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), Mapping(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), Mapping(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.