Using sparse interpolation to solve multivariate diophantine equations

Suppose that we seek to factor a multivariate polynomial a ε R = Z[ x ₁ , ..., x _n ] and a = fg with f, g in R . The multivariate Hensel lifting algorithm (MHL) developed by Wang [1] uses a prime number p and an ideal I = 〈 x ₂ − α ₂ , ..., x _n − α _n 〉 of Z _p [ x ₁ , ..., x _n ] where α ₂ , α ₃ , ..., α _n ε Z _p is an evaluation point chosen by the algorithm.