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# Maxima 5.23.2 Manual

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Maxima is a computer algebra system, implemented in Lisp.

Maxima is derived from the Macsyma system, developed at MIT in the years 1968 through 1982 as part of Project MAC. MIT turned over a copy of the Macsyma source code to the Department of Energy in 1982; that version is now known as DOE Macsyma. A copy of DOE Macsyma was maintained by Professor William F. Schelter of the University of Texas from 1982 until his death in 2001. In 1998, Schelter obtained permission from the Department of Energy to release the DOE Macsyma source code under the GNU Public License, and in 2000 he initiated the Maxima project at SourceForge to maintain and develop DOE Macsyma, now called Maxima.

Maxima infrastructure

• Introduction to Maxima |  | Sample Maxima sessions.
• Bug Detection and Reporting |  | Finding and reporting bugs in Maxima.
• Help |  | Asking for help from within a Maxima session.
• Command Line |  | Maxima command line syntax.
• Operators |  | Operators used in Maxima expressions.
• Expressions |  | Expressions in Maxima.
• Simplification |  | Simplifying expressions.
• Plotting |  | 2D and 3D graphical output.
• Input and Output |  | File input and output.
• Floating Point |  | Low level numerical routines.
• Contexts |  | Sets of assumed facts.

    Support for specific areas of mathematics

• Polynomials |  | Standard forms for polynomials, and functions operating on them.
• Constants |  | Numerical constants.
• Logarithms |  | Manipulation of expressions involving logarithms.
• Trigonometric |  | Manipulating expressions with trig and inverse trig functions.
• Special Functions |  | Special functions
• Elliptic Functions |  | Elliptic Functions and Integrals
• Limits |  | Limits of expressions.
• Differentiation |  | Differential calculus.
• Integration |  | Integral calculus.
• Equations |  | Defining and solving equations.
• Differential Equations |  | Defining and solving differential equations.
• Numerical |  | Numerical integration, Fourier transforms, etc.
• Arrays |  | Creating and working with arrays.
• Matrices and Linear Algebra |  | Matrix operations.
• Affine |  |
• itensor |  | Indicial Tensor Manipulation.
• ctensor |  | Component Tensor Manipulation.
• atensor |  | Algebraic Tensor Manipulation.
• Series |  | Taylor and power series.
• Number Theory |  | Number theory.
• Symmetries |  |
• Groups |  | Abstract algebra.

    Advanced facilities and programming

• Runtime Environment |  | Customization of the Maxima environment.
• Miscellaneous Options |  | Options with a global effect on Maxima.
• Rules and Patterns |  | User defined pattern matching and simplification rules.
• Lists |  | Manipulation of lists.
• Sets |  | Manipulation of sets.
• Function Definition |  | Defining functions.
• Program Flow |  | Defining Maxima programs.
• Debugging |  | Debugging Maxima programs.

    Additional packages

• asympa |  | Asymptotic analysis package
• augmented_lagrangian |  | augmented_lagrangian package.
• bode |  | Bode gain and phase plots.
• cobyla |  | Nonlinear optimization with inequality constraints.
• contrib_ode |  | Additional routines for ODEs
• descriptive |  | Descriptive statistics.
• diag |  | Jordan matrices.
• distrib |  | Probability distributions.
• draw |  | A Maxima-Gnuplot interface.
• drawdf |  | Direction fields with Gnuplot.
• dynamics |  | Graphics for dynamical systems and fractals.
• ezunits |  | Dimensional quantities.
• f90 |  | Maxima to fortran translator.
• ggf |  | Generating function of sequences.
• graphs |  | Graph theory package.
• grobner |  | Functions for working with Groebner bases.
• impdiff |  | Implicit derivatives.
• implicit_plot |  | Implicit plots package.
• interpol |  | Interpolation package.
• lapack |  | LAPACK functions for linear algebra.
• lbfgs |  | L-BFGS unconstrained minimization package.
• lindstedt |  | Lindstedt package.
• linearalgebra |  | Functions for linear algebra.
• lsquares |  | Least squares.
• makeOrders |  | Polynomial utility.
• minpack |  | MINPACK functions for minimization and roots
• mnewton |  | Newton's method.
• numericalio |  | Reading and writing files.
• opsubst |  | Substitutions utility.
• orthopoly |  | Orthogonal polynomials.
• plotdf |  | Direction fields plots.
• romberg |  | Romberg method for numerical integration.
• simplex |  | Linear programming.
• simplification |  | Simplification rules and functions.
• solve_rec |  | Linear recurrences.
• stats |  | Statistical inference package.
• stirling |  | Stirling formula.
• stringproc |  | String processing.
• unit |  | Units and dimensions package.
• zeilberger |  | Functions for hypergeometric summation.

