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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"><html> <head> <title>Calculate GCD and multipliers</title> <meta http-equiv="content-type" content="text/html; charset=UTF-8"> </head> <body><div style="text-align: center;"> <div class="prev" style="text-align: left; float: left;"><a href="function.gmp-gcd.html">gmp_gcd</a></div> <div class="next" style="text-align: right; float: right;"><a href="function.gmp-hamdist.html">gmp_hamdist</a></div> <div class="up"><a href="ref.gmp.html">GMP Functions</a></div> <div class="home"><a href="index.html">PHP Manual</a></div></div><hr /><div id="function.gmp-gcdext" class="refentry"> <div class="refnamediv"> <h1 class="refname">gmp_gcdext</h1> <p class="verinfo">(PHP 4 >= 4.0.4, PHP 5)</p><p class="refpurpose"><span class="refname">gmp_gcdext</span> — <span class="dc-title">Calculate GCD and multipliers</span></p> </div> <div class="refsect1 description"> <h3 class="title">Description</h3> <div class="methodsynopsis dc-description"> <span class="type">array</span> <span class="methodname"><b><b>gmp_gcdext</b></b></span> ( <span class="methodparam"><span class="type">resource</span> <tt class="parameter">$a</tt></span> , <span class="methodparam"><span class="type">resource</span> <tt class="parameter">$b</tt></span> )</div> <p class="para rdfs-comment"> Calculates g, s, and t, such that <i>a*s + b*t = g = gcd(a,b)</i>, where gcd is the greatest common divisor. Returns an array with respective elements g, s and t. </p> <p class="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: <i>a*x + b*y = c</i>. For more information, go to the <a href="http://mathworld.wolfram.com/DiophantineEquation.html" class="link external">» "Diophantine Equation" page at MathWorld</a> </p> </div> <div class="refsect1 parameters"> <h3 class="title">Parameters</h3> <p class="para"> <dl> <dt> <span class="term"><i><tt class="parameter">a</tt></i></span> <dd> <p class="para">It can be either a GMP number <a href="language.types.resource.html" class="type resource">resource</a>, or a numeric string given that it is possible to convert the latter to a number.</p> </dd> </dt> <dt> <span class="term"><i><tt class="parameter">b</tt></i></span> <dd> <p class="para">It can be either a GMP number <a href="language.types.resource.html" class="type resource">resource</a>, or a numeric string given that it is possible to convert the latter to a number.</p> </dd> </dt> </dl> </p> </div> <div class="refsect1 returnvalues"> <h3 class="title">Return Values</h3> <p class="para"> An <a href="language.types.array.html" class="type array">array</a> of GMP numbers. </p> </div> <div class="refsect1 examples"> <h3 class="title">Examples</h3> <p class="para"> <div class="example"> <p><b>Example #1 Solving a linear Diophantine equation</b></p> <div class="example-contents"><div class="phpcode"><code><span style="color: #000000"><span style="color: #0000BB"><?php<br /></span><span style="color: #FF8000">// Solve the equation a*s + b*t = g<br />// where a = 12, b = 21, g = gcd(12, 21) = 3<br /></span><span style="color: #0000BB">$a </span><span style="color: #007700">= </span><span style="color: #0000BB">gmp_init</span><span style="color: #007700">(</span><span style="color: #0000BB">12</span><span style="color: #007700">);<br /></span><span style="color: #0000BB">$b </span><span style="color: #007700">= </span><span style="color: #0000BB">gmp_init</span><span style="color: #007700">(</span><span style="color: #0000BB">21</span><span style="color: #007700">);<br /></span><span style="color: #0000BB">$g </span><span style="color: #007700">= </span><span style="color: #0000BB">gmp_gcd</span><span style="color: #007700">(</span><span style="color: #0000BB">$a</span><span style="color: #007700">, </span><span style="color: #0000BB">$b</span><span style="color: #007700">);<br /></span><span style="color: #0000BB">$r </span><span style="color: #007700">= </span><span style="color: #0000BB">gmp_gcdext</span><span style="color: #007700">(</span><span style="color: #0000BB">$a</span><span style="color: #007700">, </span><span