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

Noura Okko

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 $S_4^{SL_2}$ by using Groebner Basis; a tool which is introduced in 1965 nearly two century after Fuchs Relation.


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DOI: https://doi.org/10.5539/jmr.v10n4p49

License URL: http://creativecommons.org/licenses/by/4.0

Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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