A map of complexes $f : C \rightarrow D$ of degree $d$ is a sequence of maps $f_i : C_i \rightarrow D_{d+i}$.
We construct the zero map between two chain complexes.
i1 : R = QQ[a,b,c] o1 = R o1 : PolynomialRing |
i2 : C = freeResolution coker vars R
1 3 3 1
o2 = R <-- R <-- R <-- R
0 1 2 3
o2 : Complex
|
i3 : D = freeResolution coker matrix{{a^2, b^2, c^2}}
1 3 3 1
o3 = R <-- R <-- R <-- R
0 1 2 3
o3 : Complex
|
i4 : f = map(D, C, 0) o4 = 0 o4 : ComplexMap |
i5 : assert isWellDefined f |
i6 : assert isComplexMorphism f |
i7 : g = map(C, C, 0, Degree => 13) o7 = 0 o7 : ComplexMap |
i8 : assert isWellDefined g |
i9 : assert(degree g == 13) |
i10 : assert not isComplexMorphism g |
i11 : assert isCommutative g |
i12 : assert isHomogeneous g |
i13 : assert(source g == C) |
i14 : assert(target g == C) |
Using this function to create the identity map is the same as using id _ Complex.
i15 : assert(map(C, C, 1) === id_C) |