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Maxima 5.21.1 Manual

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

1. Introduction to Maxima   Sample Maxima sessions.
2. Bug Detection and Reporting   Finding and reporting bugs in Maxima.
3. Help   Asking for help from within a Maxima session.
4. Command Line   Maxima command line syntax.
5. Operators   Operators used in Maxima expressions.
6. Expressions   Expressions in Maxima.
7. Simplification   Simplifying expressions.
8. Plotting   2D and 3D graphical output.
9. Input and Output   File input and output.
10. Floating Point   Low level numerical routines.
11. Contexts   Sets of assumed facts. 
Support for specific areas of mathematics
12. Polynomials   Standard forms for polynomials, and functions operating on them.
13. Constants   Numerical constants.
14. Logarithms   Manipulation of expressions involving logarithms.
15. Trigonometric   Manipulating expressions with trig and inverse trig functions.
16. Special Functions   Special functions
17. Elliptic Functions   Elliptic Functions and Integrals
18. Limits   Limits of expressions.
19. Differentiation   Differential calculus.
20. Integration   Integral calculus.
21. Equations   Defining and solving equations.
22. Differential Equations   Defining and solving differential equations.
23. Numerical   Numerical integration, Fourier transforms, etc.
24. Arrays   Creating and working with arrays.
25. Matrices and Linear Algebra   Matrix operations.
26. Affine  
27. itensor   Indicial Tensor Manipulation.
28. ctensor   Component Tensor Manipulation.
29. atensor   Algebraic Tensor Manipulation.
30. Series   Taylor and power series.
31. Number Theory   Number theory.
32. Symmetries  
33. Groups   Abstract algebra. 
Advanced facilities and programming
34. Runtime Environment   Customization of the Maxima environment.
35. Miscellaneous Options   Options with a global effect on Maxima.
36. Rules and Patterns   User defined pattern matching and simplification rules.
37. Lists   Manipulation of lists.
38. Sets   Manipulation of sets.
39. Function Definition   Defining functions.
40. Program Flow   Defining Maxima programs.
41. Debugging   Debugging Maxima programs. 
Additional packages
42. augmented_lagrangian   augmented_lagrangian package.
43. bode   Bode gain and phase plots.
44. contrib_ode   Additional routines for ODEs
45. descriptive   Descriptive statistics.
46. diag   Jordan matrices.
47. distrib   Probability distributions.
48. draw   A Maxima-Gnuplot interface.
49. dynamics   Graphics for dynamical systems and fractals.
50. ezunits   Dimensional quantities.
51. f90   Maxima to fortran translator.
52. ggf   Generating function of sequences.
53. graphs   Graph theory package.
54. grobner   Functions for working with Groebner bases.
55. impdiff   Implicit derivatives.
56. implicit_plot   Implicit plots package.
57. interpol   Interpolation package.
58. lapack   LAPACK functions for linear algebra.
59. lbfgs   L-BFGS unconstrained minimization package.
60. lindstedt   Lindstedt package.
61. linearalgebra   Functions for linear algebra.
62. lsquares   Least squares.
63. makeOrders   Polynomial utility.
64. mnewton   Newton's method.
65. numericalio   Reading and writing files.
66. opsubst   Substitutions utility.
67. orthopoly   Orthogonal polynomials.
68. plotdf   Direction fields plots.
69. romberg   Romberg method for numerical integration.
70. simplex   Linear programming.
71. simplification   Simplification rules and functions.
72. solve_rec   Linear recurrences.
73. stats   Statistical inference package.
74. stirling   Stirling formula.
75. stringproc   String processing.
76. unit   Units and dimensions package.
77. zeilberger   Functions for hypergeometric summation. 

