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SpectralSequences :: SpectralSequencePage ^ List

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

Synopsis

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

See also