ACTA UNIVERSITATIS APULENSIS Special Issue KARATSUBA AND TOOM-COOK METHODS FOR MULTIVARIATE POLYNOMIALS

Karatsuba and Toom-Cook are well-known methods used to efficiently multiply univariate polynomials and long integers. For multivariate polynomials, asymptotically good approaches like Kronecker’s trick combined with FFT become truly effective only when the degree is above some threshold. In this paper we analyze Karatsuba and some of Toom-Cook methods for multivariate polynomials, considering density in a different way with respect to Kronecker, and present some algorithms for fast multivariate polynomial multiplication in practical cases, when degrees are not huge. A fast sparse polynomial multiplication algorithm is also proposed. 2000 Mathematics Subject Classification: 11A05, 11A25, 11K65, 11Y70