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#############################################################################
##
#W trans.gd GAP transitive groups library Alexander Hulpke
##
##
#Y Copyright (C) 2001, Alexander Hulpke, Colorado State University
#Y (C) 1998 School Math and Comp. Sci., University of St Andrews, Scotland
##
## This file contains the declarations for the transitive groups library
##
# ensure that the dummy binds from the library are killed
MakeReadWriteGlobal("TransitiveGroupsAvailable");
Unbind(TransitiveGroupsAvailable);
MakeReadWriteGlobal("NrTransitiveGroups");
Unbind(NrTransitiveGroups);
MakeReadWriteGlobal("TransitiveGroup");
Unbind(TransitiveGroup);
MakeReadWriteGlobal("TRANSProperties");
Unbind(TRANSProperties);
#############################################################################
##
#F TransitiveGroup(<deg>,<nr>)
##
## <#GAPDoc Label="TransitiveGroup">
## <ManSection>
## <Func Name="TransitiveGroup" Arg='deg,nr'/>
##
## <Description>
## returns the <A>nr</A>-th transitive group of degree <A>deg</A>. Both <A>deg</A> and
## <A>nr</A> must be positive integers. The transitive groups of equal degree
## are sorted with respect to their size, so for example
## <C>TransitiveGroup( <A>deg</A>, 1 )</C> is a transitive group of degree and
## size <A>deg</A>, e.g, the cyclic group of size <A>deg</A>, if <A>deg</A> is a
## prime.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareGlobalFunction("TransitiveGroup");
DeclareGlobalFunction("TransitiveGroupsAvailable");
#############################################################################
##
#F NrTransitiveGroups(<deg>)
##
## <#GAPDoc Label="NrTransitiveGroups">
## <ManSection>
## <Func Name="NrTransitiveGroups" Arg='deg'/>
##
## <Description>
## returns the number of transitive groups of degree <A>deg</A> stored in
## the library of transitive groups.
## The function returns <K>fail</K> if <A>deg</A> is
## beyond the range of the library.
## <P/>
## <Example><![CDATA[
## gap> TransitiveGroup(10,22);
## S(5)[x]2
## gap> l:=AllTransitiveGroups(NrMovedPoints,12,Size,1440,IsSolvable,false);
## [ S(6)[x]2, M_10.2(12)=A_6.E_4(12)=[S_6[1/720]{M_10}S_6]2 ]
## gap> List(l,IsSolvable);
## [ false, false ]
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareGlobalFunction("NrTransitiveGroups");
#############################################################################
##
#F MinialTransitiveIndices(<deg>)
##
DeclareGlobalFunction("MinimalTransitiveIndices");
DeclareGlobalVariable( "TRANSCOMBCACHE", "combinations cache" );
DeclareGlobalVariable( "TRANSARRCACHE", "arrangements cache" );
if IsHPCGAP then
BindGlobal("TRANSREGION", NewLibraryRegion("transitive groups region"));
else
BindGlobal("TRANSREGION", fail);
fi;
DeclareGlobalFunction("SelectTransitiveGroups");
DeclareGlobalFunction("AllTransitiveGroups");
DeclareGlobalFunction("AllLibraryTransitiveGroups");
DeclareGlobalFunction("OneTransitiveGroup");
#############################################################################
##
#E
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