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Maxima 5.39.0 Manual

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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, Input, and Output.
5. Data Types and Structures   Numbers, Strings, Lists, Arrays, and Structures.
6. Expressions   Expressions in Maxima.
7. Operators   Operators used in Maxima expressions.
8. Evaluation   Evaluating expressions.
9. Simplification   Simplifying expressions.
10. Mathematical Functions   Mathematical functions in Maxima.
11. Maximas Database   Declarations, Contexts, Facts, and Properties.
12. Plotting   2D and 3D graphical output.
13. File Input and Output   File input and output. 
Support for specific areas of mathematics
14. Polynomials   Standard forms for polynomials, and functions operating on them.
15. Special Functions   Special functions
16. Elliptic Functions   Elliptic Functions and Integrals
17. Limits   Limits of expressions.
18. Differentiation   Differential calculus.
19. Integration   Integral calculus.
20. Equations   Defining and solving equations.
21. Differential Equations   Defining and solving differential equations.
22. Numerical   Numerical integration, Fourier transforms, Equations, ODE's, etc.
23. Matrices and Linear Algebra   Matrix operations.
24. Affine  
25. itensor   Indicial Tensor Manipulation.
26. ctensor   Component Tensor Manipulation.
27. atensor   Algebraic Tensor Manipulation.
28. Sums, Products, and Series   Sums, Products, Taylor and power series.
29. Number Theory   Number theory.
30. Symmetries  
31. Groups   Abstract algebra. 
Advanced facilities and programming
32. Runtime Environment   Customization of the Maxima environment.
33. Miscellaneous Options   Options with a global effect on Maxima.
34. Rules and Patterns   User defined pattern matching and simplification rules.
35. Sets   Manipulation of sets.
36. Function Definition   Defining functions.
37. Program Flow   Defining Maxima programs.
38. Debugging   Debugging Maxima programs. 
Additional packages
39. alt-display   Alternative display package.
40. asympa   Asymptotic analysis package.
41. augmented_lagrangian   augmented_lagrangian package.
42. Bernstein   Bernstein polynomials.
43. bitwise   Manipulate bits of integers.
44. bode   Bode gain and phase plots.
45. celine   Sister Celine's method
46. clebsch_gordan   Clebsch-Gordan and Wigner coefficients
47. cobyla   Nonlinear optimization with inequality constraints.
48. contrib_ode   Additional routines for ODEs
49. descriptive   Descriptive statistics.
50. diag   Jordan matrices.
51. distrib   Probability distributions.
52. draw   A Maxima-Gnuplot interface.
53. drawdf   Direction fields with Gnuplot.
54. dynamics   3D visualization, animations and dynamical systems.
55. engineering-format   Display floats as a*10^b with b mod 3 = 0.
56. ezunits   Dimensional quantities.
57. f90   Maxima to fortran translator.
58. finance   Financial package.
59. fractals   Fractals.
60. ggf   Generating function of sequences.
61. graphs   Graph theory package.
62. grobner   Functions for working with Groebner bases.
63. impdiff   Implicit derivatives.
64. interpol   Interpolation package.
65. lapack   LAPACK functions for linear algebra.
66. lbfgs   L-BFGS unconstrained minimization package.
67. lindstedt   Lindstedt package.
68. linearalgebra   Functions for linear algebra.
69. lsquares   Least squares.
71. makeOrders   Polynomial utility.
70. minpack   MINPACK functions for minimization and roots
72. mnewton   Newton's method.
73. numericalio   Reading and writing files.
74. operatingsystem   Common operating system tasks (create/remove dirs+files,...).
75. opsubst   Substitutions utility.
76. orthopoly   Orthogonal polynomials.
77. ratpow   Determine the coefficients of polynoms.
78. romberg   Romberg method for numerical integration.
79. simplex   Linear programming.
80. simplification   Simplification rules and functions.
81. solve_rec   Linear recurrences.
82. stats   Statistical inference package.
83. stirling   Stirling formula.
84. stringproc   String processing.
85. to_poly_solve   to_poly_solve package.
86. unit   Units and dimensions package.
87. zeilberger   Functions for hypergeometric summation. 
