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#
# corefreesub: A GAP Package for calculating the core-free subgroups and their faithful transitive permutation representations
#
# Drawing of FTPR and Dot Files
#
#
##########################################
InstallMethod( DotFTPRGraph,[IsPermGroup,IsList],
function(G, genList)
local edge_dic, gen, gen_index, already_moved, num, dot_string, gen_edge, edge, isdigraph;
if not IsTransitive(G) then
return Error("The group given should be transitive");
fi;
if Size(genList) <> Size(GeneratorsOfGroup(G)) then
return Error("The size of the generators name list is different from the size of the generators of the group given");
fi;
edge_dic := [];
gen_index := 0;
for gen in GeneratorsOfGroup(G) do
already_moved := [];
Append(edge_dic, [[genList[gen_index+1],[]]]);
for num in MovedPoints(gen) do
if num in already_moved then continue;
elif OnPoints(OnPoints(num,gen),gen) = num then
Add(edge_dic[gen_index+1][2],[num,OnPoints(num,gen),false]);
Append(already_moved,[num,OnPoints(num,gen)]);
else
Add(edge_dic[gen_index+1][2],[num,OnPoints(num,gen),true]);
Append(already_moved,[num]);
fi;
od;
gen_index := gen_index + 1;
od;
dot_string := "digraph {\n";
for gen_edge in edge_dic do
for edge in gen_edge[2] do
if edge[3] then
dot_string:=Concatenation(dot_string, String(edge[1]) , " -> ", String(edge[2]), " [label = ", gen_edge[1],"];\n ");
else
dot_string:=Concatenation(dot_string, String(edge[1]) , " -> ", String(edge[2]), " [label = ", gen_edge[1],",dir=none];\n ");
fi;
od;
od;
dot_string:=Concatenation(dot_string, "}\n");
return dot_string;
end );
InstallOtherMethod( DotFTPRGraph, [IsPermGroup],
function(G)
return DotFTPRGraph(G,List([1 .. Size(GeneratorsOfGroup(G))], i -> Concatenation("r",String(i))));
end );
InstallOtherMethod( DotFTPRGraph, [IsGroup,IsGroup, IsList],
function( G, H, genList )
if IsSubgroup(G,H) and IsCoreFree(G,H) then
return DotFTPRGraph(Image(FactorCosetAction(G,H)), genList);
else
Info(InfoDrawFTPR,1,"The second group should be a subgroup of the first or it is not core-free");
return fail;
fi;
end);
InstallOtherMethod( DotFTPRGraph, [IsGroup,IsGroup],
function( G, H )
return DotFTPRGraph(G, H,List([1 .. Size(GeneratorsOfGroup(G))], i -> Concatenation("r",String(i))));
end);
InstallOtherMethod( DotFTPRGraph, [IsGeneralMapping, IsList],
function(FTPR_mapping, genList)
if IsGroupHomomorphism(FTPR_mapping) and IsBijective(FTPR_mapping) and IsPermGroup(Image(FTPR_mapping)) and IsTransitive(Image(FTPR_mapping)) then
return DotFTPRGraph(Image(FTPR_mapping), genList);
else
Info(InfoDrawFTPR,1,"The mapping provided isn't of a faithful transitive permutation representation");
return fail;
fi;
end );
InstallOtherMethod( DotFTPRGraph, [IsGeneralMapping],
function(FTPR_mapping)
return DotFTPRGraph(FTPR_mapping, List([1 .. Size(GeneratorsOfGroup(Image(FTPR_mapping)))], i -> Concatenation("r",String(i))));
end );
# The aim of the following functions is to "splash" an image or TeX directly from the dot code.
# To this effect, it adds a preamble and makes a call to the Viz CF_Splash function.
# To avoid forcing the user to install the Viz package (under development), a modified copy of the Viz Splash function is included in the file "CF_splashfromViz.g" of this package
InstallGlobalFunction( DrawFTPRGraph,
function( arg )
local opt;
opt := First(arg, k -> IsRecord(k));
if opt <> fail and IsBound(opt.viewtexfile) and opt.viewtexfile = true then return CF_Splash(arg);fi;
CF_Splash(arg);
end );
InstallGlobalFunction( TeXFTPRGraph,
function( arg )
local opt, pos;
opt := First(arg, k -> IsRecord(k));
if opt = fail then
opt := rec();
opt.viewtexfile := true;
opt.tikz := true;
Append(arg,[opt]);
else
pos := Position(arg,opt);
opt.viewtexfile := true;
opt.tikz := true;
arg[pos] := opt;
fi;
return CF_Splash(arg);
end );
InstallGlobalFunction( DrawTeXFTPRGraph,
function( arg )
local opt, pos;
opt := First(arg, k -> IsRecord(k));
if opt = fail then
opt := rec();
opt.tikz := true;
Append(arg,[opt]);
else
pos := Position(arg,opt);
opt.tikz := true;
arg[pos] := opt;
fi;
CF_Splash(arg);
end );
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