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SpectralSequences :: FilteredComplex ^ ZZ

FilteredComplex ^ ZZ -- the filtered pieces

Synopsis

Description

Returns the chain complex in (cohomological) filtration degree j. The relationship K j = K (-j) holds.

i1 : A = QQ[x,y];
i2 : C = koszul vars A;
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
i4 : K_0

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

o4 : ChainComplex
i5 : K_1

o5 = image | 1 | <-- image {1} | 1 0 | <-- image 0
                           {1} | 0 1 |      
     0                                     2
                     1

o5 : ChainComplex
i6 : K_2

      1      2      1
o6 = A  <-- A  <-- A
                    
     0      1      2

o6 : ChainComplex
i7 : K^(-1)

o7 = image | 1 | <-- image {1} | 1 0 | <-- image 0
                           {1} | 0 1 |      
     0                                     2
                     1

o7 : ChainComplex
i8 : K^(-2)

      1      2      1
o8 = A  <-- A  <-- A
                    
     0      1      2

o8 : ChainComplex
i9 : K_infinity

      1      2      1
o9 = A  <-- A  <-- A
                    
     0      1      2

o9 : ChainComplex
i10 : K_(-infinity)

o10 = image 0 <-- image 0 <-- image 0
                               
      0           1           2

o10 : ChainComplex
i11 : K^(-infinity)

       1      2      1
o11 = A  <-- A  <-- A
                     
      0      1      2

o11 : ChainComplex
i12 : K^infinity

o12 = image 0 <-- image 0 <-- image 0
                               
      0           1           2

o12 : ChainComplex

See also