    Index

• Function and Variable Index |  | Index.

     --- The Detailed Node Listing ---

    Introduction

• Introduction to Maxima |  |

    Bugs

• Bug Detection and Reporting |  |

    Help

• Lisp and Maxima |  |
• Garbage Collection |  |
• Documentation |  |
• Functions and Variables for Help |  |

    Command Line

• Introduction to Command Line |  |
• Functions and Variables for Command Line |  |

    Operators

• nary |  |
• nofix |  |
• postfix |  |
• prefix |  |
• Arithmetic operators |  |
• Relational operators |  |
• General operators |  |

    Expressions

• Introduction to Expressions |  |
• Complex |  |
• Inequality |  |
• Syntax |  |
• Functions and Variables for Expressions |  |

    Simplification

• Functions and Variables for Simplification |  |

    Plotting

• Introduction to Plotting |  |
• Plotting Formats |  |
• Functions and Variables for Plotting |  |
• Plotting Options |  |
• Gnuplot Options |  |
• Gnuplot_pipes Format Functions |  |

    Input and Output

• Comments |  |
• Files |  |
• Functions and Variables for Input and Output |  |

    Floating Point

• Functions and Variables for Floating Point |  |

    Contexts

• Functions and Variables for Contexts |  |

    Polynomials

• Introduction to Polynomials |  |
• Functions and Variables for Polynomials |  |

    Constants

• Functions and Variables for Constants |  |

    Logarithms

• Functions and Variables for Logarithms |  |

    Trigonometric

• Introduction to Trigonometric |  |
• Functions and Variables for Trigonometric |  |

    Special Functions

• Introduction to Special Functions |  |
• Bessel Functions |  |
• Airy Functions |  |
• Gamma and factorial Functions |  |
• Exponential Integrals |  |
• Error Function |  |
• Struve Functions |  |
• Hypergeometric Functions |  |
• Parabolic Cylinder Functions |  |
• Functions and Variables for Special Functions |  |

    Elliptic Functions

• Introduction to Elliptic Functions and Integrals |  |
• Functions and Variables for Elliptic Functions |  |
• Functions and Variables for Elliptic Integrals |  |

    Limits

• Functions and Variables for Limits |  |

    Differentiation

• Functions and Variables for Differentiation |  |

    Integration

• Introduction to Integration |  |
• Functions and Variables for Integration |  |

    Equations

• Functions and Variables for Equations |  |

    Differential Equations

• Introduction to Differential Equations |  |
• Functions and Variables for Differential Equations |  |

    Numerical

• Introduction to fast Fourier transform |  |
• Functions and Variables for fast Fourier transform |  |
• Introduction to Fourier series |  |
• Functions and Variables for Fourier series |  |

    Arrays

• Functions and Variables for Arrays |  |

    Matrices and Linear Algebra

• Introduction to Matrices and Linear Algebra |  |
• Dot |  |
• Vectors |  |
• eigen |  |
• Functions and Variables for Matrices and Linear Algebra |  |

    Affine

• Introduction to Affine |  |
• Functions and Variables for Affine |  |

    itensor

• Introduction to itensor |  |
• Functions and Variables for itensor |  |

    ctensor

• Introduction to ctensor |  |
• Functions and Variables for ctensor |  |

    atensor

• Introduction to atensor |  |
• Functions and Variables for atensor |  |

    Series

• Introduction to Series |  |
• Functions and Variables for Series |  |

    Number Theory

• Functions and Variables for Number Theory |  |

    Symmetries

• Introduction to Symmetries |  |
• Functions and Variables for Symmetries |  |

    Groups

• Functions and Variables for Groups |  |

    Runtime Environment

• Introduction for Runtime Environment |  |
• Interrupts |  |
• Functions and Variables for Runtime Environment |  |

    Miscellaneous Options

• Introduction to Miscellaneous Options |  |
• Share |  |
• Functions and Variables for Miscellaneous Options |  |

    Rules and Patterns

• Introduction to Rules and Patterns |  |
• Functions and Variables for Rules and Patterns |  |

