| Singular https://www.singular.uni-kl.de/forum/ |
|
| compute Groebner Basis over Galois Field (2^m) https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=1748 |
Page 1 of 1 |
| Author: | gepoLV [ Thu Jul 09, 2009 7:46 am ] |
| Post subject: | compute Groebner Basis over Galois Field (2^m) |
Hi, all, I want to know how to compute Groebner Basis over Galois Field (2^m)? For example, let m=4, given the irreducible polynomial x^4+x+1, how to generate the finite field? and when I use command "groebner", whether it will work over GF(2^4)? thanks. |
|
| Author: | bulygin [ Fri Jul 10, 2009 2:39 pm ] |
| Post subject: | Re: compute Groebner Basis over Galois Field (2^m) |
You can specify an extension with a specific minimal polynomial like this: Code: ring r=(2,a),x,dp;minpoly=a4+a+1; In fact in your case you can go with the default declaration Code: ring r=(2^4,a),x,dp; since in this case Singular uses a^4+a+1=0 as a default minimal polynomial. GB-functionality works in such rings, no problem. More on declarations of rings you can find at http://www.singular.uni-kl.de/Manual/latest/sing_28.htm#SEC38 |
|
| Author: | gepo [ Mon Jul 13, 2009 7:07 pm ] |
| Post subject: | Re: compute Groebner Basis over Galois Field (2^m) |
Thank you a lot. |
|
| Author: | gepo [ Mon Jul 13, 2009 8:49 pm ] |
| Post subject: | Re: compute Groebner Basis over Galois Field (2^m) |
In the second situation, how can i know the default irreducible polynomial? Thanks |
|
| Author: | greuel [ Fri Jul 24, 2009 1:40 am ] |
| Post subject: | Re: compute Groebner Basis over Galois Field (2^m) |
> ring r=(2^4,a),x,dp; > minpoly; 1*a^4+1*a^1+1*a^0 |
|
| Page 1 of 1 | All times are UTC + 1 hour [ DST ] |
| Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group http://www.phpbb.com/ |
|