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<h1 class="chapter"> 1. Introduction to Maxima </h1>
<p>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 "quit();". Here's a sample session:
</p>
<table><tr><td> </td><td><pre class="example">[wfs@chromium]$ maxima
Maxima 5.9.1 http://maxima.sourceforge.net
Using Lisp CMU Common Lisp 19a
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
This is a development version of Maxima. 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();
[wfs@chromium]$
</pre></td></tr></table>
<p>Maxima can search the info pages. Use the <kbd>describe</kbd> command to show
all the commands and variables containing a string, and optionally their
documentation. The question mark <code>?</code> is an abbreviation for <code>describe</code>:
</p>
<table><tr><td> </td><td><pre class="example">(%i1) ? integ
0: (maxima.info)Introduction to Elliptic Functions and Integrals.
1: Definitions for Elliptic Integrals.
2: Integration.
3: Introduction to Integration.
4: Definitions for Integration.
5: askinteger :Definitions for Simplification.
6: integerp :Definitions for Miscellaneous Options.
7: integrate :Definitions for Integration.
8: integrate_use_rootsof :Definitions for Integration.
9: integration_constant_counter :Definitions for Integration.
Enter space-separated numbers, `all' or `none': 6 5
Info from file /usr/local/info/maxima.info:
- Function: integerp (<expr>)
Returns `true' if <expr> is an integer, otherwise `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' will
ask 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) false
</pre></td></tr></table>
<p>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, <kbd>%</kbd>
refers to the most recent calculated result:
</p>
<table><tr><td> </td><td><pre class="example">(%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
(%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
(%i3) factor (%o2);
5
(%o3) 6 (y + x)
</pre></td></tr></table>
<p>Maxima knows about complex numbers and numerical constants:
</p>
<table><tr><td> </td><td><pre class="example">(%i1) cos(%pi);
(%o1) - 1
(%i2) exp(%i*%pi);
(%o2) - 1
</pre></td></tr></table>
<p>Maxima can do differential and integral calculus:
</p>
<table><tr><td> </td><td><pre class="example">(%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
(%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
(%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
</pre></td></tr></table>
<p>Maxima can solve linear systems and cubic equations:
</p>
<table><tr><td> </td><td><pre class="example">(%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
(%i2) solve (x^3 - 3*x^2 + 5*x = 15, x);
(%o2) [x = - sqrt(5) %i, x = sqrt(5) %i, x = 3]
</pre></td></tr></table>
<p>Maxima can solve nonlinear sets of equations. Note that if you don't
want a result printed, you can finish your command with <kbd>$</kbd> instead
of <kbd>;</kbd>.
</p>
<table><tr><td> </td><td><pre class="example">(%i1) eq_1: x^2 + 3*x*y + y^2 = 0$
(%i2) eq_2: 3*x + y = 1$
(%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
</pre></td></tr></table>
<p>Maxima can generate plots of one or more
functions:
</p>
<table><tr><td> </td><td><pre class="example">(%i1) eq_1: x^2 + 3*x*y + y^2 = 0$
(%i2) eq_2: 3*x + y = 1$
(%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
(%i4) kill(labels);
(%o0) done
(%i1) plot2d (sin(x)/x, [x, -20, 20]);
(%o1)
(%i2) plot2d ([atan(x), erf(x), tanh(x)], [x, -5, 5]);
(%o2)
(%i3) plot3d (sin(sqrt(x^2 + y^2))/sqrt(x^2 + y^2), [x, -12, 12], [y, -12, 12]);
(%o3)
</pre></td></tr></table>
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