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Topic review - compute Groebner Basis over Galois Field (2^m)
Author Message
greuel
  Post subject:  Re: compute Groebner Basis over Galois Field (2^m)  Reply with quote
> ring r=(2^4,a),x,dp;
> minpoly;
1*a^4+1*a^1+1*a^0
Post Posted: Fri Jul 24, 2009 1:40 am
gepo
  Post subject:  Re: compute Groebner Basis over Galois Field (2^m)  Reply with quote
In the second situation, how can i know the default irreducible polynomial?

Thanks
Post Posted: Mon Jul 13, 2009 8:49 pm
gepo
  Post subject:  Re: compute Groebner Basis over Galois Field (2^m)  Reply with quote
Thank you a lot.
Post Posted: Mon Jul 13, 2009 7:07 pm
bulygin
  Post subject:  Re: compute Groebner Basis over Galois Field (2^m)  Reply with quote
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
Post Posted: Fri Jul 10, 2009 2:39 pm
gepoLV
  Post subject:  compute Groebner Basis over Galois Field (2^m)  Reply with quote
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.
Post Posted: Thu Jul 09, 2009 7:46 am


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