3 @c 2000-04-17 Jim Van Zandt <jrv@vanzandt.mv.com> Added header,
4 @c info directory entry, reference to introduction chapter, and menu
5 @c descriptions. Rearranged chapters.
7 @c to update the menus do:
8 @c (texinfo-multiple-files-update "maxima.texi" t t)
10 @c texinfo-multiple-files-update will delete the detailed node listing!
15 @settitle Maxima @VERSION@ Manual
17 @setchapternewpage odd
19 This is a Texinfo Maxima Manual
21 Copyright 1994,2001 William F. Schelter
26 * Maxima: (maxima). A computer algebra system.
37 @include category-macros.texi
39 @c for texi2html 5.0 following lines were commented out.
42 @c @comment The title is printed in a large font.
43 @c @center @titlefont{Maxima Manual}
44 @c @center Ver. @VERSION@
46 @c @vskip 0pt plus 1filll
47 @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。
49 @c MaximaはMacsymaシステムから派生したものです。
50 @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。
51 @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;
52 @c そのバージョンは現在、DOE Macsymaとして知られています。
53 @c DOE Macsymaのコピーは、テキサス大学のWilliam F. Schelter教授によって、
54 @c 1982年から教授がなくなる2001年まで保守されました。
56 @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、
58 @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。
59 @c だから、Maximaと呼ばれています。
67 @node Top, Introduction to Maxima, (dir), (dir)
70 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。
72 MaximaはMacsymaシステムから派生したものです。
73 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。
74 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;
75 そのバージョンは現在、DOE Macsymaとして知られています。
76 DOE Macsymaのコピーは、テキサス大学のWilliam F. Schelter教授によって、
77 1982年から教授がなくなる2001年まで保守されました。
79 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、
81 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。
90 * Introduction to Maxima:: Maximaセッションの実例
91 * Bug Detection and Reporting:: Maximaのバグの発見と報告
92 * Help:: Maximaセッションの中でヘルプを見る
93 * Command Line:: Maximaコマンドライン構文法、入出力
94 * Data Types and Structures:: 数、文字列、リスト、配列、構造体
95 * Expressions:: Maximaにおける式
96 * Operators:: Maxima式の中で使われる演算子
98 * Simplification:: 式の整理
99 * Mathematical Functions:: Maximaの数学的関数
100 * Maximas Database:: 宣言、文脈、事実、プロパティ
101 * Plotting:: 2次元と3次元のグラフィカル出力
102 * File Input and Output:: ファイル入出力
106 * Polynomials:: 多項式の標準形と操作関数
107 * Special Functions:: 特殊函数
108 * Elliptic Functions:: 楕円函数と楕円積分
110 * Differentiation:: 微分法
112 * Equations:: 方程式の定義と解法
113 * Differential Equations:: 微分方程式の定義と解法
114 * Numerical:: 数値積分、Fourier変換など
115 * Matrices and Linear Algebra:: 行列演算
120 * Sums Products and Series:: 和、積、Tayler級数とべき級数
127 * Runtime Environment:: Maxima環境のカスタム化
128 * Miscellaneous Options:: Maximaでグローバルな効果を持つオプション
129 * 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
131 * Function Definition:: 関数定義
132 * Program Flow:: Maximaプログラムの定義
133 * Debugging:: Maximaプログラムのデバッグ
138 * augmented_lagrangian:: 拡張Lagrangeパッケージ
139 @c * Bernstein:: Bernstein多項式
140 * Bernstein:: @code{Bernstein}多項式
142 * cobyla:: 不等式制約を持つ非線形最適化
143 * contrib_ode:: ODEのための追加ルーチン
147 * draw:: Maxima-Gnuplotインターフェイス
148 * drawdf:: Gnuplotを使った方向場
149 * dynamics:: 力学系とフラクタルのグラフィックス
151 * f90:: MaximaからFortranへの翻訳器
155 * graphs:: グラフ理論パッケージ
156 * grobner:: Groebner基底を扱う関数
158 * implicit_plot:: 陰プロットパッケージ
160 * lapack:: 線形代数のためのLAPACK関数
161 * lbfgs:: L-BFGS無制約最小化パッケージ
162 * lindstedt:: Lindstedtパッケージ
163 * linearalgebra:: 線形代数のための関数
165 * makeOrders:: 多項式ユーティリティ
166 * minpack:: 最小化と根のためのMINPACK関数
168 * numericalio:: ファイルの読み書き
169 * opsubst:: 代入ユーティリティ
172 * romberg:: 数値積分のRomberg法
174 * simplification:: 整理のルールと関数
177 * stirling:: Stirling公式
179 @c * to_poly_solve:: to_poly_solveパッケージ
180 * to_poly_solve:: @code{to_poly_solve}パッケージ
182 * zeilberger:: 超幾何総和に関する関数
187 * Function and Variable Index:: インデックス
191 * Translator's Comments:: 訳者のコメント
