Computing Popov Forms of Polynomial Matrices

Abstract

This thesis gives a deterministic algorithm to transform a row reduced matrix to canon- ical Popov form. Given as input a row reduced matrix R over K[x], K a field, our algorithm computes the Popov form in about the same time as required to multiply together over K[x] two matrices of the same dimension and degree as R. Randomization can be used to extend the algorithm for rectangular input matrices of full row rank. Thus we give a Las Vegas algorithm that computes the Popov decomposition of matrices of full row rank. We also show that the problem of transforming a row reduced matrix to Popov form is at least as hard as polynomial matrix multiplication.