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SpectralSequences :: Page

Page -- the type of all pages

Description

A page is a collection of modules which are indexed by lists of integers. This is a parent class for the type SpectralSequencePage. The infinity page of a spectral sequence is an example of a page which is not a 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 sucessive 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);

The infinity page of the resulting spectral sequence is computed below.

i5 : E = prune spectralSequence K;
i6 : E^infinity

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

o6 : Page

See also

Types of Page :

Functions and methods returning a Page :

Methods that use a Page :

For the programmer

The object Page is a type, with ancestor classes MutableHashTable < HashTable < Thing.