HH_ZZ ChainComplex -- homology of a chain complex

HH_ZZ ChainComplex -- homology of a chain complex

Synopsis:

Function: homology -- general homology functor

Input:

an instance of class ZZ.

an instance of class ChainComplex.

Output:

an instance of class Module.

Optional arguments :

HH_i C -- homology at the i-th spot of the chain complex C.

i1 : R = ZZ/101[x,y]



o1 = R



o1 : PolynomialRing

i2 : C = chainComplex(matrix{{x,y}},matrix{{x*y},{-x^2}})



      1      2      1

o2 = R  <-- R  <-- R

                    

     0      1      2



o2 : ChainComplex

i3 : M = HH_1 C



o3 = subquotient ({1} | -y |, {1} | xy  |)

                  {1} | x  |  {1} | -x2 |



                               2

o3 : R-module, subquotient of R

i4 : prune M



o4 = cokernel {2} | x |



                            1

o4 : R-module, quotient of R

Code:

     -- ../../../Macaulay2/m2/chaincomplexes.m2:449
     homology(ZZ,ChainComplex) := Module => opts -> (i,C) -> homology(C.dd_i, C.dd_(i+1))