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| TOP module ordering https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=2976 |
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| Author: | leonada [ Wed Feb 16, 2022 11:50 pm ] |
| Post subject: | TOP module ordering |
Maybe someone knows why TOP seems to have been chosen as the only module ordering to use in free resolutions of ideals and modules. I would have though the default that makes most sense as a mathematical default would have been POT, but I would rather use a signature-based ordering in the ideal case, which means each new map in the free resolution has a slightly different ordering based on the names (signatures) of the module generators. (As an aside, I am not a fan of minimizing here, just as I am not a fan of minimizing as done in normal.lib, since it is not really mathematically driven, only minimization-driven.) |
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| Author: | hannes [ Fri Feb 18, 2022 3:57 pm ] |
| Post subject: | Re: TOP module ordering |
You can have POT or TOP for free resolutions - depending on the ordering of the ring (therefore a ring in singular has always also a module ordering, even if only ideals are defined in it). There are also different algorithm to compute free resolution, some of them use internally a diffirent ordering, for example fres (Schreyer ordering or 'signature based'), lres (dp,c or TOP), etc. |
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| Author: | leonada [ Sat Feb 19, 2022 7:26 am ] |
| Post subject: | Re: TOP module ordering |
Already ring r=0,(x,y,z), (c,dp); or ring r=0,(x,y,z),(C,dp); are big improvements for me. So maybe you can tell me where to look to get "signature-based" or Schreyer orderings in Singular, as I can't seem to find them mentioned in the online manual. |
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