random(List,Ideal) -- a random ring element of a given degree

• Function: random

• Usage:

  random(d, I)

• Inputs:
  • d, a list, or an integer, if the ring of $I$ is singly graded
  • I, an ideal, homogeneous
• Optional inputs:
  • Density => ..., default value 1,
  • Height => ..., default value 10,
  • MaximalRank => ..., default value false,
  • UpperTriangular => ..., default value false,
• Outputs:
  • a ring element, a random element in the ideal of the given degree

i1 : S = ZZ/101[a..d]

o1 = S

o1 : PolynomialRing

i2 : I = ideal(a^2, a*b^3, c*d)

             2     3
o2 = ideal (a , a*b , c*d)

o2 : Ideal of S

i3 : f = random(3, I)

        3      2       2       2                           2         2
o3 = 24a  - 36a b - 30a c - 29a d + 19a*c*d + 19b*c*d - 10c d - 29c*d

o3 : S

i4 : f % I == 0 -- so f is in the ideal I

o4 = true

i5 : degree f == {3}

o5 = true