We investigate two practical divide-and-conquer style algorithms for univariate polynomial arithmetic. First we revisit an algorithm originally described by Brent and Kung for comp...
We present algorithms to perform modular polynomial multiplication or modular dot product efficiently in a single machine word. We pack polynomials into integers and perform sever...
We use higher-order logic to verify a quantifier elimination procedure for linear arithmetic over ordered fields, where the coefficients of variables are multivariate polynomials o...
We propose a new number representation and arithmetic for the elements of the ring of integers modulo p. The socalled Polynomial Modular Number System (PMNS) allows for fast polyn...
Jean-Claude Bajard, Laurent Imbert, Thomas Plantar...
We study arithmetic operations for triangular families of polynomials, concentrating on multiplication in dimension zero. By a suitable extension of fast univariate Euclidean divi...