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Start Maxima with the command "maxima". Maxima will display version
information and a prompt. End each Maxima command with a semicolon.
End the session with the command "@code{quit();}". Here's a sample session:
@example maxima
$ maxima
Maxima 5.45.1 https://maxima.sourceforge.io
using Lisp SBCL 2.0.1.debian
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) factor(10!);
8 4 2
(%o1) 2 3 5 7
(%i2) expand ((x + y)^6);
6 5 2 4 3 3 4 2 5 6
(%o2) y + 6 x y + 15 x y + 20 x y + 15 x y + 6 x y + x
(%i3) factor (x^6 - 1);
2 2
(%o3) (x - 1) (x + 1) (x - x + 1) (x + x + 1)
(%i4) quit();
$
@end example
Maxima can search the info pages. Use the @mref{describe} command to show
information about the command or all the commands and variables containing
a string.
The question mark @mref{?} (exact search) and double question mark @mref{??}@w{}
(inexact search) are abbreviations for @code{describe}:
@example maxima
(%i1) ?? integ
0: Functions and Variables for Elliptic Integrals
1: Functions and Variables for Integration
2: Introduction to Elliptic Functions and Integrals
3: Introduction to Integration
4: askinteger (Functions and Variables for Simplification)
5: integerp (Functions and Variables for Miscellaneous Options)
6: integer_partitions (Functions and Variables for Sets)
7: integrate (Functions and Variables for Integration)
8: integrate_use_rootsof (Functions and Variables for Integration)
9: integration_constant_counter (Functions and Variables for
Integration)
10: nonnegintegerp (Functions and Variables for linearalgebra)
Enter space-separated numbers, `all' or `none': 5 4
-- Function: integerp (<expr>)
Returns `true' if <expr> is a literal numeric integer, otherwise
`false'.
`integerp' returns false if its argument is a symbol, even if the
argument is declared integer.
Examples:
(%i1) integerp (0);
(%o1) true
(%i2) integerp (1);
(%o2) true
(%i3) integerp (-17);
(%o3) true
(%i4) integerp (0.0);
(%o4) false
(%i5) integerp (1.0);
(%o5) false
(%i6) integerp (%pi);
(%o6) false
(%i7) integerp (n);
(%o7) false
(%i8) declare (n, integer);
(%o8) done
(%i9) integerp (n);
(%o9) false
-- Function: askinteger (<expr>, integer)
-- Function: askinteger (<expr>)
-- Function: askinteger (<expr>, even)
-- Function: askinteger (<expr>, odd)
`askinteger (<expr>, integer)' attempts to determine from the
`assume' database whether <expr> is an integer. `askinteger'
prompts the user if it cannot tell otherwise, and attempt to
install the information in the database if possible. `askinteger
(<expr>)' is equivalent to `askinteger (<expr>, integer)'.
`askinteger (<expr>, even)' and `askinteger (<expr>, odd)'
likewise attempt to determine if <expr> is an even integer or odd
integer, respectively.
(%o1) true
@end example
To use a result in later calculations, you can assign it to a variable or
refer to it by its automatically supplied label. In addition, @mref{%}@w{}
refers to the most recent calculated result:
@c ===beg===
@c u: expand ((x + y)^6);
@c diff (u, x);
@c factor (%o2);
@c ===end===
@example maxima
@group
(%i1) u: expand ((x + y)^6);
6 5 2 4 3 3 4 2 5 6
(%o1) y + 6 x y + 15 x y + 20 x y + 15 x y + 6 x y + x
@end group
@group
(%i2) diff (u, x);
5 4 2 3 3 2 4 5
(%o2) 6 y + 30 x y + 60 x y + 60 x y + 30 x y + 6 x
@end group
@group
(%i3) factor (%o2);
5
(%o3) 6 (y + x)
@end group
@end example
Maxima knows about complex numbers and numerical constants:
@c ===beg===
@c cos(%pi);
@c exp(%i*%pi);
@c ===end===
@example maxima
@group
(%i1) cos(%pi);
(%o1) - 1
@end group
@group
(%i2) exp(%i*%pi);
(%o2) - 1
@end group
@end example
Maxima can do differential and integral calculus:
@c ===beg===
@c u: expand ((x + y)^6);
@c diff (%, x);
@c integrate (1/(1 + x^3), x);
@c ===end===
@example maxima
@group
(%i1) u: expand ((x + y)^6);
6 5 2 4 3 3 4 2 5 6
(%o1) y + 6 x y + 15 x y + 20 x y + 15 x y + 6 x y + x
@end group
@group
(%i2) diff (%, x);
5 4 2 3 3 2 4 5
(%o2) 6 y + 30 x y + 60 x y + 60 x y + 30 x y + 6 x
@end group
@group
(%i3) integrate (1/(1 + x^3), x);
2 x - 1
2 atan(-------)
log(x - x + 1) sqrt(3) log(x + 1)
(%o3) - --------------- + ------------- + ----------
6 sqrt(3) 3
@end group
@end example
Maxima can solve linear systems and cubic equations:
@c ===beg===
@c linsolve ([3*x + 4*y = 7, 2*x + a*y = 13], [x, y]);
@c solve (x^3 - 3*x^2 + 5*x = 15, x);
@c ===end===
@example maxima
@group
(%i1) linsolve ([3*x + 4*y = 7, 2*x + a*y = 13], [x, y]);
7 a - 52 25
(%o1) [x = --------, y = -------]
3 a - 8 3 a - 8
@end group
@group
(%i2) solve (x^3 - 3*x^2 + 5*x = 15, x);
(%o2) [x = - sqrt(5) %i, x = sqrt(5) %i, x = 3]
@end group
@end example
Maxima can solve nonlinear sets of equations. Note that if you don't
want a result printed, you can finish your command with @kbd{$} instead
of @kbd{;}.
@c ===beg===
@c eq_1: x^2 + 3*x*y + y^2 = 0$
@c eq_2: 3*x + y = 1$
@c solve ([eq_1, eq_2]);
@c ===end===
@example maxima
(%i1) eq_1: x^2 + 3*x*y + y^2 = 0$
(%i2) eq_2: 3*x + y = 1$
@group
(%i3) solve ([eq_1, eq_2]);
3 sqrt(5) + 7 sqrt(5) + 3
(%o3) [[y = - -------------, x = -----------],
2 2
3 sqrt(5) - 7 sqrt(5) - 3
[y = -------------, x = - -----------]]
2 2
@end group
@end example
Maxima can generate plots of one or more functions:
@example maxima
(%i1) plot2d (sin(x)/x, [x, -20, 20])$
@end example
@altfigure{introduction1,Plot of a function}
@example maxima
(%i2) plot2d ([atan(x), erf(x), tanh(x)], [x, -5, 5], [y, -1.5, 2])$
@end example
@altfigure{introduction2,Plot of several functions}
@example maxima
@group
(%i3) plot3d (sin(sqrt(x^2 + y^2))/sqrt(x^2 + y^2),
[x, -12, 12], [y, -12, 12])$
@end group
@end example
@altfigure{introduction3,Plot of a function of two variables}
@c FOLLOWING TEXT DESCRIBES THE TCL/TK PLOT WINDOW WHICH IS NO LONGER THE DEFAULT
@c Moving the cursor to the top left corner of the plot window will pop up
@c a menu that will, among other things, let you generate a PostScript file
@c of the plot. (By default, the file is placed in your home directory.)
@c You can rotate a 3D plot.
@opencatbox{Categories:}
@category{Help}
@closecatbox
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