sinterp - Maple Programming Help

sinterp

sparse multivariate modular polynomial interpolation

 Calling Sequence sinterp(f, x, t, p)

Parameters

 f - Maple procedure x - list of variables to be interpolated t - positive integer p - prime modulus

Description

 • 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.

Examples

 > f := proc(x,y,p) local t1, t2;         t1 := x^2+y^2;         t2 := x^2-y^2;         t1 * t2 mod p;      end proc:
 > $\mathrm{sinterp}\left(f,\left[x,y\right],10,199\right)$
 ${{x}}^{{4}}{+}{198}{}{{y}}^{{4}}$ (1)