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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 | )abbrev domain LODO2 LinearOrdinaryDifferentialOperator2
++ Author: Stephen M. Watt, Manuel Bronstein
++ Date Created: 1986
++ 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{LinearOrdinaryDifferentialOperator2} defines a ring of
++ differential operators with coefficients in a differential ring A
++ and acting on an A-module M.
++ Multiplication of operators corresponds to functional composition:\br
++ \spad{(L1 * L2).(f) = L1 L2 f}
LinearOrdinaryDifferentialOperator2(A, M) : SIG == CODE where
A: DifferentialRing
M: LeftModule A with
differentiate : $ -> $
++ differentiate(x) returns the derivative of x
SIG ==> Join(LinearOrdinaryDifferentialOperatorCategory A, Eltable(M, M))
CODE ==> LinearOrdinaryDifferentialOperator(A, differentiate$A) add
elt(p:%, m:M):M ==
apply(p, differentiate, m)$ApplyUnivariateSkewPolynomial(A, M, %)
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