randomElementsFromIdeal -- Chooses random elements of given degrees in a given ideal.

Synopsis

• Usage:

  I = randomElementsFromIdeal(L,I)

• Inputs:
  • L, a list, of integers
  • I, an ideal, that should be homogeneous
• Outputs:
  • I, an ideal, generated by (at most) n homogeneous polynomials that are random linear combination of the generators of I, with degrees specified by the list L

Description

i1 : kk=ZZ/101

o1 = kk

o1 : QuotientRing

i2 : S=kk[a..c]

o2 = S

o2 : PolynomialRing

i3 : L={3,3,4,6}

o3 = {3, 3, 4, 6}

o3 : List

i4 : I = ideal(a^3,b^3, c^3)

             3   3   3
o4 = ideal (a , b , c )

o4 : Ideal of S

i5 : J=randomElementsFromIdeal(L,I)

             3      3   3      3     3        3      4     5      6
o5 = ideal (b  - 45c , a  - 26c , a*c  + 38b*c  + 34c , b*c  - 32c )

o5 : Ideal of S

See also

• Finding Extreme Examples -- Ways to use random ideals to search for (counter)-examples
• 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
• randomBinomialIdeal -- randomBinomialIdeal with binomials of given degrees
• randomPureBinomialIdeal -- randomPureBinomialIdeal with binomials of given degrees