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| Hilbert-Samuel functions https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=1682 |
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| Author: | yihuang [ Fri Aug 29, 2008 12:05 am ] |
| Post subject: | Hilbert-Samuel functions |
Hi! Let (R,m) be a Noetherian local ring. I just wonder if there is any SINGULAR codes that can compute the Poincare series of the Hilbert-Samuel functions for m-primary ideals. Thanks. |
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| Author: | Gerhard Pfister [ Mon Mar 30, 2009 9:32 pm ] |
| Post subject: | |
Singular has a command which computes the numerator Q(t) for the Hilbert-Poincare series (the denominator is (1-t)^n, n the number of variables): Code: ring A=0,(t,x,y,z),ds; ideal I=x5y2,x3,y3,xy4,xy7; intvec v = hilb(std(I),1); v; //-> 1,0,0,-2,0,0,1,0 The latter output has to be interpreted as follows: if v= (v0, ... , vd, 0) then Q(t) = sum_{i=0}^{d} vi t^i. More details can be found in the book G.-M. Greuel / G. Pfister http://www.mathematik.uni-kl.de/%7Epfister/Artikel/buchGMG.ps.gz: A Singular Introduction to Commutative Algebra, Springer 2002 second edition 2007 (pages 315 ff). |
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