chainModuleHomology -- computes the d-cohomology of an R[d]/d^2-module

Synopsis

• Usage:

  chainModuleHomology(k,M)

  chainModuleHomology M

• Inputs:
  • M, a module, whose ring is of the form R[d]/d^2 for some coefficient ring R
  • k, an integer, the cohomological degree; if omitted, then the cohomology is computed in all degrees and returned as an R[d]/d^2-module where d acts by zero.
• Outputs:
  • a module, the d-cohomology of M

Description

i1 : C = QQ[d]/d^2;

i2 : declareGenerators(C,{a=>0,b=>0,c=>0,ab=>1,ac=>1,bc=>1});

i3 : M = cospan(d*a+ab+ac, d*b-ab+bc, d*c-ac-bc, d*ab, d*ac, d*bc);

i4 : apply(5,i->prune evaluateInDegree({i},M))

        3    3
o4 = {QQ , QQ , 0, 0, 0}

o4 : List

i5 : H = chainModuleHomology(M);

i6 : apply(5,i->prune evaluateInDegree({i},H))

        1    1
o6 = {QQ , QQ , 0, 0, 0}

o6 : List

i7 : apply(5,i->prune chainModuleHomology(i,M))

        1    1
o7 = {QQ , QQ , 0, 0, 0}

o7 : List

Caveat