randomSquareFreeMonomialIdeal -- random square-free monomial ideal with given degree generators

• Usage:

  I = randomSquareFreeMonomialIdeal(L,S)

• Inputs:
  • L, a list, or sequence of non-negative integers
  • S, a ring, Polynomial ring
• Outputs:
  • I, an ideal, square-free monomial ideal with generators of specified degrees

i1 : setRandomSeed(currentTime())
 -- setting random seed to 1747319212

o1 = 1747319212

i2 : kk=ZZ/101

o2 = kk

o2 : QuotientRing

i3 : S=kk[a..e]

o3 = S

o3 : PolynomialRing

i4 : L={3,5,7}

o4 = {3, 5, 7}

o4 : List

i5 : randomSquareFreeMonomialIdeal(L, S)
low degree gens generated everything

o5 = ideal(a*c*d)

o5 : Ideal of S

i6 : randomSquareFreeMonomialIdeal(5:2, S)

o6 = ideal (b*e, b*c, c*e, a*b, a*d)

o6 : Ideal of S