randomPureBinomialIdeal -- randomPureBinomialIdeal with binomials of given degrees

Synopsis

• Usage:
I = randomPureBinomialIdeal(L,S)
• Inputs:
• L, a list, or sequence of positive integers
• S, a ring, Polynomial ring
• Outputs:
• I, an ideal, generated by random pure binomials (that is, differences of monomials without coefficients) of the given degrees

Description

 i1 : kk=ZZ/101 o1 = kk o1 : QuotientRing i2 : S=kk[a..e] o2 = S o2 : PolynomialRing i3 : L={3,3,4,6} o3 = {3, 3, 4, 6} o3 : List i4 : I=randomPureBinomialIdeal(L,S) 2 2 2 3 4 o4 = ideal (a*b*d - a*b*e, a b - b*e , c*d e - a*c*e ) o4 : Ideal of S

Caveat

The binomials are generated one at a time, and there is no checking to see whether the ideal returned is minally generated by fewer elements, so the number of minimal generators may not be what you expect.