LinearOrdinaryDifferentialOperatorsOps(A, L)

lodo.spad line 55 [edit on github]

• A : Field
• L : LinearOrdinaryDifferentialOperatorCategory(A)

LinearOrdinaryDifferentialOperatorsOps provides symmetric products and sums for linear ordinary differential operators.

directSum : (L, L, Mapping(A, A)) -> L

directSum(a, b, D) computes an operator c of minimal order such that the nullspace of c is generated by all the sums of a solution of a by a solution of b. D is the derivation to use.

symmetricPower : (L, NonNegativeInteger, Mapping(A, A)) -> L

symmetricPower(a, n, D) computes an operator c of minimal order such that the nullspace of c is generated by all the products of n solutions of a. D is the derivation to use.

symmetricProduct : (L, L, Mapping(A, A)) -> L

symmetricProduct(a, b, D) computes an operator c of minimal order such that the nullspace of c is generated by all the products of a solution of a by a solution of b. D is the derivation to use.