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<a name="Introdu_00e7_00e3o-ao-Maxima"></a>
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<h1 class="chapter"> 1. Introdu&ccedil;&atilde;o ao Maxima </h1>

<p>Inicie o Maxima com o comando &quot;maxima&quot;.  Maxima mostrar&aacute; a
informa&ccedil;&atilde;o de vers&atilde;o e uma linha de comando.  Termine
cada comando Maxima com um ponto e v&iacute;rgula.  Termine uma
sess&atilde;o com o comando &quot;quit();&quot;.  Aqui est&aacute; um exemplo de sess&atilde;o:
</p>
<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>
<p>Maxima pode fazer pesquisas nas p&aacute;ginas info do manual. Use o comando
<kbd>describe</kbd> para mostrar todos os comandos e vari&aacute;veis contendo uma
dada sequ&ecirc;ncia de caracteres, e opcionalmente a sua
documenta&ccedil;&atilde;o.  O ponto de interroga&ccedil;&atilde;o
<code>?</code> &eacute; uma abreviatura para <code>describe</code>:
</p>
<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 (&lt;expr&gt;)
     Returns `true' if &lt;expr&gt; 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>
<p>Para usar um resultado em c&aacute;lculos posteriores, pode atribuir esse
valor a uma vari&aacute;vel ou referir-se a esse mesmo valor atrav&eacute;s de seu
r&oacute;tulo gerado automaticamente.  Adicionalmente, <kbd>%</kbd> refere-se ao
mais recente resultado calculado:
</p>
<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>
<p>Maxima tem conhecimento sobre n&uacute;meros complexos e constantes num&eacute;ricas:
</p>
<pre class="example">(%i1) cos(%pi);
(%o1)                          - 1
(%i2) exp(%i*%pi);
(%o2)                          - 1
</pre>
<p>Maxima pode fazer contas de c&aacute;lculo diferencial e integrail:
</p>
<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>
<p>Maxima pode resolver sistemas lineares e equa&ccedil;&otilde;es c&uacute;bicas:
</p>
<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>
<p>Maxima pode resolver sistemas de equa&ccedil;&otilde;es n&atilde;o
lineares. Repare que se n&atilde;o quiser um resultado impresso, poder&aacute;
terminar o seu comando com <kbd>$</kbd> em lugar de encerrar com <kbd>;</kbd>.
</p>
<pre class="example">(%i1) eq_1: x^2 + 3*x*y + y^2 = 0$
(%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>
<p>Maxima pode gerar gr&aacute;ficos de uma ou mais fun&ccedil;&otilde;es:
</p>
<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>

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