Understanding maxima's output
88. Error and warning messages  
Index
A. Function and Variable Index   Index. 
 --- The Detailed Node Listing --- 

Introduction
1. Introduction to Maxima   
Bugs
2. Bug Detection and Reporting   
Help
3.1 Documentation  
3.2 Functions and Variables for Help   
Command Line
4.1 Introduction to Command Line  
4.2 Functions and Variables for Command Line  
4.3 Functions and Variables for Display   
Data Types and Structures
5.1 Numbers  
5.2 Strings  
5.3 Constants  
5.4 Lists  
5.5 Arrays  
5.6 Structures   
Expressions
6.1 Introduction to Expressions  
6.2 Nouns and Verbs  
6.3 Identifiers  
6.4 Inequality  
6.5 Functions and Variables for Expressions   
Operators
7.1 Introduction to operators  
7.2 Arithmetic operators  
7.3 Relational operators  
7.4 Logical operators  
7.5 Operators for Equations  
7.6 Assignment operators  
7.7 User defined operators   
Evaluation
8.1 Functions and Variables for Evaluation   
Simplification
9.1 Functions and Variables for Simplification   
Mathematical Functions
10.1 Functions for Numbers  
10.2 Functions for Complex Numbers  
10.3 Combinatorial Functions  
10.4 Root, Exponential and Logarithmic Functions  
10.5 Trigonometric Functions  
10.6 Random Numbers   
Maximas Database
11.1 Introduction to Maximas Database  
11.2 Functions and Variables for Properties  
11.3 Functions and Variables for Facts  
11.4 Functions and Variables for Predicates   
Plotting
12.1 Introduction to Plotting  
12.2 Plotting Formats  
12.3 Functions and Variables for Plotting  
12.4 Plotting Options  
12.5 Gnuplot Options  
12.6 Gnuplot_pipes Format Functions   
File Input and Output
13.1 Comments  
13.2 Files  
13.3 Functions and Variables for File Input and Output  
13.4 Functions and Variables for TeX Output  
13.5 Functions and Variables for Fortran Output   
Polynomials
14.1 Introduction to Polynomials  
14.2 Functions and Variables for Polynomials   
Special Functions
15.1 Introduction to Special Functions  
15.2 Bessel Functions  
15.3 Airy Functions  
15.4 Gamma and factorial Functions  
15.5 Exponential Integrals  
15.6 Error Function  
15.7 Struve Functions  
15.8 Hypergeometric Functions  
15.9 Parabolic Cylinder Functions  
15.10 Functions and Variables for Special Functions   
Elliptic Functions
16.1 Introduction to Elliptic Functions and Integrals  
16.2 Functions and Variables for Elliptic Functions  
16.3 Functions and Variables for Elliptic Integrals   
Limits
17.1 Functions and Variables for Limits   
Differentiation
18.1 Functions and Variables for Differentiation   
Integration
19.1 Introduction to Integration  
19.2 Functions and Variables for Integration   
Equations
20.1 Functions and Variables for Equations   
Differential Equations
21.1 Introduction to Differential Equations  
21.2 Functions and Variables for Differential Equations   
Numerical
22.1 Introduction to fast Fourier transform  
22.2 Functions and Variables for fast Fourier transform  
22.3 Functions for numerical solution of equations  
22.4 Introduction to numerical solution of differential equations  
22.5 Functions for numerical solution of differential equations   
Matrices and Linear Algebra
23.1 Introduction to Matrices and Linear Algebra  
23.1.1 Dot  
23.1.2 Vectors  
23.1.3 eigen  
23.2 Functions and Variables for Matrices and Linear Algebra   
Affine
24.1 Introduction to Affine  
24.2 Functions and Variables for Affine   
itensor
25.1 Introduction to itensor  
25.2 Functions and Variables for itensor   
ctensor
26.1 Introduction to ctensor  
26.2 Functions and Variables for ctensor   
atensor
27.1 Introduction to atensor  
27.2 Functions and Variables for atensor   
Sums, Products, and Series
28.1 Functions and Variables for Sums and Products  
28.2 Introduction to Series  
28.3 Functions and Variables for Series  
28.4 Introduction to Fourier series  
28.5 Functions and Variables for Fourier series   
Number Theory
29.1 Functions and Variables for Number Theory   
Symmetries
30.1 Introduction to Symmetries  
30.2 Functions and Variables for Symmetries   
Groups
31.1 Functions and Variables for Groups   
Runtime Environment
32.1 Introduction for Runtime Environment  
32.2 Interrupts  
32.3 Functions and Variables for Runtime Environment   
Miscellaneous Options
33.1 Introduction to Miscellaneous Options  
33.2 Share  
33.3 Functions and Variables for Miscellaneous Options   
Rules and Patterns
34.1 Introduction to Rules and Patterns  
34.2 Functions and Variables for Rules and Patterns   
Sets
35.1 Introduction to Sets  
35.2 Functions and Variables for Sets   
Function Definition
36.1 Introduction to Function Definition  
36.2 Function  
36.3 Macros  
36.4 Functions and Variables for Function Definition   
Program Flow
37.1 Lisp and Maxima  
37.2 Garbage Collection  
