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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 | )abbrev domain OREUP UnivariateSkewPolynomial
++ Author: Manuel Bronstein
++ Date Created: 19 October 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:
++ 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}.
UnivariateSkewPolynomial(x,R,sigma,delta) : SIG == CODE where
x : Symbol
R : Ring
sigma : Automorphism R
delta : R -> R
SIG ==> UnivariateSkewPolynomialCategory R with
coerce : Variable x -> %
++ coerce(x) returns x as a skew-polynomial.
CODE ==> SparseUnivariateSkewPolynomial(R, sigma, delta) add
Rep := SparseUnivariateSkewPolynomial(R, sigma, delta)
coerce(v:Variable(x)):% == monomial(1, 1)
coerce(p:%):OutputForm == outputForm(p, outputForm x)$Rep
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