# Singular

#### C.6.2.1 The algorithm of Conti and Traverso

The algorithm of Conti and Traverso (see [CoTr91]) computes via the extended matrix , where is the unity matrix. A lattice basis of is given by the set of vectors , where is the -th row of and the -th coordinate vector. We look at the ideal in corresponding to these vectors, namely

We introduce a further variable and adjoin the binomial to the generating set of , obtaining an ideal in the polynomial ring . is saturated w.r.t. all variables because all variables are invertible modulo . Now can be computed from by eliminating the variables .

Because of the big number of auxiliary variables needed to compute a toric ideal, this algorithm is rather slow in practice. However, it has a special importance in the application to integer programming (see Integer programming).