Epsilon is a library of functions implemented in Maple and Java for polynomial elimination and decomposition with (geometric) applications. It has 8 modules and contains more than 70 functions, which allows one to :

  • triangularize systems of multivariate (differential) polynomials;
  • decompose polynomial systems into triangular systems of various kinds (regular, normal, simple, irreducible, or with projection property);
  • decompose algebraic varieties into irreducible or unmixed subvarieties;
  • decompose polynomial ideals into primary components;
  • factorize polynomials over algebraic extension fields;
  • solve systems of polynomial equations and inequations;
  • handle and prove geometric theorems automatically.

  • Gool (by T. Liang and D. Wang)

Gool is a system for symbolic geometric computation, reasoning, and visualization. It has the following capabilities:

  • Symbolic geometric objects may be constructed and represented with certain or uncertain data;
  • Constructed objects may be modified (e.g., by changing parametric values and adding or removing assumptions);
  • Basic geometric operations and calculations with constructed objects may be performed efficiently and correctly;
  • Relations among different geometric objects can be declared and their consistency may be efficiently checked;
  • Geometric statements are formulated with simple syntax so that reasoning can be performed with advanced techniques;
  • Symbolic geometric objects can be visualized and displayed, and dynamic diagrams can be generated automatically;
  • Geometric knowledge can be represented and managed, allowing indexing and searching;
  • Geometric uncertainty and degeneracy are handled systematically and efficiently.

  • EGT System (by X. Chen and D. Wang)

The Electronic Geometry Textbook (EGT) is a dynamic software system integrating geometric knowledge and software modules developed for geometric computing and reasoning, diagram generation, and visualization in a single context of knowledge management environment to support geometry education, research, and application. The EGT system can:

  • Translate the formalized knowledge in the textbook into different natural languages (like Chinese and English) automatically;
  • Organize geometric knowledge in the database as a normal textbook in traditional style according to a proper order and generate printable documents automatically;
  • Check the consistency automatically when the textbook is modified;
  • Interact with other software modules and process the geometric knowledge in the system (computing and reasoning with geometric constraints, generating geometric diagrams, and visualizing geometric objects, etc.);
  • Retrieve the results produced by different modules and integrate them into the knowledge base automatically to realize self-learning.