@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
@settitle Maxima 5.46.0 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

@c for texi2html 5.0 following lines were commented out.
@c @titlepage
@c @sp 10
@c @comment The title is printed in a large font.
@c @center @titlefont{Maxima Manual}
@c @center Ver. 5.46.0
@c @page
@c @vskip 0pt plus 1filll
@c Maximaはコンピュータ代数システムです。Lispで実装されています。
@c  
@c MaximaはMacsymaシステムから派生したものです。
@c Macsymaシステムは、MITで1968年から1982年にかけてプロジェクトMACの一部として開発されました。
@c MITは、1982年にMacsymaソースコードのコピーをエネルギー省に引き渡しました;
@c そのバージョンは現在、DOE Macsymaとして知られています。
@c DOE Macsymaのコピーは、テキサス大学のWilliam F. Schelter教授によって、
@c 1982年から教授がなくなる2001年まで保守されました。
@c 1998年にSchelterは、
@c エネルギー省からDOE MacsymaソースコードをGNU Public Licenseの下で公開する許可を得て、
@c 2000年に彼は、
@c DOE Macsymaを保守・開発するために、MaximaプロジェクトをSourceForgeで始めました。
@c だから、Maximaと呼ばれています。
@c 
@c @end titlepage

@summarycontents
@contents

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

Maximaはコンピュータ代数システムです。Lispで実装されています。

MaximaはMacsymaシステムから派生したものです。
Macsymaシステムは、MITで1968年から1982年にかけてプロジェクトMACの一部として開発されました。
MITは、1982年にMacsymaソースコードのコピーをエネルギー省に引き渡しました;
そのバージョンは現在、DOE Macsymaとして知られています。
DOE Macsymaのコピーは、テキサス大学のWilliam F. Schelter教授によって、
1982年から教授がなくなる2001年まで保守されました。
1998年にSchelterは、
エネルギー省からDOE MacsymaソースコードをGNU Public Licenseの下で公開する許可を得て、
2000年に彼は、
DOE Macsymaを保守・開発するために、MaximaプロジェクトをSourceForgeで始めました。
だから、Maximaと呼ばれています。
@end ifnottex

@c includes

@menu
Maximaの基盤

* Introduction to Maxima::      Maximaセッションの実例
* Bug Detection and Reporting:: Maximaのバグの発見と報告
* Help::                        Maximaセッションの中でヘルプを見る
* Command Line::                Maximaコマンドライン構文法、入出力
* Data Types and Structures::   数、文字列、リスト、配列、構造体
* Expressions::                 Maximaにおける式
* Operators::                   Maxima式の中で使われる演算子
* Evaluation::                  式の評価
* Simplification::              式の整理
* Mathematical Functions::      Maximaの数学的関数
* Maximas Database::            宣言、文脈、事実、プロパティ
* Plotting::                    2次元と3次元のグラフィカル出力
* File Input and Output::       ファイル入出力

数学の特定分野のサポート

* Polynomials::                 多項式の標準形と操作関数
* Special Functions::           特殊函数
* Elliptic Functions::          楕円函数と楕円積分
* Limits::                      式の極限
* Differentiation::             微分法
* Integration::                 積分法
* Equations::                   方程式の定義と解法
* Differential Equations::      微分方程式の定義と解法
* Numerical::                   数値積分、Fourier変換など
* Matrices and Linear Algebra:: 行列演算
* Affine::                      
* itensor::                     添字テンソル操作
* ctensor::                     成分テンソル操作
* atensor::                     代数テンソル操作
* Sums Products and Series::    和、積、Tayler級数とべき級数
* Number Theory::               数論
* Symmetries::                  
* Groups::                      抽象代数

上級用機能とプログラミング

* Runtime Environment::         Maxima環境のカスタム化
* Miscellaneous Options::       Maximaでグローバルな効果を持つオプション
* Rules and Patterns::          ユーザー定義のパターンマッチングと整理ルール
* Sets::                        集合の操作
* Function Definition::         関数定義
* Program Flow::                Maximaプログラムの定義
* Debugging::                   Maximaプログラムのデバッグ

