/usr/share/axiom-20170501/src/algebra/MTSCAT.spad is in axiom-source 20170501-3.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 | )abbrev category MTSCAT MultivariateTaylorSeriesCategory
++ Author: Clifton J. Williamson
++ Date Created: 6 March 1990
++ Date Last Updated: 6 March 1990
++ Description:
++ \spadtype{MultivariateTaylorSeriesCategory} is the most general
++ multivariate Taylor series category.
MultivariateTaylorSeriesCategory(Coef,Var) : Category == SIG where
Coef : Ring
Var : OrderedSet
L ==> List
NNI ==> NonNegativeInteger
PDR ==> PartialDifferentialRing(Var)
PSC ==> PowerSeriesCategory(Coef,IndexedExponents(Var),Var)
IE ==> InnerEvalable(Var,%)
EV ==> Evalable(%)
SIG ==> Join(PDR,PSC,IE,EV) with
coefficient : (%,Var,NNI) -> %
++ \spad{coefficient(f,x,n)} returns the coefficient of \spad{x^n} in f.
coefficient : (%,L Var,L NNI) -> %
++ \spad{coefficient(f,[x1,x2,...,xk],[n1,n2,...,nk])} returns the
++ coefficient of \spad{x1^n1 * ... * xk^nk} in f.
extend : (%,NNI) -> %
++ \spad{extend(f,n)} causes all terms of f of degree
++ \spad{<= n} to be computed.
monomial : (%,Var,NNI) -> %
++ \spad{monomial(a,x,n)} returns \spad{a*x^n}.
monomial : (%,L Var,L NNI) -> %
++ \spad{monomial(a,[x1,x2,...,xk],[n1,n2,...,nk])} returns
++ \spad{a * x1^n1 * ... * xk^nk}.
order : (%,Var) -> NNI
++ \spad{order(f,x)} returns the order of f viewed as a series in x
++ may result in an infinite loop if f has no non-zero terms.
order : (%,Var,NNI) -> NNI
++ \spad{order(f,x,n)} returns \spad{min(n,order(f,x))}.
polynomial : (%,NNI) -> Polynomial Coef
++ \spad{polynomial(f,k)} returns a polynomial consisting of the sum
++ of all terms of f of degree \spad{<= k}.
polynomial : (%,NNI,NNI) -> Polynomial Coef
++ \spad{polynomial(f,k1,k2)} returns a polynomial consisting of the
++ sum of all terms of f of degree d with \spad{k1 <= d <= k2}.
if Coef has Algebra Fraction Integer then
integrate : (%,Var) -> %
++ \spad{integrate(f,x)} returns the anti-derivative of the power
++ series \spad{f(x)} with respect to the variable x with constant
++ coefficient 1. We may integrate a series when we can divide
++ coefficients by integers.
RadicalCategory
--++ We provide rational powers when we can divide coefficients
--++ by integers.
TranscendentalFunctionCategory
--++ We provide transcendental functions when we can divide
--++ coefficients by integers.
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