Maxima () is a

computer algebra system A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The de ...

(CAS) based on a 1982 version of

Macsyma Macsyma (; "Project MAC's SYmbolic MAnipulator") is one of the oldest general-purpose computer algebra systems still in wide use. It was originally developed from 1968 to 1982 at MIT's Project MAC. In 1982, Macsyma was licensed to Symbolics and ...

. It is written in

Common Lisp Common Lisp (CL) is a dialect of the Lisp programming language, published in ANSI standard document ''ANSI INCITS 226-1994 (S20018)'' (formerly ''X3.226-1994 (R1999)''). The Common Lisp HyperSpec, a hyperlinked HTML version, has been derived fro ...

and runs on all

POSIX The Portable Operating System Interface (POSIX) is a family of standards specified by the IEEE Computer Society for maintaining compatibility between operating systems. POSIX defines both the system- and user-level application programming interf ...

platforms such as

macOS macOS (; previously OS X and originally Mac OS X) is a Unix operating system developed and marketed by Apple Inc. since 2001. It is the primary operating system for Apple's Mac computers. Within the market of desktop and lapt ...

Unix Unix (; trademarked as UNIX) is a family of multitasking, multiuser computer operating systems that derive from the original AT&T Unix, whose development started in 1969 at the Bell Labs research center by Ken Thompson, Dennis Ritchie, and ot ...

BSD The Berkeley Software Distribution or Berkeley Standard Distribution (BSD) is a discontinued operating system based on Research Unix, developed and distributed by the Computer Systems Research Group (CSRG) at the University of California, Berk ...

, and

Linux Linux ( or ) is a family of open-source Unix-like operating systems based on the Linux kernel, an operating system kernel first released on September 17, 1991, by Linus Torvalds. Linux is typically packaged as a Linux distribution, which ...

, as well as under

Microsoft Windows Windows is a group of several proprietary graphical operating system families developed and marketed by Microsoft. Each family caters to a certain sector of the computing industry. For example, Windows NT for consumers, Windows Server for serv ...

and Android. It is

free software Free software or libre software is computer software distributed under terms that allow users to run the software for any purpose as well as to study, change, and distribute it and any adapted versions. Free software is a matter of liberty, no ...

released under the terms of the

GNU General Public License The GNU General Public License (GNU GPL or simply GPL) is a series of widely used free software licenses that guarantee end users the Four Freedoms (Free software), four freedoms to run, study, share, and modify the software. The license was th ...

(GPL).

History

Maxima is based on a 1982 version of

, which was developed at

MIT The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the mo ...

with funding from the

United States Department of Energy The United States Department of Energy (DOE) is an executive department of the U.S. federal government that oversees U.S. national energy policy and manages the research and development of nuclear power and nuclear weapons in the United Stat ...

and other government agencies. A version of Macsyma was maintained by

Bill Schelter William Frederick Schelter (1947 – July 30, 2001) was a professor of mathematics at The University of Texas at Austin and a Lisp developer and programmer. Schelter is credited with the development of the GNU Common Lisp (GCL) implementation ...

from 1982 until his death in 2001. In 1998, Schelter obtained permission from the Department of Energy to release his version under the GPL. That version, now called Maxima, is maintained by an independent group of users and developers. Maxima does not include any of the many modifications and enhancements made to the commercial version of Macsyma during 1982–1999. Though the core functionality remains similar, code depending on these enhancements may not work on Maxima, and bugs which were fixed in Macsyma may still be present in Maxima, and vice versa. Maxima participated in

Google Summer of Code The Google Summer of Code, often abbreviated to GSoC, is an international annual program in which Google awards stipends to contributors who successfully complete a free and open-source software coding project during the summer. , the program is ...

in 2019 under

International Neuroinformatics Coordinating Facility The International Neuroinformatics Coordinating FacilityINCF is an international non-profit organization with the mission to develop, evaluate, and endorse standards and best practices that embrace the principles of Open, FAIR, and Citable neuros ...

Symbolic calculations

Like most computer algebra systems, Maxima supports a variety of ways of reorganizing symbolic algebraic expressions, such as

polynomial factorization In mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field (mathematics), field or in the integers as the product of irreducible polynomial, irreducible ...

polynomial greatest common divisor In algebra, the greatest common divisor (frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a factor of both the two original polynomials. This concept is analogous to the greatest common di ...

calculation, expansion, separation into real and imaginary parts, and transformation of trigonometric functions to exponential and vice versa. It has a variety of techniques for simplifying algebraic expressions involving trigonometric functions, roots, and exponential functions. It can calculate symbolic

antiderivative In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function whose derivative is equal to the original function . This can be stated symbolically ...

s ("indefinite integrals"),

definite integral In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with di ...

s, and

limits Limit or Limits may refer to: Arts and media * ''Limit'' (manga), a manga by Keiko Suenobu * ''Limit'' (film), a South Korean film * Limit (music), a way to characterize harmony * "Limit" (song), a 2016 single by Luna Sea * "Limits", a 2019 ...

. It can derive closed-form

series expansion In mathematics, a series expansion is an expansion of a function into a series, or infinite sum. It is a method for calculating a function that cannot be expressed by just elementary operators (addition, subtraction, multiplication and division) ...

s as well as terms of Taylor-Maclaurin-

Laurent Laurent may refer to: *Laurent (name), a French masculine given name and a surname **Saint Laurence (aka: Saint ''Laurent''), the martyr Laurent **Pierre Alphonse Laurent, mathematician **Joseph Jean Pierre Laurent, amateur astronomer, discoverer ...

series. It can perform matrix manipulations with symbolic entries. Maxima is a general-purpose system, and special-case calculations such as factorization of large numbers, manipulation of extremely large

polynomial In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An exa ...

s, etc. are sometimes better done in specialized systems.

