Returns the two filtrations of the tensor product complex determined by the double complex. The following example illustrates the syntax.
i1 : A = QQ[x,y]; |
i2 : B = koszul vars A; |
i3 : C = koszul vars A; |
i4 : F' = (filteredComplex B) ** C
o4 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0
0 1 2 3 4
0 : image | 1 | <-- image {1} | 1 0 0 0 | <-- image {2} | 1 0 0 0 0 0 | <-- image 0 <-- image 0
{1} | 0 1 0 0 | {2} | 0 0 0 0 0 0 |
0 {1} | 0 0 0 0 | {2} | 0 0 0 0 0 0 | 3 4
{1} | 0 0 0 0 | {2} | 0 0 0 0 0 0 |
{2} | 0 0 0 0 0 0 |
1 {2} | 0 0 0 0 0 0 |
2
1 : image | 1 | <-- image {1} | 1 0 0 0 | <-- image {2} | 1 0 0 0 0 0 | <-- image {3} | 1 0 0 0 | <-- image 0
{1} | 0 1 0 0 | {2} | 0 1 0 0 0 0 | {3} | 0 1 0 0 |
0 {1} | 0 0 1 0 | {2} | 0 0 1 0 0 0 | {3} | 0 0 0 0 | 4
{1} | 0 0 0 1 | {2} | 0 0 0 1 0 0 | {3} | 0 0 0 0 |
{2} | 0 0 0 0 1 0 |
1 {2} | 0 0 0 0 0 0 | 3
2
1 4 6 4 1
2 : A <-- A <-- A <-- A <-- A
0 1 2 3 4
o4 : FilteredComplex
|
i5 : F'' = B ** (filteredComplex C)
o5 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0
0 1 2 3 4
0 : image | 1 | <-- image {1} | 0 0 0 0 | <-- image {2} | 0 0 0 0 0 0 | <-- image 0 <-- image 0
{1} | 0 0 0 0 | {2} | 0 0 0 0 0 0 |
0 {1} | 0 0 1 0 | {2} | 0 0 0 0 0 0 | 3 4
{1} | 0 0 0 1 | {2} | 0 0 0 0 0 0 |
{2} | 0 0 0 0 0 0 |
1 {2} | 0 0 0 0 0 1 |
2
1 : image | 1 | <-- image {1} | 1 0 0 0 | <-- image {2} | 0 0 0 0 0 0 | <-- image {3} | 0 0 0 0 | <-- image 0
{1} | 0 1 0 0 | {2} | 0 1 0 0 0 0 | {3} | 0 0 0 0 |
0 {1} | 0 0 1 0 | {2} | 0 0 1 0 0 0 | {3} | 0 0 1 0 | 4
{1} | 0 0 0 1 | {2} | 0 0 0 1 0 0 | {3} | 0 0 0 1 |
{2} | 0 0 0 0 1 0 |
1 {2} | 0 0 0 0 0 1 | 3
2
1 4 6 4 1
2 : A <-- A <-- A <-- A <-- A
0 1 2 3 4
o5 : FilteredComplex
|