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2019-05-22 08:33:35 -0600 commented answer What does cohomology_generators actually do?

Wow. Reading this bug report convinced me I shouldn't use sage. If even the developers think it's okay to have wrong functions with undocumented bugs... Thank god I didn't include the results in an article before knowing this.

2019-05-22 02:32:05 -0600 commented question What does cohomology_generators actually do?

The documentation is misleading then. It says explicitly (not "suggest") that the function it is finding a complement of the set of elements generated by lower-degree generators, as well as coboundaries.

2019-05-21 11:38:46 -0600 received badge  Student (source)
2019-05-21 10:48:21 -0600 asked a question What does cohomology_generators actually do?

I don't understand the output of the function "cohomology_generators" of commutative differential graded algebras. Look at this simple exmaple:

A.<x,y,z,t> = GradedCommutativeAlgebra(QQ, degrees = (2,2,1,2))
B = A.cdg_algebra({z:x-y})
B.cohomology_generators(5)

{2: [t, y, x]}

It's apparently telling me that t, x and y are all generators of the cohomology algebra in degree 2. But in cohomology, x = y, since dz = x - y!