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Maxima 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. descriptive   Descriptive statistics.
45. diag   Jordan matrices.
46. distrib   Probability distributions.
47. draw   A Maxima-Gnuplot interface.
48. dynamics   Graphics for dynamical systems and fractals.
49. eval_string   Maxima expressions as strings.
50. f90   Maxima to fortran translator.
51. ggf   Generating function of sequences.
52. grobner   Functions for working with Groebner bases.
53. impdiff   Implicit derivatives.
54. implicit_plot   Implicit plots package.
55. interpol   Interpolation package.
56. lbfgs   L-BFGS unconstrained minimization package.
57. lindstedt   Lindstedt package.
58. linearalgebra   Functions for linear algebra.
59. lsquares   Least squares.
60. makeOrders   Polynomial utility.
61. mnewton   Newton's method.
62. numericalio   Reading and writing files.
63. opsubst   Substitutions utility.
64. orthopoly   Orthogonal polynomials.
65. plotdf   Direction fields plots.
66. romberg   Romberg method for numerical integration.
67. simplex   Linear programming.
68. simplification   Simplification rules and functions.
69. solve_rec   Linear recurrences.
70. stats   Statistical inference package.
71. stirling   Stirling formula.
72. stringproc   String processing.
73. unit   Units and dimensions package.
74. zeilberger   Functions for hypergeometric summation. 

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

Introduction
1. Introduction to Maxima   
Help
3.1 Lisp and Maxima  
3.2 Garbage Collection  
3.3 Documentation  
3.4 Definitions for Help   
Command Line
4.1 Introduction to Command Line  
4.2 Definitions 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 Assignment  
6.3 Complex  
6.7 Inequality  
6.8 Syntax  
6.9 Definitions for Expressions   
Simplification
7.1 Definitions for Simplification   
Plotting
8.1 Definitions for Plotting   
Input and Output
9.1 Comments  
9.2 Files  
9.3 Definitions for Input and Output   
Floating Point
10.1 Definitions for Floating Point   
Contexts
11.1 Definitions for Contexts   
Polynomials
12.1 Introduction to Polynomials  
12.2 Definitions for Polynomials   
Constants
13.1 Definitions for Constants   
Logarithms
14.1 Definitions for Logarithms   
Trigonometric
15.1 Introduction to Trigonometric  
15.2 Definitions for Trigonometric   
Special Functions
16.1 Introduction to Special Functions  
16.2 Definitions for Special Functions   
Elliptic Functions
17.1 Introduction to Elliptic Functions and Integrals  
17.2 Definitions for Elliptic Functions  
17.3 Definitions for Elliptic Integrals   
Limits
18.1 Definitions for Limits   
Differentiation
19.1 Definitions for Differentiation   
Integration
20.1 Introduction to Integration  
20.2 Definitions for Integration   
Equations
21.1 Definitions for Equations   
Differential Equations
22.1 Introduction to Differential Equations  
22.2 Definitions for Differential Equations   
Numerical
23.1 Introduction to Numerical  
23.2 Fourier packages  
23.3 Definitions for Numerical  
23.4 Definitions for Fourier Series   
Arrays
24.1 Definitions 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 Definitions for Matrices and Linear Algebra   
Affine
26.1 Definitions for Affine   
itensor
27.1 Introduction to itensor  
27.2 Definitions for itensor   
ctensor
28.1 Introduction to ctensor  
28.2 Definitions for ctensor   
atensor
29.1 Introduction to atensor  
29.2 Definitions for atensor   
Series
30.1 Introduction to Series  
30.2 Definitions for Series   
Number Theory
31.1 Definitions for Number Theory   
Symmetries
32.1 Definitions for Symmetries   
Groups
33.1 Definitions for Groups   
Runtime Environment
34.1 Introduction for Runtime Environment  
34.2 Interrupts  
34.3 Definitions for Runtime Environment   
Miscellaneous Options
35.1 Introduction to Miscellaneous Options  
35.2 Share  
35.3 Definitions for Miscellaneous Options   
Rules and Patterns
36.1 Introduction to Rules and Patterns  
36.2 Definitions for Rules and Patterns   
Lists
37.1 Introduction to Lists  
37.2 Definitions for Lists   
Sets
38.1 Introduction to Sets  
38.2 Definitions for Sets   
Function Definition
39.1 Introduction to Function Definition  
39.2 Function  
39.3 Macros  
39.4 Definitions for Function Definition   
Program Flow
40.1 Introduction to Program Flow  
40.2 Definitions for Program Flow   
Debugging
41.3 Definitions for Debugging   

augmented_lagrangian
42.1 Definitions for augmented_lagrangian   
bode
43.1 Definitions for bode   
descriptive
44.1 Introduction to descriptive  
44.2 Definitions for data manipulation  
44.3 Definitions for descriptive statistics  
44.4 Definitions for specific multivariate descriptive statistics  
44.5 Definitions for statistical graphs   
diag
45.1 Definitions for diag   
distrib
46.1 Introduction to distrib  
46.2 Definitions for continuous distributions  
46.3 Definitions for discrete distributions   
draw
47.1 Introduction to draw  
47.2 Definitions for draw   
dynamics
48.1 Introduction to dynamics  
48.2 Definitions for dynamics   
eval_string
49.1 Definitions for eval_string   
f90
50.1 Definitions for f90   
ggf
51.1 Definitions for ggf   
grobner
52.1 Introduction to grobner  
52.2 Definitions for grobner   
impdiff
53.1 Definitions for impdiff   
implicit_plot
54.1 Definitions for implicit_plot   
interpol
55.1 Introduction to interpol  
55.2 Definitions for interpol   
lbfgs
56.1 Introduction to lbfgs  
56.2 Definitions for lbfgs   
lindstedt
57.1 Definitions for lindstedt   
linearalgebra
58.1 Introduction to linearalgebra  
58.2 Definitions for linearalgebra   
lsquares
59.1 Definitions for lsquares   
makeOrders
60.1 Definitions for makeOrders   
mnewton
61.1 Definitions for mnewton   
numericalio
62.1 Introduction to numericalio  
62.2 Definitions for numericalio   
opsubst
63.1 Definitions for opsubst   
orthopoly
64.1 Introduction to orthogonal polynomials  
64.2 Definitions for orthogonal polynomials   
plotdf
65.1 Introduction to plotdf  
65.2 Definitions for plotdf   
romberg
66.1 Definitions for romberg   
simplex
67.1 Introduction to simplex  
67.2 Definitions for simplex   
simplification
68.1 Introduction to simplification  
68.2 Definitions for simplification   
solve_rec
69.1 Introduction to solve_rec  
69.2 Definitions for solve_rec   
stats
70.1 Introduction to stats  
70.2 Definitions for inference_result  
70.3 Definitions for stats  
70.4 Definitions for special distributions   
stirling
71.1 Definitions for stirling   
stringproc
72.1 Introduction to string processing  
72.2 Definitions for input and output  
72.3 Definitions for characters  
72.4 Definitions for strings   
unit
73.1 Introduction to Units  
73.2 Definitions for Units   
zeilberger
74.1 Introduction to zeilberger  
74.2 Definitions for zeilberger   








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