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- Ruyong Feng, Xiao-Shan Gao
- ISSAC
- 2004

We give a necessary and sufficient condition for an algebraic ODE to have a rational type general solution. For an autonomous first order ODE, we give an algorithm to compute a rational general solution if it exists. The algorithm is based on the relation between rational solutions of the first order ODE and rational parametrizations of the plane algebraic… (More)

- Ruyong Feng, Xiao-Shan Gao
- J. Symb. Comput.
- 2006

We improve the algorithm given in [3]. Through analysing the structural properties of a first order autonomous ODE with a rational solution, we give a polynomial time algorithm to find a rational general solution if it exists.

- Ruyong Feng, Michael F. Singer, Min Wu
- J. Symb. Comput.
- 2010

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.

- J. M. Aroca, J. Cano, Ruyong Feng, Xiao-Shan Gao
- ISSAC
- 2005

In this paper, we give a necessary and sufficient condition for an algebraic ODE to have an algebraic general solution. For a first order autonomous ODE, we give an optimal bound for the degree of its algebraic general solutions and a polynomial-time algorithm to compute an algebraic general solution if it exists. Here an algebraic ODE means that an ODE… (More)

- Ruyong Feng, Xiao-Shan Gao, Zhenyu Huang
- J. Symb. Comput.
- 2008

In this paper, we generalize the results of Feng and Gao [Feng, R., Gao, X.S., 2006. A polynomial time algorithm to find rational general solutions of first order autonomous ODEs. J. Symbolic Comput., 41(7), 735–762] to the case of difference equations. We construct two classes of ordinary difference equations (O∆Es) whose solutions are exactly the… (More)

- Shaoshi Chen, Frédéric Chyzak, Ruyong Feng, Guofeng Fu, Ziming Li
- J. Symb. Comput.
- 2015

We present a criterion for the existence of telescopers for mixed hypergeometric terms, which is based on multiplicative and additive decompositions. The criterion enables us to determine the termination of Zeilberger’s algorithms for mixed hypergeometric inputs.

- Ruyong Feng, Michael F. Singer, Min Wu
- J. Symb. Comput.
- 2010

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… (More)

- Ruyong Feng, Xiao-Shan Gao
- IWMM/GIAE
- 2004

For a first order autonomous ODE, we give a polynomial time algorithm to decide whether it has a polynomial general solution and to compute one if it exists. Experiments show that this algorithm is quite effective in solving ODEs with high degrees and a large number of terms.

We present two criteria for the existence of telescopers for bivariate hyperexponential-hypergeometric functions. One is for the existence of telescopers with respect to the continuous variable, the other for telescopers with respect to the discrete one. Our criteria are based on a standard representations of bivariate hyperexponentialhypergeometric… (More)

- Shaoshi Chen, Ruyong Feng, Guofeng Fu, Ziming Li
- ISSAC
- 2011

A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and <i>q</i>-shift operators. We present a theorem that describes the structure of compatible rational functions. The theorem enables us to decompose a solution of such a system as a… (More)