Yuri BLINKOV 1 and Vladimir GERDT 2
1Department of Mathematics and Mechanics,
 Saratov University,
 410071 Saratov,
2Laboratory of Information Technologies,
 Joint Institute for Nuclear Research,
 141980 Dubna,
E-mail: BlinkovUA@info.sgu.ru, gerdt@jinr.ru

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

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.

  1. 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.
  2. V.P. Gerdt and Yu.A. Blinkov, Janet-like Gr\"obner Bases, Submitted to CASC-05 (Kalamata, Greece, September 12-16, 2005).