# Maxima 5.45.1s – FREE Algebra System

Maxima is a FREE computer algebra system comparable to commercial systems like Mathematica and Maple. It emphasizes symbolic mathematical computation: algebra, trigonometry, calculus, and much more. The program can calculate with exact integers and fractions, native floating-point and high-precision big floats.

Maxima is a system for the manipulation of symbolic and numerical expressions. Including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations. Besides that, the systems of linear equations, polynomials, sets, lists, vectors, matrices and tensors.

Maxima yields high precision numerical results by using exact fractions, arbitrary-precision integers and variable-precision floating-point numbers. It can plot functions and data in two and three dimensions.

The software has user-friendly front-ends, an on-line manual, plotting commands, and numerical libraries. Users can write programs in its native programming language, and many have contributed useful packages in a variety of areas over the decades.

Maxima is GPL-licensed and largely written in Common Lisp. You can download the executables for Windows, Mac, Linux, and Android. Source code is also available. An active community maintains and extends the system.

## Maxima Features:

- Specialized in symbolic operations but offering numerical capabilities too.
- Can be accessed programmatically and extended, as the underlying Lisp can be called from it.
- Complete programming language with ALGOL-like syntax but Lisp-like semantics.
- Arbitrary-precision integers.
- Rational numbers of sizes limited only by machine memory.
- Arbitrarily large floating-point numbers (“bfloats”).

Maxima is a descendant of Macsyma, the legendary computer algebra system developed in the late 1960s at the Massachusetts Institute of Technology. It is the only system based on that effort still publicly available and with an active user community. Thanks to its open source nature.

### What’s New in Maxima 5.45:

### What’s New in Maxima 5.43:

#### New items in core:

- function cartesian_product_list: Cartesian product of lists.
- function garbage_collect: trigger Lisp garbage collector.
- variables maxima_frontend, maxima_frontend_version: inform
`build_info`

which user interface is in use.

#### New items in share:

- killing.dem: a demo for Killing vector fields.
- package logic: new function logic_simplify implements K-Map reduction (Quine-McCluskey algorithm)

#### Changes in core:

- function to_cl: now autoloaded.
- package linearalgebra: autoload all functions.
- function run_testsuite: summary now not only tells which unexpectedly failed, but also which ones unexpectedly passed.
- series expansion for expintegral_si and gamma_incomplete; breaks some existing tests, see commit 47a6afd.
- function translate: generate code which translates conditional expressions with prederror = true

#### Changes in share:

- package gentran: new version (thanks to Michael Stern)
- package simplex: improvements, including symbolic inputs.
- package ode: test cases.
- package odepack: works with ECL.
- package lapack: works with ECL.
- package sarag: fix missing definition of SQUARE_FREE_ALGORITHM.
- package sarag: make certificate proof more explicit (verify certificate)
- share test suite: include tests for packages lapack, sym, and ode.
- share test suite: a few simple tests for package odepack.
- ezunits: conversion rule for nondimensional/(sum of dimensional)
- ezunits: 0 now can have a dimension.
- package draw: accepts color index number 0, 1, 2, … 17.
- package draw: accepts plot titles which are not strings.
- package wrstcse: improved range and resolution of Monte Carlo analysis.

#### User interfaces:

- SF Patch #88: Emaxima now correctly expands tabs in the comint buffer of emacs.

#### Bug fixes:

- 3549: “patch to mmref, and removing mmref.tex and maxima_pdf.texi from info directory”
- 3532: “Integrator doesn’t use a new variable internally, causing facts on the original variable to be used for the substitution variable”
- 3529: “crash with gcl due to wrong maxima startup script”
- 3524: “Discrepancy in intromax”
- 3514: “ECL: Marking rtest16/test step 50 as \”known bad\” doesn’t work”
- 3497: “ctensor documentation on the Ricci tensor is inconsistent”
- 3496: “Hardcoded interpreter path in doc/info/build_index.pl causes build fail on FreeBSD”
- 3494: “vector.dem is broken”
- 3484: “taylor of expintegral_si is wrong”
- 3470: “Error in maximize_lp “
- 3463: “Documentation: mention parameter epsilon_lp more explicitly in documentation for minimize_lp”
- 3459: “Wrong limit calculation”
- 3412: “Bug when translating functions that contain an \”if\” (in my case an implicit if)”

## Unnumbered bugs:

- mailing list 2019-05-11: “Problems with gramschmidt”
- mailing list 2019-05-06: “problem with elem() after kill(all)”
- mailing list 2019-04-02: “maxima lists”
- mailing list 2019-03-08: “GCL build broken”.
- mailing list 2019-03-08: “batch overwrites last output line”
- mailing list 2019-03-06: “the share testsuite + MAXIMA:$RESULTANT is undefined errors”
- mailing list 2018-12-03: “error in compiling function with global variable”
- mailing list 2018-11-01: “radcan(sqrt(-1/(sqrt(-3)+1))*sqrt(2))”
- commit c164f5f: SIMPEXPT was marking unsimplified expressions with SIMP
- commit 61c71db: Fix siemens/sievert typo (ezunits)

#### Build system:

- Crosscompiling: Add ‘maxima_longnames.c’ to automake
- configure: enable build with ABCL via –enable-abcl.
- Windows installer: can now include ABCL.
- Windows installer: updated external utilities.
- Windows installer: updated wxMaxima version.
- “make check” manipulates the list of tests now in a more canonical way in order to automatically run the interactive tests, as well.
- ./configure –enable-quiet-build now muffles more warnings.
- build documentation using the standard makeinfo tools.
- maxima-sbcl now supports non-ASCII user names and install dirs on MacOs and MS Windows
- “make install” now installs emaxima and imaxima in a place emacs will find by default. configure’s –emacs-prefix= option allows to choose a different directory.

#### Documentation:

- ./update_examples now interprets lines beginning with the string “input:” as text that should be sent as input.

#### Runtime:

- environment variable MAXIMA_DOC_PREFIX overrides the location the documentation is searched for.
- environment variable GCL_DISABLE_MULTIPROCESS_MEMORY_POOL disables memory-sharing between GCL-compiled Maxima processes.
- Maxima.bat now autodetects 64-bit systems and does the necessary modifications for making lapack work in SBCL if this test is positive.

Homepage – https://maxima.sourceforge.io/

Maxima (/ˈmæksɪmə/) is a computer algebra system (CAS) is written in Common Lisp and runs on all POSIX platforms such as macOS, Unix, BSD, and Linux, as well as under Microsoft Windows and Android. It is free software released under the terms of the GNU General Public License (GPL).

Size: 140 MB