MAXIMA

MAXIMA
Name	MAXIMA
Developer	William Schelter; Macsyma community
Initial release	1982 (as freefork)
Latest release	ongoing
Programming language	Common Lisp
Operating system	Cross-platform
Genre	Computer algebra system
License	BSD-style (original freefork)

MAXIMA MAXIMA is a computer algebra system originally derived from the MIT-developed Macsyma project and maintained by a community of contributors led initially by William Schelter. It provides symbolic manipulation, numerical evaluation, plotting, and programming facilities and has been used in research, education, and engineering. MAXIMA runs on Unix-like systems, Microsoft Windows, and macOS and interfaces with editors and visualization tools.

Overview

MAXIMA implements symbolic algebra, equation solving, differentiation, integration, matrix operations, and arbitrary-precision arithmetic. It traces its lineage to Project MAC, MIT, and the 1960s–1970s development of Macsyma at the Massachusetts Institute of Technology and the Symbolics corporation. The system includes a Lisp-based interpreter, numerous mathematical libraries, and front ends that integrate with TeXmacs, Emacs, and Jupyter Notebook environments.

History and Development

Development began after the original Macsyma sources were made available to the public in the 1980s, when William Schelter forked a copy and adapted it to modern Common Lisp implementations. The project evolved through contributions from individuals affiliated with institutions such as MIT, Indiana University, and independent researchers. Key moments include packaging for GNU Project-related distributions, integration with plotting libraries used by Gnuplot and gnuplot-based front ends, and updates to support modern SBCL and CLISP implementations. The MAXIMA lineage intersects with legal and licensing history involving Symbolics, Massachusetts Institute of Technology, and later stewardship by volunteer maintainers.

Architecture and Features

The system is written primarily in Common Lisp and structured as a set of Lisp files that implement symbolic kernels, simplification rules, and numeric back ends. Major components include the parser/reader, simplifier, rational and algebraic number packages, matrix and tensor libraries, and plotting interfaces that call external programs such as Gnuplot. MAXIMA supports arbitrary-precision integers via bignum implementations in Lisp, exact rational arithmetic, symbolic integration via pattern matching similar to routines developed at MIT, and differential equation solvers influenced by symbolic techniques used at Symbolics labs. Interoperability features allow interaction with Fortran-generated numerical code, export to TeX and LaTeX, and embedding in interactive environments like Emacs with modes adapted from SLIME workflows.

Usage and Applications

MAXIMA has been used in undergraduate and graduate curricula at universities such as MIT, Stanford University, and University of Cambridge for teaching calculus, linear algebra, and differential equations. In research settings, practitioners affiliated with institutions like Princeton University, Caltech, and industrial firms have applied MAXIMA to symbolic perturbation theory, analytic continuation problems, and closed-form simplifications in physics and engineering. The system is employed in preparing LaTeX-formatted homework and research manuscripts, numeric verification alongside MATLAB and Octave, and as a prototyping tool before deployment to production code in C or Fortran. Community-contributed packages extend MAXIMA toward control theory examples used in IEEE conferences, cryptographic algebra relevant to RSA-based work, and special-function manipulation encountered in NIST standards.

Community and Development

A volunteer community maintains source code repositories and mailing lists; contributors have been associated with projects at GNU Project-related organizations, university departments, and independent open-source initiatives. Development coordination has occurred on platforms that host Git repositories, with packaging for distributions maintained by volunteers connected to Debian, Ubuntu, and other Linux ecosystems. Documentation and user support are provided through community-run wikis, mailing lists, and tutorials often prepared by academics from University of California, Berkeley, University of Oxford, and other institutions. Workshops and presentations about MAXIMA have appeared at conferences organized by societies such as the Association for Symbolic Logic and panels at meetings of the American Mathematical Society.

Reception and Legacy

MAXIMA is recognized for preserving a substantial portion of the capabilities of historical Macsyma work while remaining free and extensible, earning respect among educators and researchers who value transparency and reproducibility. Reviews in academic settings compare its symbolic routines to proprietary systems developed by companies such as Wolfram Research and suites like MapleSoft’s offerings; these comparisons often highlight MAXIMA's strengths in openness and scriptability versus commercial optimization and integrated documentation from corporate products. Its long-term legacy includes influencing later computer algebra system designs, seeding tools used in open-source computational stacks alongside SageMath and inspiring pedagogical materials adopted at institutions including Harvard University and Yale University.

Category:Computer algebra systems Category:Free software programmed in Common Lisp