<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<!--Rendered using the Haskell Html Library v0.2-->
<HTML
><HEAD
><META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=UTF-8"
><TITLE
>Data.Complex</TITLE
><LINK HREF="haddock.css" REL="stylesheet" TYPE="text/css"
><SCRIPT SRC="haddock-util.js" TYPE="text/javascript"
></SCRIPT
><SCRIPT TYPE="text/javascript"
>window.onload = function () {setSynopsis("mini_Data-Complex.html")};</SCRIPT
></HEAD
><BODY
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="topbar"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD
><IMG SRC="haskell_icon.gif" WIDTH="16" HEIGHT="16" ALT=" "
></TD
><TD CLASS="title"
>base-4.1.0.0: Basic libraries</TD
><TD CLASS="topbut"
><A HREF="index.html"
>Contents</A
></TD
><TD CLASS="topbut"
><A HREF="doc-index.html"
>Index</A
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="modulebar"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD
><FONT SIZE="6"
>Data.Complex</FONT
></TD
><TD ALIGN="right"
><TABLE CLASS="narrow" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="infohead"
>Portability</TD
><TD CLASS="infoval"
>portable</TD
></TR
><TR
><TD CLASS="infohead"
>Stability</TD
><TD CLASS="infoval"
>provisional</TD
></TR
><TR
><TD CLASS="infohead"
>Maintainer</TD
><TD CLASS="infoval"
>libraries@haskell.org</TD
></TR
></TABLE
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="section4"
><B
>Contents</B
></TD
></TR
><TR
><TD
><DL
><DT
><A HREF="#1"
>Rectangular form
</A
></DT
><DT
><A HREF="#2"
>Polar form
</A
></DT
><DT
><A HREF="#3"
>Conjugate
</A
></DT
></DL
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
>Description</TD
></TR
><TR
><TD CLASS="doc"
>Complex numbers.
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
>Synopsis</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>data</SPAN
> <A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => <A HREF="#t%3AComplex"
>Complex</A
> a = !a <A HREF="#v%3A%3A%2B"
>:+</A
> !a</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3ArealPart"
>realPart</A
> :: <A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => <A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a -> a</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AimagPart"
>imagPart</A
> :: <A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => <A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a -> a</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AmkPolar"
>mkPolar</A
> :: <A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => a -> a -> <A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3Acis"
>cis</A
> :: <A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => a -> <A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3Apolar"
>polar</A
> :: <A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => <A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a -> (a, a)</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3Amagnitude"
>magnitude</A
> :: <A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => <A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a -> a</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3Aphase"
>phase</A
> :: <A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => <A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a -> a</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3Aconjugate"
>conjugate</A
> :: <A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => <A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a -> <A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
><A NAME="1"
><A NAME="1"
>Rectangular form
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>data</SPAN
> <A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => <A NAME="t:Complex"
><A NAME="t%3AComplex"
></A
></A
><B
>Complex</B
> a </TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
><P
>Complex numbers are an algebraic type.
</P
><P
>For a complex number <TT
>z</TT
>, <TT
><TT
><A HREF="Prelude.html#v%3Aabs"
>abs</A
></TT
> z</TT
> is a number with the magnitude of <TT
>z</TT
>,
but oriented in the positive real direction, whereas <TT
><TT
><A HREF="Prelude.html#v%3Asignum"
>signum</A
></TT
> z</TT
>
has the phase of <TT
>z</TT
>, but unit magnitude.
</P
></TD
></TR
><TR
><TD CLASS="section4"
>Constructors</TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="arg"
>!a <A NAME="v::+"
><A NAME="v%3A%3A%2B"
></A
></A
><B
>:+</B
> !a</TD
><TD CLASS="rdoc"
>forms a complex number from its real and imaginary
rectangular components.
