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<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><title>Chapter 5. GEL-Grundlagen</title><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot"><link rel="home" href="index.html" title="Genius-Handbuch"><link rel="up" href="index.html" title="Genius-Handbuch"><link rel="prev" href="ch04s05.html" title="2D-Darstellungen"><link rel="next" href="ch05s02.html" title="Verwendung von Variablen"></head><body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 5. GEL-Grundlagen</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="ch04s05.html">Prev</a> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="ch05s02.html">Next</a></td></tr></table><hr></div><div class="chapter"><div class="titlepage"><div><div><h1 class="title"><a name="genius-gel"></a>Chapter 5. GEL-Grundlagen</h1></div></div></div><div class="toc"><p><b>Table of Contents</b></p><dl class="toc"><dt><span class="sect1"><a href="ch05.html#genius-gel-values">Werte</a></span></dt><dd><dl><dt><span class="sect2"><a href="ch05.html#genius-gel-values-numbers">Zahlen</a></span></dt><dt><span class="sect2"><a href="ch05.html#genius-gel-values-booleans">Wahrheitswerte</a></span></dt><dt><span class="sect2"><a href="ch05.html#genius-gel-values-strings">Strings</a></span></dt><dt><span class="sect2"><a href="ch05.html#genius-gel-values-null">Null</a></span></dt></dl></dd><dt><span class="sect1"><a href="ch05s02.html">Verwendung von Variablen</a></span></dt><dd><dl><dt><span class="sect2"><a href="ch05s02.html#genius-gel-variables-setting">Setzen von Variablen</a></span></dt><dt><span class="sect2"><a href="ch05s02.html#genius-gel-variables-built-in">Eingebaute Variablen</a></span></dt><dt><span class="sect2"><a href="ch05s02.html#genius-gel-previous-result">Vorherige Ergebnisvariable</a></span></dt></dl></dd><dt><span class="sect1"><a href="ch05s03.html">Verwendung von Funktionen</a></span></dt><dd><dl><dt><span class="sect2"><a href="ch05s03.html#genius-gel-functions-defining">Definieren von Funktionen</a></span></dt><dt><span class="sect2"><a href="ch05s03.html#genius-gel-functions-variable-argument-lists">Variable Argument Lists</a></span></dt><dt><span class="sect2"><a href="ch05s03.html#genius-gel-functions-passing-functions">Übergabe von Funktionen an Funktionen</a></span></dt><dt><span class="sect2"><a href="ch05s03.html#genius-gel-functions-operations">Operationen mit Funktionen</a></span></dt></dl></dd><dt><span class="sect1"><a href="ch05s04.html">Trenner</a></span></dt><dt><span class="sect1"><a href="ch05s05.html">Kommentare</a></span></dt><dt><span class="sect1"><a href="ch05s06.html">Modulare Auswertung</a></span></dt><dt><span class="sect1"><a href="ch05s07.html">Liste der GEL-Operatoren</a></span></dt></dl></div><p lang="en">
GEL stands for Genius Extension Language. It is the language you use
to write programs in Genius. A program in GEL is simply an
expression that evaluates to a number, a matrix, or another object
in GEL.
<span class="application">Genius Mathematics Tool</span> can be used as a simple calculator, or as a
powerful theoretical research tool. The syntax is meant to
have as shallow of a learning curve as possible, especially for use
as a calculator.
</p><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a name="genius-gel-values"></a>Werte</h2></div></div></div><p lang="en">
Values in GEL can be <a class="link" href="ch05.html#genius-gel-values-numbers" title="Zahlen">numbers</a>, <a class="link" href="ch05.html#genius-gel-values-booleans" title="Wahrheitswerte">Booleans</a>, or <a class="link" href="ch05.html#genius-gel-values-strings" title="Strings">strings</a>. GEL also treats
<a class="link" href="ch08.html" title="Chapter 8. Matrizen in GEL">matrices</a> as values.
Values can be used in calculations, assigned to variables and returned from functions, among other uses.
</p><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a name="genius-gel-values-numbers"></a>Zahlen</h3></div></div></div><p lang="en">
Integers are the first type of number in GEL. Integers are written in the normal way.
</p><pre lang="en" class="programlisting">1234
</pre><p lang="en">
Hexadecimal and octal numbers can be written using C notation. For example:
</p><pre lang="en" class="programlisting">0x123ABC
01234
</pre><p lang="en">
Or you can type numbers in an arbitrary base using <code class="literal"><base>\<number></code>. Digits higher than 10 use letters in a similar way to hexadecimal. For example, a number in base 23 could be written:
</p><pre lang="en" class="programlisting">23\1234ABCD
</pre><p lang="en">
</p><p lang="en">
The second type of GEL number is rationals. Rationals are simply achieved by dividing two integers. So one could write:
</p><pre lang="en" class="programlisting">3/4
</pre><p lang="en">
to get three quarters. Rationals also accept mixed fraction notation. So in order to get one and three tenths you could write:
</p><pre lang="en" class="programlisting">1 3/10
</pre><p lang="en">
</p><p lang="en">
The next type of number is floating point. These are entered in a similar fashion to C notation. You can use <code class="literal">E</code>, <code class="literal">e</code> or <code class="literal">@</code> as the exponent delimiter. Note that using the exponent delimiter gives a float even if there is no decimal point in the number. Examples:
</p><pre lang="en" class="programlisting">1.315
7.887e77
7.887e-77
.3
0.3
77e5
</pre><p lang="en">
When Genius prints a floating point number it will always append a
<code class="computeroutput">.0</code> even if the number is whole. This is to indicate that
floating point numbers are taken as imprecise quantities. When a number is written in the
scientific notation, it is always a floating point number and thus Genius does not
print the <code class="computeroutput">.0</code>.
