<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> <link rel="stylesheet" href="style.css" type="text/css"> <meta content="text/html; charset=iso-8859-1" http-equiv="Content-Type"> <link rel="Start" href="index.html"> <link rel="previous" href="Char.html"> <link rel="next" href="Condition.html"> <link rel="Up" href="index.html"> <link title="Index of types" rel=Appendix href="index_types.html"> <link title="Index of exceptions" rel=Appendix href="index_exceptions.html"> <link title="Index of values" rel=Appendix href="index_values.html"> <link title="Index of modules" rel=Appendix href="index_modules.html"> <link title="Index of module types" rel=Appendix href="index_module_types.html"> <link title="Arg" rel="Chapter" href="Arg.html"> <link title="Arith_status" rel="Chapter" href="Arith_status.html"> <link title="Array" rel="Chapter" href="Array.html"> <link title="ArrayLabels" rel="Chapter" href="ArrayLabels.html"> <link title="Big_int" rel="Chapter" href="Big_int.html"> <link title="Bigarray" rel="Chapter" href="Bigarray.html"> <link title="Buffer" rel="Chapter" href="Buffer.html"> <link title="Callback" rel="Chapter" href="Callback.html"> <link title="CamlinternalLazy" rel="Chapter" href="CamlinternalLazy.html"> <link title="CamlinternalMod" rel="Chapter" href="CamlinternalMod.html"> <link title="CamlinternalOO" rel="Chapter" href="CamlinternalOO.html"> <link title="Char" rel="Chapter" href="Char.html"> <link title="Complex" rel="Chapter" href="Complex.html"> <link title="Condition" rel="Chapter" href="Condition.html"> <link title="Dbm" rel="Chapter" href="Dbm.html"> <link title="Digest" rel="Chapter" href="Digest.html"> <link title="Dynlink" rel="Chapter" href="Dynlink.html"> <link title="Event" rel="Chapter" href="Event.html"> <link title="Filename" rel="Chapter" href="Filename.html"> <link title="Format" rel="Chapter" href="Format.html"> <link title="Gc" rel="Chapter" href="Gc.html"> <link title="Genlex" rel="Chapter" href="Genlex.html"> <link title="Graphics" rel="Chapter" href="Graphics.html"> <link title="GraphicsX11" rel="Chapter" href="GraphicsX11.html"> <link title="Hashtbl" rel="Chapter" href="Hashtbl.html"> <link title="Int32" rel="Chapter" href="Int32.html"> <link title="Int64" rel="Chapter" href="Int64.html"> <link title="Lazy" rel="Chapter" href="Lazy.html"> <link title="Lexing" rel="Chapter" href="Lexing.html"> <link title="List" rel="Chapter" href="List.html"> <link title="ListLabels" rel="Chapter" href="ListLabels.html"> <link title="Map" rel="Chapter" href="Map.html"> <link title="Marshal" rel="Chapter" href="Marshal.html"> <link title="MoreLabels" rel="Chapter" href="MoreLabels.html"> <link title="Mutex" rel="Chapter" href="Mutex.html"> <link title="Nativeint" rel="Chapter" href="Nativeint.html"> <link title="Num" rel="Chapter" href="Num.html"> <link title="Obj" rel="Chapter" href="Obj.html"> <link title="Oo" rel="Chapter" href="Oo.html"> <link title="Parsing" rel="Chapter" href="Parsing.html"> <link title="Pervasives" rel="Chapter" href="Pervasives.html"> <link title="Printexc" rel="Chapter" href="Printexc.html"> <link title="Printf" rel="Chapter" href="Printf.html"> <link title="Queue" rel="Chapter" href="Queue.html"> <link title="Random" rel="Chapter" href="Random.html"> <link title="Scanf" rel="Chapter" href="Scanf.html"> <link title="Set" rel="Chapter" href="Set.html"> <link title="Sort" rel="Chapter" href="Sort.html"> <link title="Stack" rel="Chapter" href="Stack.html"> <link title="StdLabels" rel="Chapter" href="StdLabels.html"> <link title="Str" rel="Chapter" href="Str.html"> <link title="Stream" rel="Chapter" href="Stream.html"> <link title="String" rel="Chapter" href="String.html"> <link title="StringLabels" rel="Chapter" href="StringLabels.html"> <link title="Sys" rel="Chapter" href="Sys.html"> <link title="Thread" rel="Chapter" href="Thread.html"> <link title="ThreadUnix" rel="Chapter" href="ThreadUnix.html"> <link title="Tk" rel="Chapter" href="Tk.html"> <link title="Unix" rel="Chapter" href="Unix.html"> <link title="UnixLabels" rel="Chapter" href="UnixLabels.html"> <link title="Weak" rel="Chapter" href="Weak.html"><title>Complex</title> </head> <body> <div class="navbar"><a href="Char.html">Previous</a> <a href="index.html">Up</a> <a href="Condition.html">Next</a> </div> <center><h1>Module <a href="type_Complex.html">Complex</a></h1></center> <br> <pre><span class="keyword">module</span> Complex: <code class="code"><span class="keyword">sig</span></code> <a href="Complex.html">..</a> <code class="code"><span class="keyword">end</span></code></pre>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> <hr width="100%"> <br><code><span id="TYPEt"><span class="keyword">type</span> <code class="type"></code>t</span> = {</code><table class="typetable"> <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> <pre><span id="VALzero"><span class="keyword">val</span> zero</span> : <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 id="VALone"><span class="keyword">val</span> one</span> : <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 id="VALi"><span class="keyword">val</span> i</span> : <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 id="VALneg"><span class="keyword">val</span> neg</span> : <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 id="VALconj"><span class="keyword">val</span> conj</span> : <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 id="VALadd"><span class="keyword">val</span> add</span> : <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 id="VALsub"><span class="keyword">val</span> sub</span> : <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 id="VALmul"><span class="keyword">val</span> mul</span> : <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 id="VALinv"><span class="keyword">val</span> inv</span> : <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 id="VALdiv"><span class="keyword">val</span> div</span> : <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 id="VALsqrt"><span class="keyword">val</span> sqrt</span> : <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 id="VALnorm2"><span class="keyword">val</span> norm2</span> : <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 id="VALnorm"><span class="keyword">val</span> norm</span> : <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 id="VALarg"><span class="keyword">val</span> arg</span> : <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 id="VALpolar"><span class="keyword">val</span> polar</span> : <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 id="VALexp"><span class="keyword">val</span> exp</span> : <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 id="VALlog"><span class="keyword">val</span> log</span> : <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 id="VALpow"><span class="keyword">val</span> pow</span> : <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> </body></html>