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<a name="Introduction-to-Maxima"></a>
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<p>
Next: <a href="maxima_1.html#Bug-Detection-and-Reporting" accesskey="n" rel="next">Bug Detection and Reporting</a>, Previous: <a href="maxima_toc.html#Top" accesskey="p" rel="previous">Top</a>, Up: <a href="maxima_toc.html#Top" accesskey="u" rel="up">Top</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_423.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Introduction-to-Maxima-1"></a>
<h2 class="chapter">1 Introduction to Maxima</h2>
<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 "<code>quit();</code>". Here’s a sample session:
</p>
<div class="example">
<pre class="example">$ 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();
$
</pre></div>
<p>Maxima can search the info pages. Use the <code><a href="maxima_5.html#describe">describe</a></code> command to show
information about the command or all the commands and variables containing
a string.
The question mark <code><a href="maxima_8.html#g_t_003f">?</a></code> (exact search) and double question mark <code><a href="maxima_8.html#g_t_003f_003f">??</a></code><!-- /@w -->
(inexact search) are abbreviations for <code>describe</code>:
</p>
<div class="example">
<pre class="example">(%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
</pre></div>
<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, <code><a href="maxima_8.html#g_t_0025">%</a></code><!-- /@w -->
refers to the most recent calculated result:
</p>
<div class="example">
<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></div>
<p>Maxima knows about complex numbers and numerical constants:
</p>
<div class="example">
<pre class="example">(%i1) cos(%pi);
(%o1) - 1
(%i2) exp(%i*%pi);
(%o2) - 1
</pre></div>
<p>Maxima can do differential and integral calculus:
</p>
<div class="example">
<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></div>
<p>Maxima can solve linear systems and cubic equations:
</p>
<div class="example">
<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></div>
<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>$</kbd> instead
of <kbd>;</kbd>.
</p>
<div class="example">
<pre class="example">(%i1) eq_1: x^2 + 3*x*y + y^2 = 0$
(%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></div>
<p>Maxima can generate plots of one or more functions:
</p>
<div class="example">
<pre class="example">(%i1) plot2d (sin(x)/x, [x, -20, 20])$
</pre></div>
<img src="figures/introduction1.png" alt="figures/introduction1">
<div class="example">
<pre class="example">(%i2) plot2d ([atan(x), erf(x), tanh(x)], [x, -5, 5], [y, -1.5, 2])$
</pre></div>
<img src="figures/introduction2.png" alt="figures/introduction2">
<div class="example">
<pre class="example">(%i3) plot3d (sin(sqrt(x^2 + y^2))/sqrt(x^2 + y^2),
[x, -12, 12], [y, -12, 12])$
</pre></div>
<img src="figures/introduction3.png" alt="figures/introduction3">
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Categories:<a href="maxima_424.html#Category_003a-Help">Help</a>
·</div>
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<p>
Next: <a href="maxima_1.html#Bug-Detection-and-Reporting" accesskey="n" rel="next">Bug Detection and Reporting</a>, Previous: <a href="maxima_toc.html#Top" accesskey="p" rel="previous">Top</a>, Up: <a href="maxima_toc.html#Top" accesskey="u" rel="up">Top</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_423.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
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