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randomBinomialIdeal -- randomBinomialIdeal with binomials of given degrees

Synopsis

• Usage:
I = randomBinomialIdeal(L,S)
• Inputs:
• L, a list, or sequence of positive integers
• S, a ring, Polynomial ring
• Outputs:
• I, an ideal, generated by random binomials 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=randomBinomialIdeal(L,S) 2 2 2 2 4 o4 = ideal (a*b*d - 14b*e , b*c - 16a*b*e, a*b e - 43c*d*e , a b*e - ------------------------------------------------------------------------ 2 3 42b d*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.

Ways to use randomBinomialIdeal :

• "randomBinomialIdeal(List,Ring)"
• "randomBinomialIdeal(Sequence,Ring)"

For the programmer

The object randomBinomialIdeal is .