@c -*-texinfo-*-

@c 2000-04-17 Jim Van Zandt <jrv@vanzandt.mv.com> Added header,
@c info directory entry, reference to introduction chapter, and menu
@c descriptions.  Rearranged chapters.

@c to update the menus do: 
@c (texinfo-multiple-files-update "maxima.texi" t t)
@c
@c texinfo-multiple-files-update will delete the detailed node listing!


@c %**start of header
@synindex vr fn
@synindex cp fn
@settitle Maxima 5.33.0 Manual
@c %**end of header
@setchapternewpage odd
@ifinfo
This is a Texinfo Maxima Manual

Copyright 1994,2001 William F. Schelter

@format
INFO-DIR-SECTION Math
START-INFO-DIR-ENTRY
* Maxima: (maxima).     A computer algebra system.
END-INFO-DIR-ENTRY
@end format
@end ifinfo

@ifinfo 
@macro var {expr}
<\expr\>
@end macro
@end ifinfo

@include category-macros.texi

@titlepage
@sp 10
@comment The title is printed in a large font.
@center @titlefont{Maxima Manual}
@center Ver. 5.33.0
@page
@vskip 0pt plus 1filll
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.

@end titlepage

@summarycontents
@contents

@ifnottex
@node Top, Introduction to Maxima, (dir), (dir)
@top

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.
@end ifnottex

@c includes

@menu

@b{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, Input, and Output.
* Data Types and Structures::   Numbers, Strings, Lists, Arrays, and Structures.
* Expressions::                 Expressions in Maxima.
* Operators::                   Operators used in Maxima expressions.
* Evaluation::                  Evaluating expressions.
* Simplification::              Simplifying expressions.
* Mathematical Functions::      Mathematical functions in Maxima.
* Maximas Database::            Declarations, Contexts, Facts, and Properties.
* Plotting::                    2D and 3D graphical output.
* File Input and Output::       File input and output.

Support for specific areas of mathematics
* Polynomials::                 Standard forms for polynomials, and
                                functions operating on them.
* 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, Equations, ODE's, etc.
* Matrices and Linear Algebra:: Matrix operations.
* Affine::                      
* itensor::                     Indicial Tensor Manipulation.
* ctensor::                     Component Tensor Manipulation.
* atensor::                     Algebraic Tensor Manipulation.
* Sums Products and Series::    Sums, Products, 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.
* Sets::                        Manipulation of sets.
* Function Definition::         Defining functions.
* Program Flow::                Defining Maxima programs.
* Debugging::                   Debugging Maxima programs.

Additional packages
* alt-display::                 Alternative display package.
* asympa::                      Asymptotic analysis package.
* augmented_lagrangian::        augmented_lagrangian package.
* Bernstein::                   Bernstein polynomials.
* 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.
* finance::                     Financial package.
* fractals::                    Fractals.
* ggf::                         Generating function of sequences.
* graphs::                      Graph theory package.
* grobner::                     Functions for working with Groebner bases.
* impdiff::                     Implicit derivatives.
* 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.
* 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.
* to_poly_solve::               to_poly_solve package.
* unit::                        Units and dimensions package.
* zeilberger::                  Functions for hypergeometric summation.

Index
* Function and Variable Index:: Index.

@comment @detailmenu
 --- The Detailed Node Listing ---

Introduction
* Introduction to Maxima::

Bugs
* Bug Detection and Reporting::

Help
* Documentation::
* Functions and Variables for Help::

Command Line
* Introduction to Command Line::
* Functions and Variables for Command Line::
* Functions and Variables for Display::

Data Types and Structures
* Numbers::
* Strings::
* Constants::
* Lists::
* Arrays::
* Structures::

Expressions
* Introduction to Expressions::
* Nouns and Verbs::
* Identifiers::
* Inequality::
* Functions and Variables for Expressions::

Operators
* Introduction to operators::
* Arithmetic operators::
* Relational operators::
* Logical operators::
* Operators for Equations::
* Assignment operators::
* User defined operators::

Evaluation
* Functions and Variables for Evaluation::

Simplification
* Functions and Variables for Simplification::

Mathematical Functions
* Functions for Numbers::
* Functions for Complex Numbers::
* Combinatorial Functions::
* Root Exponential and Logarithmic Functions::
* Trigonometric Functions::
* Random Numbers::

Maximas Database
* Introduction to Maximas Database::
* Functions and Variables for Properties::
* Functions and Variables for Facts::
* Functions and Variables for Predicates::

Plotting
* Introduction to Plotting::
* Plotting Formats::
* Functions and Variables for Plotting::    
* Plotting Options::
* Gnuplot Options::
* Gnuplot_pipes Format Functions::

File Input and Output
* Comments::
* Files::
* Functions and Variables for File Input and Output::
* Functions and Variables for TeX Output::
* Functions and Variables for Fortran Output::

Polynomials
* Introduction to Polynomials::  
* Functions and Variables for Polynomials::

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::
* Functions for numerical solution of equations::
* Introduction to numerical solution of differential equations::
* Functions for numerical solution of differential equations::

