Given complex maps with the same source, this method constructs the associated map from the source to the direct sum of the targets.
First, we define some non-trivial maps of chain complexes.
i1 : R = ZZ/101[a..d]; |
i2 : D1 = (freeResolution coker matrix{{a,b,c}})[1]
1 3 3 1
o2 = R <-- R <-- R <-- R
-1 0 1 2
o2 : Complex
|
i3 : D2 = freeResolution coker matrix{{a*b,a*c,b*c}}
1 3 2
o3 = R <-- R <-- R
0 1 2
o3 : Complex
|
i4 : C = freeResolution coker matrix{{a^2,b^2,c*d}}
1 3 3 1
o4 = R <-- R <-- R <-- R
0 1 2 3
o4 : Complex
|
i5 : f = randomComplexMap(D1, C)
3 1
o5 = 0 : R <----- R : 0
0
3 3
1 : R <----------------------- R : 1
{2} | 24 -29 -10 |
{2} | -36 19 -29 |
{2} | -30 19 -8 |
1 3
2 : R <------------------------------------------------------------- R : 2
{3} | -22a-29b-24c-38d -16a+39b+21c+34d 19a-47b-39c-18d |
1
3 : 0 <----- R : 3
0
o5 : ComplexMap
|
i6 : g = randomComplexMap(D2, C)
1 1
o6 = 0 : R <----------- R : 0
| -13 |
3 3
1 : R <---------------------- R : 1
{2} | -43 -47 16 |
{2} | -15 38 22 |
{2} | -28 2 45 |
2 3
2 : R <------------------------------------------------------------- R : 2
{3} | -34a-48b-47c+47d -23a+39b+43c-17d 11a-38b+33c+40d |
{3} | 19a-16b+7c+15d -11a+48b+36c+35d 11a+46b-28c+d |
1
3 : 0 <----- R : 3
0
o6 : ComplexMap
|
i7 : h = f||g
4 1
o7 = 0 : R <--------------- R : 0
{1} | 0 |
{1} | 0 |
{1} | 0 |
{0} | -13 |
6 3
1 : R <----------------------- R : 1
{2} | 24 -29 -10 |
{2} | -36 19 -29 |
{2} | -30 19 -8 |
{2} | -43 -47 16 |
{2} | -15 38 22 |
{2} | -28 2 45 |
3 3
2 : R <------------------------------------------------------------- R : 2
{3} | -22a-29b-24c-38d -16a+39b+21c+34d 19a-47b-39c-18d |
{3} | -34a-48b-47c+47d -23a+39b+43c-17d 11a-38b+33c+40d |
{3} | 19a-16b+7c+15d -11a+48b+36c+35d 11a+46b-28c+d |
o7 : ComplexMap
|
i8 : assert isWellDefined h |
i9 : assert(target h === target f ++ target g) |
i10 : assert(source h === source f) |
This is really a shorthand for constructing complex maps via block matrices.
i11 : assert(h === map(D1 ++ D2, C, {{f},{g}}))
|