Numeric calculations

Maxima specializes in symbolic operations, but it also offers numerical capabilities such as

arbitrary-precision In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are lim ...

integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...

rational number In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ). The set of all ration ...

, and

floating-point numbers In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be ...

, limited only by space and time constraints.

Programming

Maxima includes a complete programming language with

ALGOL ALGOL (; short for "Algorithmic Language") is a family of imperative computer programming languages originally developed in 1958. ALGOL heavily influenced many other languages and was the standard method for algorithm description used by the ...

-like syntax but

Lisp A lisp is a speech impairment in which a person misarticulates sibilants (, , , , , , , ). These misarticulations often result in unclear speech. Types * A frontal lisp occurs when the tongue is placed anterior to the target. Interdental lisping ...

-like

semantics Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy Philosophy (f ...

. It is written in

and can be accessed programmatically and extended, as the underlying Lisp can be called from Maxima. It uses

gnuplot gnuplot is a command-line and GUI program that can generate two- and three-dimensional plots of functions, data, and data fits. The program runs on all major computers and operating systems (Linux, Unix, Microsoft Windows, macOS, FreeDOS, an ...

for drawing. For calculations using floating point and arrays heavily, Maxima has translators from the Maxima language to other programming languages (notably Fortran), which may execute more efficiently.

Interfaces

Various

graphical user interface The GUI ( "UI" by itself is still usually pronounced . or ), graphical user interface, is a form of user interface that allows users to interact with electronic devices through graphical icons and audio indicator such as primary notation, inste ...

s (GUIs) are available for Maxima: * wxMaxima is a graphical front-end using

wxWidgets wxWidgets (formerly wxWindows) is a widget toolkit and tools library for creating graphical user interfaces (GUIs) for cross-platform applications. wxWidgets enables a program's GUI code to compile and run on several computer platforms with mini ...

. * There is a kernel for

Project Jupyter Project Jupyter () is a project with goals to develop open-source software, open standards, and services for interactive computing across multiple programming languages. It was spun off from IPython in 2014 by Fernando Pérez and Brian Granger ...

, a flexible,

notebook A notebook (also known as a notepad, writing pad, drawing pad, or legal pad) is a book or stack of paper pages that are often ruled and used for purposes such as note-taking, journaling or other writing, drawing, or scrapbooking. History ...

-style GUI written in

Python Python may refer to: Snakes * Pythonidae, a family of nonvenomous snakes found in Africa, Asia, and Australia ** ''Python'' (genus), a genus of Pythonidae found in Africa and Asia * Python (mythology), a mythical serpent Computing * Python (pro ...

. * GMaxima is a Maxima interface using

GTK+ GTK (formerly GIMP ToolKit and GTK+) is a free and open-source cross-platform widget toolkit for creating graphical user interfaces (GUIs). It is licensed under the terms of the GNU Lesser General Public License, allowing both free and proprie ...

. *

Cantor A cantor or chanter is a person who leads people in singing or sometimes in prayer. In formal Jewish worship, a cantor is a person who sings solo verses or passages to which the choir or congregation responds. In Judaism, a cantor sings and lead ...

, using Qt, can interface with Maxima (along with

SageMath SageMath (previously Sage or SAGE, "System for Algebra and Geometry Experimentation") is a computer algebra system (CAS) with features covering many aspects of mathematics, including algebra, combinatorics, graph theory, numerical analysis, numbe ...

, R, and

KAlgebra KAlgebra is a mathematical graph calculator included in the KDE education package. While it is based on the MathML content markup language, knowledge of MathML is not required for use. The calculator includes numerical, logical, symbolic, and ...

) * The

GNU TeXmacs GNU TeXmacs is a scientific word processor and typesetting component of the GNU Project. It originated as GNU Emacs with TeX functionalities, though it shares no code with those programs, while using TeX fonts. It is written and maintained by Jori ...

and

LyX LyX (styled as ; pronounced ) (Based on 3 developers, they say it can be pronounced "Licks", "Lucks" and "Leeks") is an open source, graphical user interface document processor based on the LaTeX typesetting system. Unlike most word processors, ...

mathematical editor programs can be used to provide an interactive GUI for Maxima, as can SageMath. Other options include the Imaxima front end, as well as an

Emacs Emacs , originally named EMACS (an acronym for "Editor MACroS"), is a family of text editors that are characterized by their extensibility. The manual for the most widely used variant, GNU Emacs, describes it as "the extensible, customizable, s ...

and

XEmacs XEmacs is a graphical- and console-based text editor which runs on almost any Unix-like operating system as well as Microsoft Windows. XEmacs is a fork, based on a version of GNU Emacs from the late 1980s. Any user can download, use, and modify XE ...

interaction mode which is activated by Imaxima. * Kayali * Climaxima, a

CLIM The Common Lisp Interface Manager (CLIM) is a Common Lisp-based programming interface for creating user interfaces, i.e., graphical user interfaces (GUIs). It provides an application programming interface (API) to user interface facilities for the ...

-based front-end.

References

External links

* {{Authority control Common Lisp (programming language) software Computer algebra system software for Linux Computer algebra system software for macOS Computer algebra system software for Windows Cross-platform free software Free computer algebra systems Free educational software Free software programmed in Lisp Software that uses wxWidgets