FAST RESOLUTION OF INTEGER VANDERMONDE SYSTEMS

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The resolution of polynomial interpolation problems with integer coefficients directly involves the open issue of the integer inversion of a general Vandermonde matrix defined over the field ℤ/p ℤ, for p prime number. The purpose of this paper is to demonstrate the possibility to invert a Vandermonde matrix with integer mod p coefficients and exactly compute the integer inverse matrix in the ring Mat(ℤ/p ℤ) of square matrices over ℤ/p ℤ through the new fast algorithm InVanderMOD. The explicit formula derived for the integer inversion of Vandermonde matrices entirely develops inside the field of the integers mod p , with due consideration to the operation of integer division. The inversion procedure InVanderMOD is valid for any prime number p and competitive in terms of computational effort, since its computational cost is less than O(n 3 ) .