194 --- The Detailed Node Listing ---
198 * Introduction to Maxima::
202 * Bug Detection and Reporting::
207 * Functions and Variables for Help::
211 * Introduction to Command Line::
212 * Functions and Variables for Command Line::
213 * Functions and Variables for Display::
226 * Introduction to Expressions::
230 * Functions and Variables for Expressions::
234 * Introduction to operators::
235 * Arithmetic operators::
236 * Relational operators::
237 * Logical operators::
238 * Operators for Equations::
239 * Assignment operators::
240 * User defined operators::
244 * Functions and Variables for Evaluation::
248 * Functions and Variables for Simplification::
252 * Functions for Numbers::
253 * Functions for Complex Numbers::
254 * Combinatorial Functions::
255 * Root Exponential and Logarithmic Functions::
256 * Trigonometric Functions::
261 * Introduction to Maximas Database::
262 * Functions and Variables for Properties::
263 * Functions and Variables for Facts::
264 * Functions and Variables for Predicates::
268 * Introduction to Plotting::
270 * Functions and Variables for Plotting::
273 * Gnuplot_pipes Format Functions::
279 * Functions and Variables for File Input and Output::
283 * Introduction to Polynomials::
284 * Functions and Variables for Polynomials::
288 * Introduction to Special Functions::
291 * Gamma and factorial Functions::
292 * Exponential Integrals::
295 * Hypergeometric Functions::
296 * Parabolic Cylinder Functions::
297 * Functions and Variables for Special Functions::
301 * Introduction to Elliptic Functions and Integrals::
302 * Functions and Variables for Elliptic Functions::
303 * Functions and Variables for Elliptic Integrals::
307 * Functions and Variables for Limits::
311 * Functions and Variables for Differentiation::
315 * Introduction to Integration::
316 * Functions and Variables for Integration::
320 * Functions and Variables for Equations::
324 * Introduction to Differential Equations::
325 * Functions and Variables for Differential Equations::
329 * Introduction to fast Fourier transform::
330 * Functions and Variables for fast Fourier transform::
331 * Introduction to Fourier series::
332 * Functions and Variables for Fourier series::
336 * Introduction to Matrices and Linear Algebra::
340 * Functions and Variables for Matrices and Linear Algebra::
344 * Introduction to Affine::
345 * Functions and Variables for Affine::
349 * Introduction to itensor::
350 * Functions and Variables for itensor::
354 * Introduction to ctensor::
355 * Functions and Variables for ctensor::
359 * Introduction to atensor::
360 * Functions and Variables for atensor::
364 * Sums and Products::
365 * Introduction to Series::
366 * Functions and Variables for Series::
371 * Functions and Variables for Number Theory::
375 * Introduction to Symmetries::
376 * Functions and Variables for Symmetries::
380 * Functions and Variables for Groups::
384 * Introduction for Runtime Environment::
386 * Functions and Variables for Runtime Environment::
390 * Introduction to Miscellaneous Options::
392 * Functions and Variables for Miscellaneous Options::
396 * Introduction to Rules and Patterns::
397 * Functions and Variables for Rules and Patterns::
401 * Introduction to Sets::
402 * Functions and Variables for Sets::
406 * Introduction to Function Definition::
409 * Functions and Variables for Function Definition::
414 * Garbage Collection::
415 * Introduction to Program Flow::
416 * Functions and Variables for Program Flow::
420 * Functions and Variables for Debugging::
424 * Introduction to asympa::
425 * Functions and variables for asympa::
429 * Functions and Variables for augmented_lagrangian::
433 * Functions and Variables for Bernstein::
437 * Functions and Variables for bode::
