mirror of
https://github.com/sigmasternchen/php-doc-en
synced 2025-03-19 10:28:54 +00:00
96c9d88bad
git-svn-id: https://svn.php.net/repository/phpdoc/en/trunk@297028 c90b9560-bf6c-de11-be94-00142212c4b1
112 lines
3 KiB
XML
112 lines
3 KiB
XML
<?xml version="1.0" encoding="utf-8"?>
|
|
<!-- $Revision$ -->
|
|
<refentry xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://docbook.org/ns/docbook" xml:id="function.gmp-gcdext">
|
|
<refnamediv>
|
|
<refname>gmp_gcdext</refname>
|
|
<refpurpose>Calculate GCD and multipliers</refpurpose>
|
|
</refnamediv>
|
|
|
|
<refsect1 role="description">
|
|
&reftitle.description;
|
|
<methodsynopsis>
|
|
<type>array</type><methodname>gmp_gcdext</methodname>
|
|
<methodparam><type>resource</type><parameter>a</parameter></methodparam>
|
|
<methodparam><type>resource</type><parameter>b</parameter></methodparam>
|
|
</methodsynopsis>
|
|
<para>
|
|
Calculates g, s, and t, such that <literal>a*s + b*t = g =
|
|
gcd(a,b)</literal>, where gcd is the greatest common divisor. Returns
|
|
an array with respective elements g, s and t.
|
|
</para>
|
|
<para>
|
|
This function can be used to solve linear Diophantine equations in two
|
|
variables. These are equations that allow only integer solutions and have the form:
|
|
<literal>a*x + b*y = c</literal>.
|
|
For more information, go to the <link xlink:href="&url.diophantine-equation;">"Diophantine
|
|
Equation" page at MathWorld</link>
|
|
</para>
|
|
</refsect1>
|
|
|
|
<refsect1 role="parameters">
|
|
&reftitle.parameters;
|
|
<para>
|
|
<variablelist>
|
|
<varlistentry>
|
|
<term><parameter>a</parameter></term>
|
|
<listitem>
|
|
&gmp.parameter;
|
|
</listitem>
|
|
</varlistentry>
|
|
<varlistentry>
|
|
<term><parameter>b</parameter></term>
|
|
<listitem>
|
|
&gmp.parameter;
|
|
</listitem>
|
|
</varlistentry>
|
|
</variablelist>
|
|
</para>
|
|
</refsect1>
|
|
|
|
<refsect1 role="returnvalues">
|
|
&reftitle.returnvalues;
|
|
<para>
|
|
An <type>array</type> of GMP numbers.
|
|
</para>
|
|
</refsect1>
|
|
|
|
<refsect1 role="examples">
|
|
&reftitle.examples;
|
|
<para>
|
|
<example>
|
|
<title>Solving a linear Diophantine equation</title>
|
|
<programlisting role="php">
|
|
<![CDATA[
|
|
<?php
|
|
// Solve the equation a*s + b*t = g
|
|
// where a = 12, b = 21, g = gcd(12, 21) = 3
|
|
$a = gmp_init(12);
|
|
$b = gmp_init(21);
|
|
$g = gmp_gcd($a, $b);
|
|
$r = gmp_gcdext($a, $b);
|
|
|
|
$check_gcd = (gmp_strval($g) == gmp_strval($r['g']));
|
|
$eq_res = gmp_add(gmp_mul($a, $r['s']), gmp_mul($b, $r['t']));
|
|
$check_res = (gmp_strval($g) == gmp_strval($eq_res));
|
|
|
|
if ($check_gcd && $check_res) {
|
|
$fmt = "Solution: %d*%d + %d*%d = %d\n";
|
|
printf($fmt, gmp_strval($a), gmp_strval($r['s']), gmp_strval($b),
|
|
gmp_strval($r['t']), gmp_strval($r['g']));
|
|
} else {
|
|
echo "Error while solving the equation\n";
|
|
}
|
|
|
|
// output: Solution: 12*2 + 21*-1 = 3
|
|
?>
|
|
]]>
|
|
</programlisting>
|
|
</example>
|
|
</para>
|
|
</refsect1>
|
|
</refentry>
|
|
|
|
<!-- Keep this comment at the end of the file
|
|
Local variables:
|
|
mode: sgml
|
|
sgml-omittag:t
|
|
sgml-shorttag:t
|
|
sgml-minimize-attributes:nil
|
|
sgml-always-quote-attributes:t
|
|
sgml-indent-step:1
|
|
sgml-indent-data:t
|
|
indent-tabs-mode:nil
|
|
sgml-parent-document:nil
|
|
sgml-default-dtd-file:"~/.phpdoc/manual.ced"
|
|
sgml-exposed-tags:nil
|
|
sgml-local-catalogs:nil
|
|
sgml-local-ecat-files:nil
|
|
End:
|
|
vim600: syn=xml fen fdm=syntax fdl=2 si
|
|
vim: et tw=78 syn=sgml
|
|
vi: ts=1 sw=1
|
|
-->
|