Singular Manual: Conti and Traverso

| #### C.6.2.1 The algorithm of Conti and Traverso The algorithm of Conti and Traverso (see [CoTr91]) computes 750#750 via the extended matrix 751#751, where 752#752 is the 753#753 unity matrix. A lattice basis of 195#195 is given by the set of vectors 754#754, where 755#755 is the 55#55-th row of 190#190 and 756#756 the 55#55-th coordinate vector. We look at the ideal in 757#757 corresponding to these vectors, namely 758#758 We introduce a further variable 501#501 and adjoin the binomial 759#759 to the generating set of 760#760, obtaining an ideal 761#761 in the polynomial ring 762#762. 761#761 is saturated w.r.t. all variables because all variables are invertible modulo 761#761. Now 750#750 can be computed from 761#761 by eliminating the variables 763#763. 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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