441 * Introduction to cobyla::
442 * Functions and Variables for cobyla::
443 * Examples for cobyla::
447 * Introduction to contrib_ode::
448 * Functions and Variables for contrib_ode::
449 * Possible improvements to contrib_ode::
450 * Test cases for contrib_ode::
451 * References for contrib_ode::
455 * Introduction to descriptive::
456 * Functions and Variables for data manipulation::
457 * Functions and Variables for descriptive statistics::
458 * Functions and Variables for statistical graphs::
462 * Functions and Variables for diag::
466 * Introduction to distrib::
467 * Functions and Variables for continuous distributions::
468 * Functions and Variables for discrete distributions::
472 * Introduction to draw::
473 * Functions and Variables for draw::
474 * Functions and Variables for pictures::
475 * Functions and Variables for worldmap::
479 * Introduction to drawdf::
480 * Functions and Variables for drawdf::
484 * Introduction to dynamics::
485 * Functions and Variables for dynamics::
489 * Introduction to ezunits::
490 * Introduction to physical_constants::
491 * Functions and Variables for ezunits::
495 * Functions and Variables for f90::
499 * Introduction to finance::
500 * Functions and Variables for finance::
504 * Introduction to fractals::
505 * Definitions for IFS fractals::
506 * Definitions for complex fractals::
507 * Definitions for Koch snowflakes::
508 * Definitions for Peano maps::
512 * Functions and Variables for ggf::
516 * Introduction to graphs::
517 * Functions and Variables for graphs::
521 * Introduction to grobner::
522 * Functions and Variables for grobner::
526 * Functions and Variables for impdiff::
530 * Functions and Variables for implicit_plot::
534 * Introduction to interpol::
535 * Functions and Variables for interpol::
539 * Introduction to lapack::
540 * Functions and Variables for lapack::
544 * Introduction to lbfgs::
545 * Functions and Variables for lbfgs::
549 * Functions and Variables for lindstedt::
553 * Introduction to linearalgebra::
554 * Functions and Variables for linearalgebra::
558 * Introduction to lsquares::
559 * Functions and Variables for lsquares::
563 * Functions and Variables for makeOrders::
567 * Introduction to minpack::
568 * Functions and Variables for minpack::
572 * Introduction to mnewton::
573 * Functions and Variables for mnewton::
577 * Introduction to numericalio::
578 * Functions and Variables for plain-text input and output::
579 * Functions and Variables for binary input and output::
583 * Functions and Variables for opsubst::
587 * Introduction to orthogonal polynomials::
588 * Functions and Variables for orthogonal polynomials::
592 * Introduction to plotdf::
593 * Functions and Variables for plotdf::
597 * Functions and Variables for romberg::
601 * Introduction to simplex::
602 * Functions and Variables for simplex::
606 * Introduction to simplification::
617 * Introduction to solve_rec::
618 * Functions and Variables for solve_rec::
622 * Introduction to stats::
623 * Functions and Variables for inference_result::
624 * Functions and Variables for stats::
625 * Functions and Variables for special distributions::
629 * Functions and Variables for stirling::
633 * Introduction to string processing::
634 * Functions and Variables for input and output::
635 * Functions and Variables for characters::
636 * Functions and Variables for strings::
640 * Functions and Variables for to_poly_solve::
644 * Introduction to Units::
645 * Functions and Variables for Units::
649 * Introduction to zeilberger::
650 * Functions and Variables for zeilberger::
652 @comment @end detailmenu
655 @c Put the @node lines here, rather than in the @included files,
656 @c so emacs can automatically update them with C-c C-u C-e.