</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="section4"
><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Complex')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:Complex" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Data-Typeable.html#t%3ATypeable1"
>Typeable1</A
> <A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => <A HREF="Data-Eq.html#t%3AEq"
>Eq</A
> (<A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => <A HREF="Prelude.html#t%3AFloating"
>Floating</A
> (<A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => <A HREF="Prelude.html#t%3AFractional"
>Fractional</A
> (<A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
>(<A HREF="Data-Data.html#t%3AData"
>Data</A
> a, <A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a) => <A HREF="Data-Data.html#t%3AData"
>Data</A
> (<A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => <A HREF="Prelude.html#t%3ANum"
>Num</A
> (<A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
>(<A HREF="Text-Read.html#t%3ARead"
>Read</A
> a, <A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a) => <A HREF="Text-Read.html#t%3ARead"
>Read</A
> (<A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => <A HREF="Text-Show.html#t%3AShow"
>Show</A
> (<A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a)</TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:realPart"
><A NAME="v%3ArealPart"
></A
></A
><B
>realPart</B
> :: <A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => <A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a -> a</TD
></TR
><TR
><TD CLASS="doc"
>Extracts the real part of a complex number.
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:imagPart"
><A NAME="v%3AimagPart"
></A
></A
><B
>imagPart</B
> :: <A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => <A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a -> a</TD
></TR
><TR
><TD CLASS="doc"
>Extracts the imaginary part of a complex number.
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
><A NAME="2"
><A NAME="2"
>Polar form
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:mkPolar"
><A NAME="v%3AmkPolar"
></A
></A
><B
>mkPolar</B
> :: <A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => a -> a -> <A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a</TD
></TR
><TR
><TD CLASS="doc"
>Form a complex number from polar components of magnitude and phase.
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:cis"
><A NAME="v%3Acis"
></A
></A
><B
>cis</B
> :: <A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => a -> <A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a</TD
></TR
><TR
><TD CLASS="doc"
><TT
><TT
><A HREF="Data-Complex.html#v%3Acis"
>cis</A
></TT
> t</TT
> is a complex value with magnitude <TT
>1</TT
>
and phase <TT
>t</TT
> (modulo <TT
>2*<TT
><A HREF="Prelude.html#v%3Api"
>pi</A
></TT
></TT
>).
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:polar"
><A NAME="v%3Apolar"
></A
></A
><B
>polar</B
> :: <A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => <A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a -> (a, a)</TD
></TR
><TR
><TD CLASS="doc"
>The function <TT
><A HREF="Data-Complex.html#v%3Apolar"
>polar</A
></TT
> takes a complex number and
returns a (magnitude, phase) pair in canonical form:
the magnitude is nonnegative, and the phase in the range <TT
>(-<TT
><A HREF="Prelude.html#v%3Api"
>pi</A
></TT
>, <TT
><A HREF="Prelude.html#v%3Api"
>pi</A
></TT
>]</TT
>;
if the magnitude is zero, then so is the phase.
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:magnitude"
><A NAME="v%3Amagnitude"
></A
></A
><B
>magnitude</B
> :: <A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => <A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a -> a</TD
></TR
><TR
><TD CLASS="doc"
>The nonnegative magnitude of a complex number.
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:phase"
><A NAME="v%3Aphase"
></A
></A
><B
>phase</B
> :: <A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => <A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a -> a</TD
></TR
><TR
><TD CLASS="doc"
>The phase of a complex number, in the range <TT
>(-<TT
><A HREF="Prelude.html#v%3Api"
>pi</A
></TT
>, <TT
><A HREF="Prelude.html#v%3Api"
>pi</A
></TT
>]</TT
>.
If the magnitude is zero, then so is the phase.
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
><A NAME="3"
><A NAME="3"
>Conjugate
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:conjugate"
><A NAME="v%3Aconjugate"
></A
></A
><B
>conjugate</B
> :: <A HREF="Prelude.html#t%3ARealFloat"
>RealFloat</A
> a => <A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a -> <A HREF="Data-Complex.html#t%3AComplex"
>Complex</A
> a</TD
></TR
><TR
><TD CLASS="doc"
>The conjugate of a complex number.
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="botbar"
>Produced by <A HREF="http://www.haskell.org/haddock/"
>Haddock</A
> version 2.4.2</TD
></TR
></TABLE
></BODY
></HTML
>
distrib
>
Mandriva
>
2010.0
>
i586
>
media
>
contrib-release
>
by-pkgid
>
70ec89744a04da80369b4702b2c37256
>
files
>
209
