 (-1131)) (-5 *2 (-1152)))) @@ -3465,11 +2557,6 @@ ((*1 *2 *1) (-12 (-5 *2 (-506)) (-5 *1 (-1175)))) ((*1 *2 *1) (-12 (-5 *2 (-225)) (-5 *1 (-1175)))) ((*1 *2 *1) (-12 (-5 *2 (-564)) (-5 *1 (-1175))))) -(((*1 *1 *1) - (-12 (-5 *1 (-594 *2)) (-4 *2 (-38 (-407 (-564)))) (-4 *2 (-1045))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1181 (-641 *4))) (-4 *4 (-846)) - (-5 *2 (-641 (-641 *4))) (-5 *1 (-1180 *4))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) @@ -3486,42 +2573,74 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) +(((*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 *2 *1) + (-12 + (-5 *2 + (-641 + (-2 (|:| |scalar| (-407 (-564))) (|:| |coeff| (-1166 *3)) + (|:| |logand| (-1166 *3))))) + (-5 *1 (-585 *3)) (-4 *3 (-363))))) (((*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 *2 *1) (-12 (-4 *1 (-254 *2)) (-4 *2 (-1209))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-1172 (-407 (-564)))) (-5 *1 (-190))))) -(((*1 *1 *1) (-12 (-4 *1 (-166 *2)) (-4 *2 (-172)))) - ((*1 *1 *1 *1) (-4 *1 (-473))) - ((*1 *1 *1) (-12 (-4 *1 (-793 *2)) (-4 *2 (-172)))) - ((*1 *2 *2) (-12 (-5 *2 (-641 (-564))) (-5 *1 (-879)))) - ((*1 *1 *1) (-5 *1 (-967))) - ((*1 *1 *1) (-12 (-4 *1 (-993 *2)) (-4 *2 (-172))))) -(((*1 *2 *2) (-12 (-5 *2 (-564)) (-5 *1 (-553))))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-1152)) (-5 *2 (-312)) (-5 *1 (-825))))) -(((*1 *2 *3 *4 *4 *3) - (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *2 (-1031)) - (-5 *1 (-748))))) -(((*1 *2 *2) - (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) - (-4 *2 (-13 (-430 *3) (-998)))))) -(((*1 *2 *1) - (-12 (-4 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(-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-645 *3 *4 *5)) (-4 *3 (-1094)) - (-4 *4 (-23)) (-14 *5 *4)))) +(((*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 (-1170)) (-4 *5 (-147)) + (-4 *5 (-13 (-452) (-1034 (-564)) (-637 (-564)))) (-5 *2 (-316 *5)) + (-5 *1 (-588 *5))))) +(((*1 *2 *2) + (-12 (-5 *2 (-641 *6)) (-4 *6 (-1059 *3 *4 *5)) (-4 *3 (-147)) + (-4 *3 (-307)) (-4 *3 (-556)) (-4 *4 (-789)) (-4 *5 (-846)) + (-5 *1 (-973 *3 *4 *5 *6))))) +(((*1 *2 *1 *3) + (-12 (-4 *1 (-554 *3)) (-4 *3 (-13 (-404) (-1194))) (-5 *2 (-112))))) +(((*1 *2 *1) + (|partial| -12 (-4 *1 (-166 *3)) (-4 *3 (-172)) (-4 *3 (-545)) + (-5 *2 (-407 (-564))))) + ((*1 *2 *1) + (|partial| -12 (-5 *2 (-407 (-564))) (-5 *1 (-418 *3)) (-4 *3 (-545)) + (-4 *3 (-556)))) + ((*1 *2 *1) (|partial| -12 (-4 *1 (-545)) (-5 *2 (-407 (-564))))) + ((*1 *2 *1) + (|partial| -12 (-4 *1 (-793 *3)) (-4 *3 (-172)) (-4 *3 (-545)) + (-5 *2 (-407 (-564))))) + ((*1 *2 *1) + (|partial| -12 (-5 *2 (-407 (-564))) (-5 *1 (-829 *3)) (-4 *3 (-545)) + (-4 *3 (-1094)))) + ((*1 *2 *1) + (|partial| -12 (-5 *2 (-407 (-564))) (-5 *1 (-839 *3)) (-4 *3 (-545)) + (-4 *3 (-1094)))) + ((*1 *2 *1) + (|partial| -12 (-4 *1 (-993 *3)) (-4 *3 (-172)) (-4 *3 (-545)) + (-5 *2 (-407 (-564))))) + ((*1 *2 *3) + (|partial| -12 (-5 *2 (-407 (-564))) (-5 *1 (-1004 *3)) + (-4 *3 (-1034 *2))))) (((*1 *2 *1) (-12 (-4 *1 (-326 *3 *4)) (-4 *3 (-1045)) (-4 *4 (-788)) (-5 *2 (-112)))) ((*1 *2 *1) (-12 (-4 *1 (-430 *3)) (-4 *3 (-1094)) (-5 *2 (-112))))) (((*1 *2 *1 *3 *4) (-12 (-5 *3 (-468)) (-5 *4 (-917)) (-5 *2 (-1264)) (-5 *1 (-1260))))) -(((*1 *2 *1) - (-12 (-5 *2 (-641 (-2 (|:| |gen| *3) (|:| -1755 (-564))))) - (-5 *1 (-361 *3)) (-4 *3 (-1094)))) - ((*1 *2 *1) - (-12 (-5 *2 (-641 (-2 (|:| |gen| *3) (|:| -1755 (-767))))) - (-5 *1 (-386 *3)) (-4 *3 (-1094)))) - ((*1 *2 *1) - (-12 (-5 *2 (-641 (-2 (|:| -3616 *3) (|:| -1384 (-564))))) - (-5 *1 (-418 *3)) (-4 *3 (-556)))) - ((*1 *2 *1) - (-12 (-5 *2 (-641 (-2 (|:| |gen| *3) (|:| -1755 (-767))))) - (-5 *1 (-815 *3)) (-4 *3 (-846))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1202 *2 *3 *4 *5)) (-4 *2 (-556)) (-4 *3 (-789)) - (-4 *4 (-846)) (-4 *5 (-1059 *2 *3 *4))))) -(((*1 *2 *3 *3 *4 *4 *4 *4 *3) - (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *2 (-1031)) - (-5 *1 (-748))))) -(((*1 *2) (-12 (-5 *2 (-564)) (-5 *1 (-467)))) - ((*1 *2 *2) (-12 (-5 *2 (-564)) (-5 *1 (-467)))) - ((*1 *2) (-12 (-5 *2 (-564)) (-5 *1 (-923))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *5 (-112)) (-4 *4 (-13 (-363) (-844))) (-5 *2 (-418 *3)) + (-5 *1 (-181 *4 *3)) (-4 *3 (-1235 (-169 *4))))) + ((*1 *2 *3 *4) + (-12 (-4 *4 (-13 (-363) (-844))) (-5 *2 (-418 *3)) + (-5 *1 (-181 *4 *3)) (-4 *3 (-1235 (-169 *4)))))) +(((*1 *2 *1 *2) (-12 (-5 *2 (-641 (-1152))) (-5 *1 (-1189))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-767)) (-4 *1 (-1235 *4)) (-4 *4 (-1045)) + (-5 *2 (-1259 *4))))) +(((*1 *2 *3) (-12 (-5 *3 (-939 *2)) (-5 *1 (-978 *2)) (-4 *2 (-1045))))) (((*1 *2 *3) - (-12 (-5 *3 (-1259 *5)) (-4 *5 (-637 *4)) (-4 *4 (-556)) - (-5 *2 (-112)) (-5 *1 (-636 *4 *5))))) -(((*1 *1 *1 *1) (-12 (-5 *1 (-778 *2)) (-4 *2 (-1045))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1170)) - (-4 *5 (-13 (-556) (-1034 (-564)) (-637 (-564)))) - (-5 *2 - (-2 (|:| |func| *3) (|:| |kers| (-641 (-610 *3))) - (|:| |vals| (-641 *3)))) - (-5 *1 (-277 *5 *3)) (-4 *3 (-13 (-27) (-1194) (-430 *5)))))) + (-12 (-5 *3 (-1259 (-641 (-2 (|:| -2128 *4) (|:| -2083 (-1114)))))) + (-4 *4 (-349)) (-5 *2 (-685 *4)) (-5 *1 (-346 *4))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) @@ -3595,9 +2729,6 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-816)) (-14 *5 (-1170)) (-5 *2 (-641 (-1232 *5 *4))) - (-5 *1 (-1108 *4 *5)) (-5 *3 (-1232 *5 *4))))) (((*1 *1 *1) (-4 *1 (-243))) ((*1 *1 *1) (-12 (-4 *2 (-172)) (-5 *1 (-289 *2 *3 *4 *5 *6 *7)) @@ -3605,7 +2736,7 @@ (-14 *6 (-1 (-3 *4 "failed") *4 *4)) (-14 *7 (-1 (-3 *3 "failed") *3 *3 *4)))) ((*1 *1 *1) - (-2822 (-12 (-5 *1 (-294 *2)) (-4 *2 (-363)) (-4 *2 (-1209))) + (-2807 (-12 (-5 *1 (-294 *2)) (-4 *2 (-363)) (-4 *2 (-1209))) (-12 (-5 *1 (-294 *2)) (-4 *2 (-473)) (-4 *2 (-1209))))) ((*1 *1 *1) (-4 *1 (-473))) ((*1 *2 *2) (-12 (-5 *2 (-1259 *3)) (-4 *3 (-349)) (-5 *1 (-528 *3)))) @@ -3614,16 +2745,77 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *1) (-12 (-4 *1 (-793 *2)) (-4 *2 (-172)) (-4 *2 (-363))))) -(((*1 *2 *3 *3 *4 *4 *3 *4 *4 *3 *3 *3) - (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *2 (-1031)) - (-5 *1 (-748))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-641 (-948 *6))) (-5 *4 (-641 (-1170))) + (-4 *6 (-13 (-556) (-1034 *5))) (-4 *5 (-556)) + (-5 *2 (-641 (-641 (-294 (-407 (-948 *6)))))) (-5 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(-1094)))) @@ -3631,9 +2823,6 @@ ((*1 *1 *1) (-12 (-5 *1 (-1134 *2 *3)) (-4 *2 (-13 (-1094) (-34))) (-4 *3 (-13 (-1094) (-34)))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1059 *2 *3 *4)) (-4 *2 (-1045)) (-4 *3 (-789)) - (-4 *4 (-846)) (-4 *2 (-452))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) @@ -3650,23 +2839,6 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-641 (-948 *4))) (-5 *3 (-641 (-1170))) (-4 *4 (-452)) - (-5 *1 (-914 *4))))) -(((*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 *2 *3 *4 *5) - (-12 (-5 *5 (-112)) (-4 *4 (-13 (-363) (-844))) (-5 *2 (-418 *3)) - (-5 *1 (-181 *4 *3)) (-4 *3 (-1235 (-169 *4))))) - ((*1 *2 *3 *4) - (-12 (-4 *4 (-13 (-363) (-844))) (-5 *2 (-418 *3)) - (-5 *1 (-181 *4 *3)) (-4 *3 (-1235 (-169 *4)))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-641 (-948 *6))) (-5 *4 (-641 (-1170))) - (-4 *6 (-13 (-556) (-1034 *5))) (-4 *5 (-556)) - (-5 *2 (-641 (-641 (-294 (-407 (-948 *6)))))) (-5 *1 (-1035 *5 *6))))) (((*1 *2 *3 *3 *4 *5) (-12 (-5 *3 (-641 (-685 *6))) (-5 *4 (-112)) (-5 *5 (-564)) (-5 *2 (-685 *6)) (-5 *1 (-1025 *6)) (-4 *6 (-363)) (-4 *6 (-1045)))) @@ -3676,18 +2848,32 @@ ((*1 *2 *3 *3 *4) (-12 (-5 *3 (-641 (-685 *5))) (-5 *4 (-564)) (-5 *2 (-685 *5)) (-5 *1 (-1025 *5)) (-4 *5 (-363)) (-4 *5 (-1045))))) -(((*1 *1 *1 *1) (-5 *1 (-112))) ((*1 *1 *1 *1) (-4 *1 (-123)))) -(((*1 *2 *3 *4 *5 *5 *6) - (-12 (-5 *5 (-610 *4)) (-5 *6 (-1170)) - (-4 *4 (-13 (-430 *7) (-27) (-1194))) - (-4 *7 (-13 (-452) (-1034 (-564)) (-147) (-637 (-564)))) - (-5 *2 - (-2 (|:| |particular| (-3 *4 "failed")) (|:| -3423 (-641 *4)))) - (-5 *1 (-566 *7 *4 *3)) (-4 *3 (-652 *4)) (-4 *3 (-1094))))) -(((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-407 (-948 *4))) (-5 *3 (-1170)) - (-4 *4 (-13 (-556) (-1034 (-564)) 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*5 (-789))))) +(((*1 *2) + (-12 (-4 *4 (-363)) (-5 *2 (-767)) (-5 *1 (-328 *3 *4)) + (-4 *3 (-329 *4)))) + ((*1 *2) (-12 (-4 *1 (-1278 *3)) (-4 *3 (-363)) (-5 *2 (-767))))) (((*1 *2 *3) (-12 (-5 *3 (-1170)) (-4 *4 (-13 (-452) (-1034 (-564)) (-637 (-564)))) (-5 *2 (-52)) @@ -3738,30 +2924,66 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *2 *3 *3 *4) - (-12 (-5 *3 (-225)) (-5 *4 (-564)) (-5 *2 (-1031)) (-5 *1 (-754))))) -(((*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 *3 *4 *4 *4 *4 *5 *5 *4) + (-12 (-5 *3 (-1152)) (-5 *4 (-564)) (-5 *5 (-685 (-169 (-225)))) + (-5 *2 (-1031)) (-5 *1 (-750))))) +(((*1 *2 *3 *1) + (-12 (-4 *4 (-363)) (-4 *5 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*4)))) + ((*1 *2 *1) + (|partial| -12 (-4 *3 (-1106)) (-4 *3 (-1094)) + (-5 *2 (-2 (|:| |var| (-610 *1)) (|:| -1410 (-564)))) + (-4 *1 (-430 *3)))) + ((*1 *2 *1) + (|partial| -12 (-5 *2 (-2 (|:| |val| (-888 *3)) (|:| -1410 (-767)))) + (-5 *1 (-888 *3)) (-4 *3 (-1094)))) + ((*1 *2 *1) + (|partial| -12 (-4 *1 (-945 *3 *4 *5)) (-4 *3 (-1045)) (-4 *4 (-789)) + (-4 *5 (-846)) (-5 *2 (-2 (|:| |var| *5) (|:| -1410 (-767)))))) + ((*1 *2 *3) + (|partial| -12 (-4 *4 (-789)) (-4 *5 (-846)) (-4 *6 (-1045)) + (-4 *7 (-945 *6 *4 *5)) + (-5 *2 (-2 (|:| |var| *5) (|:| -1410 (-564)))) + (-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 *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)))) @@ -3797,10 +3019,6 @@ (-12 (-5 *3 "first") (|has| *1 (-6 -4408)) (-4 *1 (-1247 *2)) (-4 *2 (-1209))))) (((*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 *3) (-12 (-5 *3 (-1170)) (-4 *4 (-13 (-452) (-1034 (-564)) (-637 (-564)))) (-5 *2 (-52)) (-5 *1 (-315 *4 *5)) (-4 *5 (-13 (-27) (-1194) (-430 *4))))) @@ -3850,43 +3068,53 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *2 *3 *3 *3 *4 *3) - (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *2 (-1031)) - (-5 *1 (-750))))) -(((*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 *1) (-12 (-5 *2 (-112)) (-5 *1 (-280))))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-1152)) (-5 *2 (-112)) (-5 *1 (-825))))) -(((*1 *2 *3 *4 *4 *4 *3 *3 *5 *5 *3) - (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *5 (-225)) - (-5 *2 (-1031)) (-5 *1 (-747))))) -(((*1 *1 *1) (-5 *1 (-225))) ((*1 *1 *1) (-5 *1 (-379))) - ((*1 *1) (-5 *1 (-379)))) -(((*1 *2) - (|partial| -12 (-4 *4 (-1213)) (-4 *5 (-1235 (-407 *2))) - (-4 *2 (-1235 *4)) (-5 *1 (-341 *3 *4 *2 *5)) - (-4 *3 (-342 *4 *2 *5)))) - ((*1 *2) - (|partial| -12 (-4 *1 (-342 *3 *2 *4)) (-4 *3 (-1213)) - (-4 *4 (-1235 (-407 *2))) (-4 *2 (-1235 *3))))) -(((*1 *2 *3 *3 *3 *3 *4 *4 *4 *4 *4 *3 *3 *3) - (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *2 (-1031)) - (-5 *1 (-748))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-112)) (-4 *5 (-13 (-452) (-1034 (-564)) (-637 (-564)))) +(((*1 *2 *1) + (-12 (-5 *2 (-641 (-1195 *3))) (-5 *1 (-1195 *3)) (-4 *3 (-1094))))) +(((*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| *3) (|:| -3577 *4)))) + (-5 *1 (-1102 *5 *6 *7 *3 *4)) (-4 *4 (-1065 *5 *6 *7 *3))))) +(((*1 *2 *3 *1) + (-12 (|has| *1 (-6 -4407)) (-4 *1 (-489 *3)) (-4 *3 (-1209)) + (-4 *3 (-1094)) (-5 *2 (-112)))) + ((*1 *2 *3 *1) + (-12 (-5 *3 (-901 *4)) (-4 *4 (-1094)) (-5 *2 (-112)) + (-5 *1 (-900 *4)))) + ((*1 *2 *3 *1) + (-12 (-5 *3 (-917)) (-5 *2 (-112)) (-5 *1 (-1095 *4 *5)) (-14 *4 *3) + (-14 *5 *3)))) +(((*1 *2 *3 *3 *4 *4 *4 *4 *3 *3 *3 *3 *5 *3 *6) + (-12 (-5 *3 (-564)) (-5 *5 (-685 (-225))) + (-5 *6 (-3 (|:| |fn| (-388)) (|:| |fp| (-70 APROD)))) (-5 *4 (-225)) + (-5 *2 (-1031)) (-5 *1 (-752))))) +(((*1 *2 *3 *4 *5 *5 *6) + (-12 (-5 *5 (-610 *4)) (-5 *6 (-1170)) + (-4 *4 (-13 (-430 *7) (-27) (-1194))) + (-4 *7 (-13 (-452) (-1034 (-564)) (-147) (-637 (-564)))) (-5 *2 - (-3 (|:| |%expansion| (-313 *5 *3 *6 *7)) - (|:| |%problem| (-2 (|:| |func| (-1152)) (|:| |prob| (-1152)))))) - (-5 *1 (-420 *5 *3 *6 *7)) (-4 *3 (-13 (-27) (-1194) (-430 *5))) - (-14 *6 (-1170)) (-14 *7 *3)))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-767)) (-4 *1 (-1276 *3 *4)) (-4 *3 (-846)) - (-4 *4 (-1045)) (-4 *4 (-172)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-1276 *2 *3)) (-4 *2 (-846)) (-4 *3 (-1045)) - (-4 *3 (-172))))) + (-2 (|:| |particular| (-3 *4 "failed")) (|:| -1298 (-641 *4)))) + (-5 *1 (-566 *7 *4 *3)) (-4 *3 (-652 *4)) (-4 *3 (-1094))))) +(((*1 *1 *1 *1) + (-12 (|has| *1 (-6 -4408)) (-4 *1 (-244 *2)) (-4 *2 (-1209))))) +(((*1 *2 *1) + (-12 (-4 *1 (-554 *3)) (-4 *3 (-13 (-404) (-1194))) (-5 *2 (-112)))) + ((*1 *2 *1) (-12 (-4 *1 (-844)) (-5 *2 (-112)))) + ((*1 *2 *3 *1) + (-12 (-4 *1 (-1062 *4 *3)) (-4 *4 (-13 (-844) (-363))) + (-4 *3 (-1235 *4)) (-5 *2 (-112))))) +(((*1 *2 *3) + (-12 (-5 *3 (-225)) (-5 *2 (-112)) (-5 *1 (-299 *4 *5)) (-14 *4 *3) + (-14 *5 *3))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-1088 (-839 (-225)))) (-5 *3 (-225)) (-5 *2 (-112)) + (-5 *1 (-305)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-363)) (-4 *4 (-789)) (-4 *5 (-846)) (-5 *2 (-112)) + (-5 *1 (-504 *3 *4 *5 *6)) (-4 *6 (-945 *3 *4 *5))))) +(((*1 *2 *3 *3) + (-12 (-5 *2 (-1150 (-641 (-564)))) (-5 *1 (-879)) + (-5 *3 (-641 (-564)))))) (((*1 *2 *3) (-12 (-5 *3 (-1170)) (-4 *4 (-13 (-452) (-1034 (-564)) (-637 (-564)))) (-5 *2 (-52)) @@ -3945,7 +3173,16 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *1 *2) (-12 (-5 *2 (-641 (-330))) (-5 *1 (-330))))) +(((*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 *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 *4) (-12 (-5 *3 (-641 *8)) (-5 *4 (-136 *5 *6 *7)) (-14 *5 (-564)) (-14 *6 (-767)) (-4 *7 (-172)) (-4 *8 (-172)) @@ -3955,64 +3192,25 @@ (-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 *1 *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 *1 *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 *1) - (-12 (-4 *1 (-342 *3 *4 *5)) (-4 *3 (-1213)) (-4 *4 (-1235 *3)) - (-4 *5 (-1235 (-407 *4))) (-5 *2 (-112))))) -(((*1 *1 *1) (-12 (-5 *1 (-1195 *2)) (-4 *2 (-1094))))) -(((*1 *2 *3 *4 *5 *6) - (-12 (-5 *5 (-767)) (-5 *6 (-112)) (-4 *7 (-452)) (-4 *8 (-789)) - (-4 *9 (-846)) (-4 *3 (-1059 *7 *8 *9)) - (-5 *2 - (-2 (|:| |done| (-641 *4)) - (|:| |todo| (-641 (-2 (|:| |val| (-641 *3)) (|:| -3505 *4)))))) - (-5 *1 (-1063 *7 *8 *9 *3 *4)) (-4 *4 (-1065 *7 *8 *9 *3)))) - ((*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)) (|:| -3505 *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 *7)) - (-5 *2 - (-2 (|:| |done| (-641 *4)) - (|:| |todo| (-641 (-2 (|:| |val| (-641 *3)) (|:| -3505 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((*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))))) (((*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-998))))) @@ -4207,55 +3367,42 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *2 *3 *4 *4 *4 *3) - (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *2 (-1031)) - (-5 *1 (-747))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-112) (-114) (-114))) (-5 *1 (-114))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-363)) (-4 *5 (-556)) +(((*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 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(-1209)))) - ((*1 *2 *3 *1) - (|partial| -12 (-4 *1 (-608 *3 *2)) (-4 *3 (-1094)) (-4 *2 (-1094)))) - ((*1 *1 *2 *1 *3) - (-12 (-5 *2 (-1 (-112) *4)) (-5 *3 (-564)) (-4 *4 (-1094)) - (-5 *1 (-733 *4)))) - ((*1 *1 *2 *1 *3) - (-12 (-5 *3 (-564)) (-5 *1 (-733 *2)) (-4 *2 (-1094)))) - ((*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 *2 *3) - (-12 (-4 *3 (-307)) (-5 *1 (-455 *3 *2)) (-4 *2 (-1235 *3)))) - ((*1 *2 *2 *3) - (-12 (-4 *3 (-307)) (-5 *1 (-460 *3 *2)) (-4 *2 (-1235 *3)))) - ((*1 *2 *2 *3) - (-12 (-4 *3 (-307)) (-14 *4 *3) (-14 *5 (-1 *3 *3 (-767))) - (-5 *1 (-539 *3 *2 *4 *5)) (-4 *2 (-1235 *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)))) +(((*1 *2 *3) + (-12 (-5 *3 (-316 (-225))) (-5 *2 (-316 (-379))) (-5 *1 (-305))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) @@ -4272,14 +3419,6 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *1 *1 *1) (-5 *1 (-858)))) -(((*1 *2 *1 *1) - (-12 (-4 *3 (-556)) (-4 *3 (-1045)) - (-5 *2 (-2 (|:| -2715 *1) (|:| -4198 *1))) (-4 *1 (-848 *3)))) - ((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-99 *5)) (-4 *5 (-556)) (-4 *5 (-1045)) - (-5 *2 (-2 (|:| -2715 *3) (|:| -4198 *3))) (-5 *1 (-849 *5 *3)) - (-4 *3 (-848 *5))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-917)) (-4 *1 (-329 *3)) (-4 *3 (-363)) (-4 *3 (-368)))) ((*1 *2 *1) (-12 (-4 *1 (-329 *2)) (-4 *2 (-363)))) @@ -4291,27 +3430,36 @@ ((*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 *2 *1 *3 *4) - (-12 (-5 *3 (-917)) (-5 *4 (-870)) (-5 *2 (-1264)) (-5 *1 (-1260)))) - ((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-917)) (-5 *4 (-1152)) (-5 *2 (-1264)) (-5 *1 (-1260)))) - ((*1 *2 *1 *3) (-12 (-5 *3 (-1152)) (-5 *2 (-1264)) (-5 *1 (-1261))))) +(((*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) + (-12 (-4 *4 (-556)) + (-5 *2 (-2 (|:| |coef2| *3) (|:| |subResultant| *3))) + (-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 *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 (-641 (-685 *5))) (-4 *5 (-307)) (-4 *5 (-1045)) - (-5 *2 (-1259 (-1259 *5))) (-5 *1 (-1025 *5)) (-5 *4 (-1259 *5))))) -(((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-641 (-1166 *4))) (-5 *3 (-1166 *4)) - (-4 *4 (-905)) (-5 *1 (-659 *4))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-767)) (-4 *1 (-652 *3)) (-4 *3 (-1045)) (-4 *3 (-363)))) - ((*1 *2 *2 *3 *4) - (-12 (-5 *3 (-767)) (-5 *4 (-1 *5 *5)) (-4 *5 (-363)) - (-5 *1 (-655 *5 *2)) (-4 *2 (-652 *5))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-1259 *4)) (-5 *3 (-767)) (-4 *4 (-349)) - (-5 *1 (-528 *4))))) -(((*1 *2 *3) - (-12 (-5 *2 (-1172 (-407 (-564)))) (-5 *1 (-190)) (-5 *3 (-564))))) + (-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))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) @@ -4331,7 +3479,7 @@ (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -3374 (-641 (-225))))) + (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -3430 (-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)) @@ -4353,7 +3501,7 @@ (-5 *1 (-946 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-363) - (-10 -8 (-15 -2488 ($ *7)) (-15 -2388 (*7 $)) (-15 -2402 (*7 $))))))) + (-10 -8 (-15 -2423 ($ *7)) (-15 -2324 (*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)))) @@ -4363,51 +3511,65 @@ ((*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 (-1096 (-1096 *3))) (-5 *1 (-900 *3)) (-4 *3 (-1094))))) -(((*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 *1) - (-12 (-5 *2 (-174 (-407 (-564)))) (-5 *1 (-117 *3)) (-14 *3 (-564)))) - ((*1 *1 *2 *3 *3) - (-12 (-5 *3 (-1150 *2)) (-4 *2 (-307)) (-5 *1 (-174 *2)))) - ((*1 *1 *2) (-12 (-5 *2 (-407 *3)) (-4 *3 (-307)) (-5 *1 (-174 *3)))) - ((*1 *2 *3) - (-12 (-5 *2 (-174 (-564))) (-5 *1 (-761 *3)) (-4 *3 (-404)))) - ((*1 *2 *1) - (-12 (-5 *2 (-174 (-407 (-564)))) (-5 *1 (-867 *3)) (-14 *3 (-564)))) - ((*1 *2 *1) - (-12 (-14 *3 (-564)) (-5 *2 (-174 (-407 (-564)))) - (-5 *1 (-868 *3 *4)) (-4 *4 (-865 *3))))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-767)) (-4 *3 (-1045)) (-4 *1 (-683 *3 *4 *5)) - (-4 *4 (-373 *3)) (-4 *5 (-373 *3)))) - ((*1 *1 *2) - (-12 (-4 *2 (-1045)) (-4 *1 (-1117 *3 *2 *4 *5)) (-4 *4 (-238 *3 *2)) - (-4 *5 (-238 *3 *2))))) + (-12 (-5 *2 (-3 (|:| |fst| (-434)) (|:| -1836 "void"))) + (-5 *1 (-437))))) (((*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 *1 *2) (-12 (-5 *1 (-227 *2)) (-4 *2 (-13 (-363) (-1194)))))) +(((*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 *3) - (-12 (-5 *2 (-1172 (-407 (-564)))) (-5 *1 (-190)) (-5 *3 (-564))))) -(((*1 *2 *1) (-12 (-5 *2 (-858)) (-5 *1 (-52))))) -(((*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) (|:| -3505 *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)) (|:| -3505 *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) (|:| -3505 *9)))) - (-5 *1 (-1102 *6 *7 *4 *8 *9))))) -(((*1 *1 *2 *3) (-12 (-5 *2 (-767)) (-5 *1 (-59 *3)) (-4 *3 (-1209)))) - ((*1 *1 *2) (-12 (-5 *2 (-641 *3)) (-4 *3 (-1209)) (-5 *1 (-59 *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))))))))) + ((*1 *2) + (-12 (-5 *2 (-767)) (-5 *1 (-353 *3 *4)) (-4 *3 (-349)) + (-14 *4 (-917))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) @@ -4424,18 +3586,6 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *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 *2 *3 *4 *2) (-12 (-5 *3 (-1166 (-407 (-1166 *2)))) (-5 *4 (-610 *2)) (-4 *2 (-13 (-430 *5) (-27) (-1194))) @@ -4452,37 +3602,61 @@ (-4 *6 (-1045)) (-4 *2 (-13 (-363) - (-10 -8 (-15 -2488 ($ *7)) (-15 -2388 (*7 $)) (-15 -2402 (*7 $))))) + (-10 -8 (-15 -2423 ($ *7)) (-15 -2324 (*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 *2 *2 *2) - (-12 (-5 *2 (-685 *3)) - (-4 *3 (-13 (-307) (-10 -8 (-15 -4154 ((-418 $) $))))) - (-4 *4 (-1235 *3)) (-5 *1 (-499 *3 *4 *5)) (-4 *5 (-409 *3 *4))))) -(((*1 *2 *1 *3 *4 *4 *4 *4 *5 *5 *5 *5 *6 *5 *6 *5) - (-12 (-5 *3 (-917)) (-5 *4 (-225)) (-5 *5 (-564)) (-5 *6 (-870)) - (-5 *2 (-1264)) (-5 *1 (-1260))))) -(((*1 *1 *1) (-4 *1 (-627))) - ((*1 *2 *2) - (-12 (-4 *3 (-556)) (-5 *1 (-628 *3 *2)) - (-4 *2 (-13 (-430 *3) (-998) (-1194)))))) -(((*1 *1 *1 *1) (-4 *1 (-143))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-556)) (-5 *1 (-158 *3 *2)) (-4 *2 (-430 *3)))) - ((*1 *2 *2 *2) (-12 (-5 *1 (-159 *2)) (-4 *2 (-545))))) +(((*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 (-112)) (-5 *1 (-1195 *3)) (-4 *3 (-1094))))) -(((*1 *1) (-5 *1 (-186)))) -(((*1 *1 *1 *1) (-4 *1 (-963)))) + (-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 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) - (|:| -1510 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) + (|:| -3090 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *2 (-2 @@ -4500,7 +3674,7 @@ (-3 (|:| |str| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -1510 + (|:| -3090 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -4508,13 +3682,7 @@ "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-559))))) -(((*1 *2) (-12 (-5 *2 (-1264)) (-5 *1 (-799))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5) - (-12 (-5 *3 (-1 (-379) (-379))) (-5 *4 (-379)) - (-5 *2 - (-2 (|:| -2195 *4) (|:| -1456 *4) (|:| |totalpts| (-564)) - (|:| |success| (-112)))) - (-5 *1 (-785)) (-5 *5 (-564))))) +(((*1 *1) (-5 *1 (-186)))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *1 *1 *1) (-5 *1 (-225))) ((*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) @@ -4535,9 +3703,6 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *1 *2) - (-12 (-5 *2 (-1136 *3 *4)) (-14 *3 (-917)) (-4 *4 (-363)) - (-5 *1 (-989 *3 *4))))) (((*1 *1 *2 *3) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1045)) (-4 *3 (-788)))) ((*1 *1 *2 *3) @@ -4545,10 +3710,10 @@ (-4 *2 (-363)) (-14 *5 (-989 *4 *2)))) ((*1 *1 *2 *3) (-12 (-5 *3 (-709 *5 *6 *7)) (-4 *5 (-846)) - (-4 *6 (-238 (-2245 *4) (-767))) + (-4 *6 (-238 (-2181 *4) (-767))) (-14 *7 - (-1 (-112) (-2 (|:| -2151 *5) (|:| -1384 *6)) - (-2 (|:| -2151 *5) (|:| -1384 *6)))) + (-1 (-112) (-2 (|:| -2083 *5) (|:| -1410 *6)) + (-2 (|:| -2083 *5) (|:| -1410 *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) @@ -4578,26 +3743,76 @@ ((*1 *1 *1 *2 *3) (-12 (-4 *1 (-969 *4 *3 *2)) (-4 *4 (-1045)) (-4 *3 (-788)) (-4 *2 (-846))))) +(((*1 *2 *3 *4 *3) + (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *2 (-1031)) + (-5 *1 (-743))))) (((*1 *2 *2) - (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) - (-4 *2 (-13 (-430 *3) (-998)))))) -(((*1 *2 *1) (-12 (-4 *1 (-1128 *3)) (-4 *3 (-1045)) (-5 *2 (-112))))) -(((*1 *1 *2) - (|partial| -12 (-5 *2 (-1274 *3 *4)) (-4 *3 (-846)) (-4 *4 (-172)) - (-5 *1 (-660 *3 *4)))) + (|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)))) ((*1 *2 *1) - (|partial| -12 (-5 *2 (-660 *3 *4)) (-5 *1 (-1279 *3 *4)) - (-4 *3 (-846)) (-4 *4 (-172))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-1170)) (-4 *4 (-452)) (-4 *4 (-1094)) - (-5 *1 (-573 *4 *2)) (-4 *2 (-284)) (-4 *2 (-430 *4))))) + (-12 (-4 *3 (-556)) (-5 *2 (-564)) (-5 *1 (-621 *3 *4)) + (-4 *4 (-1235 *3)))) + ((*1 *2 *1 *3 *2) + (-12 (-5 *2 (-767)) (-4 *1 (-736 *4 *3)) (-4 *4 (-1045)) + (-4 *3 (-846)))) + ((*1 *2 *1 *3) + (-12 (-4 *1 (-736 *4 *3)) (-4 *4 (-1045)) (-4 *3 (-846)) + (-5 *2 (-767)))) + ((*1 *2 *1) (-12 (-4 *1 (-865 *3)) (-5 *2 (-767)))) + ((*1 *2 *1) (-12 (-5 *2 (-767)) (-5 *1 (-900 *3)) (-4 *3 (-1094)))) + ((*1 *2 *1) (-12 (-5 *2 (-767)) (-5 *1 (-901 *3)) (-4 *3 (-1094)))) + ((*1 *2 *3) + (|partial| -12 (-5 *3 (-336 *5 *6 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(-917)) + (-4 *4 (-1045))))) (((*1 *1) (-5 *1 (-186)))) -(((*1 *2 *2) (-12 (-5 *2 (-379)) (-5 *1 (-97))))) -(((*1 *2 *3 *1) - (-12 (-5 *3 (-901 *4)) (-4 *4 (-1094)) (-5 *2 (-641 (-767))) - (-5 *1 (-900 *4))))) -(((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-467)))) - ((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-467))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) @@ -4617,43 +3832,47 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *2 *3 *4 *5 *4) - (-12 (-5 *3 (-685 (-225))) (-5 *4 (-564)) (-5 *5 (-112)) - (-5 *2 (-1031)) (-5 *1 (-741))))) +(((*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 *1 *2 *2) (-12 (-5 *1 (-294 *2)) (-4 *2 (-1209)))) ((*1 *1 *2 *3) (-12 (-5 *2 (-1170)) (-5 *3 (-1152)) (-5 *1 (-985)))) ((*1 *1 *2 *3) (-12 (-5 *2 (-1170)) (-5 *3 (-1088 *4)) (-4 *4 (-1209)) (-5 *1 (-1086 *4))))) +(((*1 *1 *1 *1 *1) (-5 *1 (-858))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-641 (-858))) (-5 *1 (-858))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-820))))) +(((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-767)) (-4 *5 (-556)) + (-5 *2 (-2 (|:| |coef2| *3) (|:| |subResultant| *3))) + (-5 *1 (-965 *5 *3)) (-4 *3 (-1235 *5))))) (((*1 *2 *3) - (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1094)) (-4 *5 (-1094)) - (-4 *6 (-1094)) (-5 *2 (-1 *6 *5 *4)) (-5 *1 (-680 *4 *5 *6))))) -(((*1 *2 *1) - (-12 (-4 *1 (-691 *3)) (-4 *3 (-1094)) - (-5 *2 (-641 (-2 (|:| -3740 *3) (|:| -3969 (-767)))))))) -(((*1 *2 *1) - (-12 (-5 *2 (-1166 (-407 (-948 *3)))) (-5 *1 (-453 *3 *4 *5 *6)) - (-4 *3 (-556)) (-4 *3 (-172)) (-14 *4 (-917)) - (-14 *5 (-641 (-1170))) (-14 *6 (-1259 (-685 *3)))))) + (-12 (-5 *3 (-641 *2)) (-4 *2 (-430 *4)) (-5 *1 (-158 *4 *2)) + (-4 *4 (-556))))) +(((*1 *2 *1 *1) + (-12 (-4 *1 (-1006 *3)) (-4 *3 (-1209)) (-4 *3 (-1094)) + (-5 *2 (-112))))) (((*1 *2 *3) - (-12 (-5 *3 (-641 (-2 (|:| -3616 *4) (|:| -2851 (-564))))) - (-4 *4 (-1235 (-564))) (-5 *2 (-733 (-767))) (-5 *1 (-442 *4)))) + (-12 (-4 *4 (-13 (-307) (-147))) (-4 *5 (-13 (-846) (-612 (-1170)))) + (-4 *6 (-789)) (-5 *2 (-407 (-948 *4))) (-5 *1 (-920 *4 *5 *6 *3)) + (-4 *3 (-945 *4 *6 *5)))) ((*1 *2 *3) - (-12 (-5 *3 (-418 *5)) (-4 *5 (-1235 *4)) (-4 *4 (-1045)) - (-5 *2 (-733 (-767))) (-5 *1 (-444 *4 *5))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-641 *2)) (-4 *2 (-945 *4 *5 *6)) (-4 *4 (-452)) - (-4 *5 (-789)) (-4 *6 (-846)) (-5 *1 (-449 *4 *5 *6 *2))))) + (-12 (-5 *3 (-685 *7)) (-4 *7 (-945 *4 *6 *5)) + (-4 *4 (-13 (-307) (-147))) (-4 *5 (-13 (-846) (-612 (-1170)))) + (-4 *6 (-789)) (-5 *2 (-685 (-407 (-948 *4)))) + (-5 *1 (-920 *4 *5 *6 *7)))) + ((*1 *2 *3) + (-12 (-5 *3 (-641 *7)) (-4 *7 (-945 *4 *6 *5)) + (-4 *4 (-13 (-307) (-147))) (-4 *5 (-13 (-846) (-612 (-1170)))) + (-4 *6 (-789)) (-5 *2 (-641 (-407 (-948 *4)))) + (-5 *1 (-920 *4 *5 *6 *7))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1 *6 *5 *4)) (-4 *5 (-1094)) (-4 *4 (-1094)) + (-4 *6 (-1094)) (-5 *2 (-1 *6 *5)) (-5 *1 (-680 *5 *4 *6))))) +(((*1 *2 *1) (-12 (-5 *2 (-1264)) (-5 *1 (-818))))) (((*1 *1) (-5 *1 (-186)))) -(((*1 *2 *3 *3 *3 *4 *5) - (-12 (-5 *5 (-641 (-641 (-225)))) (-5 *4 (-225)) - (-5 *2 (-641 (-939 *4))) (-5 *1 (-1205)) (-5 *3 (-939 *4))))) -(((*1 *1) - (-12 (-4 *1 (-404)) (-2416 (|has| *1 (-6 -4398))) - (-2416 (|has| *1 (-6 -4390))))) - ((*1 *2 *1) (-12 (-4 *1 (-425 *2)) (-4 *2 (-1094)) (-4 *2 (-846)))) - ((*1 *2 *1) (-12 (-4 *1 (-826 *2)) (-4 *2 (-846)))) - ((*1 *1) (-4 *1 (-840))) ((*1 *1 *1 *1) (-4 *1 (-846)))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) @@ -4673,42 +3892,31 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *1 *1 *1) (-4 *1 (-545)))) +(((*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 (-4 *4 (-13 (-363) (-147) (-1034 (-407 (-564))))) - (-4 *5 (-1235 *4)) - (-5 *2 (-641 (-2 (|:| |deg| (-767)) (|:| -1654 *5)))) - (-5 *1 (-805 *4 *5 *3 *6)) (-4 *3 (-652 *5)) - (-4 *6 (-652 (-407 *5)))))) -(((*1 *2) - (-12 (-4 *4 (-172)) (-5 *2 (-1166 (-948 *4))) (-5 *1 (-416 *3 *4)) - (-4 *3 (-417 *4)))) - ((*1 *2) - (-12 (-4 *1 (-417 *3)) (-4 *3 (-172)) (-4 *3 (-363)) - (-5 *2 (-1166 (-948 *3))))) - ((*1 *2) - (-12 (-5 *2 (-1166 (-407 (-948 *3)))) (-5 *1 (-453 *3 *4 *5 *6)) - (-4 *3 (-556)) (-4 *3 (-172)) (-14 *4 (-917)) - (-14 *5 (-641 (-1170))) (-14 *6 (-1259 (-685 *3)))))) -(((*1 *2 *1 *1) (-12 (-4 *1 (-34)) (-5 *2 (-112))))) + (-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 *2 *2 *3) - (|partial| -12 - (-5 *3 (-641 (-2 (|:| |func| *2) (|:| |pole| (-112))))) - (-4 *2 (-13 (-430 *4) (-998))) (-4 *4 (-556)) - (-5 *1 (-276 *4 *2))))) -(((*1 *2 *1 *1) - (-12 (-4 *1 (-1006 *3)) (-4 *3 (-1209)) (-4 *3 (-1094)) - (-5 *2 (-112))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-979 *2)) (-4 *2 (-1194))))) + (-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 - (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -3374 (-641 (-225))))) - (-5 *2 (-379)) (-5 *1 (-267)))) + (-12 (-5 *3 (-641 (-225))) (-5 *2 (-641 (-1152))) (-5 *1 (-192)))) ((*1 *2 *3) - (-12 (-5 *3 (-1259 (-316 (-225)))) (-5 *2 (-379)) (-5 *1 (-305))))) -(((*1 *2 *1) (-12 (-5 *1 (-1204 *2)) (-4 *2 (-970))))) -(((*1 *2 *1) (-12 (-5 *2 (-1264)) (-5 *1 (-818))))) + (-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))))) (((*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-998))))) @@ -4725,74 +3933,50 @@ (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3)))) ((*1 *1 *1) (-4 *1 (-1197)))) -(((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-885 *5 *3)) (-5 *4 (-888 *5)) (-4 *5 (-1094)) - (-4 *3 (-166 *6)) (-4 (-948 *6) (-882 *5)) - (-4 *6 (-13 (-882 *5) (-172))) (-5 *1 (-178 *5 *6 *3)))) - ((*1 *2 *1 *3 *2) - (-12 (-5 *2 (-885 *4 *1)) (-5 *3 (-888 *4)) (-4 *1 (-882 *4)) - (-4 *4 (-1094)))) - ((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-885 *5 *6)) (-5 *4 (-888 *5)) (-4 *5 (-1094)) - (-4 *6 (-13 (-1094) (-1034 *3))) (-4 *3 (-882 *5)) - (-5 *1 (-927 *5 *3 *6)))) - ((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-885 *5 *3)) (-4 *5 (-1094)) - (-4 *3 (-13 (-430 *6) (-612 *4) (-882 *5) (-1034 (-610 $)))) - (-5 *4 (-888 *5)) (-4 *6 (-13 (-556) (-882 *5))) - (-5 *1 (-928 *5 *6 *3)))) - ((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-885 (-564) *3)) (-5 *4 (-888 (-564))) (-4 *3 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"prime")) (|:| |fctr| *4) + (|:| |xpnt| (-564)))) + (-4 *4 (-13 (-1235 *3) (-556) (-10 -8 (-15 -2123 ($ $ $))))) + (-4 *3 (-556)) (-5 *1 (-1238 *3 *4))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-294 (-407 (-948 *5)))) (-5 *4 (-1170)) + (-4 *5 (-13 (-307) (-147))) + (-5 *2 (-1159 (-641 (-316 *5)) (-641 (-294 (-316 *5))))) + (-5 *1 (-1123 *5)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-407 (-948 *5))) (-5 *4 (-1170)) + (-4 *5 (-13 (-307) (-147))) + (-5 *2 (-1159 (-641 (-316 *5)) (-641 (-294 (-316 *5))))) + (-5 *1 (-1123 *5))))) +(((*1 *2 *3) (-12 (-5 *3 (-858)) (-5 *2 (-1152)) (-5 *1 (-706))))) (((*1 *2 *3) (-12 (-5 *3 (-52)) (-5 *1 (-51 *2)) (-4 *2 (-1209)))) ((*1 *1 *2) (-12 (-5 *2 (-948 (-379))) (-5 *1 (-339 *3 *4 *5)) @@ -7894,11 +7969,11 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) - (|:| -1510 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) + (|:| -3090 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (|:| |mdnia| (-2 (|:| |fn| (-316 (-225))) - (|:| -1510 (-641 (-1088 (-839 (-225))))) + (|:| -3090 (-641 (-1088 (-839 (-225))))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))))) (-5 *1 (-765)))) ((*1 *2 *1) @@ -7914,13 +7989,13 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-316 (-225))) (|:| -3374 (-641 (-225))) + (-2 (|:| |fn| (-316 (-225))) (|:| -3430 (-641 (-225))) (|:| |lb| (-641 (-839 (-225)))) (|:| |cf| (-641 (-316 (-225)))) (|:| |ub| (-641 (-839 (-225)))))) (|:| |lsa| (-2 (|:| |lfn| (-641 (-316 (-225)))) - (|:| -3374 (-641 (-225))))))) + (|:| -3430 (-641 (-225))))))) (-5 *1 (-837)))) ((*1 *2 *1) (-12 @@ -7939,26 +8014,26 @@ (-4 *4 (-789)) (-4 *5 (-846)) (-4 *1 (-972 *3 *4 *5 *6)))) ((*1 *2 *1) (-12 (-4 *1 (-1034 *2)) (-4 *2 (-1209)))) ((*1 *1 *2) - (-2822 + (-2807 (-12 (-5 *2 (-948 *3)) - (-12 (-2416 (-4 *3 (-38 (-407 (-564))))) - (-2416 (-4 *3 (-38 (-564)))) (-4 *5 (-612 (-1170)))) + (-12 (-2351 (-4 *3 (-38 (-407 (-564))))) + (-2351 (-4 *3 (-38 (-564)))) (-4 *5 (-612 (-1170)))) (-4 *3 (-1045)) (-4 *1 (-1059 *3 *4 *5)) (-4 *4 (-789)) (-4 *5 (-846))) (-12 (-5 *2 (-948 *3)) - (-12 (-2416 (-4 *3 (-545))) (-2416 (-4 *3 (-38 (-407 (-564))))) + (-12 (-2351 (-4 *3 (-545))) (-2351 (-4 *3 (-38 (-407 (-564))))) (-4 *3 (-38 (-564))) (-4 *5 (-612 (-1170)))) (-4 *3 (-1045)) (-4 *1 (-1059 *3 *4 *5)) (-4 *4 (-789)) (-4 *5 (-846))) (-12 (-5 *2 (-948 *3)) - (-12 (-2416 (-4 *3 (-988 (-564)))) (-4 *3 (-38 (-407 (-564)))) + (-12 (-2351 (-4 *3 (-988 (-564)))) (-4 *3 (-38 (-407 (-564)))) (-4 *5 (-612 (-1170)))) (-4 *3 (-1045)) (-4 *1 (-1059 *3 *4 *5)) (-4 *4 (-789)) (-4 *5 (-846))))) ((*1 *1 *2) - (-2822 + (-2807 (-12 (-5 *2 (-948 (-564))) (-4 *1 (-1059 *3 *4 *5)) - (-12 (-2416 (-4 *3 (-38 (-407 (-564))))) (-4 *3 (-38 (-564))) + (-12 (-2351 (-4 *3 (-38 (-407 (-564))))) (-4 *3 (-38 (-564))) (-4 *5 (-612 (-1170)))) (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *5 (-846))) (-12 (-5 *2 (-948 (-564))) (-4 *1 (-1059 *3 *4 *5)) @@ -7968,39 +8043,50 @@ (-12 (-5 *2 (-948 (-407 (-564)))) (-4 *1 (-1059 *3 *4 *5)) (-4 *3 (-38 (-407 (-564)))) (-4 *5 (-612 (-1170))) (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *5 (-846))))) -(((*1 *1 *1 *1) (-5 *1 (-858)))) -(((*1 *2 *3) - (-12 (-4 *4 (-556)) (-4 *5 (-789)) (-4 *6 (-846)) (-5 *2 (-112)) - (-5 *1 (-973 *4 *5 *6 *3)) (-4 *3 (-1059 *4 *5 *6))))) -(((*1 *2 *3) - (-12 (-5 *3 (-641 (-917))) (-5 *2 (-900 (-564))) (-5 *1 (-913))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-641 (-767))) (-5 *1 (-1158 *3 *4)) (-14 *3 (-917)) - (-4 *4 (-1045))))) -(((*1 *2 *3) - (-12 (-5 *2 (-610 *4)) (-5 *1 (-609 *3 *4)) (-4 *3 (-1094)) - (-4 *4 (-1094))))) -(((*1 *2 *3 *3 *3 *4 *3) - (-12 (-5 *3 (-564)) (-5 *4 (-685 (-169 (-225)))) (-5 *2 (-1031)) - (-5 *1 (-750))))) -(((*1 *2 *3) - (-12 (-4 *2 (-363)) (-4 *2 (-844)) (-5 *1 (-941 *2 *3)) - (-4 *3 (-1235 *2))))) +(((*1 *2 *2 *2 *2 *2 *3) + (-12 (-5 *2 (-685 *4)) (-5 *3 (-767)) (-4 *4 (-1045)) + (-5 *1 (-686 *4))))) +(((*1 *2) + (-12 (-4 *4 (-172)) (-5 *2 (-112)) (-5 *1 (-366 *3 *4)) + (-4 *3 (-367 *4)))) + ((*1 *2) (-12 (-4 *1 (-367 *3)) (-4 *3 (-172)) (-5 *2 (-112))))) +(((*1 *2 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(-564))) (|:| -2308 (-316 (-379))) (|:| CF (-316 (-169 (-379)))) (|:| |switch| (-1169)))) (-5 *1 (-1169))))) -(((*1 *1 *1) - (-12 (-5 *1 (-594 *2)) (-4 *2 (-38 (-407 (-564)))) (-4 *2 (-1045))))) +(((*1 *2 *3 *3 *4 *5) + (-12 (-5 *3 (-641 (-948 *6))) (-5 *4 (-641 (-1170))) (-4 *6 (-452)) + (-5 *2 (-641 (-641 *7))) (-5 *1 (-538 *6 *7 *5)) (-4 *7 (-363)) + (-4 *5 (-13 (-363) (-844)))))) (((*1 *1 *1 *2) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1045)) (-4 *3 (-788)) (-4 *2 (-363)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-564)) (-5 *1 (-225)))) ((*1 *1 *1 *1) - (-2822 (-12 (-5 *1 (-294 *2)) (-4 *2 (-363)) (-4 *2 (-1209))) + (-2807 (-12 (-5 *1 (-294 *2)) (-4 *2 (-363)) (-4 *2 (-1209))) (-12 (-5 *1 (-294 *2)) (-4 *2 (-473)) (-4 *2 (-1209))))) ((*1 *1 *1 *1) (-4 *1 (-363))) ((*1 *1 *1 *2) (-12 (-5 *2 (-564)) (-5 *1 (-379)))) @@ -8131,91 +8206,56 @@ ((*1 *1 *1 *2) (-12 (-5 *1 (-1282 *2 *3)) (-4 *2 (-363)) (-4 *2 (-1045)) (-4 *3 (-842))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-641 *6)) (-4 *6 (-1059 *3 *4 *5)) (-4 *3 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"End point continuity not yet evaluated"))) - (|:| |singularitiesStream| - (-3 (|:| |str| (-1150 (-225))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -1510 - (-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))))) + (-2 (|:| |sysok| (-112)) (|:| |z0| (-641 *7)) (|:| |n0| (-641 *7)))) + (-5 *1 (-920 *4 *5 *6 *7)) (-5 *3 (-641 *7))))) +(((*1 *2) + (-12 (-4 *4 (-172)) (-5 *2 (-112)) (-5 *1 (-366 *3 *4)) + (-4 *3 (-367 *4)))) + ((*1 *2) (-12 (-4 *1 (-367 *3)) (-4 *3 (-172)) (-5 *2 (-112))))) +(((*1 *1 *2) (-12 (-5 *2 (-641 (-1088 (-407 (-564))))) (-5 *1 (-263)))) + ((*1 *1 *2) (-12 (-5 *2 (-641 (-1088 (-379)))) (-5 *1 (-263))))) +(((*1 *2 *2 *3 *2) + (-12 (-5 *3 (-767)) (-4 *4 (-349)) (-5 *1 (-216 *4 *2)) + (-4 *2 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(-12 + (-5 *2 (-2 (|:| -2487 (-641 (-1170))) (|:| -1904 (-641 (-1170))))) + (-5 *1 (-1211))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-641 (-948 *4))) (-5 *3 (-641 (-1170))) (-4 *4 (-452)) + (-5 *1 (-914 *4))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-316 (-564))) (|:| -2371 (-316 (-379))) + (-3 (|:| I (-316 (-564))) (|:| -2308 (-316 (-379))) (|:| CF (-316 (-169 (-379)))) (|:| |switch| (-1169)))) (-5 *1 (-1169))))) -(((*1 *1 *2) (-12 (-5 *2 (-870)) (-5 *1 (-263)))) - ((*1 *1 *2) (-12 (-5 *2 (-379)) (-5 *1 (-263))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1152)) (-5 *2 (-1264)) (-5 *1 (-818))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-939 *5)) (-4 *5 (-1045)) (-5 *2 (-767)) + (-5 *1 (-1158 *4 *5)) (-14 *4 (-917)))) + ((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-641 (-767))) (-5 *3 (-767)) (-5 *1 (-1158 *4 *5)) + (-14 *4 (-917)) (-4 *5 (-1045)))) + ((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-641 (-767))) (-5 *3 (-939 *5)) (-4 *5 (-1045)) + (-5 *1 (-1158 *4 *5)) (-14 *4 (-917))))) (((*1 *1 *1 *1) (-4 *1 (-21))) ((*1 *1 *1) (-4 *1 (-21))) ((*1 *1 *1 *1) (|partial| -5 *1 (-134))) ((*1 *1 *1 *1) (-12 (-5 *1 (-214 *2)) (-4 *2 (-13 (-846) - (-10 -8 (-15 -4363 ((-1152) $ (-1170))) (-15 -1679 ((-1264) $)) - (-15 -1443 ((-1264) $))))))) + (-10 -8 (-15 -4366 ((-1152) $ (-1170))) (-15 -1629 ((-1264) $)) + (-15 -3668 ((-1264) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-294 *2)) (-4 *2 (-21)) (-4 *2 (-1209)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-294 *2)) (-4 *2 (-21)) (-4 *2 (-1209)))) ((*1 *1 *1 *1) @@ -8235,52 +8275,63 @@ ((*1 *2 *2 *2) (-12 (-5 *2 (-939 (-225))) (-5 *1 (-1205)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1257 *2)) (-4 *2 (-1209)) (-4 *2 (-21)))) ((*1 *1 *1) (-12 (-4 *1 (-1257 *2)) (-4 *2 (-1209)) (-4 *2 (-21))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-641 (-767))) (-5 *3 (-171)) (-5 *1 (-1158 *4 *5)) + (-14 *4 (-917)) (-4 *5 (-1045))))) +(((*1 *1 *2) + (-12 (-5 *2 (-641 *6)) (-4 *6 (-945 *3 *4 *5)) (-4 *3 (-363)) + (-4 *4 (-789)) (-4 *5 (-846)) (-5 *1 (-504 *3 *4 *5 *6))))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-1 *7 *7)) (-4 *7 (-1235 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(|:| -2308 (-316 (-379))) (|:| CF (-316 (-169 (-379)))) (|:| |switch| (-1169)))) (-5 *1 (-1169))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1088 (-839 (-225)))) (-5 *2 (-225)) (-5 *1 (-192)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1088 (-839 (-225)))) (-5 *2 (-225)) (-5 *1 (-300)))) +(((*1 *2 *1) + (|partial| -12 (-4 *3 (-1106)) (-4 *3 (-1094)) (-5 *2 (-641 *1)) + (-4 *1 (-430 *3)))) + ((*1 *2 *1) + (|partial| -12 (-5 *2 (-641 (-888 *3))) (-5 *1 (-888 *3)) + (-4 *3 (-1094)))) + ((*1 *2 *1) + (|partial| -12 (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *5 (-846)) + (-5 *2 (-641 *1)) (-4 *1 (-945 *3 *4 *5)))) ((*1 *2 *3) - (-12 (-5 *3 (-1088 (-839 (-225)))) (-5 *2 (-225)) (-5 *1 (-305))))) + (|partial| -12 (-4 *4 (-789)) (-4 *5 (-846)) (-4 *6 (-1045)) + (-4 *7 (-945 *6 *4 *5)) (-5 *2 (-641 *3)) + (-5 *1 (-946 *4 *5 *6 *7 *3)) + (-4 *3 + (-13 (-363) + (-10 -8 (-15 -2423 ($ *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))))) (((*1 *1 *1 *1) (-4 *1 (-25))) ((*1 *1 *1 *1) (-5 *1 (-157))) ((*1 *1 *1 *1) (-12 (-5 *1 (-214 *2)) (-4 *2 (-13 (-846) - (-10 -8 (-15 -4363 ((-1152) $ (-1170))) (-15 -1679 ((-1264) $)) - (-15 -1443 ((-1264) $))))))) + (-10 -8 (-15 -4366 ((-1152) $ (-1170))) (-15 -1629 ((-1264) $)) + (-15 -3668 ((-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) @@ -8303,55 +8354,37 @@ (-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 *2 *3) - (-12 (-4 *4 (-38 (-407 (-564)))) - (-5 *2 (-2 (|:| -3649 (-1150 *4)) (|:| -3661 (-1150 *4)))) - (-5 *1 (-1156 *4)) (-5 *3 (-1150 *4))))) -(((*1 *1 *1 *1) (-4 *1 (-657)))) +(((*1 *1 *2) (-12 (-5 *2 (-564)) (-5 *1 (-858))))) (((*1 *2 *2 *2) - (-12 (-4 *3 (-363)) (-5 *1 (-762 *2 *3)) (-4 *2 (-704 *3)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-848 *2)) (-4 *2 (-1045)) (-4 *2 (-363))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-407 (-948 *3))) (-5 *1 (-453 *3 *4 *5 *6)) - (-4 *3 (-556)) (-4 *3 (-172)) (-14 *4 (-917)) - (-14 *5 (-641 (-1170))) (-14 *6 (-1259 (-685 *3)))))) -(((*1 *2 *3) - (-12 (-5 *2 (-2 (|:| -3522 (-564)) (|:| -3862 (-641 *3)))) - (-5 *1 (-442 *3)) (-4 *3 (-1235 (-564)))))) -(((*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| *3) (|:| -3505 *4)))) - (-5 *1 (-1066 *5 *6 *7 *3 *4)) (-4 *4 (-1065 *5 *6 *7 *3))))) -(((*1 *1 *1 *1 *2) - (-12 (-4 *1 (-1059 *3 *4 *2)) (-4 *3 (-1045)) (-4 *4 (-789)) - (-4 *2 (-846)))) + (|partial| -12 (-4 *3 (-363)) (-5 *1 (-762 *2 *3)) (-4 *2 (-704 *3)))) ((*1 *1 *1 *1) - (-12 (-4 *1 (-1059 *2 *3 *4)) (-4 *2 (-1045)) (-4 *3 (-789)) - (-4 *4 (-846))))) -(((*1 *2 *1) - (-12 (-5 *2 (-858)) (-5 *1 (-1150 *3)) (-4 *3 (-1094)) - (-4 *3 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(-5 *2 (-1031)) (-5 *1 (-754))))) +(((*1 *1 *1 *1) (-4 *1 (-657)))) +(((*1 *1 *1) + (-12 (-5 *1 (-594 *2)) (-4 *2 (-38 (-407 (-564)))) (-4 *2 (-1045))))) +(((*1 *2 *2) + (-12 (-5 *2 (-641 *6)) (-4 *6 (-945 *3 *4 *5)) (-4 *3 (-452)) + (-4 *4 (-789)) (-4 *5 (-846)) (-5 *1 (-449 *3 *4 *5 *6))))) +(((*1 *2 *3 *4 *2) + (-12 (-5 *2 (-641 (-641 (-641 *5)))) (-5 *3 (-1 (-112) *5 *5)) + (-5 *4 (-641 *5)) (-4 *5 (-846)) (-5 *1 (-1180 *5))))) +(((*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 *2) (-12 (-5 *2 - (-3 (|:| I (-316 (-564))) (|:| -2371 (-316 (-379))) + (-3 (|:| I (-316 (-564))) (|:| -2308 (-316 (-379))) (|:| CF (-316 (-169 (-379)))) (|:| |switch| (-1169)))) (-5 *1 (-1169))))) (((*1 *2 *3 *4) @@ -8373,9 +8406,16 @@ ((*1 *2 *1) (-12 (-4 *1 (-1276 *3 *4)) (-4 *3 (-846)) (-4 *4 (-1045)) (-5 *2 (-641 *3))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-45 (-1152) (-770))) (-5 *1 (-114))))) -(((*1 *2 *2) (-12 (-5 *2 (-564)) (-5 *1 (-923))))) +(((*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 *2 *1) (|partial| -12 (-5 *2 (-641 *1)) (-4 *1 (-916))))) (((*1 *1 *1 *1) (-4 *1 (-657)))) +(((*1 *2 *2 *3) + (|partial| -12 (-5 *3 (-1 *6 *6)) (-4 *6 (-1235 *5)) + (-4 *5 (-13 (-27) (-430 *4))) (-4 *4 (-13 (-556) (-1034 (-564)))) + (-4 *7 (-1235 (-407 *6))) (-5 *1 (-552 *4 *5 *6 *7 *2)) + (-4 *2 (-342 *5 *6 *7))))) (((*1 *2 *1) (|partial| -12 (-4 *3 (-452)) (-4 *4 (-846)) (-4 *5 (-789)) (-5 *2 (-112)) (-5 *1 (-983 *3 *4 *5 *6)) @@ -8384,256 +8424,179 @@ (-12 (-5 *2 (-112)) (-5 *1 (-1134 *3 *4)) (-4 *3 (-13 (-1094) (-34))) (-4 *4 (-13 (-1094) (-34)))))) (((*1 *2 *3) - (-12 (-5 *3 (-1259 (-685 *4))) (-4 *4 (-172)) - (-5 *2 (-1259 (-685 (-948 *4)))) (-5 *1 (-189 *4))))) -(((*1 *2 *3 *3 *2) - (|partial| -12 (-5 *2 (-767)) - (-4 *3 (-13 (-722) (-368) (-10 -7 (-15 ** (*3 *3 (-564)))))) - (-5 *1 (-246 *3))))) -(((*1 *2 *3) - (|partial| -12 (-4 *4 (-1213)) (-4 *5 (-1235 *4)) - (-5 *2 (-2 (|:| |radicand| (-407 *5)) (|:| |deg| (-767)))) - (-5 *1 (-148 *4 *5 *3)) (-4 *3 (-1235 (-407 *5)))))) + (-12 (-5 *3 (-917)) (-5 *2 (-1166 *4)) (-5 *1 (-587 *4)) + (-4 *4 (-349))))) (((*1 *2) - (-12 (-4 *4 (-172)) (-5 *2 (-1166 (-948 *4))) (-5 *1 (-416 *3 *4)) - (-4 *3 (-417 *4)))) - ((*1 *2) - (-12 (-4 *1 (-417 *3)) (-4 *3 (-172)) (-4 *3 (-363)) - (-5 *2 (-1166 (-948 *3))))) - ((*1 *2) - (-12 (-5 *2 (-1166 (-407 (-948 *3)))) (-5 *1 (-453 *3 *4 *5 *6)) + (-12 (-5 *2 (-407 (-948 *3))) (-5 *1 (-453 *3 *4 *5 *6)) (-4 *3 (-556)) (-4 *3 (-172)) (-14 *4 (-917)) (-14 *5 (-641 (-1170))) (-14 *6 (-1259 (-685 *3)))))) -(((*1 *2 *1) (-12 (-4 *1 (-367 *3)) (-4 *3 (-172)) (-5 *2 (-1166 *3))))) -(((*1 *2 *2) - (-12 (-4 *3 (-452)) (-5 *1 (-1200 *3 *2)) - (-4 *2 (-13 (-430 *3) (-1194)))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-529))))) 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*4)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-434)) (|:| -1921 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-434)) (|:| -1836 "void"))) (-5 *3 (-641 (-948 (-564)))) (-5 *4 (-112)) (-5 *1 (-437)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-434)) (|:| -1921 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-434)) (|:| -1836 "void"))) (-5 *3 (-641 (-1170))) (-5 *4 (-112)) (-5 *1 (-437)))) ((*1 *2 *1) (-12 (-5 *2 (-1150 *3)) (-5 *1 (-599 *3)) (-4 *3 (-1209)))) @@ -11110,24 +11638,24 @@ ((*1 *1 *2 *3) (-12 (-5 *1 (-709 *2 *3 *4)) (-4 *2 (-846)) (-4 *3 (-1094)) (-14 *4 - (-1 (-112) (-2 (|:| -2151 *2) (|:| -1384 *3)) - (-2 (|:| -2151 *2) (|:| -1384 *3)))))) + (-1 (-112) (-2 (|:| -2083 *2) (|:| -1410 *3)) + (-2 (|:| -2083 *2) (|:| -1410 *3)))))) ((*1 *1 *2 *3) (-12 (-5 *2 (-506)) (-5 *3 (-1112)) (-5 *1 (-834)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-869 *2 *3)) (-4 *2 (-1209)) (-4 *3 (-1209)))) ((*1 *1 *2) - (-12 (-5 *2 (-641 (-2 (|:| -1982 (-1170)) (|:| -3740 *4)))) + (-12 (-5 *2 (-641 (-2 (|:| 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(|:| -1921 "void"))) + (-14 *4 (-3 (|:| |fst| (-434)) (|:| -1836 "void"))) (-14 *5 (-641 (-1170))) (-14 *6 (-1174)))) ((*1 *1 *2) (-12 (-5 *2 (-331 *4)) (-4 *4 (-13 (-846) (-21))) @@ -11402,14 +11956,14 @@ ((*1 *1 *2) (-12 (-5 *2 (-434)) (-5 *1 (-437)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -3193 (-641 (-330))))) + (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -3228 (-641 (-330))))) (-4 *1 (-440)))) ((*1 *1 *2) (-12 (-5 *2 (-330)) (-4 *1 (-440)))) ((*1 *1 *2) (-12 (-5 *2 (-641 (-330))) (-4 *1 (-440)))) ((*1 *1 *2) (-12 (-5 *2 (-1259 (-695))) (-4 *1 (-440)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -3193 (-641 (-330))))) + (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -3228 (-641 (-330))))) (-4 *1 (-441)))) ((*1 *1 *2) (-12 (-5 *2 (-330)) (-4 *1 (-441)))) ((*1 *1 *2) (-12 (-5 *2 (-641 (-330))) (-4 *1 (-441)))) @@ -11478,7 +12032,7 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-641 (-2 (|:| -4373 *3) (|:| -3258 *4)))) + (-12 (-5 *2 (-641 (-2 (|:| -4376 *3) (|:| -3290 *4)))) (-4 *3 (-1045)) (-4 *4 (-722)) (-5 *1 (-731 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-564)) (-4 *1 (-759)))) ((*1 *1 *2) @@ -11487,25 +12041,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) - (|:| -1510 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) + (|:| -3090 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (|:| |mdnia| (-2 (|:| |fn| (-316 (-225))) - (|:| -1510 (-641 (-1088 (-839 (-225))))) + (|:| -3090 (-641 (-1088 (-839 (-225))))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))))) (-5 *1 (-765)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-316 (-225))) - (|:| -1510 (-641 (-1088 (-839 (-225))))) (|:| |abserr| (-225)) + (|:| -3090 (-641 (-1088 (-839 (-225))))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *1 (-765)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) - (|:| -1510 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) + (|:| -3090 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *1 (-765)))) ((*1 *2 *3) (-12 (-5 *2 (-770)) (-5 *1 (-769 *3)) (-4 *3 (-1209)))) @@ -11523,23 +12077,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-316 (-225))) (|:| -3374 (-641 (-225))) + (-2 (|:| |fn| (-316 (-225))) (|:| -3430 (-641 (-225))) (|:| |lb| (-641 (-839 (-225)))) (|:| |cf| (-641 (-316 (-225)))) (|:| |ub| (-641 (-839 (-225)))))) (|:| |lsa| (-2 (|:| |lfn| (-641 (-316 (-225)))) - (|:| -3374 (-641 (-225))))))) + (|:| -3430 (-641 (-225))))))) (-5 *1 (-837)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -3374 (-641 (-225))))) + (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -3430 (-641 (-225))))) (-5 *1 (-837)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-316 (-225))) (|:| -3374 (-641 (-225))) + (-2 (|:| |fn| (-316 (-225))) (|:| -3430 (-641 (-225))) (|:| |lb| (-641 (-839 (-225)))) (|:| |cf| (-641 (-316 (-225)))) (|:| |ub| (-641 (-839 (-225)))))) (-5 *1 (-837)))) 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(-225)) + (|:| |relerr| (-225)))) + (-5 *2 (-379)) (-5 *1 (-192))))) (((*1 *2 *3) - (-12 (-4 *4 (-556)) (-5 *2 (-767)) (-5 *1 (-43 *4 *3)) - (-4 *3 (-417 *4))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1252 *3 *2)) - (-4 *2 (-1250 *3))))) -(((*1 *2 *1) - (-12 (-4 *1 (-602 *2 *3)) (-4 *3 (-1209)) (-4 *2 (-1094)) - (-4 *2 (-846))))) + (-12 (-4 *1 (-905)) (-5 *2 (-418 (-1166 *1))) (-5 *3 (-1166 *1))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4407)) (-4 *1 (-151 *3)) (-4 *3 (-1209)))) @@ -15132,190 +15605,152 @@ (-4 *5 (-789)) (-4 *3 (-846)) (-4 *2 (-1059 *4 *5 *3)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-767)) (-5 *1 (-1206 *2)) (-4 *2 (-1209))))) -(((*1 *1 *2) (-12 (-5 *2 (-1152)) (-5 *1 (-858))))) -(((*1 *2 *3) (-12 (-5 *3 (-1152)) (-5 *2 (-52)) (-5 *1 (-825))))) -(((*1 *2 *3) (-12 (-5 *3 (-1152)) (-5 *2 (-379)) (-5 *1 (-782))))) -(((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-525))))) -(((*1 *1 *2) (-12 (-5 *2 (-641 *3)) (-4 *3 (-846)) (-5 *1 (-126 *3))))) -(((*1 *2 *1) - (-12 (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *5 (-846)) (-5 *2 (-641 *1)) - (-4 *1 (-1059 *3 *4 *5))))) -(((*1 *2 *3) (-12 (-5 *2 (-407 (-564))) (-5 *1 (-561)) (-5 *3 (-564))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-641 (-858))) (-5 *1 (-858)))) - ((*1 *2 *1) - (-12 +(((*1 *2 *3 *4 *5 *6) + (-12 (-5 *5 (-767)) (-5 *6 (-112)) (-4 *7 (-452)) (-4 *8 (-789)) + (-4 *9 (-846)) (-4 *3 (-1059 *7 *8 *9)) (-5 *2 - (-2 (|:| -3099 (-641 (-858))) (|:| -2773 (-641 (-858))) - (|:| |presup| (-641 (-858))) (|:| -2272 (-641 (-858))) - (|:| |args| (-641 (-858))))) - (-5 *1 (-1170))))) -(((*1 *1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1209)))) - ((*1 *1 *2 *1) (-12 (-5 *1 (-121 *2)) (-4 *2 (-846)))) - ((*1 *1 *2 *1) (-12 (-5 *1 (-126 *2)) (-4 *2 (-846)))) - ((*1 *1 *1 *1 *2) - (-12 (-5 *2 (-564)) (-4 *1 (-282 *3)) (-4 *3 (-1209)))) - ((*1 *1 *2 *1 *3) - (-12 (-5 *3 (-564)) (-4 *1 (-282 *2)) (-4 *2 (-1209)))) - ((*1 *1 *2) - (-12 + (-2 (|:| |done| (-641 *4)) + (|:| |todo| (-641 (-2 (|:| |val| (-641 *3)) (|:| -3577 *4)))))) + (-5 *1 (-1063 *7 *8 *9 *3 *4)) (-4 *4 (-1065 *7 *8 *9 *3)))) + ((*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 - (|:| -1982 - (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) - (|:| -1510 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) - (|:| |relerr| (-225)))) - (|:| -3740 - (-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"))) - (|:| -1510 - (-3 (|:| |finite| "The range is finite") - (|:| |lowerInfinite| - "The bottom of range is infinite") - 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*8 (-307)) + (-5 *2 (-641 (-767))) (-5 *1 (-738 *6 *7 *8 *9)) (-5 *5 (-767))))) (((*1 *2 *3) (-12 (-4 *5 (-13 (-612 *2) (-172))) (-5 *2 (-888 *4)) (-5 *1 (-170 *4 *5 *3)) (-4 *4 (-1094)) (-4 *3 (-166 *5)))) @@ -17361,9 +17353,9 @@ (-12 (-5 *2 (-948 *3)) (-4 *3 (-1045)) (-4 *1 (-1059 *3 *4 *5)) (-4 *5 (-612 (-1170))) (-4 *4 (-789)) (-4 *5 (-846)))) ((*1 *1 *2) - (-2822 + (-2807 (-12 (-5 *2 (-948 (-564))) (-4 *1 (-1059 *3 *4 *5)) - (-12 (-2416 (-4 *3 (-38 (-407 (-564))))) (-4 *3 (-38 (-564))) + (-12 (-2351 (-4 *3 (-38 (-407 (-564))))) (-4 *3 (-38 (-564))) (-4 *5 (-612 (-1170)))) (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *5 (-846))) (-12 (-5 *2 (-948 (-564))) (-4 *1 (-1059 *3 *4 *5)) @@ -17374,12 +17366,12 @@ (-4 *3 (-38 (-407 (-564)))) (-4 *5 (-612 (-1170))) (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *5 (-846)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-641 *7)) (|:| -3505 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-641 *7)) (|:| -3577 *8))) (-4 *7 (-1059 *4 *5 *6)) (-4 *8 (-1065 *4 *5 *6 *7)) (-4 *4 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