Abstract
This chapter discusses the use of computers in Galois theory. The problem of calculating the Galois group of a polynomial over the rationals is remarkable among mathematical algorithms for the paucity of its input–output. A single polynomial is given as input, and a single group code or the Cayley table of a group is returned as output. The chapter describes the computational difficulties that arise in computing such groups. It has been noticed that although the splitting fields whose automorphism groups are the Galois groups of polynomials over the rationals are infinite fields, the problem of calculating these automorphism groups is actually a finite problem. Simpler methods are given by van der Waerden in the case in which the polynomial has degree less than or equal to 4.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
