hilbertFunction(ZZ,DualSpace)

• Function: hilbertFunction

• Usage:

  k = hilbertFunction(d,S)

  T = hilbertFunction(S)

  K = hilbertFunction(D,S)

• Inputs:
  • d, an integer, an integer, or a list of arguments
  • S, an instance of the type DualSpace, a dual space
• Outputs:
  • T, a tally, of dimensions for each degree
  • k, an integer, dimensions
  • K, a list, of dimensions

i1 : R = CC[x,y];

i2 : I = (ideal {x,y})^4;

o2 : Ideal of R

i3 : D = zeroDimensionalDual(origin R, I)

o3 = | 1 y x .5y2 xy .5x2 .166667y3 .5xy2 .5x2y .166667x3 |

o3 : DualSpace

i4 : hilbertFunction D

o4 = Tally{0 => 1}
           1 => 2
           2 => 3
           3 => 4

o4 : Tally