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

:D :) :( :o :shock: :? 8) :lol: :x :P :oops: :cry: :evil: :twisted: :roll: :wink: :!: :?: :idea: :arrow: :| :mrgreen:
Font size:
Font colour
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 - Groebner bases with vs without parameters
Author Message
  Post subject:  Groebner bases with vs without parameters  Reply with quote
Dear Singular Forum,

I would like to perform polynomial division in a polynomial ring with parameters. Here is an example that I have in mind:
ring r=(0, y(1)),(z(1), z(2), z(3), z(4), z(5)),dp;
ideal f = z(1)*z(2)*z(3)*z(4)*z(5)-y(1)*z(2)^5+z(3)^5+z(4)^5+z(5)^5+z(1)^5;
ideal j = jacob(f);
ideal gb = groebner(j,"par2var");
poly p = 24*y(1)^4*z(2)^20;
list q = division(p,j);

This yields (note result of the division is zero and there are rational expressions in the parameter)

For efficiency reasons I would like to perform the same computation treating y(1) as a ring variable. I observed that with several parameters treated as ring variables the Groebner basis computation is much faster than if they are treated as parameters. So here is the same example as above
ring r = 0, (y(1), z(1), z(2), z(3), z(4), z(5)), dp;
ideal f = z(1)*z(2)*z(3)*z(4)*z(5)-y(1)*z(2)^5+z(3)^5+z(4)^5+z(5)^5+z(1)^5;
int i;
ideal j=diff(f,z(1));
ideal gb = groebner(j);
poly p = 24*y(1)^4*z(2)^20;
list q = division(p,j);

The result, however, is very different. In particular the result of the division is not zero anymore.

How do I have to modify the code in order to reproduce the correct result of the division in the ring with parameter ?

Thanks for the help in advance.
Post Posted: Tue Sep 19, 2017 2:44 pm

It is currently Thu Feb 21, 2019 3:31 pm
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group