Computation of Galois groups of rational polynomials
Fieker, Claus
Klüners, Jürgen
Computational Theory and Mathematics
General Mathematics
Computational Galois theory, in particular the problem of computing the Galois group of a given polynomial, is a very old problem. Currently, the best algorithmic solution is Stauduhar’s method. Computationally, one of the key challenges in the application of Stauduhar’s method is to find, for a given pair of groups H<G, a G-relative H-invariant, that is a multivariate polynomial F that is H-invariant, but not G-invariant. While generic, theoretical methods are known to find such F, in general they yield impractical answers. We give a general method for computing invariants of large degree which improves on previous known methods, as well as various special invariants that are derived from the structure of the groups. We then apply our new invariants to the task of computing the Galois groups of polynomials over the rational numbers, resulting in the first practical degree independent algorithm.
Wiley
2014
info:eu-repo/semantics/article
doc-type:article
text
http://purl.org/coar/resource_type/c_6501
https://ris.uni-paderborn.de/record/34845
Fieker C, Klüners J. Computation of Galois groups of rational polynomials. <i>LMS Journal of Computation and Mathematics</i>. 2014;17(1):141-158. doi:<a href="https://doi.org/10.1112/s1461157013000302">10.1112/s1461157013000302</a>
eng
info:eu-repo/semantics/altIdentifier/doi/10.1112/s1461157013000302
info:eu-repo/semantics/altIdentifier/issn/1461-1570
info:eu-repo/semantics/altIdentifier/arxiv/1211.3588
info:eu-repo/semantics/closedAccess