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Macaulay2Doc :: hilbertSeries(PolynomialRing)

hilbertSeries(PolynomialRing) -- compute the Hilbert series of a ring

Synopsis

Description

We compute the Hilbert series of a ring.
i1 : R = ZZ/101[x, Degrees => {2}]/ideal(x^2);
i2 : s = hilbertSeries R

           4
      1 - T
o2 = --------
           2
     (1 - T )

o2 : Expression of class Divide
i3 : numerator s

          4
o3 = 1 - T

o3 : ZZ[T]
i4 : poincare R

          4
o4 = 1 - T

o4 : ZZ[T]
Recall that the variables of the power series are the variables of the degrees ring.
i5 : R=ZZ/101[x, Degrees => {{1,1}}]/ideal(x^2);
i6 : s = hilbertSeries R

           2 2
      1 - T T
           0 1
o6 = ----------
     (1 - T T )
           0 1

o6 : Expression of class Divide
i7 : numerator s

          2 2
o7 = 1 - T T
          0 1

o7 : ZZ[T ..T ]
         0   1
i8 : poincare R

          2 2
o8 = 1 - T T
          0 1

o8 : ZZ[T ..T ]
         0   1