Given a complex $C$, this method produces the natural quasi-isomorphism from a complex $F$ all of whose terms are free modules to the complex $C$. The algorithm used minimizes the ranks of the free modules in $F$.
i1 : R = ZZ/101[a,b,c]; |
i2 : I = ideal(a^2, a*b, b*c)
2
o2 = ideal (a , a*b, b*c)
o2 : Ideal of R
|
i3 : C = freeResolution I
1 3 2
o3 = R <-- R <-- R
0 1 2
o3 : Complex
|
i4 : f = augmentationMap C
1
o4 = 0 : cokernel | a2 ab bc | <--------- R : 0
| 1 |
o4 : ComplexMap
|
i5 : assert isWellDefined f |
i6 : assert isComplexMorphism f |
i7 : assert isQuasiIsomorphism f |
i8 : g = resolutionMap complex comodule I
1
o8 = 0 : cokernel | a2 ab bc | <--------- R : 0
| 1 |
o8 : ComplexMap
|
i9 : assert(f == g) |
The object augmentationMap is a method function.