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- W1574268181 abstract "The main motivation of our work is to create an efficient algorithm that decides hypertranscendence of solutions of linear differential and difference equations, via the parameterized differential and difference Galois theories. The results of our paper lead to an algorithm that calculates the Galois group of a parameterized linear differential equation whose differential operator is a composition of two completely reducible differential operators. We do this for the differential equations whose coefficients are rational functions. P. Berman and M.F. Singer presented such an algorithm for differential equations without parameters. We use their algorithm as a part of our algorithm. As a corollary, we find an effective criterion for the algebraic independence of the solutions and all their derivatives with respect to the parameter. We show how to use this to calculate the Galois group of third order linear differential equations with parameters. Our results can also be applied to design an algorithm that calculates the Galois group of a parameterized linear difference equation." @default.
- W1574268181 created "2016-06-24" @default.
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- W1574268181 date "2015-05-26" @default.
- W1574268181 modified "2023-09-27" @default.
- W1574268181 title "Calculating Galois groups of differential equations with parameters" @default.
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