Division of generalized polynomials using the comrade matrix

AbstractLet a(λ) and b(λ) be two polynomials expressed in generalized form, i.e. relative to a given orthogonal basis. It is shown how their greatest common divisor d(λ), the quotient a(λ)/d(λ), and the quotient and remainder on division of a(λ) by b(λ) can be determined simultaneously, without any conversion into standard power form. This is done by applying elementary row operations to the matrix b(A), where A is the comrade matrix associated with a(λ)