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<link title="Weak" rel="Chapter" href="Weak.html"><title>Complex</title>
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<center><h1>Module <a href="type_Complex.html">Complex</a></h1></center>
<br>
<pre><span class="keyword">module</span> Complex: <code class="type">sig end</code></pre><div class="info">
Complex numbers.
<p>
This module provides arithmetic operations on complex numbers.
Complex numbers are represented by their real and imaginary parts
(cartesian representation). Each part is represented by a
double-precision floating-point number (type <code class="code">float</code>).<br>
</div>
<hr width="100%">
<br><code><span class="keyword">type</span> <a name="TYPEt"></a>t = {<br></code><table border="0" cellpadding="1">
<tr>
<td align="left" valign="top" >
<code> </code></td>
<td align="left" valign="top" >
<code>re : <code class="type">float</code>;</code></td>
</tr>
<tr>
<td align="left" valign="top" >
<code> </code></td>
<td align="left" valign="top" >
<code>im : <code class="type">float</code>;</code></td>
</tr></table>
}
<div class="info">
The type of complex numbers. <code class="code">re</code> is the real part and <code class="code">im</code> the
imaginary part.<br>
</div>
<br>
<pre><span class="keyword">val</span> <a name="VALzero"></a>zero : <code class="type"><a href="Complex.html#TYPEt">t</a></code></pre><div class="info">
The complex number <code class="code">0</code>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALone"></a>one : <code class="type"><a href="Complex.html#TYPEt">t</a></code></pre><div class="info">
The complex number <code class="code">1</code>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALi"></a>i : <code class="type"><a href="Complex.html#TYPEt">t</a></code></pre><div class="info">
The complex number <code class="code">i</code>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALneg"></a>neg : <code class="type"><a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info">
Unary negation.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALconj"></a>conj : <code class="type"><a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info">
Conjugate: given the complex <code class="code">x + i.y</code>, returns <code class="code">x - i.y</code>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALadd"></a>add : <code class="type"><a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info">
Addition<br>
</div>
<pre><span class="keyword">val</span> <a name="VALsub"></a>sub : <code class="type"><a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info">
Subtraction<br>
</div>
<pre><span class="keyword">val</span> <a name="VALmul"></a>mul : <code class="type"><a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info">
Multiplication<br>
</div>
<pre><span class="keyword">val</span> <a name="VALinv"></a>inv : <code class="type"><a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info">
Multiplicative inverse (<code class="code">1/z</code>).<br>
</div>
<pre><span class="keyword">val</span> <a name="VALdiv"></a>div : <code class="type"><a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info">
Division<br>
</div>
<pre><span class="keyword">val</span> <a name="VALsqrt"></a>sqrt : <code class="type"><a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info">
Square root. The result <code class="code">x + i.y</code> is such that <code class="code">x > 0</code> or
<code class="code">x = 0</code> and <code class="code">y >= 0</code>.
This function has a discontinuity along the negative real axis.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALnorm2"></a>norm2 : <code class="type"><a href="Complex.html#TYPEt">t</a> -> float</code></pre><div class="info">
Norm squared: given <code class="code">x + i.y</code>, returns <code class="code">x^2 + y^2</code>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALnorm"></a>norm : <code class="type"><a href="Complex.html#TYPEt">t</a> -> float</code></pre><div class="info">
Norm: given <code class="code">x + i.y</code>, returns <code class="code">sqrt(x^2 + y^2)</code>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALarg"></a>arg : <code class="type"><a href="Complex.html#TYPEt">t</a> -> float</code></pre><div class="info">
Argument. The argument of a complex number is the angle
in the complex plane between the positive real axis and a line
passing through zero and the number. This angle ranges from
<code class="code">-pi</code> to <code class="code">pi</code>. This function has a discontinuity along the
negative real axis.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALpolar"></a>polar : <code class="type">float -> float -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info">
<code class="code">polar norm arg</code> returns the complex having norm <code class="code">norm</code>
and argument <code class="code">arg</code>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALexp"></a>exp : <code class="type"><a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info">
Exponentiation. <code class="code">exp z</code> returns <code class="code">e</code> to the <code class="code">z</code> power.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALlog"></a>log : <code class="type"><a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info">
Natural logarithm (in base <code class="code">e</code>).<br>
</div>
<pre><span class="keyword">val</span> <a name="VALpow"></a>pow : <code class="type"><a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info">
Power function. <code class="code">pow z1 z2</code> returns <code class="code">z1</code> to the <code class="code">z2</code> power.<br>
</div>
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