A Symplectic Kovacic's Algorithm in Dimension 4
| Affiliation auteurs | Affiliation ok |
| Titre | A Symplectic Kovacic's Algorithm in Dimension 4 |
| Type de publication | Conference Paper |
| Year of Publication | 2018 |
| Auteurs | Combot T, Sanabria C |
| Conference Name | ISSAC'18: PROCEEDINGS OF THE 2018 ACM INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION |
| Publisher | Assoc Comp Machinery; Assoc Comp Machinery Special Interest Grp Symbol & Algebra Manipulat; City Univ New York, Grad Ctr; Natl Secur Agcy; Natl Sci Fdn; Maplesoft; Fachgruppe Computeralgebra |
| Conference Location | 1515 BROADWAY, NEW YORK, NY 10036-9998 USA |
| ISBN Number | 978-1-4503-5550-6 |
| Mots-clés | Differential Galois theory, Kovacic's algorithm, Liouvillian functions, Symplectic differential systems |
| Résumé | Let L be a 4th order linear differential operator with coefficients in K(z), with K a computable algebraically closed field. The operator L is called symplectic when up to rational gauge transformation, the fundamental matrix of solutions X satisfies X-t JX = J where J is the standard symplectic matrix. It is called projectively symplectic when it is projectively equivalent to a symplectic operator. We design an algorithm to test if L is projectively symplectic. Furthermore, based on Kovacic's algorithm, we design an algorithm that computes Liouvillian solutions of projectively symplectic operators of order 4. Moreover, using Klein's Theorem, algebraic solutions are given as pullbacks of standard hypergeometric equations. |
| DOI | 10.1145/3208976.3209005 |