A symplectic Kovacic's algorithm in dimension 4 [article]

Thierry Combot, Camilo Sanabria
2018 arXiv   pre-print
Let L be a 4th order 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 J X=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
more » ... , 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.
arXiv:1802.01023v1 fatcat:thp4fhn2qzhldjnxr72kf4heui