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
|