# ReduceLODE(F, L, UP, A, LO)ΒΆ

- 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`

.