style="color: #0000BB">$b</span><span style="color: #007700">);<br /><br /></span><span style="color: #0000BB">$check_gcd </span><span style="color: #007700">= (</span><span style="color: #0000BB">gmp_strval</span><span style="color: #007700">(</span><span style="color: #0000BB">$g</span><span style="color: #007700">) == </span><span style="color: #0000BB">gmp_strval</span><span style="color: #007700">(</span><span style="color: #0000BB">$r</span><span style="color: #007700">[</span><span style="color: #DD0000">'g'</span><span style="color: #007700">]));<br /></span><span style="color: #0000BB">$eq_res </span><span style="color: #007700">= </span><span style="color: #0000BB">gmp_add</span><span style="color: #007700">(</span><span style="color: #0000BB">gmp_mul</span><span style="color: #007700">(</span><span style="color: #0000BB">$a</span><span style="color: #007700">, </span><span style="color: #0000BB">$r</span><span style="color: #007700">[</span><span style="color: #DD0000">'s'</span><span style="color: #007700">]), </span><span style="color: #0000BB">gmp_mul</span><span style="color: #007700">(</span><span style="color: #0000BB">$b</span><span style="color: #007700">, </span><span style="color: #0000BB">$r</span><span style="color: #007700">[</span><span style="color: #DD0000">'t'</span><span style="color: #007700">]));<br /></span><span style="color: #0000BB">$check_res </span><span style="color: #007700">= (</span><span style="color: #0000BB">gmp_strval</span><span style="color: #007700">(</span><span style="color: #0000BB">$g</span><span style="color: #007700">) == </span><span style="color: #0000BB">gmp_strval</span><span style="color: #007700">(</span><span style="color: #0000BB">$eq_res</span><span style="color: #007700">));<br /><br />if (</span><span style="color: #0000BB">$check_gcd </span><span style="color: #007700">&& </span><span style="color: #0000BB">$check_res</span><span style="color: #007700">) {<br /> </span><span style="color: #0000BB">$fmt </span><span style="color: #007700">= </span><span style="color: #DD0000">"Solution: %d*%d + %d*%d = %d\n"</span><span style="color: #007700">;<br /> </span><span style="color: #0000BB">printf</span><span style="color: #007700">(</span><span style="color: #0000BB">$fmt</span><span style="color: #007700">, </span><span style="color: #0000BB">gmp_strval</span><span style="color: #007700">(</span><span style="color: #0000BB">$a</span><span style="color: #007700">), </span><span style="color: #0000BB">gmp_strval</span><span style="color: #007700">(</span><span style="color: #0000BB">$r</span><span style="color: #007700">[</span><span style="color: #DD0000">'s'</span><span style="color: #007700">]), </span><span style="color: #0000BB">gmp_strval</span><span style="color: #007700">(</span><span style="color: #0000BB">$b</span><span style="color: #007700">),<br /> </span><span style="color: #0000BB">gmp_strval</span><span style="color: #007700">(</span><span style="color: #0000BB">$r</span><span style="color: #007700">[</span><span style="color: #DD0000">'t'</span><span style="color: #007700">]), </span><span style="color: #0000BB">gmp_strval</span><span style="color: #007700">(</span><span style="color: #0000BB">$r</span><span style="color: #007700">[</span><span style="color: #DD0000">'g'</span><span style="color: #007700">]));<br />} else {<br /> echo </span><span style="color: #DD0000">"Error while solving the equation\n"</span><span style="color: #007700">;<br />}<br /><br /></span><span style="color: #FF8000">// output: Solution: 12*2 + 21*-1 = 3<br /></span><span style="color: #0000BB">?></span></span></code></div> </div> </div> </p> </div></div><hr /><div style="text-align: center;"> <div class="prev" style="text-align: left; float: left;"><a href="function.gmp-gcd.html">gmp_gcd</a></div> <div class="next" style="text-align: right; float: right;"><a href="function.gmp-hamdist.html">gmp_hamdist</a></div> <div class="up"><a href="ref.gmp.html">GMP Functions</a></div> <div class="home"><a href="index.html">PHP Manual</a></div></div></body></html>⌨️ 快捷键说明
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