Timeline for Algorithm to check is representation irreducible ? Algorithm to decompose the reducible one ?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Sep 15 at 8:20 | comment | added | Derek Holt | @student Factorization of polynomials over finite fields is very fast in practice using the standard probabilistic algorithms, and accounts for a very small proportion of the running time of the algorithm. Allan Steel from the Magma group in Sydney has made a lot of progress with decomposing modules over the integers and over number fields. You can find details in his PhD thesis, available from his webpage. | |
| Sep 15 at 0:37 | comment | added | Student | This has been inspiring me over the past few days. Some older papers are difficult to find. A modern account is given in sec 1.3 of Lux and Pahlings' Representations of Groups. There, two basic variants were given. The meataxe based on Norton's irreducibility criterion only works for finite fields. A workaround is the Holt-Rees algorithm. However, one step of the later requires factorizing single-variable polynomials over the field, which no definite algorithm solves. Over the integer ring $Z$, check Parker's paper on The Integral Meataxe. | |
| Nov 10, 2012 at 16:49 | vote | accept | Alexander Chervov | ||
| Nov 4, 2012 at 10:54 | comment | added | Alexander Chervov | Thank you very much ! I will accept your answers, but let me think over them for a while. May ask you about the complexity of the algorithms you mention - are they polynomial (if yes what degree), again both "worst case" and "average". May I also kindly ask you to look at mathoverflow.net/questions/111444/… | |
| Nov 3, 2012 at 22:20 | history | answered | Derek Holt | CC BY-SA 3.0 |