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Macaulay2Doc :: poincare(Ring)

poincare(Ring) -- assemble degrees of an ring into a polynomial

Synopsis

Description

We compute the Poincare polynomial of a ring.
i1 : R=ZZ/101[x]/ideal(x^2);
i2 : poincare R

          2
o2 = 1 - T

o2 : ZZ[T]
i3 : numerator hilbertSeries R

          2
o3 = 1 - T

o3 : ZZ[T]
Recall that the variables of the polynomial are the variables of the degrees ring.
i4 : R=ZZ/101[x, Degrees => {{1,1}}]/ideal(x^2);
i5 : poincare R

          2 2
o5 = 1 - T T
          0 1

o5 : ZZ[T , T ]
         0   1
i6 : numerator hilbertSeries R

          2 2
o6 = 1 - T T
          0 1

o6 : ZZ[T , T ]
         0   1