dinterp - Maple Help

dinterp

probabilistic degree interpolation

 Calling Sequence dinterp(f, n, k, d, p)

Parameters

 f - a Maple procedure n, k, d - integers p - prime modulus

Description

 • 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.

Examples

 > f := proc(x,y,z,p) x^2+y^3+z^4 mod p end proc:
 > $\mathrm{dinterp}\left(f,3,1,6,997\right)$
 ${2}$ (1)
 > $\mathrm{dinterp}\left(f,3,2,6,997\right)$
 ${3}$ (2)
 > $\mathrm{dinterp}\left(f,3,3,6,997\right)$
 ${4}$ (3)