filteredComplex(ChainComplex) -- obtain a filtered complex from a chain complex

i1 : needsPackage "SpectralSequences"

o1 = SpectralSequences

o1 : Package

i2 : A = QQ[x,y]

o2 = A

o2 : PolynomialRing

i3 : C = koszul vars A

      1      2      1
o3 = A  <-- A  <-- A
                    
     0      1      2

o3 : ChainComplex

i4 : K = filteredComplex C

o4 = -1 : image 0 <-- image 0 <-- image 0
                                   
          0           1           2

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

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

          1      2      1
     2 : A  <-- A  <-- A
                        
         0      1      2

o4 : FilteredComplex