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

i1 : A = QQ[x,y]

o1 = A

o1 : PolynomialRing

i2 : C = koszulComplex vars A

      1      2      1
o2 = A  <-- A  <-- A
                    
     0      1      2

o2 : Complex

i3 : K = filteredComplex C

o3 = -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

o3 : FilteredComplex