| Singular https://www.singular.uni-kl.de/forum/ |
|
| Reduced Groebner Basis https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=2539 |
Page 1 of 1 |
| Author: | rambiz [ Thu Jun 09, 2016 4:44 pm ] |
| Post subject: | Reduced Groebner Basis |
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? |
|
| Author: | hannes [ Fri Jun 10, 2016 11:00 am ] |
| Post subject: | Re: Reduced Groebner Basis |
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) |
|
| Author: | rambiz [ Sat Jun 11, 2016 4:20 pm ] |
| Post subject: | Re: Reduced Groebner Basis |
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. |
|
| Page 1 of 1 | All times are UTC + 1 hour [ DST ] |
| Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group http://www.phpbb.com/ |
|