37.3 Introduction to Program Flow  
37.4 Functions and Variables for Program Flow   
Debugging
38.3 Functions and Variables for Debugging   
alt-display
39.1 Introduction to alt-display  
39.2 Functions and Variables for alt-display   
asympa
40.1 Introduction to asympa  
40.2 Functions and variables for asympa   
augmented_lagrangian
41.1 Functions and Variables for augmented_lagrangian   
Bernstein
42.1 Functions and Variables for Bernstein   
Bitwise
43.1 Functions and Variables for bitwise   
bode
44.1 Functions and Variables for bode   
clebsch_gordan
46.1 Functions and Variables for clebsch_gordan   
cobyla
47.1 Introduction to cobyla  
47.2 Functions and Variables for cobyla  
47.3 Examples for cobyla   
contrib_ode
48.1 Introduction to contrib_ode  
48.2 Functions and Variables for contrib_ode  
48.3 Possible improvements to contrib_ode  
48.4 Test cases for contrib_ode  
48.5 References for contrib_ode   
descriptive
49.1 Introduction to descriptive  
49.2 Functions and Variables for data manipulation  
49.3 Functions and Variables for descriptive statistics  
49.4 Functions and Variables for statistical graphs   
diag
50.1 Functions and Variables for diag   
distrib
51.1 Introduction to distrib  
51.2 Functions and Variables for continuous distributions  
51.3 Functions and Variables for discrete distributions   
draw
52.1 Introduction to draw  
52.2 Functions and Variables for draw  
52.3 Functions and Variables for pictures  
52.4 Functions and Variables for worldmap   
drawdf
53.1 Introduction to drawdf  
53.2 Functions and Variables for drawdf   
dynamics
54.1 The dynamics package  
54.2 Graphical analysis of discrete dynamical systems  
54.3 Visualization with VTK   
ezunits
56.1 Introduction to ezunits  
56.2 Introduction to physical_constants  
56.3 Functions and Variables for ezunits   
f90
57.1 Functions and Variables for f90   
finance
58.1 Introduction to finance  
58.2 Functions and Variables for finance   
fractals
59.1 Introduction to fractals  
59.2 Definitions for IFS fractals  
59.3 Definitions for complex fractals  
59.4 Definitions for Koch snowflakes  
59.5 Definitions for Peano maps   
ggf
60.1 Functions and Variables for ggf   
graphs
61.1 Introduction to graphs  
61.2 Functions and Variables for graphs   
grobner
62.1 Introduction to grobner  
62.2 Functions and Variables for grobner   
impdiff
63.1 Functions and Variables for impdiff   
interpol
64.1 Introduction to interpol  
64.2 Functions and Variables for interpol   
lapack
65.1 Introduction to lapack  
65.2 Functions and Variables for lapack   
lbfgs
66.1 Introduction to lbfgs  
66.2 Functions and Variables for lbfgs   
lindstedt
67.1 Functions and Variables for lindstedt   
linearalgebra
68.1 Introduction to linearalgebra  
68.2 Functions and Variables for linearalgebra   
lsquares
69.1 Introduction to lsquares  
69.2 Functions and Variables for lsquares   
makeOrders
71.1 Functions and Variables for makeOrders   
minpack
70.1 Introduction to minpack  
70.2 Functions and Variables for minpack   
mnewton
72.1 Introduction to mnewton  
72.2 Functions and Variables for mnewton   
numericalio
73.1 Introduction to numericalio  
73.2 Functions and Variables for plain-text input and output  
73.3 Functions and Variables for binary input and output   
operatingsystem
74.1 Introduction to operatingsystem  
74.2 Directory operations  
74.4 Environment operations   
opsubst
75.1 Functions and Variables for opsubst   
orthopoly
76.1 Introduction to orthogonal polynomials  
76.2 Functions and Variables for orthogonal polynomials   
ratpow
77.1 Functions and Variables for ratpow   
romberg
78.1 Functions and Variables for romberg   
simplex
79.1 Introduction to simplex  
79.2 Functions and Variables for simplex   
simplification
80.1 Introduction to simplification  
80.2 Package absimp  
80.3 Package facexp  
80.4 Package functs  
80.5 Package ineq  
80.6 Package rducon  
80.7 Package scifac  
80.8 Package sqdnst   
solve_rec
81.1 Introduction to solve_rec  
81.2 Functions and Variables for solve_rec   
stats
82.1 Introduction to stats  
82.2 Functions and Variables for inference_result  
82.3 Functions and Variables for stats  
82.4 Functions and Variables for special distributions   
stirling
83.1 Functions and Variables for stirling   
stringproc
84.1 Introduction to String Processing  
84.2 Input and Output  
84.3 Characters  
84.4 String Processing  
84.5 Octets and Utilities for Cryptography   
to_poly_solve
85.1 Functions and Variables for to_poly_solve   
unit
86.1 Introduction to Units  
86.2 Functions and Variables for Units   
zeilberger
87.1 Introduction to zeilberger  
87.2 Functions and Variables for zeilberger   
Understanding maxima's output
88.1 Error messages  
88.2 Warning messages  

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