The coimage of a ZZ/d-graded factorization map $f : C \to D$ is the ZZ/d-graded factorization $E$ whose $i-th$ term is $coimage(f_i)$, and whose differential is induced from the differential on the source.
i1 : S = ZZ/101[a,b];
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i2 : R = S/(a^3+b^3);
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i3 : m = ideal vars R
o3 = ideal (a, b)
o3 : Ideal of R
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i4 : C = tailMF m
2 2 2
o4 = S <-- S <-- S
0 1 0
o4 : ZZdFactorization
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i5 : D = tailMF (m^2)
3 3 3
o5 = S <-- S <-- S
0 1 0
o5 : ZZdFactorization
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i6 : f = randomFactorizationMap(C, D, Cycle => true, InternalDegree => 2)
2 3
o6 = 0 : S <------------------------------------------------------------------------------ S : 0
{2} | -34a3+15a2b-31ab2-38b3 -29a3+35a2b+6ab2+38b3 -22a3-5a2b+41ab2-30b3 |
{3} | -38a2-16ab+39b2 -10a2-29ab-8b2 21a2+34ab+19b2 |
2 3
1 : S <------------------------------------------------------------------------------ S : 1
{4} | -34a3-14a2b-12ab2-19b3 29a3+44a2b-35ab2+39b3 -22a3-39a2b+48ab2-8b3 |
{4} | -38a3+8a2b+3ab2-30b3 10a3+21a2b-40ab2+38b3 21a3+18a2b+32ab2-38b3 |
o6 : ZZdFactorizationMap
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i7 : isWellDefined coimage f
o7 = true
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i8 : inducedMap(coimage f, D)
3
o8 = 0 : cokernel {3} | -29a5-27a4b+a3b2+2a2b3+10ab4+50b5 | <----------------- S : 0
{3} | -19a5-38a4b+30a3b2+14a2b3+29ab4+21b5 | {3} | 1 0 0 |
{3} | a5+37a4b+a3b2+29a2b3-24ab4-30b5 | {3} | 0 1 0 |
{3} | 0 0 1 |
3
1 : cokernel {5} | -29a5+a4b-37a3b2+38a2b3+44ab4+30b5 | <----------------- S : 1
{5} | 19a5-10a4b-47a3b2+34a2b3+40ab4+50b5 | {5} | 1 0 0 |
{5} | a5+17a4b+47a3b2+12a2b3-22ab4+21b5 | {5} | 0 1 0 |
{5} | 0 0 1 |
o8 : ZZdFactorizationMap
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i9 : prune coimage f
o9 = cokernel {3} | -29a5-27a4b+a3b2+2a2b3+10ab4+50b5 | <-- cokernel {5} | -29a5+a4b-37a3b2+38a2b3+44ab4+30b5 | <-- cokernel {3} | -29a5-27a4b+a3b2+2a2b3+10ab4+50b5 |
{3} | -19a5-38a4b+30a3b2+14a2b3+29ab4+21b5 | {5} | 19a5-10a4b-47a3b2+34a2b3+40ab4+50b5 | {3} | -19a5-38a4b+30a3b2+14a2b3+29ab4+21b5 |
{3} | a5+37a4b+a3b2+29a2b3-24ab4-30b5 | {5} | a5+17a4b+47a3b2+12a2b3-22ab4+21b5 | {3} | a5+37a4b+a3b2+29a2b3-24ab4-30b5 |
0 1 0
o9 : ZZdFactorization
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i10 : potential coimage f
3 3
o10 = a + b
o10 : S
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