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You can not define, say a cosinus over a finite field, but you can define polynomials as follows:
sage: K = GF(7)
sage: K
Finite Field of size 7
sage: R.<x,y> = K[]
sage: R
Multivariate Polynomial Ring in x, y over Finite Field of size 7
sage: P = 1+x^2+x*y^3
sage: P
x*y^3 + x^2 + 1
sage: P.parent()
Multivariate Polynomial Ring in x, y over Finite Field of size 7
sage: P(2,3)
3
sage: P(2,10)
3
sage: P(2,10).parent()
Finite Field of size 7
