Oid is an open source, interactive, extensible software system for experimenting with matroids. Since matroids are a generalization of many other combinatorial objects such as graphs, matrices, and linearspaces, a software system for matroids inherently handles all these objects. Oid also has a library of classes can be assembled into programs that are optimized for special applications.
Copyright (2001-2005) Robert Kingan and Sandra Kingan. Oid is distributed under the GNU General Public License, version 2 or later. More information on this license is available at the GNU website
The details of Oid's design are published in the paper A software system for matroids which appears in the 2005 DIMACS Series in Discrete Mathematics and Theoretical Computer Science titled Graphs and Discovery, Volume 69, 287 - 296.
The Matroid Generation Program - this program uses Oid's library of classes to generate isomorph-free simple matroids representable over GF(q), for any prime power q. The generation is exhaustive over GF(2) and GF(3) but not exhaustive over higher fields due to lack of unique representability.
matroids.c: this program was written in 1996 in ANSI C. It calculates circuits, cocircuits, bases, hyperplanes etc. for binary matroids.
Links to combinatorial software
DISCRETA: a program to construct t-designs with prescribed automorphism group
Genreg: a very fast structure generator for regular graphs.
Graffiti and Automated Conjecture-Making: Graffiti is a program of Siemion Fajtlowicz, a mathematician at the University of Houston. Its development began around 1985. Development of Graffiti was preceded by "Little Paul" written by Fajtlowicz's student Shui-Tain Chen. Graffiti was co-developed with Ermelinda DeLaVina from 1990 to 1993. Graffiti makes conjectures in various subfields of mathematics and in chemistry. In principle, it is domain-independent and not limited to these areas.
Graphlet: a toolkit for graph editors and graph algorithms
Graphviz: an open source graph drawing program.
GRaph INterface (GRIN): Grin is a powerful tool in the Graph theory with many capabilities. Grin is easy to use; you don`t need any computer experience to get start. You can create, edit, and research the Graphs and NetWorks. Graphs can be stored on a disk and loaded from disk. You can edit graphs interactively.
The Macek Project: this project is a set of tools and routines for reasonably efficient combinatorial computations with representable matroids, especially for matroid constructions and for some structural tests.
MOLGEN: this system is devoted to the computation of all structural formulae (=connectivity isomers) that correspond to a given molecular formula, with (optional) further conditions (e.g. substructures).
MOLGEN-MS: this program is devoted to computer aided molecular structure elucidation. MOLGEN-MS is mainly adapted to low resolution electron impact mass spectra but also includes tools which allow to process high resolution data and results from atomic analysis. Even information gained from IR or NMR interpretation can be added.
MOLGEN-QSPR: this is an integrated software tool for structure generation, descriptor calculation, and regression analysis in combinatorial chemistry.
nauty: nauty is a program for computing automorphism groups of graphs and digraphs. It can also produce a canonical labelling.
plantri and fullgen: plantri and fullgen are programs for generation of certain types of planar graph. fullgen generates fullerenes, which are planar cubic graphs having only faces of size 5 or 6. There is also an option for forbidding adjacent pentagons.
Symplectic matroid program: a program that identifies Symplectic matroids.
TOPCOM: a package for computing triangulations of point configurations and oriented matroids
GraPHhedron: a computer-assisted system which helps to obtainconjectures in graph theory. It uses a polyhedral approach to findstrongest relations among a set of graph invariants. This approachprovides a formal framework allowing to identify interesting and tightrelations among the selected set of invariants.
Graphs and Discovery: this is the home page of the DIMACS working group on Graphs and Discovery and has details about the first workshop held in November 2001.
Workshop on Computes and Discovery: this is the second meeting of the DIMACS working group on Graphs and Discovery held in June 2004.
OpenMath and MathML: OpenMath is an emerging standard for representing mathematical objects with their semantics, allowing them to be exchanged between computer programs, stored in databases, or published on the worldwide web. While the original designers were mainly developers of computer algebra systems, it is now attracting interest from other areas of scientific computation and from many publishers of electronic documents with a significant mathematical content. There is a strong relationship to the MathML recommendation from the Worldwide Web Consortium, and a large overlap between the two developer communities. MathML deals principally with the presentation of mathematical objects, while OpenMath is solely concerned with their semantic meaning or content. While MathML does have some limited facilities for dealing with content, it also allows semantic information encoded in OpenMath to be embedded inside a MathML structure. Thus the two technologies may be seen as highly complementary.