# OrePolynomialMatrixOperations(F, LO)¶

undocumented

rowEchelon: (Matrix LO, F, List Vector F) -> Record(mat: Matrix LO, vecs: List Vector F)

rowEchelon(m, c, lv) returns [m2, lv2] such that m2 is the row echelon form of the matrix m. lv2 is transformed lv using c as parameter to apply.

rowEchelon: Matrix LO -> Matrix LO

rowEchelon(m) returns the row echelon form of the matrix m.

solve: (Matrix LO, F, List Vector F, (LO, List F) -> Record(particular: List Record(ratpart: F, coeffs: Vector F), basis: List F)) -> Union(Record(particular: List Record(ratpart: Vector F, coeffs: Vector F), basis: List Vector F), failed)

solve(m, c, lv, solf) returns “failed” of [[vp1, …, vp_m], [b1, …, bl]] such that bi-s are basis of solutions of homogeneous system m bi = 0. Each vpi = [r, [c1, …, cn]] is a particular solution of a parametric matrix equation m r = sum ci vi where lv = [v1, …, vn]. solf is scalar solver, c is a parameter to apply (needed for action of LO on F). “failed” means that system is underdetermined.