Back to Forum | View unanswered posts | View active topics



Post new topic Reply to topic  Page 1 of 1
  [ 2 posts ] 
  Print view | E-mail friend Previous topic | Next topic 
Author Message
Hanno
 Post subject: Computing minimal resolutions of graded modules
PostPosted: Tue Aug 06, 2013 8:18 am 
Hello,

First of all: thank you very much for developing this great software!

I'm having trouble handling graded modules and computing their minimal resolutions:

1) How can I assign gradings to the generators in a free module over a graded polynomial ring?
2) I tried to compute the minimal resolution of the graded module Q[a]*e + Q[a] * f / (a*e+f) (with deg(a)=deg(f)=1, deg(e)=0), but didn't know how to define the gradings, and the ungraded approach

Code:
ring r = 0,a,lp;
matrix A[2][1] = 1,a;
module M = module(A);
resolution RES = mres(M,0);
RES;


suggested ranks 2 and 1 in the minimal resolution. Applying the function prune to the module, however, does eliminate the irrelevant generator f.

What am I doing wrong?

Thank you!
Hanno


Report this post
Top
  
Reply with quote  
malex
 Post subject: Re: Computing minimal resolutions of graded modules
PostPosted: Tue Aug 06, 2013 1:44 pm 

Joined: Tue Jun 23, 2009 10:33 pm
Posts: 51
Location: Kaiserslautern
you could try using the following new feature (probably in the development version of Singular - spielwiese)


New orderings for modules

Quote:
One can assign weights to module components, when defining a monomial ordering. For example

Code:
ring R = 0, (x,y,z), (am(1,2,3,   10,20,30,40), dp, C);
deg(x*gen(1));
==> 11


will assign weights 1,2,3 to x,y,z respectively, and weights 10,20,30,40,0,0,... to components of any free module defined over R. This ordering will first sort by this weighted degree, then by dp on the ring monomials and then will give priority to the large component index.


Report this post
Top
 Profile  
Reply with quote  
Display posts from previous:  Sort by  
Post new topic Reply to topic  Page 1 of 1
  [ 2 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 11:04 am
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group