Given an integer valued function f : (x1,...,xn, p) -> Z that evaluates a polynomial in n variables modulo p, and a degree bound d on the kth variable, determine probabilistically the degree of the kth variable.

The dinterp function may return FAIL if it encounters a division by zero when evaluating f.  It may also return a result for the degree of the kth variable which is too low.  The probability that this happens can be decreased by using a larger modulus.  A 12 to 20 digit modulus is considered ideal.

f := proc(x,y,z,p) x^2+y^3+z^4 mod p end proc:

$\mathrm{dinterp}\left(f\,3\,1\,6\,997\right)$

$2$

$\mathrm{dinterp}\left(f\,3\,2\,6\,997\right)$

$3$

$\mathrm{dinterp}\left(f\,3\,3\,6\,997\right)$

$4$