    Lists

• Introduction to Lists |  |
• Functions and Variables for Lists |  |

    Sets

• Introduction to Sets |  |
• Functions and Variables for Sets |  |

    Function Definition

• Introduction to Function Definition |  |
• Function |  |
• Macros |  |
• Functions and Variables for Function Definition |  |

    Program Flow

• Introduction to Program Flow |  |
• Functions and Variables for Program Flow |  |

    Debugging

• Functions and Variables for Debugging |  |

    asympa

• Introduction to asympa |  |
• Functions and variables for asympa |  |

    augmented_lagrangian

• Functions and Variables for augmented_lagrangian |  |

    bode

• Functions and Variables for bode |  |

    cobyla

• Introduction to cobyla |  |
• Functions and Variables for cobyla |  |
• Examples for cobyla |  |

    contrib_ode

• Introduction to contrib_ode |  |
• Functions and Variables for contrib_ode |  |
• Possible improvements to contrib_ode |  |
• Test cases for contrib_ode |  |
• References for contrib_ode |  |

    descriptive

• Introduction to descriptive |  |
• Functions and Variables for data manipulation |  |
• Functions and Variables for descriptive statistics |  |
• Functions and Variables for statistical graphs |  |

    diag

• Functions and Variables for diag |  |

    distrib

• Introduction to distrib |  |
• Functions and Variables for continuous distributions |  |
• Functions and Variables for discrete distributions |  |

    draw

• Introduction to draw |  |
• Functions and Variables for draw |  |
• Functions and Variables for pictures |  |
• Functions and Variables for worldmap |  |

    drawdf

• Introduction to drawdf |  |
• Functions and Variables for drawdf |  |

    dynamics

• Introduction to dynamics |  |
• Functions and Variables for dynamics |  |

    ezunits

• Introduction to ezunits |  |
• Introduction to physical_constants |  |
• Functions and Variables for ezunits |  |

    f90

• Functions and Variables for f90 |  |

    ggf

• Functions and Variables for ggf |  |

    graphs

• Introduction to graphs |  |
• Functions and Variables for graphs |  |

    grobner

• Introduction to grobner |  |
• Functions and Variables for grobner |  |

    impdiff

• Functions and Variables for impdiff |  |

    implicit_plot

• Functions and Variables for implicit_plot |  |

    interpol

• Introduction to interpol |  |
• Functions and Variables for interpol |  |

    lapack

• Introduction to lapack |  |
• Functions and Variables for lapack |  |

    lbfgs

• Introduction to lbfgs |  |
• Functions and Variables for lbfgs |  |

    lindstedt

• Functions and Variables for lindstedt |  |

    linearalgebra

• Introduction to linearalgebra |  |
• Functions and Variables for linearalgebra |  |

    lsquares

    * Introduction to lsquares

• Functions and Variables for lsquares |  |

    makeOrders

• Functions and Variables for makeOrders |  |

    minpack

• Introduction to minpack |  |
• Functions and Variables for minpack |  |

    mnewton

• Introduction to mnewton |  |
• Functions and Variables for mnewton |  |

    numericalio

• Introduction to numericalio |  |
• Functions and Variables for plain-text input and output |  |
• Functions and Variables for binary input and output |  |

    opsubst

• Functions and Variables for opsubst |  |

    orthopoly

• Introduction to orthogonal polynomials |  |
• Functions and Variables for orthogonal polynomials |  |

    plotdf

• Introduction to plotdf |  |
• Functions and Variables for plotdf |  |

    romberg

• Functions and Variables for romberg |  |

    simplex

• Introduction to simplex |  |
• Functions and Variables for simplex |  |

    simplification

• Introduction to simplification |  |
• Package absimp |  |
• Package facexp |  |
• Package functs |  |
• Package ineq |  |
• Package rducon |  |
• Package scifac |  |
• Package sqdnst |  |

    solve_rec

• Introduction to solve_rec |  |
• Functions and Variables for solve_rec |  |

    stats

• Introduction to stats |  |
• Functions and Variables for inference_result |  |
• Functions and Variables for stats |  |
• Functions and Variables for special distributions |  |

    stirling

• Functions and Variables for stirling |  |

    stringproc

• Introduction to string processing |  |
• Functions and Variables for input and output |  |
• Functions and Variables for characters |  |
• Functions and Variables for strings |  |

    unit

• Introduction to Units |  |
• Functions and Variables for Units |  |

    zeilberger

• Introduction to zeilberger |  |
• Functions and Variables for zeilberger |  |

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