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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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<Chapter Label="Intro">

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<Heading>Introduction</Heading>    

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<Section Label="IntroAims">

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<Heading>General aims of &Congruence; package</Heading>

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<Index Key="IsCongruenceSubgroup"><C>IsCongruenceSubgroup</C></Index>

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The &GAP; package &Congruence; provides functions to construct several

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types of canonical congruence subgroups in <M>SL_2(&ZZ;)</M>, and also 

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intersections of a finite number of such subgroups. 

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<P/>

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Furthermore, it implements the algorithm for generating Farey symbols for

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congruence subgroups and using them to produce a system of independent

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generators for these subgroups. 

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<P/>

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Using the package, one can also determine indices of congruence subgroups and

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their intersections in <M>SL_2(&ZZ;)</M> and in other congruence subgroups,

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generate their random elements and check element memberships. Success of other

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group theoretical constructions mostly depends on whether they could be

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expressed in terms of group generators or not.

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<P/>

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For the theoretical backround, we refer to <Cite Key="LLT-Hecke" />,

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<Cite Key="LLT-Algorithm" />, <Cite Key="CLT" /> and <Cite Key="Kulkarni" />.

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</Section>

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<!-- ********************************************************* -->

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<Section Label="IntroInstall">

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<Heading>Installation and system requirements</Heading>

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&Congruence; is distributed in standard formats (<File>tar.gz</File>, 

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<File>tar.bz2</File>, <File>-win.zip</File>) and can be obtained from 

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<URL>http://www.cs.st-andrews.ac.uk/~alexk/congruence/</URL>. 

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<P/>

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&Congruence; does not  use  external  binaries and,  therefore,  works  without 

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restrictions on the operating system.  

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It requires at least version  &GAP;&nbsp;4.5, and no compatibility with 

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previous releases of &GAP;&nbsp;4 is guaranteed.

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<P/>

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Installation of the package is standard and follows the guidelines from the 

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&GAP; manual (see <Ref Sect="Installing a GAP Package" BookName="ref"/>.  

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After the package is installed, you can start &GAP; and load 

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the &Congruence; package using the command:

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<Log>

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<![CDATA[

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gap> LoadPackage("congruence");

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]]>

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</Log>

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</Section>

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</Chapter>

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