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<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><title>Chapter 5. Основы GEL</title><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot"><link rel="home" href="index.html" title="Руководство пользователя Genius"><link rel="up" href="index.html" title="Руководство пользователя Genius"><link rel="prev" href="ch04s05.html" title="Графики поверхностей"><link rel="next" href="ch05s02.html" title="Использование переменных"></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. Основы GEL</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. Основы GEL</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">Значения</a></span></dt><dd><dl><dt><span class="sect2"><a href="ch05.html#genius-gel-values-numbers">Числа</a></span></dt><dt><span class="sect2"><a href="ch05.html#genius-gel-values-booleans">Логические значения</a></span></dt><dt><span class="sect2"><a href="ch05.html#genius-gel-values-strings">Строки</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">Использование переменных</a></span></dt><dd><dl><dt><span class="sect2"><a href="ch05s02.html#genius-gel-variables-setting">Присваивание значения переменным</a></span></dt><dt><span class="sect2"><a href="ch05s02.html#genius-gel-variables-built-in">Встроенные переменные</a></span></dt><dt><span class="sect2"><a href="ch05s02.html#genius-gel-previous-result">Переменные с результатом предыдущего вычисления</a></span></dt></dl></dd><dt><span class="sect1"><a href="ch05s03.html">Использование функций</a></span></dt><dd><dl><dt><span class="sect2"><a href="ch05s03.html#genius-gel-functions-defining">Определение функций</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">Passing Functions to Functions</a></span></dt><dt><span class="sect2"><a href="ch05s03.html#genius-gel-functions-operations">Операции с функциями</a></span></dt></dl></dd><dt><span class="sect1"><a href="ch05s04.html">Разделитель</a></span></dt><dt><span class="sect1"><a href="ch05s05.html">Comments</a></span></dt><dt><span class="sect1"><a href="ch05s06.html">Modular Evaluation</a></span></dt><dt><span class="sect1"><a href="ch05s07.html">Список операторов GEL</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>Значения</h2></div></div></div><p lang="en">
Values in GEL can be <a class="link" href="ch05.html#genius-gel-values-numbers" title="Числа">numbers</a>, <a class="link" href="ch05.html#genius-gel-values-booleans" title="Логические значения">Booleans</a>, or <a class="link" href="ch05.html#genius-gel-values-strings" title="Строки">strings</a>. GEL also treats
<a class="link" href="ch08.html" title="Chapter 8. Матрицы в 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>Числа</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>При вводе мнимых чисел перед символом <code class="literal">i</code> должно стоять число. Если использовать символ <code class="literal">i</code> сам по себе, Genius интерпретирует его как ссылку на переменную <code class="varname">i</code>. Если нужно указать саму мнимую единицу <code class="literal">i</code>, используйте вместо неё <code class="literal">1i</code>.</p><p>Чтобы использовать смешанные дроби в мнимых числах, нужно взять смешанную дробь в круглые скобки: (например, <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>Логические значения</h3></div></div></div><p>Genius также поддерживает логические значения. Определены две логические константы: <code class="constant">true</code> и <code class="constant">false</code>; их можно использовать, как и любую переменную. В качестве псевдонимов к ним можно также использовать <code class="constant">True</code>, <code class="constant">TRUE</code>, <code class="constant">False</code> и <code class="constant">FALSE</code>.</p><p>Там, где требуется логическое выражение, можно использовать логическое значение или любое выражение, дающее в результате число или логическое значение. Если Genius нужно использовать число как логическое значение, он будет интерпретировать 0 как <code class="constant">false</code> и любое другое число как <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>Строки</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>Некоторые функции возвращают <code class="constant">null</code>, если невозможно вернуть значение или произошла ошибка. Также <code class="constant">null</code> используется как пустой вектор или матрица, или пустая ссылка.</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">Графики поверхностей </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Использование переменных</td></tr></table></div></body></html>
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