This paper generalizes the well-known Sch6nhage-Strassen algorithm for multiplying large integers to an algorithm for dividing polynomials with coefficients from an arbitrary, not necessarily commutative, not always associative, algebra d, and obtains a method not requiring division that is valid for any algebra.Expand

New probabilistic algorithms are presented for factoring univariate polynomials over finite fields, using fast matrix multiplication techniques and the new baby step/giant step techniques.Expand

Douglas Wiedemann’s (1986) landmark approach to solving sparse linear systems over finite fields provides the symbolic counterpart to non-combinatorial numerical methods for solving sparse linear… Expand

It is proved that by use of certain randomizations on the input system the parallel speed up is roughly by the number of vectors in the blocks when using as many processors.Expand

Algorithms are developed that adopt a novel implicit representation for multivariate polynomials and rational functions with rational coefficients, that of black boxes for their evaluation. It is… Expand

New baby steps/giant steps algorithms of asymptotically fast running time for dense matrix problems that deterministically compute the determinant, characteristic polynomial and adjoint of A with n3.2+o(1) and O(n2.697263) ring additions, subtractions and multiplications are presented.Expand

This paper can probabilistically determine all those sparse irreducible factors of a polynomial given by a straight-line program that have less than a given number of monomials.Expand

International Symposium on Symbolic and Algebraic…

9 July 2006

TLDR

This work presents an algorithm based on a version of the structured total least norm (STLN) method and demonstrates that the algorithm in practice computes globally minimal approximations on a diverse set of benchmark polynomials.Expand

International Symposium on Symbolic and Algebraic…

4 July 1988

TLDR

This work considers the problem of interpolating sparse multivariate polynomials from their values and presents efficient algorithms for finding the rank of certain special Toeplitz systems arising in the Ben-Or and Tiwari algorithm and for solving transposed Vandermonde systems of equations.Expand

International Symposium on Symbolic and Algebraic…

3 August 2003

TLDR

Using an absolute irreducibility criterion due to Ruppert, this work is able to find useful separation bounds, in several norms, for bivariate polynomials, and derive new, more effective Noether forms for polynmials of arbitrarily many variables.Expand