Back to Forum | View unanswered posts | View active topics





Post a reply
Username:
Note:If not registered, provide any username. For more comfort, register here.
Subject:
Message body:
Enter your message here, it may contain no more than 60000 characters. 

Smilies
:D :) :( :o :shock: :? 8) :lol: :x :P :oops: :cry: :evil: :twisted: :roll: :wink: :!: :?: :idea: :arrow: :| :mrgreen:
Font size:
Font colour
Options:
BBCode is ON
[img] is ON
[flash] is OFF
[url] is ON
Smilies are ON
Disable BBCode
Disable smilies
Do not automatically parse URLs
Confirmation of post
To prevent automated posts the board requires you to enter a confirmation code. The code is displayed in the image you should see below. If you are visually impaired or cannot otherwise read this code please contact the %sBoard Administrator%s.
Confirmation code:
Enter the code exactly as it appears. All letters are case insensitive, there is no zero.
   

Topic review - Reduced Groebner Basis
Author Message
rambiz
  Post subject:  Re: Reduced Groebner Basis  Reply with quote
Thank you for the clarification. For sure it is a matter of definition! Nonetheless I think a few words about the definition of the Reduced Groebner Basis used by the Singular developers would be helpful. It can definitely confuse a few new users.
Post Posted: Sat Jun 11, 2016 4:20 pm
hannes
  Post subject:  Re: Reduced Groebner Basis  Reply with quote
No, that depends on the definition.
Any (skalar) multiples of the elements of a Groebner basis form also
also a Groebner basis.
(see http://www.singular.uni-kl.de/Manual/4-0-3/sing_900.htm)
Some authors divied all elements by the leading coeficient
(and get then a unique Groebner basis, if it is completely reduced)
Post Posted: Fri Jun 10, 2016 11:00 am
rambiz
  Post subject:  Reduced Groebner Basis  Reply with quote
Hi all;
the coefficients of the leading terms of the generators of a reduced Groebner basis should be equal to one (1) as far as I know. Now consider the following code:
Code:
> ring r=0,(x,y),lp;
> ideal i=x4+x2+xy3+2,x2+y2-1;
> option(redSB);
> ideal g=std(i);
> g;
g[1]=2y8-7y6+17y4-24y2+16
g[2]=16x-6y7+13y5-23y3+20y
>


Here the leading terms have the coefficients 2 and 16. How comes? What am I missing?
Post Posted: Thu Jun 09, 2016 4:44 pm


It is currently Fri May 13, 2022 11:02 am
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group