### D.13.1 cimonom_lib

Library:
  cimonom.lib
Purpose:
  Determines if the toric ideal of an affine monomial curve is a complete intersection

Authors:
  I.Bermejo, ibermejo@ull.es
  I.Garcia-Marco, iggarcia@ull.es
  J.-J.Salazar-Gonzalez, jjsalaza@ull.es

Overview:
  A library for determining if the toric ideal of an affine monomial curve is a complete intersection with NO NEED of computing explicitly a system of generators of such ideal. It also contains procedures to obtain the minimum positive multiple of an integer which is in a semigroup of positive integers. The procedures are based on a paper by Isabel Bermejo, Ignacio Garcia and Juan Jose Salazar-Gonzalez: 'An algorithm to check whether the toric ideal of an affine monomial curve is a complete intersection', Preprint.

Procedures:

> D.13.1.1 BelongSemig |  | checks whether n is in the semigroup generated by v;
> D.13.1.2 MinMult |  | computes k, the minimum positive integer such that k*a is in the semigroup of positive integers generated by the elements in b.
> D.13.1.3 CompInt |  | checks wether I(d) is a complete intersection or not.

See also: Integer programming.

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