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https://github.com/sigmasternchen/php-doc-en
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b4aa07cd65
git-svn-id: https://svn.php.net/repository/phpdoc/en/trunk@146318 c90b9560-bf6c-de11-be94-00142212c4b1
81 lines
2.4 KiB
XML
81 lines
2.4 KiB
XML
<?xml version="1.0" encoding="iso-8859-1"?>
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<!-- $Revision: 1.5 $ -->
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<!-- splitted from ./en/functions/gmp.xml, last change in rev 1.1 -->
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<refentry id="function.gmp-gcdext">
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<refnamediv>
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<refname>gmp_gcdext</refname>
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<refpurpose>Calculate GCD and multipliers</refpurpose>
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</refnamediv>
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<refsect1>
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<title>Description</title>
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<methodsynopsis>
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<type>array</type><methodname>gmp_gcdext</methodname>
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<methodparam><type>resource</type><parameter>a</parameter></methodparam>
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<methodparam><type>resource</type><parameter>b</parameter></methodparam>
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</methodsynopsis>
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<para>
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Calculates g, s, and t, such that <literal>a*s + b*t = g =
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gcd(a,b)</literal>, where gcd is the greatest common divisor. Returns
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an array with respective elements g, s and t.
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</para>
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<para>
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This function can be used to solve linear Diophantine equations in two
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variables. These are equations that allow only integer solutions and have the form:
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<literal>a*x + b*y = c</literal>.
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For more information, go to the <ulink url="&url.diophantine-equation;">"Diophantine
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Equation" page at MathWorld</ulink>
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</para>
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<para>
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<example>
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<title>Solving a linear Diophantine equation</title>
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<programlisting role="php">
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<![CDATA[
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<?php
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// Solve the equation a*s + b*t = g
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// where a = 12, b = 21, g = gcd(12, 21) = 3
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$a = gmp_init(12);
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$b = gmp_init(21);
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$g = gmp_gcd($a, $b);
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$r = gmp_gcdext($a, $b);
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$check_gcd = (gmp_strval($g) == gmp_strval($r['g']));
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$eq_res = gmp_add(gmp_mul($a, $r['s']), gmp_mul($b, $r['t']));
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$check_res = (gmp_strval($g) == gmp_strval($eq_res));
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if ($check_gcd && $check_res) {
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$fmt = "Solution: %d*%d + %d*%d = %d\n";
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printf($fmt, gmp_strval($a), gmp_strval($r['s']), gmp_strval($b),
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gmp_strval($r['t']), gmp_strval($r['g']));
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} else {
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echo "Error while solving the equation\n";
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}
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// output: Solution: 12*2 + 21*-1 = 3
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?>
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]]>
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</programlisting>
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</example>
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</para>
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</refsect1>
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</refentry>
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<!-- Keep this comment at the end of the file
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Local variables:
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mode: sgml
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sgml-omittag:t
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sgml-shorttag:t
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sgml-minimize-attributes:nil
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sgml-always-quote-attributes:t
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sgml-indent-step:1
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sgml-indent-data:t
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indent-tabs-mode:nil
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sgml-parent-document:nil
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sgml-default-dtd-file:"../../../../manual.ced"
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sgml-exposed-tags:nil
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sgml-local-catalogs:nil
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sgml-local-ecat-files:nil
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End:
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vim600: syn=xml fen fdm=syntax fdl=2 si
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vim: et tw=78 syn=sgml
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vi: ts=1 sw=1
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-->
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