Software Packages

All the software packages listed here are free under the condition that no commercial interests are involved. Please cite the relevant book or paper if you used these packages in your work.

Xiao-Shan Gao

MMP: Mathematics Mechanization Platform

MMP is a software platform under development, which is supported by a Chinese National Key Basic Research Project ``Mathematics Mechanization and Platform for Automated Reasoning.'' The aim of MMP is to realize some of the goals proposed by Wu to mechanize basic mathematical activities including automated solution of algebraic and differential equations and automated theorem proving and discovering. MMP is based on algorithms from symbolic computation and automated reasoning, and in particular the Wu-Ritt characteristic set (CS) method. Based on the CS method, we also implement application packages in automated geometric theorem proving and discovering, automated geometric diagram generation, algebraic differential equation solving, robotics, mechanism design, and CAGD.

X.S. Gao, D.K. Wang, Q Liao, and H. Yang, Equation Solving and Machien Proving - Problem Solving with MMP (in Chinese ), Science Press, Beijing, 2006.

GEX: Geometry Expert

GEX is a software system for dynamic diagram drawing and automated geometry theorem proving and discovering.

X.S. Gao, J. Z. Zhang, and S.C. Chou, Geometry Expert (in Chinese), Nine Chapters Pub., Taiwan, 1998.

Java Geometry Expert

Java GEX is an internet based version of Geometry Expert.

MMP/Geometer

A new version of GEX with ability of automated geometric diagram construction.

X.S. Gao and Q. Lin, MMP/Geometer - A Software Package for Automated Geometric Reasoning, Proc. of Automated Deduction in Geometry, 44-66, Springer, Berlin.

LGP: A Local Generic Position Method for Solving Bivariate Polynomial Systems

This is a maple package which can be used to solve bivariate polynomial systems.

J.S Cheng, X.S. Gao, and J Li, Root Isolation for Bivariate Polynomial Systems with Local Generic Position Method. {\em Proc. ISSAC 2009}, 103-109, ACM Press, New York, 2009.

Decomposition of Ordinary Difference Polynomials

This is a maple package which can be used to decompose nonlinear difference polynomials.

M. Zhang and X.S. Gao, Decomposition of Ordinary Difference Polynomials, MM-Preprints, Vol. 25, 248-263, 2006.

Find polynomial solutions to 1st order autonomous ODE

This is a maple package which can be used to find the polynomial (general) solutions for first order autonomous ODEs. Here are several examples.

R. Feng and X.S. Gao, Polynomial General Solution for First Order ODEs with Constant Coefficients, MM-Preprints, No. 22, 2003.