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What does cohomology_generators actually do?

asked 2019-05-21 09:46:44 -0500

wututut gravatar image

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!

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Strictly speaking the documentation does not claim that the list is anyhow minimal. However the stated algorithm does suggest that this is attempted. Do you see anything wrong with the algorithm or its implementation (approx. 40 lines of code)?

rburing gravatar imagerburing ( 2019-05-21 12:46:39 -0500 )edit

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.

wututut gravatar imagewututut ( 2019-05-22 02:32:05 -0500 )edit

I said "suggest" because the code obviously doesn't work, as you demonstrated.

rburing gravatar imagerburing ( 2019-05-22 03:09:40 -0500 )edit

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answered 2019-05-21 21:46:52 -0500

updated 2019-05-21 21:47:59 -0500

This should be improved once the changes at https://trac.sagemath.org/ticket/27045 are merged into Sage.

Oh, and if you want to know "What does cohomology_generators actually do?", evaluate B.cohomology_generators?? to read the source code.

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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.

wututut gravatar imagewututut ( 2019-05-22 08:33:35 -0500 )edit

I don't understand your comment at all. Which parts indicate that developers think it's okay to have "wrong functions with undocumented bugs"? I see a discussion, with one person clarifying the changes they are proposing, and others critiquing and trying to improve those changes. Once it is made clear that there is a bug in the old code, no one argued about fixing it.

John Palmieri gravatar imageJohn Palmieri ( 2019-05-22 12:03:33 -0500 )edit

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Asked: 2019-05-21 09:46:44 -0500

Seen: 109 times

Last updated: May 21