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dinterp

probabilistic degree interpolation

 

Calling Sequence

Parameters

Description

Examples

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:

dinterpf,3,1,6,997

2

(1)

dinterpf,3,2,6,997

3

(2)

dinterpf,3,3,6,997

4

(3)

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