Approximate Polynomial GCD over Integers with Digits-wise Lattice

For the given coprime polynomials over integers, we change their coefficients slightly over integers so that they have a greatest common divisor (GCD) over integers. That is an approximate polynomial GCD over integers. There are only two algorithms known for this problem. One is based on an algorithm for approximate integer GCDs. The other is based on the well-known subresultant mapping and the lattice basis reduction. In this paper, we give an improved algorithm of the latter with a new lattice construction process by which we can restrict the range of perturbations. This helps us for computing approximate polynomial GCD over integers of the input erroneous polynomials having a priori errors on some digits of their coefficients.