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<title>Calculate GCD and multipliers</title>
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<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" id="refsect1-function.gmp-gcdext-description">
<h3 class="title">Description</h3>
<div class="methodsynopsis dc-description">
<span class="type">array</span> <span class="methodname"><strong>gmp_gcdext</strong></span>
( <span class="methodparam"><span class="type">resource</span> <code class="parameter">$a</code></span>
, <span class="methodparam"><span class="type">resource</span> <code class="parameter">$b</code></span>
)</div>
<p class="para rdfs-comment">
Calculates g, s, and t, such that <em>a*s + b*t = g =
gcd(a,b)</em>, 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:
<em>a*x + b*y = c</em>.
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" id="refsect1-function.gmp-gcdext-parameters">
<h3 class="title">Parameters</h3>
<p class="para">
<dl>
<dt>
<span class="term"><em><code class="parameter">a</code></em></span>
<dd>
<p class="para">It can be either a GMP number <span class="type"><a href="language.types.resource.html" class="type resource">resource</a></span>, or a
numeric string given that it is possible to convert the latter to a number.</p>
</dd>
</dt>
<dt>
<span class="term"><em><code class="parameter">b</code></em></span>
<dd>
<p class="para">It can be either a GMP number <span class="type"><a href="language.types.resource.html" class="type resource">resource</a></span>, 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" id="refsect1-function.gmp-gcdext-returnvalues">
<h3 class="title">Return Values</h3>
<p class="para">
An <span class="type"><a href="language.types.array.html" class="type array">array</a></span> of GMP numbers.
</p>
</div>
<div class="refsect1 examples" id="refsect1-function.gmp-gcdext-examples">
<h3 class="title">Examples</h3>
<p class="para">
<div class="example" id="example-3411">
<p><strong>Example #1 Solving a linear Diophantine equation</strong></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>
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