Reproduction of Fuchs Relation for the Group $S_4^{SL_2}$ by Using Groebner Bases

Noura Okko

Journal of Mathematics Research, 2018, vol. 10, issue 4, 49-53

Abstract: In 1872, Lazarus Fuchs used a new tool which is The Invariant Theory to construct the minimal polynomial of an algebraic solution of a differential equation of second order. He expressed the coefficient of the equation in terms of the (semi-)invariants of its differential Galois group. In this paper we will give another method to obtain Fuchs Relation: for the octahedral groupe by using Groebner Basis; a tool which is introduced in 1965 nearly two century after Fuchs Relation.

Keywords: Differential Galois Theory; Algebraic Solutions; Groebner Basis; Invariant Theory; Representation Theory (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.ccsenet.org/journal/index.php/jmr/article/download/75638/41773 (application/pdf)
http://www.ccsenet.org/journal/index.php/jmr/article/view/75638 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ibn:jmrjnl:v:10:y:2018:i:4:p:49

Access Statistics for this article

More articles in Journal of Mathematics Research from Canadian Center of Science and Education Contact information at EDIRC.
Bibliographic data for series maintained by Canadian Center of Science and Education ().