Saratov University,

410071 Saratov,

RUSSIA

and

Joint Institute for Nuclear Research,

141980 Dubna,

RUSSIA

E-mail: BlinkovUA@info.sgu.ru, gerdt@jinr.ru

**Open Source Software Implementing Gr\"obner Bases Methods
for Systems of Equations**

**Abstract:**

In this talk we present the first version of open source software GINV
(Gr\"obner INVolutive) oriented to creation of library of symbolic algorithms
for investigating system of algebraic, differential and difference equations
of polynomial type based on their converting to the Gr\"oobner basis form.
At present, the library contains the algorithms for constructing involutive
Janet bases with integer coefficients [1] for polynomial ideals and modules
and Janet-like bases for polynomial ideals. The reduced Gr\"oobner bases
are also output. The library written in C++ and documented in Russian and
English with doxygen. The interfaces developed for basic classes allow
a user to implement easily new algorithms and data structures. The input
and output data arranged as xml files what allows to reuse results of computation
as input information, and to store extra information on the problem under
computation in a separate file. There is also a set of utilities written
in Python to work with xml files. Currently, a graphical interface is under
construction to work with the input and output data using the PyQt library.
The GINV software is available on the Web page http://invo.jinr.ru.
We shall demonstrate the software by a number of examples.

- V.P. Gerdt, Involutive Algorithms for Computing Gr\"obner Bases. Proceedings of the NATO Advanced Research Workshop "Computational commutative and noncommutative algebraic geometry" (Chishinau, June 6-11, 2004), IOS Press, to appear.
- V.P. Gerdt and Yu.A. Blinkov, Janet-like Gr\"obner Bases, Submitted to CASC-05 (Kalamata, Greece, September 12-16, 2005).