The success of the symbolic mathematical computation discipline is striking. The theoretical
advances have been continuous and significant: Gröbner bases, the Risch integration …

We gather together several bounds on the sizes of coefficients which can appear in factors
of polynomials in Z [x]; we include a new bound which was latent in a paper by Mignotte, and …

In this paper we present a generic algorithm for factoring polynomials over global fields F. As
efficient implementations of that algorithm for number fields and function fields differ …

A new algorithm is presented for computing an integer polynomial similar to the GCD of two
polynomials 7~(z) and v (z) EZ [z], deg (u (~))= n 2 deg (v (z)). Our approach uses structured …

An efficient algorithm is proposed for factoring polynomials over an algebraic extension field
defined by a polynomial ring modulo a maximal ideal. If the maximal ideal is given by its …

The aim of this paper is to exploit the algorithms of paper Experimental Math. 8 (1999) in
order to produce a new algebraic method for computing efficiently absolute Lagrange …

A new efficient algorithm is proposed for factoring polynomials over an algebraic extension
field. The extension field is defined by a polynomial ring modulo a maximal ideal. If the …

Trager's algorithm for factoringa univariate polynomialover an algebraic number field
computes thenorm of the polynomial and then factors the norm over the integers. It has been …

Publisher Summary This chapter describes several algorithms for factorization and greatest
common divisor (GCD) computation of polynomials over algebraic extension fields. These …

The problem of interpolating a sparse polynomial has always been one of the central objects
of research in the area of computer algebra. It is the key part of many algorithms such as …