### D.4.18 monomialideal_lib

Library:
  monomialideal.lib
Purpose:
  Primary and irreducible decompositions of monomial ideals
Authors:
  I.Bermejo, ibermejo@ull.es
  E.Garcia-Llorente, evgarcia@ull.es
  Ph.Gimenez, pgimenez@agt.uva.es

Overview:
  A library for computing a primary and the irreducible decompositions of a monomial ideal using several methods.
  In this library we also take advantage of the fact that the ideal is monomial to make some computations that are Grobner free in this case (radical, intersection, quotient...).

Procedures:

> D.4.18.1 isMonomial |  | checks whether an ideal id is monomial
> D.4.18.2 minbaseMon |  | computes the minimal monomial generating set of a monomial ideal id
> D.4.18.3 gcdMon |  | computes the gcd of two monomials f, g
> D.4.18.4 lcmMon |  | computes the lcm of two monomials f, g
> D.4.18.5 membershipMon |  | checks whether a polynomial f belongs to a monomial ideal id
> D.4.18.6 intersectMon |  | intersection of monomial ideals id1 and id2
> D.4.18.7 quotientMon |  | quotient ideal id1:id2
> D.4.18.8 radicalMon |  | computes the radical of a monomial ideal id
> D.4.18.9 isprimeMon |  | checks whether a monomial ideal id is prime
> D.4.18.10 isprimaryMon |  | checks whether a monomial ideal id is primary
> D.4.18.11 isirreducibleMon |  | checks whether a monomial ideal id is irreducible
> D.4.18.12 isartinianMon |  | checks whether a monomial ideal id is artininan
> D.4.18.13 isgenericMon |  | checks whether a monomial ideal id is generic
> D.4.18.14 dimMon |  | dimension of a monomial ideal id
> D.4.18.15 irreddecMon |  | computes the irreducible decomposition of a monomial ideal id
> D.4.18.16 primdecMon |  | computes a minimal primary decomposition of a monomial ideal id

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