basis(List,SpectralSequencePage) -- generators of a particular degree

Synopsis

Function: basis
Usage:

B = basis(L, E)
Inputs:
- L, a list,
- E, a spectral sequence page,
Optional inputs:
- Degree => ..., default value null,
- Limit => ..., default value infinity,
- SourceRing => ..., default value null,
- Strategy => ..., default value null,
- Truncate => ..., default value false,
- Variables => ..., default value null,
Outputs:
- B, a matrix, Note!! The output should actually be a page!!;

Description

Returns generators for the requested (multi)degree of the spectral sequence page. It is designed to extend the function basis which can be applied to modules, for instance.

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 : E^3

     +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------+--------------------------------------------------------------------------------+----------------------------------------+
o6 = |cokernel {4} | -d -b -d -c 0  0  -c 0  0  0  -d 0  0  0  0  -d -c 0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  ||0                                                                                                                                               |0                                                                                       |0                                                                               |0                                       |
     |         {4} | c  a  0  0  0  -d 0  -b 0  -d 0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |         {4} | 0  0  b  a  c  0  0  0  -d 0  0  -d 0  -d 0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  ||{-3, 4}                                                                                                                                         |{-2, 4}                                                                                 |{-1, 4}                                                                         |{0, 4}                                  |
     |         {4} | 0  0  0  0  -d c  b  a  0  0  0  0  -d 0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |         {4} | 0  0  0  0  0  0  0  0  c  b  a  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  b  a  0  0  0  0  c  0  0  0  -d 0  0  -d 0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d c  b  a  0  0  0  0  -d 0  0  0  0  0  -d 0  0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  0  0  0  0  0  0  0  0  0  0  0  0  c  0  0  0  -d 0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  -d 0  0  0  -d 0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d c  b  a  0  -d 0  0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0  -d 0  0  0  0  0  0  -d 0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0  0  0  -d 0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  -d 0  0  0  -d ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  -d 0  ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0  0  ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  ||                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |{-4, 4}                                                                                                                                                                                                                                                      |                                                                                                                                                |                                                                                        |                                                                                |                                        |
     +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------+--------------------------------------------------------------------------------+----------------------------------------+
     |0                                                                                                                                                                                                                                                            |cokernel {3} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||0                                                                                       |0                                                                               |0                                       |
     |                                                                                                                                                                                                                                                             |         {3} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                                                                                        |                                                                                |                                        |
     |{-4, 3}                                                                                                                                                                                                                                                      |         {3} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||{-2, 3}                                                                                 |{-1, 3}                                                                         |{0, 3}                                  |
     |                                                                                                                                                                                                                                                             |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 ||                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 ||                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 ||                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a ||                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |{-3, 3}                                                                                                                                         |                                                                                        |                                                                                |                                        |
     +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------+--------------------------------------------------------------------------------+----------------------------------------+
     |0                                                                                                                                                                                                                                                            |0                                                                                                                                               |cokernel {2} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||cokernel {4} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||0                                       |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |         {2} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                                        |
     |{-4, 2}                                                                                                                                                                                                                                                      |{-3, 2}                                                                                                                                         |         {2} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||{0, 2}                                  |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                                        |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 ||                                        |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 ||                                        |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 ||                                        |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a ||                                        |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a ||                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |                                                                                        |{-1, 2}                                                                         |                                        |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |{-2, 2}                                                                                 |                                                                                |                                        |
     +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------+--------------------------------------------------------------------------------+----------------------------------------+
     |0                                                                                                                                                                                                                                                            |0                                                                                                                                               |0                                                                                       |cokernel {1} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 |                                |cokernel {3} | d c b a 0 0 0 0 0 0 0 0 ||
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |                                                                                        |         {1} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |                                |         {3} | 0 0 0 0 d c b a 0 0 0 0 ||
     |{-4, 1}                                                                                                                                                                                                                                                      |{-3, 1}                                                                                                                                         |{-2, 1}                                                                                 |         {1} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |                                |         {3} | 0 0 0 0 0 0 0 0 d c b a ||
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |                                                                                        |         {1} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |                                |                                        |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |                                                                                        |                                                                                |{0, 1}                                  |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |                                                                                        |{-1, 1}                                                                         |                                        |
     +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------+--------------------------------------------------------------------------------+----------------------------------------+
     |0                                                                                                                                                                                                                                                            |0                                                                                                                                               |0                                                                                       |0                                                                               |cokernel | d c b a |                    |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |{-4, 0}                                                                                                                                                                                                                                                      |{-3, 0}                                                                                                                                         |{-2, 0}                                                                                 |{-1, 0}                                                                         |{0, 0}                                  |
     +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------+--------------------------------------------------------------------------------+----------------------------------------+

o6 : SpectralSequencePage

i7 : basis(0,E^3)

     +------+
o7 = || 1 | |
     |      |
     |{0, 0}|
     +------+

o7 : Page

Ways to use this method: