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| Homology and non-commutative base-ring https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=1899 |
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| Author: | noncommuting [ Tue Jan 04, 2011 3:10 am ] |
| Post subject: | Homology and non-commutative base-ring |
I have been using the homology command with a non-commutative base ring. Is there any reason that the answer I am getting would not be correct? Thanks in advance. |
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| Author: | gorzel [ Tue Jan 04, 2011 5:01 pm ] |
| Post subject: | Re: Homology and non-commutative base-ring |
If you have the impression that some results are not correct -- and if you want to get an answer here -- then present the comptuation you have done. |
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| Author: | noncommuting [ Tue Jan 04, 2011 6:51 pm ] |
| Post subject: | Re: Homology and non-commutative base-ring |
My apologies for the possibly confusing context of the question. The answer I am getting is the answer that I wanted, that the homology vanishes. The example is too complicated to do by hand. However, I will say that the ring is (almost) a Weyl-algebra. I want a "proof" that this homology vanishes -- which is why I want to check if anything about the homology command is critically assuming the ring to be commutative. Because homolog_lib is listed as a commutative algebra library, I am a bit hesitant. |
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| Author: | malex [ Tue Jan 04, 2011 8:28 pm ] |
| Post subject: | Re: Homology and non-commutative base-ring |
AFAIK 'homology' only uses 'modulo' command and module-concatination which will work fine in any non-commutative setting. Therefore if you are content with the idea behind it (section Compute: of its manual entry) it should work for you. ps: Happy New Year! |
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| Author: | levandov [ Fri Oct 14, 2011 6:26 pm ] |
| Post subject: | Re: Homology and non-commutative base-ring |
noncommuting wrote: My apologies for the possibly confusing context of the question. The answer I am getting is the answer that I wanted, that the homology vanishes. The example is too complicated to do by hand. However, I will say that the ring is (almost) a Weyl-algebra. I want a "proof" that this homology vanishes -- which is why I want to check if anything about the homology command is critically assuming the ring to be commutative. Because homolog_lib is listed as a commutative algebra library, I am a bit hesitant. There is an ongoing work on the nchomalg.lib, which implements homological computations for G-algebras (which Singular:Plural supports). Contact me or post your computation here for being 100% sure. Indeed there is a possibility that some computations can be incorrect. homolog.lib can only work by chance in non-commutative ring. Regards, Viktor |
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