Post new topic Reply to topic  [ 3 posts ] 
Author Message
 Post subject: TOP module ordering
PostPosted: Wed Feb 16, 2022 11:50 pm 

Joined: Mon Jan 31, 2011 9:50 pm
Posts: 12
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.)


Report this post
Top
 Profile  
Reply with quote  
 Post subject: Re: TOP module ordering
PostPosted: Fri Feb 18, 2022 3:57 pm 

Joined: Wed May 25, 2005 4:16 pm
Posts: 275
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.


Report this post
Top
 Profile  
Reply with quote  
 Post subject: Re: TOP module ordering
PostPosted: Sat Feb 19, 2022 7:26 am 

Joined: Mon Jan 31, 2011 9:50 pm
Posts: 12
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.


Report this post
Top
 Profile  
Reply with quote  
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 3 posts ] 

You can post new topics in this forum
You can reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

It is currently Fri May 13, 2022 10:54 am
cron
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group