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HH DGAlgebra -- The homology algebra of a DG algebra

Description

Returns the homology algebra of A, caching the result inside A so subsequent calls are fast. This is a convenience wrapper around homologyAlgebra that supports the HH shorthand.

i1 : R = ZZ/101[a,b,c] / ideal(a^3, b^3, c^3, a^2*b^2*c^2)

o1 = R

o1 : QuotientRing
 
i2 : A = koszulComplexDGA R

o2 = {Ring => R                          }
      Underlying algebra => R[T   ..T   ]
                               1,1   1,3
      Differential => {a, b, c}

o2 : DGAlgebra
 
i3 : HA = HH A
Finding easy relations           :  -- used 0.0315046s (cpu); 0.0287475s (thread); 0s (gc)

o3 = HA

o3 : QuotientRing
 
i4 : numgens HA

o4 = 10
 
i5 : apply(maxDegree A + 1, i -> numgens prune homology(i, A))

o5 = {1, 4, 6, 3}

o5 : List

For DG algebras with even-degree generators (such as acyclic closures of non-regular rings), call homologyAlgebra directly and supply GenDegreeLimit and RelDegreeLimit explicitly.

See also

Ways to use this method:

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/DGAlgebras/doc.m2:8166:0.