idealSheafGens -- creates a list of subsets of the minimal generators that generate a given ideal up to saturation

Synopsis

• Usage:

  idealSheafGens(n,I,irr)

  idealSheafGens(n,I,X)

• Inputs:
  • I, an ideal,
  • n, an integer, size of subset of minimal generators of I that may generate I up to saturation with irr
  • irr, an ideal, irrelevant ideal
  • X, a normal toric variety, normal toric variety whose Cox ring contains I
• Optional inputs:
  • GeneralElements => ..., default value false, combines generators of same degree into a general linear combination
• Outputs:
  • a list, all ideals generated by subsets of size n of generators of I that generate I up to saturation with irr

Description

i1 : R = ZZ/101[x_0,x_1,x_2,x_3,x_4,Degrees=>{2:{1,0},3:{0,1}}];

i2 : B = intersect(ideal(x_0,x_1),ideal(x_2,x_3,x_4));

o2 : Ideal of R

i3 : I = ideal(x_0^2*x_2^2+x_1^2*x_3^2+x_0*x_1*x_4^2, x_0^3*x_4+x_1^3*(x_2+x_3));

o3 : Ideal of R

i4 : idealSheafGens(2,I,B)

              2 2    2 2        2   3      3      3
o4 = {ideal (x x  + x x  + x x x , x x  + x x  + x x )}
              0 2    1 3    0 1 4   1 2    1 3    0 4

o4 : List