With the help of computer symbolic computation software e.g., Maple , abundant interaction solutions of sine-Gordon equation are obtained by means of a constructed Wronskian form expansion method. The method is based upon the forms and structures of Wronskian solutions of sine-Gordon equation, and the functions used in the Wronskian determinants do not satisfy linear partial differential equati...

We introduce a general algebraic setting for describing linear boundary problems in a symbolic computation context, with emphasis on the case of partial differential equations. The general setting is then applied to the Cauchy problem for completely reducible partial differential equations with constant coefficients. While we concentrate on the theoretical features in this paper, the underlying...

In this note we provide further evidence for a conjecture of Gillis, Reznick, and Zeilberger on the positivity of the diagonal coefficients of a multivariate rational function. Kauers had proven this conjecture for up to 6 variables using computer algebra. We present a variation of his approach that allows us to prove positivity of the coefficients up to 17 variables using symbolic computation.

What do you do to start reading symbolic and algebraic computation international symposium issac 88 rome italy july 4 8 1988 p? Searching the book that you love to read first or find an interesting book that will make you want to read? Everybody has difference with their reason of reading a book. Actuary, reading habit must be from earlier. Many people may be love to read, but not a book. It's ...

The success of the symbolic mathematical computation discipline is striking. The theoretical advances have been continuous and signiicant: Grr obner, Risch, LLL, WZ, etc. From the beginning in the early 60s, it has been the tradition of our discipline to create software that makes our ideas readily available to scientists, engineers, and educators: SAC-1, Reduce, Macsyma, etc. The commercial vi...

In this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modified Riemann-Liouville derivative. With the aid of symbolic computation, we choose the space-time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation in mathematical physics with a source to illustrate the validity a...

This paper is a step to bring closer together two views of computing with mathematical objects: the view of “symbolic computation” and the view of “computer algebra.” Symbolic computation may be seen as working with expression trees representing mathematical formulae and applying various rules to transform them. Computer algebra may be seen as developing constructive algorithms to compute algeb...

Symbolic computation is one of the computational domains that requires large computational resources. Computer Algebra Systems (CAS), the main tools used for symbolic computations, are mainly designed to be used as software tools installed on standalone machines that do not provide the required resources for solving large symbolic computation problems. In order to support symbolic computations ...

Randomizers are popularly used to prevent various types of attacks on batch-verification schemes. Recently, several algorithms based upon symbolic computation are proposed for the batch verification of ECDSA signatures. In this article, we demonstrate that the concept of randomizers can be easily embedded in these symbolic-computation algorithms. The performance degradation caused by randomizer...