{"intvolume":"        17","status":"public","abstract":[{"text":"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.","lang":"eng"}],"date_created":"2022-12-22T10:53:44Z","publication":"LMS Journal of Computation and Mathematics","year":"2014","type":"journal_article","keyword":["Computational Theory and Mathematics","General Mathematics"],"language":[{"iso":"eng"}],"publisher":"Wiley","issue":"1","volume":17,"external_id":{"arxiv":["1211.3588"]},"_id":"34845","doi":"10.1112/s1461157013000302","publication_identifier":{"issn":["1461-1570"]},"user_id":"93826","department":[{"_id":"102"}],"publication_status":"published","page":"141-158","date_updated":"2023-03-06T09:43:56Z","author":[{"full_name":"Fieker, Claus","first_name":"Claus","last_name":"Fieker"},{"id":"21202","first_name":"Jürgen","last_name":"Klüners","full_name":"Klüners, Jürgen"}],"citation":{"ama":"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>","mla":"Fieker, Claus, and Jürgen Klüners. “Computation of Galois Groups of Rational Polynomials.” <i>LMS Journal of Computation and Mathematics</i>, vol. 17, no. 1, Wiley, 2014, pp. 141–58, doi:<a href=\"https://doi.org/10.1112/s1461157013000302\">10.1112/s1461157013000302</a>.","ieee":"C. Fieker and J. Klüners, “Computation of Galois groups of rational polynomials,” <i>LMS Journal of Computation and Mathematics</i>, vol. 17, no. 1, pp. 141–158, 2014, doi: <a href=\"https://doi.org/10.1112/s1461157013000302\">10.1112/s1461157013000302</a>.","apa":"Fieker, C., &#38; Klüners, J. (2014). Computation of Galois groups of rational polynomials. <i>LMS Journal of Computation and Mathematics</i>, <i>17</i>(1), 141–158. <a href=\"https://doi.org/10.1112/s1461157013000302\">https://doi.org/10.1112/s1461157013000302</a>","short":"C. Fieker, J. Klüners, LMS Journal of Computation and Mathematics 17 (2014) 141–158.","chicago":"Fieker, Claus, and Jürgen Klüners. “Computation of Galois Groups of Rational Polynomials.” <i>LMS Journal of Computation and Mathematics</i> 17, no. 1 (2014): 141–58. <a href=\"https://doi.org/10.1112/s1461157013000302\">https://doi.org/10.1112/s1461157013000302</a>.","bibtex":"@article{Fieker_Klüners_2014, title={Computation of Galois groups of rational polynomials}, volume={17}, DOI={<a href=\"https://doi.org/10.1112/s1461157013000302\">10.1112/s1461157013000302</a>}, number={1}, journal={LMS Journal of Computation and Mathematics}, publisher={Wiley}, author={Fieker, Claus and Klüners, Jürgen}, year={2014}, pages={141–158} }"},"title":"Computation of Galois groups of rational polynomials"}