have the same results. If you consider that GF9 is the 3-dimensional vector space over GF3, then addition of vectors and scalar product work as a vector space without any modification.GF3[2] + GF9[7]GF9[6] andGF9[2] + GF9[7]GF9[6]

The Galois Field Package allows addition and multiplication with integers. An integer k in a mixed expression is recognized as Sum[GF9[1],{i,k}], when we compute in GF9. Hence k is translated to the regular representation k (mod p), where p is the characteristic of the field.

This feature guarantees that the next theorem works for both variables and algebraic variables.3 + GF9[4]GF9[4]4 GF9[3]GF9[3]DeclareVariables[GF9,x]5 xx GF9[2]

**Theorem 3.*** (x+y) ^{p} = x^{p} + y^{p} over a finite field with characteristic p*.

And also Derivation over a finite field works.Expand[ (x+y)^3]( x, y are variables of GF9 ) 3 3 x + yExpand[ (X + Y)^3](X, Y are algebraic variables of GF9) 3 3 X + YExpand[ (u + v)^3 ]( u, v are just symbols in Mathematica) 3 2 2 3 u + 3 u v + 3 u v + v

DeclareVariables[GF9,a,b,c]DeclareAlgebraicVariables[GF9,X]D[a X^2 + b X + c, X]b + a X GF9[2]