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NoetherianOperators :: hilbertFunction(ZZ,DualSpace)

hilbertFunction(ZZ,DualSpace)

Synopsis

Description

counts the dimension of the dual space in each degree. A single degree can be specified, or a list of degrees. If no degree is specified, then a Tally is returned pairing each degree with its dimension.

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