</p><p lang="en">
The final type of number in GEL is the complex numbers. You can enter a complex number as a sum of real and imaginary parts. To add an imaginary part, append an <code class="literal">i</code>. Here are examples of entering complex numbers:
</p><pre lang="en" class="programlisting">1+2i
8.01i
77*e^(1.3i)
</pre><p lang="en">
</p><div class="important" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Important</h3><p lang="en">
When entering imaginary numbers, a number must be in front of the <code class="literal">i</code>. If you use <code class="literal">i</code> by itself, Genius will interpret this as referring to the variable <code class="varname">i</code>. If you need to refer to <code class="literal">i</code> by itself, use <code class="literal">1i</code> instead.
</p><p lang="en">
In order to use mixed fraction notation with imaginary numbers you must have the mixed fraction in parentheses. (i.e., <strong class="userinput"><code>(1 2/5)i</code></strong>)
</p></div></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a name="genius-gel-values-booleans"></a>Wahrheitswerte</h3></div></div></div><p lang="en">
Genius also supports native Boolean values. The two Boolean constants are
defined as <code class="constant">true</code> and <code class="constant">false</code>; these
identifiers can be used like any other variable. You can also use the
identifiers <code class="constant">True</code>, <code class="constant">TRUE</code>,
<code class="constant">False</code> and <code class="constant">FALSE</code> as aliases for the
above.
</p><p lang="en">
At any place where a Boolean expression is expected, you can use a Boolean
value or any expression that produces either a number or a Boolean. If
Genius needs to evaluate a number as a Boolean it will interpret
0 as <code class="constant">false</code> and any other number as
<code class="constant">true</code>.
</p><p lang="en">
In addition, you can do arithmetic with Boolean values. For example:
</p><pre lang="en" class="programlisting">( (1 + true) - false ) * true
</pre><p lang="en">
is the same as:
</p><pre lang="en" class="programlisting">( (true or true) or not false ) and true
</pre><p lang="en">
Only addition, subtraction and multiplication are supported. If you mix numbers with Booleans in an expression then the numbers are converted to Booleans as described above. This means that, for example:
</p><pre lang="en" class="programlisting">1 == true
</pre><p lang="en">
always evaluates to <code class="constant">true</code> since 1 will be converted to <code class="constant">true</code> before being compared to <code class="constant">true</code>.
</p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a name="genius-gel-values-strings"></a>Strings</h3></div></div></div><p lang="en">
Like numbers and Booleans, strings in GEL can be stored as values inside variables and passed to functions. You can also concatenate a string with another value using the plus operator. For example:
</p><pre lang="en" class="programlisting">a=2+3;"The result is: "+a
</pre><p lang="en">
will create the string:
</p><pre lang="en" class="programlisting">The result is: 5
</pre><p lang="en">
You can also use C-like escape sequences such as <code class="literal">\n</code>,<code class="literal">\t</code>,<code class="literal">\b</code>,<code class="literal">\a</code> and <code class="literal">\r</code>. To get a <code class="literal">\</code> or <code class="literal">"</code> into the string you can quote it with a <code class="literal">\</code>. For example:
</p><pre lang="en" class="programlisting">"Slash: \\ Quotes: \" Tabs: \t1\t2\t3"
</pre><p lang="en">
will make a string:
</p><pre lang="en" class="programlisting">Slash: \ Quotes: " Tabs: 1 2 3
</pre><p lang="en">
Do note however that when a string is returned from a function, escapes are
quoted, so that the output can be used as input. If you wish to print the
string as it is (without escapes), use the
<a class="link" href="ch11s02.html#gel-function-print"><code class="function">print</code></a>
or
<a class="link" href="ch11s02.html#gel-function-printn"><code class="function">printn</code></a> functions.
</p><p lang="en">
In addition, you can use the library function <a class="link" href="ch11s02.html#gel-function-string"><code class="function">string</code></a> to convert anything to a string. For example:
</p><pre lang="en" class="programlisting">string(22)
</pre><p lang="en">
will return
</p><pre lang="en" class="programlisting">"22"
</pre><p lang="en">
Strings can also be compared with <code class="literal">==</code> (equal), <code class="literal">!=</code> (not equal) and <code class="literal"><=></code> (comparison) operators
</p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a name="genius-gel-values-null"></a>Null</h3></div></div></div><p lang="en">
There is a special value called
<code class="constant">null</code>. No operations can be performed on
it, and nothing is printed when it is returned. Therefore,
<code class="constant">null</code> is useful when you do not want output from an
expression. The value <code class="constant">null</code> can be obtained as an expression when you
type <code class="literal">.</code>, the constant <code class="constant">null</code> or nothing.
By nothing we mean that if you end an expression with
a separator <code class="literal">;</code>, it is equivalent to ending it with a
separator followed by a <code class="constant">null</code>.
</p><p lang="en">
Example:
</p><pre lang="en" class="programlisting">x=5;.
x=5;
</pre><p lang="en">
</p><p lang="en">
Some functions return <code class="constant">null</code> when no value can be returned
or an error happened. Also <code class="constant">null</code> is used as an empty vector
or matrix, or an empty reference.
</p></div></div></div><div class="navfooter"><hr><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="ch04s05.html">Prev</a> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="ch05s02.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">2D-Darstellungen </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Verwendung von Variablen</td></tr></table></div></body></html>
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