Polynomial GCD Derived through Monic Polynomial Subtractions

Numerical Univariate Polynomial GCD

We formalize the notion of approximate GCD for univariate poly-nomials given with limited accuracy and then address the problem of its computation. Algebraic concepts are applied in order to provide a solid foundation for a numerical approach. We exhibit the limitations of the euclidean algorithm through experiments, show that existing methods only solve part of the problem and assert its worst...

GCDHEU: Heuristic Polynomial GCD Algorithm Based on Integer GCD Computation

A heuristic algorithm, GCDHEU, is described for polynomial GCD computation over the integers. The algorithm is based on evaluation at a single large integer value (for each variable), integer GCD computation, and a single-point interpolation scheme. Timing comparisons show that this algorithm is very efficient for most univariate problems and it is also the algorithm of choice for many problems...

The Probability That a Random Monic p-adic Polynomial Splits

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...

Numerical Computation of a Polynomial GCD and Extensions

In the rst part of this paper, we deene approximate polynomial gcds (greatest common divisors) and extended gcds provided that approximations to the zeros of the input polynomials are available. We relate our novel deenition to the older and weaker ones, based on perturbation of the coeecients of the input polynomials, we demonstrate some deeciency of the latter deenitions (which our deenition ...