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SpectralSequences :: filteredComplex(SpectralSequence)

filteredComplex(SpectralSequence) -- obtain the filtered complex associated to the spectral sequence

Synopsis

Description

Produces the filtered complex which determined the spectral sequence. Consider the spectral sequence $E$ which arises from a nested list of simplicial complexes.

i1 : A = QQ[a,b,c,d];
i2 : D = simplicialComplex {a*d*c, a*b, a*c, b*c};
i3 : F2D = D;
i4 : F1D = simplicialComplex {a*c, d};
i5 : F0D = simplicialComplex {a,d};
i6 : K = filteredComplex {F2D, F1D, F0D};
i7 : E = spectralSequence(K) ;

The underlying filtered chain complex can be recovered from the spectral sequence by:

i8 : C = filteredComplex E

o8 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0
                                               
          -1          0           1           2

     0 : image | 1 | <-- image | 1 0 | <-- image 0 <-- image 0
                               | 0 0 |                  
         -1                    | 0 0 |     1           2
                               | 0 1 |
                          
                         0

     1 : image | 1 | <-- image | 1 0 0 | <-- image | 0 | <-- image 0
                               | 0 0 0 |           | 1 |      
         -1                    | 0 1 0 |           | 0 |     2
                               | 0 0 1 |           | 0 |
                                                   | 0 |
                         0                    
                                             1

           1       4       5       1
     2 : QQ  <-- QQ  <-- QQ  <-- QQ
                                  
         -1      0       1       2

o8 : FilteredComplex