Index
78. Indices   Index. 
 --- The Detailed Node Listing ---

Introduction
1. Introduction to Maxima   
Bugs
2. Bug Detection and Reporting   
Help
3.1 Lisp and Maxima  
3.2 Garbage Collection  
3.3 Documentation  
3.4 Functions and Variables for Help   
Command Line
4.1 Introduction to Command Line  
4.2 Functions and Variables for Command Line   
Operators
5.1 nary  
5.2 nofix  
5.3 postfix  
5.4 prefix  
5.5 Arithmetic operators  
5.6 Relational operators  
5.7 General operators   
Expressions
6.1 Introduction to Expressions  
6.2 Complex  
6.6 Inequality  
6.7 Syntax  
6.8 Functions and Variables for Expressions   
Simplification
7.1 Functions and Variables for Simplification   
Plotting
8.1 Introduction to Plotting  
8.2 Plotting Formats  
8.3 Functions and Variables for Plotting  
8.4 Plotting Options  
8.5 Gnuplot Options  
8.6 Gnuplot_pipes Format Functions   
Input and Output
9.1 Comments  
9.2 Files  
9.3 Functions and Variables for Input and Output   
Floating Point
10.1 Functions and Variables for Floating Point   
Contexts
11.1 Functions and Variables for Contexts   
Polynomials
12.1 Introduction to Polynomials  
12.2 Functions and Variables for Polynomials   
Constants
13.1 Functions and Variables for Constants   
Logarithms
14.1 Functions and Variables for Logarithms   
Trigonometric
15.1 Introduction to Trigonometric  
15.2 Functions and Variables for Trigonometric   
Special Functions
16.1 Introduction to Special Functions  
16.2 Bessel Functions  
16.3 Airy Functions  
16.4 Gamma and factorial Functions  
16.5 Exponential Integrals  
16.6 Error Function  
16.7 Struve Functions  
16.8 Hypergeometric Functions  
16.9 Parabolic Cylinder Functions  
16.10 Functions and Variables for Special Functions   
Elliptic Functions
17.1 Introduction to Elliptic Functions and Integrals  
17.2 Functions and Variables for Elliptic Functions  
17.3 Functions and Variables for Elliptic Integrals   
Limits
18.1 Functions and Variables for Limits   
Differentiation
19.1 Functions and Variables for Differentiation   
Integration
20.1 Introduction to Integration  
20.2 Functions and Variables for Integration   
Equations
21.1 Functions and Variables for Equations   
Differential Equations
22.1 Introduction to Differential Equations  
22.2 Functions and Variables for Differential Equations   
Numerical
23.1 Introduction to fast Fourier transform  
23.2 Functions and Variables for fast Fourier transform  
23.3 Introduction to Fourier series  
23.4 Functions and Variables for Fourier series   
Arrays
24.1 Functions and Variables for Arrays   
Matrices and Linear Algebra
25.1 Introduction to Matrices and Linear Algebra  
25.1.1 Dot  
25.1.2 Vectors  
25.1.3 eigen  
25.2 Functions and Variables for Matrices and Linear Algebra   
Affine
26.1 Introduction to Affine  
26.2 Functions and Variables for Affine   
itensor
27.1 Introduction to itensor  
27.2 Functions and Variables for itensor   
ctensor
28.1 Introduction to ctensor  
28.2 Functions and Variables for ctensor   
atensor
29.1 Introduction to atensor  
29.2 Functions and Variables for atensor   
Series
30.1 Introduction to Series  
30.2 Functions and Variables for Series   
Number Theory
31.1 Functions and Variables for Number Theory   
Symmetries
32.1 Introduction to Symmetries  
32.2 Functions and Variables for Symmetries   
Groups
33.1 Functions and Variables for Groups   
Runtime Environment
34.1 Introduction for Runtime Environment  
34.2 Interrupts  
34.3 Functions and Variables for Runtime Environment   
Miscellaneous Options
35.1 Introduction to Miscellaneous Options  
35.2 Share  
35.3 Functions and Variables for Miscellaneous Options   
Rules and Patterns
36.1 Introduction to Rules and Patterns  
36.2 Functions and Variables for Rules and Patterns   
Lists
37.1 Introduction to Lists  
37.2 Functions and Variables for Lists   
Sets
38.1 Introduction to Sets  
38.2 Functions and Variables for Sets   
Function Definition
39.1 Introduction to Function Definition  
39.2 Function  
39.3 Macros  
39.4 Functions and Variables for Function Definition   
Program Flow
40.1 Introduction to Program Flow  
40.2 Functions and Variables for Program Flow   
Debugging
41.3 Functions and Variables for Debugging   

