Description
We compute the
Hilbert series of
R/I, the quotient of the ambient ring by the ideal. Caution: For an ideal
I running
hilbertSeries I calculates the Hilbert series of
R/I.
i1 : R = ZZ/101[x, Degrees => {2}];

i2 : I = ideal x^2
2
o2 = ideal x
o2 : Ideal of R

i3 : s = hilbertSeries I
4
1  T
o3 = 
2
(1  T )
o3 : Expression of class Divide

i4 : numerator s
4
o4 = 1  T
o4 : ZZ[T]

i5 : poincare I
4
o5 = 1  T
o5 : ZZ[T]

i6 : reduceHilbert s
2
1 + T
o6 = 
1
o6 : Expression of class Divide

Recall that the variables of the power series are the variables of the
degrees ring.
i7 : R=ZZ/101[x, Degrees => {{1,1}}];

i8 : I = ideal x^2;
o8 : Ideal of R

i9 : s = hilbertSeries I
2 2
1  T T
0 1
o9 = 
(1  T T )
0 1
o9 : Expression of class Divide

i10 : numerator s
2 2
o10 = 1  T T
0 1
o10 : ZZ[T ..T ]
0 1

i11 : poincare I
2 2
o11 = 1  T T
0 1
o11 : ZZ[T ..T ]
0 1

i12 : reduceHilbert s
1 + T T
0 1
o12 = 
1
o12 : Expression of class Divide
