1976/01/01 by Barry Trager · 190 citations
Computer Science · Mathematics · #Polynomial and algebraic computation #Numerical Methods and Algorithms #Numerical methods for differential equations #Factorization of polynomials #Mathematics #Algebraic extension #Rational function #Algebraic function #Field (mathematics) #Algebra over a field #Simple (philosophy) #Algebraic number #Constructive #Transcendental function #Polynomial #Factoring #Degree (music) #Function field of an algebraic variety #Factorization #Square-free polynomial #Irreducible polynomial #Pure mathematics #Algorithm #Computer science #Matrix polynomial #Mathematical analysis #Differential equation #Process (computing)
paper · doi:10.1145/800205.806338
openalex publication_date 1976/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
This paper presents a new, simple, and efficient algorithm for factoring polynomials in several variables over an algebraic number field. The algorithm is then used iteratively, to construct the splitting field of a polynomial over the integers. Finally the factorization and splitting field algorithms are applied to the problem of determining the transcendental part of the integral of a rational function. In particular, a constructive procedure is given for finding the least degree extension field in which the integral can be expressed.