An algorithm to compute Liouvillian solutions of prime order linear difference-differential equations
نویسندگان
چکیده
A normal form is given for integrable linear difference-differential equations {σ(Y ) = AY, δ(Y ) = BY }, which is irreducible over C(x, t) and solvable in terms of liouvillian solutions. We refine this normal form and devise an algorithm to compute all liouvillian solutions of such kind of systems of prime order.
منابع مشابه
Liouvillian Solutions of Difference-Differential Equations
For a field k with an automorphism σ and a derivation δ, we introduce the notion of liouvillian solutions of linear difference-differential systems {σ(Y ) = AY, δ(Y ) = BY } over k and characterize the existence of liouvillian solutions in terms of the Galois group of the systems. We will give an algorithm to decide whether such a system has liouvillian solutions when k = C(x, t), σ(x) = x+ 1, ...
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For a field k with an automorphism σ and a derivation δ, we introduce the notion of liouvillian solutions of linear difference-differential systems {σ(Y ) = AY, δ(Y ) = BY } over k and characterize the existence of liouvillian solutions in terms of the Galois group of the systems. We will give an algorithm to decide whether such a system has liouvillian solutions when k = C(x, t), σ(x) = x + 1,...
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عنوان ژورنال:
- J. Symb. Comput.
دوره 45 شماره
صفحات -
تاریخ انتشار 2010