その他のパッケージ

* asympa::                      漸近解析パッケージ
* augmented_lagrangian::        拡張Lagrangeパッケージ
@c * Bernstein::                   Bernstein多項式
* Bernstein::                   @code{Bernstein}多項式
* bode::                        Bode線図
* cobyla::                      不等式制約を持つ非線形最適化
* contrib_ode::                 ODEのための追加ルーチン
* descriptive::                 記述統計
* diag::                        Jordan行列
* distrib::                     確率分布
* draw::                        Maxima-Gnuplotインターフェイス
* drawdf::                      Gnuplotを使った方向場
* dynamics::                    力学系とフラクタルのグラフィックス
* ezunits::                     次元量
* f90::                         MaximaからFortranへの翻訳器
* finance::                     金融パッケージ
* fractals::                    フラクタル
* ggf::                         数列の母函数
* graphs::                      グラフ理論パッケージ
* grobner::                     Groebner基底を扱う関数
* impdiff::                     陰導函数
* implicit_plot::               陰プロットパッケージ
* interpol::                    内挿バッケージ
* lapack::                      線形代数のためのLAPACK関数
* lbfgs::                       L-BFGS無制約最小化パッケージ
* lindstedt::                   Lindstedtパッケージ
* linearalgebra::               線形代数のための関数
* lsquares::                    最小二乗
* makeOrders::                  多項式ユーティリティ
* minpack::                     最小化と根のためのMINPACK関数
* mnewton::                     Newton法
* numericalio::                 ファイルの読み書き
* opsubst::                     代入ユーティリティ
* orthopoly::                   直交多項式
* plotdf::                      方向場プロット
* romberg::                     数値積分のRomberg法
* simplex::                     線形計画
* simplification::              整理のルールと関数
* solve_rec::                   線形漸化式
* stats::                       統計的推定パッケージ
* stirling::                    Stirling公式
* stringproc::                  文字列処理
@c * to_poly_solve::               to_poly_solveパッケージ
* to_poly_solve::               @code{to_poly_solve}パッケージ
* unit::                        単位と次元パッケージ
* zeilberger::                  超幾何総和に関する関数


索引

* Function and Variable Index:: インデックス

訳者後書き

* Translator's Comments::       訳者のコメント

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

手引き

* Introduction to Maxima::

バグ

* Bug Detection and Reporting::

ヘルプ

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

コマンドライン

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

データ型と構造体

* Numbers::
* Strings::
* Constants::
* Lists::
* Arrays::
* Structures::

式

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

演算子

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

評価

* Functions and Variables for Evaluation::

式整理

* Functions and Variables for Simplification::  

数学的関数

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

Maximaのデータベース

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

プロット

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

ファイル入出力

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

多項式

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

特殊函数

* 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::  

楕円函数

* Introduction to Elliptic Functions and Integrals::
* Functions and Variables for Elliptic Functions::
* Functions and Variables for Elliptic Integrals::

極限

* Functions and Variables for Limits::      

微分

* Functions and Variables for Differentiation::  

積分

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

方程式

* Functions and Variables for Equations::   

微分方程式

* Introduction to Differential Equations::  
* Functions and Variables for Differential Equations::  

数値

* Introduction to fast Fourier transform::                     
* Functions and Variables for fast Fourier transform::
* Introduction to Fourier series::
* Functions and Variables for Fourier series::

行列と線形代数

* Introduction to Matrices and Linear Algebra::  
* Dot::                         
* Vectors::                     
* eigen::
* Functions and Variables for Matrices and Linear Algebra::  

アフィン

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

指標テンソル

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

成分テンソル

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

代数テンソル

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

和、積、級数

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

数論

* Functions and Variables for Number Theory::  

対称群

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

群

* Functions and Variables for Groups::      

ランタイム環境

* Introduction for Runtime Environment::  
* Interrupts::                  
* Functions and Variables for Runtime Environment::  

様々なオプション

* Introduction to Miscellaneous Options::  
* Share::                       
* Functions and Variables for Miscellaneous Options::  

規則とパターン

* Introduction to Rules and Patterns::  
* Functions and Variables for Rules and Patterns::  

集合

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

関数定義

* Introduction to Function Definition::  
* Function::                    
* Macros::                      
* Functions and Variables for Function Definition::  

プログラムフロー

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

デバッグ

* Functions and Variables for Debugging::   

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::

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::

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, asympa, Program Flow, Top
@chapter Debugging
@include Debugging.texi

@node asympa, augmented_lagrangian, Debugging, 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, implicit_plot, grobner, Top
@chapter impdiff
@include impdiff.texi

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

@node interpol, lapack, implicit_plot, 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, plotdf, opsubst, Top
@chapter orthopoly
@include orthopoly.texi

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

@node romberg, simplex, plotdf, 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, Translator's Comments, zeilberger, Top
@chapter Indices
@include Indices.texi

@node Translator's Comments,  , Function and Variable Index, Top
@appendix Translator's Comments
@include Translator.texi

@c end includes

