Sophie: ghc-0:6.10.4-1mdv2010.0 i586

ghc-6.10.4-1mdv2010.0.i586.rpm

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>Data.Ratio</TITLE
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>base-4.1.0.0: Basic libraries</TD
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><A HREF="index.html"
>Contents</A
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>Index</A
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>Data.Ratio</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"
>stable</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 CLASS="section1"
>Description</TD
></TR
><TR
><TD CLASS="doc"
>Standard functions on rational 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%3AIntegral"
>Integral</A
> a =&gt; <A HREF="#t%3ARatio"
>Ratio</A
> a</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>type</SPAN
> <A HREF="#t%3ARational"
>Rational</A
> = <A HREF="Data-Ratio.html#t%3ARatio"
>Ratio</A
> <A HREF="../integer/GHC-Integer.html#t%3AInteger"
>Integer</A
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3A%25"
>(%)</A
> :: <A HREF="Prelude.html#t%3AIntegral"
>Integral</A
> a =&gt; a -&gt; a -&gt; <A HREF="Data-Ratio.html#t%3ARatio"
>Ratio</A
> a</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3Anumerator"
>numerator</A
> :: <A HREF="Prelude.html#t%3AIntegral"
>Integral</A
> a =&gt; <A HREF="Data-Ratio.html#t%3ARatio"
>Ratio</A
> a -&gt; a</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3Adenominator"
>denominator</A
> :: <A HREF="Prelude.html#t%3AIntegral"
>Integral</A
> a =&gt; <A HREF="Data-Ratio.html#t%3ARatio"
>Ratio</A
> a -&gt; a</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AapproxRational"
>approxRational</A
> :: <A HREF="Prelude.html#t%3ARealFrac"
>RealFrac</A
> a =&gt; a -&gt; a -&gt; <A HREF="Data-Ratio.html#t%3ARational"
>Rational</A
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
>Documentation</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>data</SPAN
> <A HREF="Prelude.html#t%3AIntegral"
>Integral</A
> a =&gt; <A NAME="t:Ratio"
><A NAME="t%3ARatio"
></A
></A
><B
>Ratio</B
> a </TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
>Rational numbers, with numerator and denominator of some <TT
><A HREF="Prelude.html#t%3AIntegral"
>Integral</A
></TT
> type.
</TD
></TR
><TR
><TD CLASS="section4"
><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Ratio')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:Ratio" 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-Ratio.html#t%3ARatio"
>Ratio</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Prelude.html#t%3AIntegral"
>Integral</A
> a =&gt; <A HREF="Prelude.html#t%3AEnum"
>Enum</A
> (<A HREF="Data-Ratio.html#t%3ARatio"
>Ratio</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Prelude.html#t%3AIntegral"
>Integral</A
> a =&gt; <A HREF="Data-Eq.html#t%3AEq"
>Eq</A
> (<A HREF="Data-Ratio.html#t%3ARatio"
>Ratio</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Prelude.html#t%3AIntegral"
>Integral</A
> a =&gt; <A HREF="Prelude.html#t%3AFractional"
>Fractional</A
> (<A HREF="Data-Ratio.html#t%3ARatio"
>Ratio</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
>(<A HREF="Data-Data.html#t%3AData"
>Data</A
> a, <A HREF="Prelude.html#t%3AIntegral"
>Integral</A
> a) =&gt; <A HREF="Data-Data.html#t%3AData"
>Data</A
> (<A HREF="Data-Ratio.html#t%3ARatio"
>Ratio</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Prelude.html#t%3AIntegral"
>Integral</A
> a =&gt; <A HREF="Prelude.html#t%3ANum"
>Num</A
> (<A HREF="Data-Ratio.html#t%3ARatio"
>Ratio</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Prelude.html#t%3AIntegral"
>Integral</A
> a =&gt; <A HREF="Data-Ord.html#t%3AOrd"
>Ord</A
> (<A HREF="Data-Ratio.html#t%3ARatio"
>Ratio</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
>(<A HREF="Prelude.html#t%3AIntegral"
>Integral</A
> a, <A HREF="Text-Read.html#t%3ARead"
>Read</A
> a) =&gt; <A HREF="Text-Read.html#t%3ARead"
>Read</A
> (<A HREF="Data-Ratio.html#t%3ARatio"
>Ratio</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Prelude.html#t%3AIntegral"
>Integral</A
> a =&gt; <A HREF="Prelude.html#t%3AReal"
>Real</A
> (<A HREF="Data-Ratio.html#t%3ARatio"
>Ratio</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Prelude.html#t%3AIntegral"
>Integral</A
> a =&gt; <A HREF="Prelude.html#t%3ARealFrac"
>RealFrac</A
> (<A HREF="Data-Ratio.html#t%3ARatio"
>Ratio</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Prelude.html#t%3AIntegral"
>Integral</A
> a =&gt; <A HREF="Text-Show.html#t%3AShow"
>Show</A
> (<A HREF="Data-Ratio.html#t%3ARatio"
>Ratio</A
> a)</TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>type</SPAN
> <A NAME="t:Rational"
><A NAME="t%3ARational"
></A
></A
><B
>Rational</B
> = <A HREF="Data-Ratio.html#t%3ARatio"
>Ratio</A
> <A HREF="../integer/GHC-Integer.html#t%3AInteger"
>Integer</A
></TD
></TR
><TR
><TD CLASS="doc"
>Arbitrary-precision rational numbers, represented as a ratio of
 two <TT
><A HREF="../integer/GHC-Integer.html#t%3AInteger"
>Integer</A
></TT
> values.  A rational number may be constructed using
 the <TT
><A HREF="Data-Ratio.html#v%3A%25"
>%</A
></TT
> operator.
