MaplePrimes - answers and comments on Question, Groebner Basis over GF(2^m)

Sage

alec — Sat, 24 Jan 2009 13:14:39 Z

Even if that is possible in Maple, it is much easier to use more mathematically oriented CAS, such as Sage, for instance. For example,

sage: k.<a>=GF(16)
sage: R.<x,y>=k['x,y']
sage:  I=ideal(x^2-a*y,x^3-(a^2+1))
sage: print I.groebner_basis()
[x^2 + (a)*y, x*y + (a^3 + a + 1), y^2 + (a^3 + a^2)*x]

Alec

Thank you so much. But What

gepo — Sat, 24 Jan 2009 18:09:53 Z

Thank you so much. But What i want to do is to do some programming using maple.

Any other ideas?

Well, the problem is I have

gepo — Sat, 24 Jan 2009 19:46:44 Z

Well, the problem is I have already completed part of the programming. So now it is difficult for me to transfer my codes to sage or other platform.

If maple cannot offer such operations, I will try to implement it in maple. But now I have some problems.

I am not quite understanding the concept of "a polynomial over Galois Field"? whether"over some field" means the coefficients of the polynomial should be in some field? For example, make 4x^2+5x+6 over GF(4). Whether this means the coefficients 4,5,6 should be changed in GF(4). Here, we should notice that GF(4) is not Z_4.

Yes, I also tried that. I

gepo — Sat, 24 Jan 2009 20:37:00 Z

Yes, I also tried that. I met the same problems.

Maybe there are other ways to issue it.

Thank you, Alex. I really appreciate your help.

Right tools for the job

alec — Sat, 24 Jan 2009 21:54:07 Z

As I suggested earlier, it is better to use right tools for the job. If one needs statistics - use R (it is included in Sage, too, by the way). If one needs mathematics - use Sage.

Maple has included a Physics package recently, but the Mathematics package is still missing.

Note that Maple is easily accessible from Sage, too, like maple("2+2;"), for example, so you could use your existing Maple code from Sage, too, if necessary.

Alec

In Mupad

alec — Sun, 25 Jan 2009 08:31:37 Z

Also, here is an example in Mupad 5.1.0 (which is a part of Matlab 7.7.0 (R2008b)).

k:=Dom::GaloisField(2, 4, a^4+a+1):

k::Name:="k":

groebner::gbasis([poly(x^2+a*y,[x,y],k),poly(x^3+(a^2+1),[x,y],k)]);

[poly(x^2 + a*y,[x,y],k),poly(x*y + a + a^3 + 1,[x,y],k),poly((a^3 + a^2)*x + y^2,[x,y],k)]

Alec

PS It's not related to that topic, but I had some fun including Mupad's output inside <maple> and </maple> tags above :) Looks better in Mupad though,

Alec