Assume that f is a procedure which, given n integers and a prime p, returns an integer in Z mod p. Then sinterp returns a polynomial in x whose values modulo p equal those of f. The list x must contain n variables. The function sinterp uses sparse interpolation.

For the interpolation to succeed, the modulus p should be sufficiently large.  If it is not, FAIL is returned.

The degree bound t is a bound on the total degree of the polynomial being interpolated.

f := proc(x,y,p) local t1, t2;
        t1 := x^2+y^2;
        t2 := x^2-y^2;
        t1 * t2 mod p;
     end proc:

$\mathrm{sinterp}\left(f\,\left[x\,y\right]\,10\,199\right)$

$x^4+198y^4$