Back to Forum | View unanswered posts | View active topics



Post new topic Reply to topic  Page 1 of 1
  [ 5 posts ] 
  Print view | E-mail friend Previous topic | Next topic 
Author Message
John Perry
 Post subject: representation obtained by reduction?
PostPosted: Fri Oct 17, 2008 11:34 pm 

Joined: Fri Oct 17, 2008 11:22 pm
Posts: 7
Suppose that B is an ideal, f is a polynomial, and r is obtained via
r = reduce(f,B);
Then there exists a list H of polynomials such that
f == H1*B1 + ... + Hm*Bm + r

Does Singular have a function/option to determine H, after computing r?


Report this post
Top
 Profile  
Reply with quote  
bricken
 Post subject:
PostPosted: Thu Oct 30, 2008 9:52 am 

Joined: Fri Apr 29, 2005 10:57 am
Posts: 3
Hi John!
Lift might do the job.
http://www.singular.uni-kl.de/Manual/3-0-4/sing_235.htm
Michael


Report this post
Top
 Profile  
Reply with quote  
John Perry
 Post subject: Lift yes, but...
PostPosted: Thu Oct 30, 2008 11:13 pm 

Joined: Fri Oct 17, 2008 11:22 pm
Posts: 7
bricken wrote:
Hi John!
Lift might do the job.
http://www.singular.uni-kl.de/Manual/3-0-4/sing_235.htm
Michael
Thanks, that helps a great deal. I don't know that it's as efficient as I'd like, maybe you can say. To use lift to "recover" the H's, I understand that I need to type
Code:
r = reduce(f,B);
lift(B,f-r);
When Singular performs the reduction, it computes H once.

Then, when Singular computes the lift, it computes H a second time.

I'd prefer to compute H only the first time, and recover it without having Singular go through it again.


Report this post
Top
 Profile  
Reply with quote  
greuel
 Post subject:
PostPosted: Sat Nov 15, 2008 3:12 am 

Joined: Mon Aug 29, 2005 9:22 am
Posts: 41
Location: Kaiserslautern, Germany
Hi,
I guess 'division' is what you want.


Report this post
Top
 Profile  
Reply with quote  
Guest
 Post subject:
PostPosted: Sat Nov 15, 2008 5:59 am 
greuel wrote:
Hi,
I guess 'division' is what you want.

Thanks. Unfortunately, B is not necessarily a standard basis, and division appears to compute a standard basis of B before doing the division. For example,
Code:
> ring R=0,(x,y),dp;
> ideal l = xy+1,y2+1;
> poly f = x-y;
> division(f,l);
[1]:
   _[1,1]=-y
   _[2,1]=x
[2]:
   _[1]=0
[3]:
   _[1,1]=1
The answer I want is
Code:
[1]:
    _[1,1]=0
    _[2,1]=0
[2]:
    _[1]=x-y
[3]:
    _[1,1]=1
If I read the documentation correctly, division computes a standard basis, then lifts to l; I want the result from the non-standard basis. Is there an option to turn that behavior off?


Report this post
Top
  
Reply with quote  
Display posts from previous:  Sort by  
Post new topic Reply to topic  Page 1 of 1
  [ 5 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 11:03 am
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group