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

Support for specific areas of mathematics
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.
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. eval_string		Maxima expressions as strings.
51. f90		Maxima to fortran translator.
52. ggf		Generating function of sequences.
53. grobner		Functions for working with Groebner bases.
54. impdiff		Implicit derivatives.
55. implicit_plot		Implicit plots package.
56. interpol		Interpolation package.
57. lbfgs		L-BFGS unconstrained minimization package.
58. lindstedt		Lindstedt package.
59. linearalgebra		Functions for linear algebra.
60. lsquares		Least squares.
61. makeOrders		Polynomial utility.
62. mnewton		Newton's method.
63. numericalio		Reading and writing files.
64. opsubst		Substitutions utility.
65. orthopoly		Orthogonal polynomials.
66. plotdf		Direction fields plots.
67. romberg		Romberg method for numerical integration.
68. simplex		Linear programming.
69. simplification		Simplification rules and functions.
70. solve_rec		Linear recurrences.
71. stats		Statistical inference package.
72. stirling		Stirling formula.
73. stringproc		String processing.
74. unit		Units and dimensions package.
75. zeilberger		Functions for hypergeometric summation.
Index
76. 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 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 Assignment
6.3 Complex
6.7 Inequality
6.8 Syntax
6.9 Functions and Variables for Expressions
Simplification
7.1 Functions and Variables for Simplification
Plotting
8.1 Functions and Variables for Plotting
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 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 Numerical
23.2 Fourier packages
23.3 Functions and Variables for Numerical
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 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 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
eval_string
50.1 Functions and Variables for eval_string
f90
51.1 Functions and Variables for f90
ggf
52.1 Functions and Variables for ggf
grobner
53.1 Introduction to grobner
53.2 Functions and Variables for grobner
impdiff
54.1 Functions and Variables for impdiff
implicit_plot
55.1 Functions and Variables for implicit_plot
interpol
56.1 Introduction to interpol
56.2 Functions and Variables for interpol
lbfgs
57.1 Introduction to lbfgs
57.2 Functions and Variables for lbfgs
lindstedt
58.1 Functions and Variables for lindstedt
linearalgebra
59.1 Introduction to linearalgebra
59.2 Functions and Variables for linearalgebra
lsquares
60.1 Functions and Variables for lsquares
makeOrders
61.1 Functions and Variables for makeOrders
mnewton
62.1 Functions and Variables for mnewton
numericalio
63.1 Introduction to numericalio
63.2 Functions and Variables for numericalio
opsubst
64.1 Functions and Variables for opsubst
orthopoly
65.1 Introduction to orthogonal polynomials
65.2 Functions and Variables for orthogonal polynomials
plotdf
66.1 Introduction to plotdf
66.2 Functions and Variables for plotdf
romberg
67.1 Functions and Variables for romberg
simplex
68.1 Introduction to simplex
68.2 Functions and Variables for simplex
simplification
69.1 Introduction to simplification
69.2 Functions and Variables for simplification
solve_rec
70.1 Introduction to solve_rec
70.2 Functions and Variables for solve_rec
stats
71.1 Introduction to stats
71.2 Functions and Variables for inference_result
71.3 Functions and Variables for stats
71.4 Functions and Variables for special distributions
stirling
72.1 Functions and Variables for stirling
stringproc
73.1 Introduction to string processing
73.2 Functions and Variables for input and output
73.3 Functions and Variables for characters
73.4 Functions and Variables for strings
unit
74.1 Introduction to Units
74.2 Functions and Variables for Units
zeilberger
75.1 Introduction to zeilberger
75.2 Functions and Variables for zeilberger

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