PseudoLinearNormalForm K

pseudolin.spad line 1 [edit on github]

• K: Field

PseudoLinearNormalForm provides a function for computing a block-companion form for pseudo-linear operators.

changeBase: (Matrix K, Matrix K, Automorphism K, K -> K) -> Matrix K

changeBase(M, A, sig, der): computes the new matrix of a pseudo-linear transform given by the matrix M under the change of base A

companionBlocks: (Matrix K, List Vector K) -> List Record(C: Matrix K, lg: List Vector K)

companionBlocks(m, lv) returns [[C_1, lg_1], ..., [C_k, lg_k]] such that each C_i is a companion block and m = diagonal(C_1, ..., C_k).

normalForm: (Matrix K, Automorphism K, K -> K) -> Record(R: Matrix K, A: Matrix K, Ainv: Matrix K)

normalForm(M, sig, der) returns [R, A, A^{-1}] such that the pseudo-linear operator whose matrix in the basis y is M had matrix R in the basis z = A y. der is a sig-derivation.