next | previous | forward | backward | up | top | index | toc | Macaulay2 website
Macaulay2Doc :: poincare(Ideal)

poincare(Ideal) -- assemble degrees of the quotient of the ambient ring by an ideal into a polynomial

Synopsis

Description

We compute the Poincare polynomial of the quotient of the ambient ring by an ideal.
i1 : R = ZZ/101[w..z];
i2 : I = monomialCurveIdeal(R,{1,3,4});

o2 : Ideal of R
i3 : poincare I

          2     3     4    5
o3 = 1 - T  - 3T  + 4T  - T

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

                2    3
o4 = 1 + 2T + 2T  - 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 : I = ideal x^2;

o6 : Ideal of R
i7 : poincare I

          2 2
o7 = 1 - T T
          0 1

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

o8 = 1 + T T
          0 1

o8 : ZZ[T ..T ]
         0   1

Caveat

As is often the case, calling this function on an ideal I actually computes it for R/I where R is the ring of I.