augmented_lagrangian
42.1 Functions and Variables for augmented_lagrangian   
bode
43.1 Functions and Variables for bode   
contrib_ode
44.1 Introduction to contrib_ode  
44.2 Functions and Variables for contrib_ode  
44.3 Possible improvements to contrib_ode  
44.4 Test cases for contrib_ode  
44.5 References for contrib_ode   
descriptive
45.1 Introduction to descriptive  
45.2 Functions and Variables for data manipulation  
45.3 Functions and Variables for descriptive statistics  
45.4 Functions and Variables for specific multivariate descriptive statistics  
45.5 Functions and Variables for statistical graphs   
diag
46.1 Functions and Variables for diag   
distrib
47.1 Introduction to distrib  
47.2 Functions and Variables for continuous distributions  
47.3 Functions and Variables for discrete distributions   
draw
48.1 Introduction to draw  
48.2 Functions and Variables for draw  
48.3 Functions and Variables for pictures  
48.4 Functions and Variables for worldmap   
dynamics
49.1 Introduction to dynamics  
49.2 Functions and Variables for dynamics   
ezunits
50.1 Introduction to ezunits  
50.2 Introduction to physical_constants  
50.3 Functions and Variables for ezunits   
f90
51.1 Functions and Variables for f90   
ggf
52.1 Functions and Variables for ggf   
graphs
53.1 Introduction to graphs  
53.2 Functions and Variables for graphs   
grobner
54.1 Introduction to grobner  
54.2 Functions and Variables for grobner   
impdiff
55.1 Functions and Variables for impdiff   
implicit_plot
56.1 Functions and Variables for implicit_plot   
interpol
57.1 Introduction to interpol  
57.2 Functions and Variables for interpol   
lapack
58.1 Introduction to lapack  
58.2 Functions and Variables for lapack   
lbfgs
59.1 Introduction to lbfgs  
59.2 Functions and Variables for lbfgs   
lindstedt
60.1 Functions and Variables for lindstedt   
linearalgebra
61.1 Introduction to linearalgebra  
61.2 Functions and Variables for linearalgebra   
lsquares

* Introduction to lsquares
62.2 Functions and Variables for lsquares   
makeOrders
63.1 Functions and Variables for makeOrders   
mnewton
64.1 Introduction to mnewton  
64.2 Functions and Variables for mnewton   
numericalio
65.1 Introduction to numericalio  
65.2 Functions and Variables for plain-text input and output  
65.3 Functions and Variables for binary input and output   
opsubst
66.1 Functions and Variables for opsubst   
orthopoly
67.1 Introduction to orthogonal polynomials  
67.2 Functions and Variables for orthogonal polynomials   
plotdf
68.1 Introduction to plotdf  
68.2 Functions and Variables for plotdf   
romberg
69.1 Functions and Variables for romberg   
simplex
70.1 Introduction to simplex  
70.2 Functions and Variables for simplex   
simplification
71.1 Introduction to simplification  
71.2 Package absimp  
71.3 Package facexp  
71.4 Package functs  
71.5 Package ineq  
71.6 Package rducon  
71.7 Package scifac  
71.8 Package sqdnst   
solve_rec
72.1 Introduction to solve_rec  
72.2 Functions and Variables for solve_rec   
stats
73.1 Introduction to stats  
73.2 Functions and Variables for inference_result  
73.3 Functions and Variables for stats  
73.4 Functions and Variables for special distributions   
stirling
74.1 Functions and Variables for stirling   
stringproc
75.1 Introduction to string processing  
75.2 Functions and Variables for input and output  
75.3 Functions and Variables for characters  
75.4 Functions and Variables for strings   
unit
76.1 Introduction to Units  
76.2 Functions and Variables for Units   
zeilberger
77.1 Introduction to zeilberger  
77.2 Functions and Variables for zeilberger   










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