657 @c nota bene: C-c C-u C-a and texinfo-multiple-files-update will delete
658 @c the detailed node listing!
660 @node Introduction to Maxima, Bug Detection and Reporting, Top, Top
661 @chapter Introduction to Maxima
662 @include Introduction.texi
664 @node Bug Detection and Reporting, Help, Introduction to Maxima, Top
665 @chapter Bug Detection and Reporting
668 @node Help, Command Line, Bug Detection and Reporting, Top
672 @node Command Line, Data Types and Structures, Help, Top
673 @chapter Command Line
674 @include Command.texi
676 @node Data Types and Structures, Expressions, Command Line, Top
677 @chapter Data Types and Structures
678 @include DataTypes.texi
679 @include Constants.texi
682 @include defstruct.texi
684 @node Expressions, Operators, Data Types and Structures, Top
686 @include Expressions.texi
688 @node Operators, Evaluation, Expressions, Top
690 @include Operators.texi
692 @node Evaluation, Simplification, Operators, Top
694 @include Evaluation.texi
696 @node Simplification, Mathematical Functions, Evaluation, Top
697 @chapter Simplification
698 @include Simplification.texi
700 @node Mathematical Functions, Maximas Database, Simplification, Top
701 @chapter Mathematical Functions
702 @include MathFunctions.texi
704 @node Maximas Database, Plotting, Mathematical Functions, Top
705 @chapter Maximas Database
706 @include Database.texi
708 @node Plotting, File Input and Output, Maximas Database, Top
710 @include Plotting.texi
712 @node File Input and Output, Polynomials, Plotting, Top
713 @chapter File Input and Output
716 @node Polynomials, Special Functions, File Input and Output, Top
718 @include Polynomials.texi
720 @node Special Functions, Elliptic Functions, Polynomials, Top
721 @chapter Special Functions
722 @include Special.texi
724 @node Elliptic Functions, Limits, Special Functions, Top
725 @chapter Elliptic Functions
726 @include Elliptic.texi
728 @node Limits, Differentiation, Elliptic Functions, Top
732 @node Differentiation, Integration, Limits, Top
733 @chapter Differentiation
734 @include Differentiation.texi
736 @node Integration, Equations, Differentiation, Top
738 @include Integration.texi
740 @node Equations, Differential Equations, Integration, Top
742 @include Equations.texi
744 @node Differential Equations, Numerical, Equations, Top
745 @chapter Differential Equations
746 @include Differential.texi
748 @c @include NonCommutative.texi
750 @node Numerical, Matrices and Linear Algebra, Differential Equations, Top
752 @include Numerical.texi
754 @node Matrices and Linear Algebra, Affine, Numerical, Top
755 @chapter Matrices and Linear Algebra
756 @include Matrices.texi
758 @node Affine, itensor, Matrices and Linear Algebra, Top
762 @node itensor, ctensor, Affine, Top
764 @include Itensor.texi
766 @node ctensor, atensor, itensor, Top
768 @include Ctensor.texi
770 @node atensor, Sums Products and Series, ctensor, Top
772 @include Atensor.texi
774 @node Sums Products and Series, Number Theory, atensor, Top
775 @chapter Sums, Products, and Series
778 @node Number Theory, Symmetries, Sums Products and Series, Top
779 @chapter Number Theory
782 @node Symmetries, Groups, Number Theory, Top
784 @include Symmetries.texi
786 @node Groups, Runtime Environment, Symmetries, Top
790 @node Runtime Environment, Miscellaneous Options, Groups, Top
791 @chapter Runtime Environment
792 @include Runtime.texi
794 @node Miscellaneous Options, Rules and Patterns, Runtime Environment, Top
795 @chapter Miscellaneous Options
796 @include Miscellaneous.texi
798 @node Rules and Patterns, Sets, Miscellaneous Options, Top