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:%"
><A NAME="v%3A%25"
></A
></A
><B
>(%)</B
> :: <A HREF="Prelude.html#t%3AIntegral"
>Integral</A
> a =&gt; a -&gt; a -&gt; <A HREF="Data-Ratio.html#t%3ARatio"
>Ratio</A
> a</TD
></TR
><TR
><TD CLASS="doc"
>Forms the ratio of two integral numbers.
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:numerator"
><A NAME="v%3Anumerator"
></A
></A
><B
>numerator</B
> :: <A HREF="Prelude.html#t%3AIntegral"
>Integral</A
> a =&gt; <A HREF="Data-Ratio.html#t%3ARatio"
>Ratio</A
> a -&gt; a</TD
></TR
><TR
><TD CLASS="doc"
>Extract the numerator of the ratio in reduced form:
 the numerator and denominator have no common factor and the denominator
 is positive.
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:denominator"
><A NAME="v%3Adenominator"
></A
></A
><B
>denominator</B
> :: <A HREF="Prelude.html#t%3AIntegral"
>Integral</A
> a =&gt; <A HREF="Data-Ratio.html#t%3ARatio"
>Ratio</A
> a -&gt; a</TD
></TR
><TR
><TD CLASS="doc"
>Extract the denominator of the ratio in reduced form:
 the numerator and denominator have no common factor and the denominator
 is positive.
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:approxRational"
><A NAME="v%3AapproxRational"
></A
></A
><B
>approxRational</B
> :: <A HREF="Prelude.html#t%3ARealFrac"
>RealFrac</A
> a =&gt; a -&gt; a -&gt; <A HREF="Data-Ratio.html#t%3ARational"
>Rational</A
></TD
></TR
><TR
><TD CLASS="doc"
><P
><TT
><A HREF="Data-Ratio.html#v%3AapproxRational"
>approxRational</A
></TT
>, applied to two real fractional numbers <TT
>x</TT
> and <TT
>epsilon</TT
>,
 returns the simplest rational number within <TT
>epsilon</TT
> of <TT
>x</TT
>.
 A rational number <TT
>y</TT
> is said to be <EM
>simpler</EM
> than another <TT
>y'</TT
> if
</P
><UL
><LI
> <TT
><TT
><A HREF="Prelude.html#v%3Aabs"
>abs</A
></TT
> (<TT
><A HREF="Data-Ratio.html#v%3Anumerator"
>numerator</A
></TT
> y) &lt;= <TT
><A HREF="Prelude.html#v%3Aabs"
>abs</A
></TT
> (<TT
><A HREF="Data-Ratio.html#v%3Anumerator"
>numerator</A
></TT
> y')</TT
>, and
</LI
><LI
> <TT
><TT
><A HREF="Data-Ratio.html#v%3Adenominator"
>denominator</A
></TT
> y &lt;= <TT
><A HREF="Data-Ratio.html#v%3Adenominator"
>denominator</A
></TT
> y'</TT
>.
</LI
></UL
><P
>Any real interval contains a unique simplest rational;
 in particular, note that <TT
>0/1</TT
> is the simplest rational of all.
</P
></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
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