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         2   3
o4 = ideal (a*b*d - 14b*e , b*c  - 16a*b*e, a*b e - 43c*d*e , a b*e - 42b d*e )

o4 : Ideal of S

Caveat

See also

• randomIdeal -- randomIdeal made from a given set of monomials
• randomMonomialIdeal -- random monomial ideal with given degree generators
• randomSquareFreeMonomialIdeal -- random square-free monomial ideal with given degree generators
• randomMonomial -- Choose a random monomial of given degree in a given ring
• randomPureBinomialIdeal -- randomPureBinomialIdeal with binomials of given degrees
• randomElementsFromIdeal -- Chooses random elements of given degrees in a given ideal.