A complex map $f : C \to D$ of degree $d$ is a sequence of maps $f_i : C_i \to D_{i+d}$. This method allows one to access the individual $f_i$.
i1 : S = ZZ/101[a..c]; |
i2 : C = freeResolution coker matrix{{a^2, b^2, c^2}}
1 3 3 1
o2 = S <-- S <-- S <-- S
0 1 2 3
o2 : Complex
|
i3 : D = freeResolution coker vars S
1 3 3 1
o3 = S <-- S <-- S <-- S
0 1 2 3
o3 : Complex
|
i4 : f = randomComplexMap(D, C)
1 1
o4 = 0 : S <---------- S : 0
| 24 |
3 3
1 : S <-------------------------------------------------- S : 1
{1} | -36a-30b-29c -29a-24b-38c -39a-18b-13c |
{1} | 19a+19b-10c -16a+39b+21c -43a-15b-28c |
{1} | -29a-8b-22c 34a+19b-47c -47a+38b+2c |
3 3
2 : S <------------------------------------------------------------------------------------------------------ S : 2
{2} | 16a2+22ab-34b2+45ac-48bc-47c2 35a2+11ab+33b2-38ac+40bc+11c2 -37a2-13ab+30b2-10ac-18bc+39c2 |
{2} | 47a2+19ab+7b2-16ac+15bc-23c2 46a2-28ab-3b2+ac+22bc-47c2 27a2-22ab-9b2+32ac-32bc-20c2 |
{2} | 39a2+43ab-11b2-17ac+48bc+36c2 -23a2-7ab+29b2+2ac-47bc+15c2 24a2-30ab-15b2-48ac+39bc |
1 1
3 : S <------------------------------------------------------------------- S : 3
{3} | 33a3-49a2b-19ab2+44b3-33a2c+17abc-39b2c-20ac2+36bc2+9c3 |
o4 : ComplexMap
|
i5 : f_2
o5 = {2} | 16a2+22ab-34b2+45ac-48bc-47c2 35a2+11ab+33b2-38ac+40bc+11c2
{2} | 47a2+19ab+7b2-16ac+15bc-23c2 46a2-28ab-3b2+ac+22bc-47c2
{2} | 39a2+43ab-11b2-17ac+48bc+36c2 -23a2-7ab+29b2+2ac-47bc+15c2
------------------------------------------------------------------------
-37a2-13ab+30b2-10ac-18bc+39c2 |
27a2-22ab-9b2+32ac-32bc-20c2 |
24a2-30ab-15b2-48ac+39bc |
3 3
o5 : Matrix S <--- S
|
i6 : f_0
o6 = | 24 |
1 1
o6 : Matrix S <--- S
|
Indices that are outside of the concentration are automatically zero.
i7 : concentration f o7 = (0, 3) o7 : Sequence |
i8 : f_-1 o8 = 0 o8 : Matrix 0 <--- 0 |
i9 : f_3
o9 = {3} | 33a3-49a2b-19ab2+44b3-33a2c+17abc-39b2c-20ac2+36bc2+9c3 |
1 1
o9 : Matrix S <--- S
|
i10 : f_4 o10 = 0 o10 : Matrix 0 <--- 0 |