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::     

Sums, Products, and Series
* Functions and Variables for Sums and Products::
* Introduction to Series::
* Functions and Variables for Series::
* Introduction to Fourier series::
* Functions and Variables for Fourier 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::

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
* Lisp and Maxima::
* Garbage Collection::
* Introduction to Program Flow::  
* Functions and Variables for Program Flow::  

Debugging
* Functions and Variables for Debugging::   

alt-display
* Introduction to alt-display::
* Functions and Variables for alt-display::

asympa
* Introduction to asympa::
* Functions and variables for asympa::

augmented_lagrangian
* Functions and Variables for augmented_lagrangian::

Bernstein
* Functions and Variables for Bernstein::

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::

finance
* Introduction to finance::
* Functions and Variables for finance::

fractals
* Introduction to fractals::
* Definitions for IFS fractals::
* Definitions for complex fractals::
* Definitions for Koch snowflakes::
* Definitions for Peano maps::

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::

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::

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::

to_poly_solve
* Functions and Variables for to_poly_solve::

unit
* Introduction to Units::       
* Functions and Variables for Units::

zeilberger
* Introduction to zeilberger::
* Functions and Variables for zeilberger::

@comment @end detailmenu
@end menu

@c  Put the @node lines here, rather than in the @included files,
@c  so emacs can automatically update them with C-c C-u C-e.
@c  nota bene: C-c C-u C-a and texinfo-multiple-files-update will delete
@c  the detailed node listing!

@node Introduction to Maxima, Bug Detection and Reporting, Top, Top
@chapter Introduction to Maxima
@include Introduction.texi

@node Bug Detection and Reporting, Help, Introduction to Maxima, Top
@chapter Bug Detection and Reporting
@include Bugs.texi

@node Help, Command Line, Bug Detection and Reporting, Top
@chapter Help
@include Help.texi

@node Command Line, Data Types and Structures, Help, Top
@chapter Command Line
@include Command.texi

@node Data Types and Structures, Expressions, Command Line, Top
@chapter Data Types and Structures
@include DataTypes.texi
@include Constants.texi
@include Lists.texi
@include Arrays.texi
@include defstruct.texi

@node Expressions, Operators, Data Types and Structures, Top
@chapter Expressions
@include Expressions.texi

@node Operators, Evaluation, Expressions, Top
@chapter Operators
@include Operators.texi

@node Evaluation, Simplification, Operators, Top
@chapter Evaluation
@include Evaluation.texi

@node Simplification, Mathematical Functions, Evaluation, Top
@chapter Simplification
@include Simplification.texi

@node Mathematical Functions, Maximas Database, Simplification, Top
@chapter Mathematical Functions
@include MathFunctions.texi

@node Maximas Database, Plotting, Mathematical Functions, Top
@chapter Maximas Database
@include Database.texi

@node Plotting, File Input and Output, Maximas Database, Top
@chapter Plotting
@include Plotting.texi

@node File Input and Output, Polynomials, Plotting, Top
@chapter File Input and Output
@include Input.texi

@node Polynomials, Special Functions, File Input and Output, Top
@chapter Polynomials
@include Polynomials.texi

@node Special Functions, Elliptic Functions, Polynomials, Top
@chapter Special Functions
@include Special.texi

@node Elliptic Functions, Limits, Special Functions, Top
@chapter Elliptic Functions
@include Elliptic.texi

@node Limits, Differentiation, Elliptic Functions, Top
@chapter Limits
@include Limits.texi

@node Differentiation, Integration, Limits, Top
@chapter Differentiation
@include Differentiation.texi

@node Integration, Equations, Differentiation, Top
@chapter Integration
@include Integration.texi

@node Equations, Differential Equations, Integration, Top
@chapter Equations
@include Equations.texi

@node Differential Equations, Numerical, Equations, Top
@chapter Differential Equations
@include Differential.texi

@c @include NonCommutative.texi

@node Numerical, Matrices and Linear Algebra, Differential Equations, Top
@chapter Numerical
@include Numerical.texi

@node Matrices and Linear Algebra, Affine, Numerical, Top
@chapter Matrices and Linear Algebra
@include Matrices.texi

@node Affine, itensor, Matrices and Linear Algebra, Top
@chapter Affine
@include Affine.texi

@node itensor, ctensor, Affine, Top
@chapter itensor
@include Itensor.texi

@node ctensor, atensor, itensor, Top
@chapter ctensor
@include Ctensor.texi

@node atensor, Sums Products and Series, ctensor, Top
@chapter atensor
@include Atensor.texi

@node Sums Products and Series, Number Theory, atensor, Top
@chapter Sums, Products, and Series
@include Series.texi

@node Number Theory, Symmetries, Sums Products and Series, Top
@chapter Number Theory
@include Number.texi

@node Symmetries, Groups, Number Theory, Top
@chapter Symmetries
@include Symmetries.texi

@node Groups, Runtime Environment, Symmetries, Top
@chapter Groups
@include Groups.texi

