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Macaulay2Doc :: poincare(Module)

poincare(Module) -- assemble degrees of an module into a polynomial

Synopsis

Description

We compute the Poincare polynomial of a module.
i1 : R = ZZ/101[w..z];
i2 : M = module monomialCurveIdeal(R,{1,3,4});
i3 : poincare M

      2     3     4    5
o3 = T  + 3T  - 4T  + T

o3 : ZZ[T]
i4 : numerator reduceHilbert hilbertSeries M

      2     3     4    5
o4 = T  + 3T  - 4T  + T

o4 : ZZ[T]
Recall that the variables of the polynomial are the variables of the degrees ring.
i5 : R=ZZ/101[x, Degrees => {{1,1}}];
i6 : M = module ideal x^2;
i7 : poincare M

      2 2
o7 = T T
      0 1

o7 : ZZ[T ..T ]
         0   1
i8 : numerator reduceHilbert hilbertSeries M

      2 2
o8 = T T
      0 1

o8 : ZZ[T ..T ]
         0   1