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

## 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