799 @chapter Rules and Patterns
802 @node Sets, Function Definition, Rules and Patterns, Top
806 @node Function Definition, Program Flow, Sets, Top
807 @chapter Function Definition
808 @include Function.texi
810 @node Program Flow, Debugging, Function Definition, Top
811 @chapter Program Flow
812 @include Program.texi
814 @node Debugging, asympa, Program Flow, Top
816 @include Debugging.texi
818 @node asympa, augmented_lagrangian, Debugging, Top
822 @node augmented_lagrangian, Bernstein, asympa, Top
823 @chapter augmented_lagrangian
824 @include augmented_lagrangian.texi
826 @node Bernstein, bode, augmented_lagrangian, Top
828 @include bernstein.texi
830 @node bode, cobyla, Bernstein, Top
834 @node cobyla, contrib_ode, bode, Top
838 @node contrib_ode, descriptive, cobyla, Top
840 @include contrib_ode.texi
842 @node descriptive, diag, contrib_ode, Top
844 @include descriptive.texi
846 @node diag, distrib, descriptive, Top
850 @node distrib, draw, diag, Top
852 @include distrib.texi
854 @node draw, drawdf, distrib, Top
858 @node drawdf, dynamics, draw, Top
862 @node dynamics, ezunits, drawdf, Top
864 @include dynamics.texi
866 @node ezunits, f90, dynamics, Top
868 @include ezunits.texi
870 @node f90, finance, ezunits, Top
874 @node finance, fractals, f90, Top
876 @include finance.texi
878 @node fractals, ggf, finance, Top
880 @include fractals.texi
882 @node ggf, graphs, fractals, Top
886 @node graphs, grobner, ggf, Top
890 @node grobner, impdiff, graphs, Top
892 @include grobner.texi
894 @node impdiff, implicit_plot, grobner, Top
896 @include impdiff.texi
898 @node implicit_plot, interpol, impdiff, Top
899 @chapter implicit_plot
900 @include implicit_plot.texi
902 @node interpol, lapack, implicit_plot, Top
904 @include interpol.texi
906 @node lapack, lbfgs, interpol, Top
910 @node lbfgs, lindstedt, lapack, Top
914 @node lindstedt, linearalgebra, lbfgs, Top
916 @include lindstedt.texi
918 @node linearalgebra, lsquares, lindstedt, Top
919 @chapter linearalgebra
920 @include linearalgebra.texi
922 @node lsquares, minpack, linearalgebra, Top
924 @include lsquares.texi
926 @node minpack, makeOrders, lsquares, Top
928 @include minpack.texi
930 @node makeOrders, mnewton, minpack, Top
932 @include makeOrders.texi
934 @node mnewton, numericalio, makeOrders, Top
936 @include mnewton.texi
938 @node numericalio, opsubst, mnewton, Top
940 @include numericalio.texi
942 @node opsubst, orthopoly, numericalio, Top
944 @include opsubst.texi
946 @node orthopoly, plotdf, opsubst, Top
948 @include orthopoly.texi
950 @node plotdf, romberg, orthopoly, Top
954 @node romberg, simplex, plotdf, Top
956 @include romberg.texi
958 @node simplex, simplification, romberg, Top
960 @include simplex.texi
962 @node simplification, solve_rec, simplex, Top
963 @chapter simplification
964 @include simplifications.texi
966 @node solve_rec, stats, simplification, Top
968 @include solve_rec.texi
970 @node stats, stirling, solve_rec, Top
974 @node stirling, stringproc, stats, Top
976 @include stirling.texi
978 @node stringproc, to_poly_solve, stirling, Top
980 @include stringproc.texi
982 @node to_poly_solve, unit, stringproc, Top
983 @chapter to_poly_solve
984 @include to_poly_solve.texi
986 @node unit, zeilberger, to_poly_solve, Top
990 @node zeilberger, Function and Variable Index, unit, Top
992 @include zeilberger.texi
994 @node Function and Variable Index, Translator's Comments, zeilberger, Top
996 @include Indices.texi
998 @node Translator's Comments, , Function and Variable Index, Top
999 @appendix Translator's Comments
1000 @include Translator.texi