hilbertPolynomial(SpectralSequencePage) -- the Hilbert polynomial of a spectral sequence page

Synopsis

Function: hilbertPolynomial
Usage:

H = hilbertPolynomial(E)
Inputs:
- E, a spectral sequence page,
Optional inputs:
- Projective => ..., default value true,
Outputs:
- H, a Page,

Description

Returns the Hilbert polynomials of all modules of the spectral sequence page

As a specific example consider the filtered complex $K$ below, obtained by multiplying the minimal free resolution of the rational quartic space curve by successive powers of the irrelevant ideal.

i1 : B = QQ[a..d];

i2 : J = ideal vars B;

o2 : Ideal of B

i3 : C = complete res monomialCurveIdeal(B,{1,3,4});

i4 : K = filteredComplex(J,C,4);

We compute the degree $0$ piece of the $E^3$ page below.

i5 : E = prune spectralSequence K;

i6 : hilbertPolynomial(E^3)

     +-------------+
o6 = |- 3*P  + 4*P |
     |     0      1|
     |             |
     |{-4, 4}      |
     +-------------+

o6 : Page