# LinearOrdinaryDifferentialOperatorsOps(A, L)ΒΆ

lodo.spad line 55 [edit on github]

`LinearOrdinaryDifferentialOperatorsOps`

provides symmetric products and sums for linear ordinary differential operators.

- directSum: (L, L, 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, 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, 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.