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};
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i3 : F2D = D; |
i4 : F1D = simplicialComplex {a*c, d};
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i5 : F0D = simplicialComplex {a,d};
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i6 : K = filteredComplex {F2D, F1D, F0D};
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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
|