/usr/share/gap/grp/simple.gd is in gap-libs 4r7p5-2.
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##
#W simple.gd GAP Library Alexander Hulpke
##
##
#Y Copyright (C) 2011 The GAP Group
##
## This file contains basic constructions for simple groups of bounded size,
## if necessary by calling the `atlasrep' package.
##
#############################################################################
##
#F SimpleGroup( <id> [,<param1>[,<param2>[] )
##
## <#GAPDoc Label="SimpleGroup">
## <ManSection>
## <Func Name="SimpleGroup" Arg='id [,param]'/>
##
## <Description>
## This function will construct <B>an</B> instance of the specified simple group.
## Groups are specified via their name in ATLAS style notation, with parameters added
## if necessary. The intelligence applied to parsing the name is limited, and at the
## moment no proper extensions can be constructed.
## For groups who do not have a permutation representation of small degree the
## ATLASREP package might need to be installed to construct theses groups.
## <Example><![CDATA[
## gap> g:=SimpleGroup("M(23)");
## M23
## gap> Size(g);
## 10200960
## gap> g:=SimpleGroup("PSL",3,5);
## PSL(3,5)
## gap> Size(g);
## 372000
## gap> g:=SimpleGroup("PSp6",2);
## PSp(6,2)
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareGlobalFunction("SimpleGroup");
#############################################################################
##
#F EpimorphismFromClassical( <G> )
##
## <#GAPDoc Label="EpimorphismFromClassical">
## <ManSection>
## <Func Name="EpimorphismFromClassical" Arg='G'/>
##
## <Description>
## For an (almost) simple group this homomorphsim will try to construct an
## epimorphism from a classical group onto it (or return fail if it does
## not work or is not yet implemented).
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareGlobalFunction("EpimorphismFromClassical");
#############################################################################
##
#F SimpleGroupsIterator( [<start>,<end>] )
##
## <#GAPDoc Label="SimpleGroupsIterator">
## <ManSection>
## <Func Name="SimpleGroupsIterator" Arg='[start[,end]]'/>
##
## <Description>
## This function returns an iterator that will run over all simple groups, starting
## at order <A>start</A> if specified, up to order <M>10^{18}</M> (or -- if specified
## -- order <A>end</A>). If the option <A>NOPSL2</A> is given, groups of type
## <M>PSL_2(q)</M> are omitted.
## <Example><![CDATA[
## gap> it:=SimpleGroupsIterator(20000);
## <iterator>
## gap> List([1..8],x->NextIterator(it));
## [ A8, PSL(3,4), PSL(2,37), PSp(4,3), Sz(8), PSL(2,32), PSL(2,41),
## PSL(2,43) ]
## gap> it:=SimpleGroupsIterator(1,2000);;
## gap> l:=[];;for i in it do Add(l,i);od;l;
## [ A5, PSL(2,7), A6, PSL(2,8), PSL(2,11), PSL(2,13) ]
## gap> it:=SimpleGroupsIterator(20000,100000:NOPSL2);;
## gap> l:=[];;for i in it do Add(l,i);od;l;
## [ A8, PSL(3,4), PSp(4,3), Sz(8), PSU(3,4), M12 ]
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
DeclareGlobalFunction("SimpleGroupsIterator");
#############################################################################
##
#F ClassicalIsomorphismTypeFiniteSimpleGroup(<G>] )
##
## <#GAPDoc Label="ClassicalIsomorphismTypeFiniteSimpleGroup">
## <ManSection>
## <Func Name="ClassicalIsomorphismTypeFiniteSimpleGroup" Arg='G'/>
## This function returns a result equivalent to (and based on)
## <Ref Func="IsomorphismTypeInfoFiniteSimpleGroup"/>, but returns a
## classically names series (consistent with
## <Ref Func="SimpleGroup"/>) and the parameter always in a list. This makes it
## easier to parse the result.
## <Description>
## <Example><![CDATA[
## gap> ClassicalIsomorphismTypeFiniteSimpleGroup(SimpleGroup("O+",8,2));
## rec( parameter := [ 8, 2 ], series := "O+" )
## gap> IsomorphismTypeInfoFiniteSimpleGroup(SimpleGroup("O+",8,2));
## rec( name := "D(4,2) = O+(8,2)", parameter := [ 4, 2 ], series := "D" )
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
DeclareGlobalFunction("ClassicalIsomorphismTypeFiniteSimpleGroup");
DeclareAttribute("DataAboutSimpleGroup",IsGroup);
#############################################################################
##
#F SufficientlySmallDegreeSimpleGroupOrder(n)
##
## <#GAPDoc Label="SufficientlySmallDegreeSimpleGroupOrder">
## <ManSection>
## <Func Name="SufficientlySmallDegreeSimpleGroupOrder" Arg='n'/>
## For an order <M>n</M> this function returns a heuristic bound for a
## small permutation degree of a simple group of that exact order.
## This function
## can be used to decide whether it is woth to try the `SmallerDegree'
## reduction.
## <#/GAPDoc>
DeclareGlobalFunction("SufficientlySmallDegreeSimpleGroupOrder");
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