use indeterminate with coefficient over Galois field with matlab

Question

good morning,

can any one tell me how use indeterminates in Matlab with coefficient from Galois field .$F_4=\{0,1,2,3\}$ and ,$a_1,a_2$ two indeterminates ,sow : $$(1a_1)+(1a_1)=0$$ over $F_2$ or

$$(1a_1)(1a_2)+(2a_1)(1a_2)=(3a_1)(2a_2)$$.the last example i write is addition of multivarible polynomial and i am not shire if it correct. i have generate $F(4)$ with :

m = 2;

els = gf([0:2^m-1]',m);

and two symbols in matlab with

syms a1;

syms a2;

and whene id do the multiplication :

els(2)*a1 i have the following message :

Answer 1

It seems that you only need arithmetic in the Galois field to solve the equations. You mentioned in a comment that you might need to compute the determinant of a matrix containing elements from GF$(2^m)$. You can compute the determinant in MATLAB by using the det() function.

The following example shows how to use the det() function for a matrix of GF($16$) elements.

els = gf(0:15,4);

det([els(4) els(7);els(10) els(5)]) gives you $15$.

I hope that helps.