SpectralSequencePage ^ List -- the module in the i,j position on the page

Operator: ^
Usage:

M = P^L
Inputs:
- P, a spectral sequence page,
- L, a list, A list L = \{i,j\} of integers
Outputs:
- M, a module,

Description

Returns the module in the \{i,j\} \ position in the spectral sequence page. (Using cohomological or upper indexing conventions.) The relationship $E^{-i,-j} = E_{i,j}$ holds.

i1 : A = QQ[x,y]

o1 = A

o1 : PolynomialRing

i2 : C = koszul vars A;

i3 : K = filteredComplex C;

i4 : E = spectralSequence K

o4 = E

o4 : SpectralSequence

i5 : E_0

     +-----------------+-----------------------+------+
     |                 |                       | 1    |
o5 = |image | 1 0 0 0 ||image {1} | 1 0 0 0 0 ||A     |
     |                 |      {1} | 0 1 0 0 0 ||      |
     |{0, 0}           |                       |{2, 0}|
     |                 |{1, 0}                 |      |
     +-----------------+-----------------------+------+

o5 : SpectralSequencePage

i6 : E_0 ^{-1,0}

o6 = image {1} | 1 0 0 0 0 |
           {1} | 0 1 0 0 0 |

                             2
o6 : A-module, submodule of A

i7 : E^0 _{1,0}

o7 = image {1} | 1 0 0 0 0 |
           {1} | 0 1 0 0 0 |

                             2
o7 : A-module, submodule of A

Ways to use this method:

SpectralSequencePage ^ List -- the module in the i,j position on the page

The source of this document is in SpectralSequences.m2:3527:0.

SpectralSequencePage ^ List -- the module in the i,j position on the page

Description

See also

Ways to use this method: