Singular Manual: Conti and Traverso

| #### C.6.2.1 The algorithm of Conti and Traverso The algorithm of Conti and Traverso (see [CoTr91]) computes 752#752 via the extended matrix 753#753, where 754#754 is the 755#755 unity matrix. A lattice basis of 196#196 is given by the set of vectors 756#756, where 757#757 is the 55#55-th row of 191#191 and 758#758 the 55#55-th coordinate vector. We look at the ideal in 759#759 corresponding to these vectors, namely 760#760 We introduce a further variable 503#503 and adjoin the binomial 761#761 to the generating set of 762#762, obtaining an ideal 763#763 in the polynomial ring 764#764. 763#763 is saturated w.r.t. all variables because all variables are invertible modulo 763#763. Now 752#752 can be computed from 763#763 by eliminating the variables 765#765. 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).

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