A multiple polynomial general number field sieve

We assume that the reader is familiar with the General Number Field Sieve (GNFS). This article describes a way to use more than two polynomials. Two, three and four polynomials are compared both for classical and for a special form of lattice sieving (line sieving). We present theoretical expectations and experimental results. With our present polynomial search algorithm, using more than two polynomials speeds up classical sieving considerably but not line sieving. Line sieving for two polynomials is the fastest way of sieving we tried so far.