getGenElts -- general elements of an ideal cutting down the codimension

• Usage:

  getGenElts(I, n)

• Inputs:
  • I, an ideal,
  • n, an integer, the number of general elements to produce
• Optional inputs:
  • minTerms => an integer, default value -1, the minimum number of generators of I to combine when forming a general element; the default value -1 uses all generators
  • numCandidates => an integer, default value 3, the number of random candidates tried at each step
• Outputs:
  • a list, a list of n general elements of I

i1 : R = QQ[x,y,z];

i2 : I = ideal "xy,yz,zx";

o2 : Ideal of R

i3 : setRandomSeed 0;
 -- setting random seed to 0

i4 : getGenElts(I, 2)

      7      7      3     5      7      3
o4 = {-x*y + -x*z + -y*z, -x*y + -x*z + -y*z}
      9      4      4     6      8      2

o4 : List