Euclidean remainders for generalized polynomials

AbstractGiven two polynomials a(λ) and b(λ) expressed in generalized form (i.e. relative to a given orthogonal basis), it is shown how the complete set of euclidean remainders can be determined, also in generalized form. The computational scheme involves reducing the matrix b(A), where A is the comrade matrix associated with a(λ), by elementary row operations to a quasitriangular form. As a by-product, solutions to a set of linear congruences are also obtained