@node Runtime Environment, Miscellaneous Options, Groups, Top
@chapter Runtime Environment
@include Runtime.texi

@node Miscellaneous Options, Rules and Patterns, Runtime Environment, Top
@chapter Miscellaneous Options
@include Miscellaneous.texi

@node Rules and Patterns, Sets, Miscellaneous Options, Top
@chapter Rules and Patterns
@include Rules.texi

@node Sets, Function Definition, Rules and Patterns, Top
@chapter Sets
@include nset.texi

@node Function Definition, Program Flow, Sets, Top
@chapter Function Definition
@include Function.texi

@node Program Flow, Debugging, Function Definition, Top
@chapter Program Flow
@include Program.texi

@node Debugging, alt-display, Program Flow, Top
@chapter Debugging
@include Debugging.texi

@node alt-display, asympa, Debugging, Top
@chapter alt-display
@include alt-display.texi

@node asympa, augmented_lagrangian, alt-display, Top
@chapter asympa
@include asympa.texi

@node augmented_lagrangian, Bernstein, asympa, Top
@chapter augmented_lagrangian
@include augmented_lagrangian.texi

@node Bernstein, bode, augmented_lagrangian, Top
@chapter Bernstein
@include bernstein.texi

@node bode, cobyla, Bernstein, Top
@chapter bode
@include bode.texi

@node cobyla, contrib_ode, bode, Top
@chapter cobyla
@include cobyla.texi

@node contrib_ode, descriptive, cobyla, Top
@chapter contrib_ode
@include contrib_ode.texi

@node descriptive, diag, contrib_ode, Top
@chapter descriptive
@include descriptive.texi

@node diag, distrib, descriptive, Top
@chapter diag
@include diag.texi

@node distrib, draw, diag, Top
@chapter distrib
@include distrib.texi

@node draw, drawdf, distrib, Top
@chapter draw
@include draw.texi

@node drawdf, dynamics, draw, Top
@chapter drawdf
@include drawdf.texi

@node dynamics, ezunits, drawdf, Top
@chapter dynamics
@include dynamics.texi

@node ezunits, f90, dynamics, Top
@chapter ezunits
@include ezunits.texi

@node f90, finance, ezunits, Top
@chapter f90
@include f90.texi

@node finance, fractals, f90, Top
@chapter finance
@include finance.texi

@node fractals, ggf, finance, Top
@chapter fractals
@include fractals.texi

@node ggf, graphs, fractals, Top
@chapter ggf
@include ggf.texi

@node graphs, grobner, ggf, Top
@chapter graphs
@include graphs.texi

@node grobner, impdiff, graphs, Top
@chapter grobner
@include grobner.texi

@node impdiff, interpol, grobner, Top
@chapter impdiff
@include impdiff.texi

@node interpol, lapack, impdiff, Top
@chapter interpol
@include interpol.texi

@node lapack, lbfgs, interpol, Top
@chapter lapack
@include lapack.texi

@node lbfgs, lindstedt, lapack, Top
@chapter lbfgs
@include lbfgs.texi

@node lindstedt, linearalgebra, lbfgs, Top
@chapter lindstedt
@include lindstedt.texi

@node linearalgebra, lsquares, lindstedt, Top
@chapter linearalgebra
@include linearalgebra.texi

@node lsquares, minpack, linearalgebra, Top
@chapter lsquares
@include lsquares.texi

@node minpack, makeOrders, lsquares, Top
@chapter minpack
@include minpack.texi

@node makeOrders, mnewton, minpack, Top
@chapter makeOrders
@include makeOrders.texi

@node mnewton, numericalio, makeOrders, Top
@chapter mnewton
@include mnewton.texi

@node numericalio, opsubst, mnewton, Top
@chapter numericalio
@include numericalio.texi

@node opsubst, orthopoly, numericalio, Top
@chapter opsubst
@include opsubst.texi

@node orthopoly, romberg, opsubst, Top
@chapter orthopoly
@include orthopoly.texi

@node romberg, simplex, orthopoly, Top
@chapter romberg
@include romberg.texi

@node simplex, simplification, romberg, Top
@chapter simplex
@include simplex.texi

@node simplification, solve_rec, simplex, Top
@chapter simplification
@include simplifications.texi

@node solve_rec, stats, simplification, Top
@chapter solve_rec
@include solve_rec.texi

@node stats, stirling, solve_rec, Top
@chapter stats
@include stats.texi

@node stirling, stringproc, stats, Top
@chapter stirling
@include stirling.texi

@node stringproc, to_poly_solve, stirling, Top
@chapter stringproc
@include stringproc.texi

@node to_poly_solve, unit, stringproc, Top
@chapter to_poly_solve
@include to_poly_solve.texi

@node unit, zeilberger, to_poly_solve, Top
@chapter unit
@include unit.texi

@node zeilberger, Function and Variable Index, unit, Top
@chapter zeilberger
@include zeilberger.texi

@node Function and Variable Index,  , zeilberger, Top
@chapter Indices
@include Indices.texi

@c end includes

