Given simplicial module 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 simplicial modules.
i1 : R = ZZ/101[a..d];
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i2 : D1 = simplicialModule((freeResolution coker matrix{{a,b,c}})[1], Degeneracy => true)
3 6 10
o2 = R <-- R <-- R <-- ...
0 1 2
o2 : SimplicialModule
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i3 : D2 = simplicialModule(freeResolution coker matrix{{a*b,a*c,b*c}}, Degeneracy => true)
1 4 9
o3 = R <-- R <-- R <-- ...
0 1 2
o3 : SimplicialModule
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i4 : C = simplicialModule(freeResolution coker matrix{{a^2,b^2,c*d}}, Degeneracy => true)
1 4 10 20
o4 = R <-- R <-- R <-- R <-- ...
0 1 2 3
o4 : SimplicialModule
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i5 : f = randomSimplicialMap(D1, C)
3 1
o5 = 0 : R <----- R : 0
0
6 4
1 : R <------------------------- R : 1
{1} | 0 0 0 0 |
{1} | 0 0 0 0 |
{1} | 0 0 0 0 |
{2} | 0 24 -29 -10 |
{2} | 0 -36 19 -29 |
{2} | 0 -30 19 -8 |
10 10
2 : R <--------------------------------------------------------------------------------------- R : 2
{1} | 0 0 0 0 0 0 0 0 0 0 |
{1} | 0 0 0 0 0 0 0 0 0 0 |
{1} | 0 0 0 0 0 0 0 0 0 0 |
{2} | 0 24 -29 -10 0 0 0 0 0 0 |
{2} | 0 -36 19 -29 0 0 0 0 0 0 |
{2} | 0 -30 19 -8 0 0 0 0 0 0 |
{2} | 0 0 0 0 24 -29 -10 0 0 0 |
{2} | 0 0 0 0 -36 19 -29 0 0 0 |
{2} | 0 0 0 0 -30 19 -8 0 0 0 |
{3} | 0 0 0 0 0 0 0 -22a-29b-24c-38d -16a+39b+21c+34d 19a-47b-39c-18d |
o5 : SimplicialModuleMap
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i6 : g = randomSimplicialMap(D2, C)
1 1
o6 = 0 : R <----------- R : 0
| -13 |
4 4
1 : R <-------------------------- R : 1
{0} | -13 0 0 0 |
{2} | 0 -43 -47 16 |
{2} | 0 -15 38 22 |
{2} | 0 -28 2 45 |
9 10
2 : R <--------------------------------------------------------------------------------------- R : 2
{0} | -13 0 0 0 0 0 0 0 0 0 |
{2} | 0 -43 -47 16 0 0 0 0 0 0 |
{2} | 0 -15 38 22 0 0 0 0 0 0 |
{2} | 0 -28 2 45 0 0 0 0 0 0 |
{2} | 0 0 0 0 -43 -47 16 0 0 0 |
{2} | 0 0 0 0 -15 38 22 0 0 0 |
{2} | 0 0 0 0 -28 2 45 0 0 0 |
{3} | 0 0 0 0 0 0 0 -34a-48b-47c+47d -23a+39b+43c-17d 11a-38b+33c+40d |
{3} | 0 0 0 0 0 0 0 19a-16b+7c+15d -11a+48b+36c+35d 11a+46b-28c+d |
o6 : SimplicialModuleMap
|