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D.15.4 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 decomposition of a monomial ideal using several methods.
In addition, taking advantage of the fact that the ideals under consideration are monomial, the library offers some basic operations on ideals which are Groebner free in the monomial case (radical, intersection, ideal quotient...). Note, however, that the general Singular kernel commands for these operations are usually faster. In a future edition of Singular, the specialized algorithms will also be implemented in the Singular kernel.

Literature: Miller, Ezra and Sturmfels, Bernd: Combinatorial Commutative Algebra, Springer 2004

Procedures:

D.15.4.1 isMonomial  checks whether an ideal id is monomial
D.15.4.2 minbaseMon  computes the minimal monomial generating set of a monomial ideal id
D.15.4.3 gcdMon  computes the gcd of two monomials f, g
D.15.4.4 lcmMon  computes the lcm of two monomials f, g
D.15.4.5 membershipMon  checks whether a polynomial f belongs to a monomial ideal id
D.15.4.6 intersectMon  intersection of monomial ideals id1 and id2
D.15.4.7 quotientMon  quotient ideal id1:id2
D.15.4.8 radicalMon  computes the radical of a monomial ideal id
D.15.4.9 isprimeMon  checks whether a monomial ideal id is prime
D.15.4.10 isprimaryMon  checks whether a monomial ideal id is primary
D.15.4.11 isirreducibleMon  checks whether a monomial ideal id is irreducible
D.15.4.12 isartinianMon  checks whether a monomial ideal id is artininan
D.15.4.13 isgenericMon  checks whether a monomial ideal id is generic, i.e., no two minimal generators of it agree in the exponent of any variable that actually appears in both of them
D.15.4.14 dimMon  dimension of a monomial ideal id
D.15.4.15 irreddecMon  computes the irreducible decomposition of a monomial ideal id
D.15.4.16 primdecMon  computes a minimal primary decomposition of a monomial ideal id


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