ReduceLODE(F, L, UP, A, LO)

odeef.spad line 189 [edit on github]

• F : Field
• L : LinearOrdinaryDifferentialOperatorCategory(F)
• UP : UnivariatePolynomialCategory(F)
• A : MonogenicAlgebra(F, UP)
• LO : LinearOrdinaryDifferentialOperatorCategory(A)

Elimination of an algebraic from the coefficients of a linear ordinary differential equation.

reduceLODE : (LO, A) -> Record(mat : Matrix(L), vec : Vector(F))

reduceLODE(op, g) returns [m, v] such that any solution in A of op z = g is of the form z = (z_1, ..., z_m) . (b_1, ..., b_m) where the b_i's are the basis of A over F returned by basis() from A, and the z_i's satisfy the differential system M.z = v.

reduceLODE : (LO, List(A)) -> Record(mat : Matrix(L), vecs : List(Vector(F)))

reduceLODE(op, [g1, ..., gn]) returns [m, [v1, ..., vn]] such that any solution in A of op z = c1*g1 + ... + cn*gn where ci are constants satisfy the differential system M.z = c1*v1 + ... + cn*vn