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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 | )abbrev package APPLYORE ApplyUnivariateSkewPolynomial
++ Author: Manuel Bronstein
++ Date Created: 7 December 1993
++ Date Last Updated: 1 February 1994
++ References:
++ Bron95 On radical solutions of linear ordinary differential equations
++ Abra01 On Solutions of Linear Functional Systems
++ Muld95 Primitives: Orepoly and Lodo
++ Description:
++ \spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate
++ skew polynomials to be applied to appropriate modules.
ApplyUnivariateSkewPolynomial(R,M,P) : SIG == CODE where
R:Ring
M: LeftModule R
P: UnivariateSkewPolynomialCategory R
SIG ==> with
apply : (P, M -> M, M) -> M
++ apply(p, f, m) returns \spad{p(m)} where the action is given
++ by \spad{x m = f(m)}.
++ \spad{f} must be an R-pseudo linear map on M.
CODE ==> add
apply(p, f, m) ==
w:M := 0
mn:M := m
for i in 0..degree p repeat
w := w + coefficient(p, i) * mn
mn := f mn
w
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