Given a map $d$ of complexes having degree -1 and whose source and targets are equal, this method constructs the chain complex whose differential is $d$. This constructor does not verify that $d^2 = 0$.
i1 : S = ZZ/101[x_1..x_4]; |
i2 : F = freeResolution coker vars S
1 4 6 4 1
o2 = S <-- S <-- S <-- S <-- S
0 1 2 3 4
o2 : Complex
|
i3 : d = randomComplexMap(F, F, Cycle => true, InternalDegree => -1, Degree => -1)
1
o3 = -1 : 0 <----- S : 0
0
1 4
0 : S <---------------------- S : 1
| -29 30 -36 -24 |
4 6
1 : S <--------------------------------- S : 2
{1} | -30 36 0 24 0 0 |
{1} | -29 0 36 0 24 0 |
{1} | 0 -29 30 0 0 24 |
{1} | 0 0 0 -29 30 -36 |
6 4
2 : S <--------------------------- S : 3
{2} | -36 -24 0 0 |
{2} | -30 0 -24 0 |
{2} | -29 0 0 -24 |
{2} | 0 -30 36 0 |
{2} | 0 -29 0 36 |
{2} | 0 0 -29 30 |
4 1
3 : S <--------------- S : 4
{3} | 24 |
{3} | -36 |
{3} | -30 |
{3} | -29 |
o3 : ComplexMap
|
i4 : d^2 o4 = 0 o4 : ComplexMap |
i5 : C = complex d
1 4 6 4 1
o5 = S <-- S <-- S <-- S <-- S
0 1 2 3 4
o5 : Complex
|
i6 : assert isWellDefined C |
i7 : assert all(0..4, i -> dd^C_i == d_i) |
i8 : e = randomComplexMap(F, F, InternalDegree => -1, Degree => -1)
1
o8 = -1 : 0 <----- S : 0
0
1 4
0 : S <--------------------- S : 1
| 19 19 -10 -29 |
4 6
1 : S <----------------------------------- S : 2
{1} | -8 -38 34 -18 -28 16 |
{1} | -22 -16 19 -13 -47 22 |
{1} | -29 39 -47 -43 38 45 |
{1} | -24 21 -39 -15 2 -34 |
6 4
2 : S <--------------------------- S : 3
{2} | -48 15 48 40 |
{2} | -47 -23 36 11 |
{2} | 47 39 35 46 |
{2} | 19 43 11 -28 |
{2} | -16 -17 -38 1 |
{2} | 7 -11 33 -3 |
4 1
3 : S <--------------- S : 4
{3} | 22 |
{3} | -47 |
{3} | -23 |
{3} | -7 |
o8 : ComplexMap
|
i9 : D = complex e
1 4 6 4 1
o9 = S <-- S <-- S <-- S <-- S
0 1 2 3 4
o9 : Complex
|
i10 : debugLevel = 1 o10 = 1 |
i11 : assert not isWellDefined D -- expected maps in the differential to compose to zero -- differentials at indices (2, 1) fail this condition |