Post new topic Reply to topic  [ 1 post ] 
Author Message
 Post subject: How to Compute Homology of a Graded Chain Complex
PostPosted: Mon Jun 05, 2017 4:27 am 

Joined: Fri Jun 02, 2017 11:18 am
Posts: 1
I'm new to singular. I'd like to compute the Betti numbers of a graded k[x,y]-module M arising as a homology module of a chain complex of free graded k[x,y]-modules, and I'm running into difficulties: I'm using the "homology" command to obtain a presentation of M, but this seems to discard information about the graded structure on M. I wonder if my trouble is related to bug #67 in the Singular issue tracker.

In any case, I'd appreciate your advice on how to circumvent this problem. Below is some Singular code which demonstrates the issue in detail:

Code:
LIB "homolog.lib";
ring R=2,(x,y),dp;

//d2 will represent a homomorphism of free graded k[x,y]-modules
module d2;
d2[1]=x*gen(3)+x*gen(2)+x*gen(1);
d2[2]=y*gen(3)+y*gen(2)+y*gen(1);
intvec grades_C1=1,1,1;
attrib(d2,"isHomog",grades_C1);

//d1 will also represent a homomorphism of free graded k[x,y]-modules
module d1;
d1[1]=gen(3)+gen(2);
d1[2]=gen(1)+gen(3);
d1[3]=gen(1)+gen(2);
intvec grades_C0=1,1,1;
attrib(d1,"isHomog",grades_C0);

module triv=0;
//Compute a presentation for M:=ker(d1)/im(d2)
def M=homology(d2,d1,triv,triv);

//Next command outputs the grade information for the generators of M.
//Note the null output; homology apparently is not returning a graded object, whereas
//the generator for M should live at grade 1.
attrib(M,"isHomog");

//Compute a free resolution of M
resolution resM=res(M,0);

//Since the grading was lost for M, the Betti numbers are off by 1.
print(betti(resM), "betti");


Report this post
Top
 Profile  
Reply with quote  
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 1 post ] 

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 Tue Nov 21, 2017 9:56 am
cron
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group