A map of complexes $f : C \rightarrow D$ of degree $d$ is a sequence of maps $f_i : C_i \rightarrow D_{d+i}$. No relationship between the maps $f_i$ and and the differentials of either $C$ or $D$ is assumed.
We construct a map of chain complexes by specifying a function which determines the maps between the terms.
i1 : R = ZZ/101[x]/x^3; |
i2 : M = coker vars R
o2 = cokernel | x |
1
o2 : R-module, quotient of R
|
i3 : C = freeResolution(M, LengthLimit => 6)
1 1 1 1 1 1 1
o3 = R <-- R <-- R <-- R <-- R <-- R <-- R
0 1 2 3 4 5 6
o3 : Complex
|
i4 : D = C[1]
1 1 1 1 1 1 1
o4 = R <-- R <-- R <-- R <-- R <-- R <-- R
-1 0 1 2 3 4 5
o4 : Complex
|
i5 : f = map(D, C, i ->
if odd i then
map(D_i, C_i, {{x}})
else map(D_i, C_i, {{x^2}})
)
1 1
o5 = 0 : R <-------------- R : 0
{1} | x2 |
1 1
1 : R <------------- R : 1
{3} | x |
1 1
2 : R <-------------- R : 2
{4} | x2 |
1 1
3 : R <------------- R : 3
{6} | x |
1 1
4 : R <-------------- R : 4
{7} | x2 |
1 1
5 : R <------------- R : 5
{9} | x |
o5 : ComplexMap
|
i6 : assert isWellDefined f |
i7 : assert isCommutative f |
i8 : assert(source f == C) |
i9 : assert(target f == D) |