randomIdeal -- randomIdeal made from a given set of monomials

• Usage:

  I = randomIdeal(L,m)

• Inputs:
  • L, a list, or sequence of positive integers
  • m, a matrix, 1xn matrix of homogeneous polynomials in a ring S
• Outputs:
  • I, an ideal, generated by random linear combinations of degrees given by L of the given polynomials

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 : m = matrix{{a^3,b^4+c^4,d^5}}

o4 = | a3 b4+c4 d5 |

             1      3
o4 : Matrix S  <-- S

i5 : I=randomIdeal(L,m)

             3   4    4     5        5        5      6     5
o5 = ideal (a , b  + c , a*d  + 42b*d  - 27c*d  + 41d  - 2d e)

o5 : Ideal of S