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#############################################################################
##
#W matgrp.gi Bettina Eick
##
## This file contains the header functions to handle the 3- and
## 4-dimensional almost crystallographic integral matrix groups.
##
#############################################################################
##
#F AlmostCrystallographicDim3( type, param )
##
InstallGlobalFunction( AlmostCrystallographicDim3,
function( type, param )
local g, G, info;
# type is integer or string
if IsString( type ) then
g := Int( type );
elif IsInt( type ) then
g := type;
else
g := false;
fi;
if not g in [1..17] then
Error("type does not define a valid ac-group type");
fi;
# check parameters
if IsBool( param ) then
param := List( [1..ACDim3Param[g]], x -> Random(Integers) );
if param[1] = 0 then param[1] := Random(Integers)^2 + 1; fi;
elif IsInt( param ) then
param := List( [1..ACDim3Param[g]], x -> param );
elif Length( param ) <> ACDim3Param[g] then
Error("parameter should be a list of length ", ACDim3Param[g] );
fi;
# get group
if Length( param ) = 4 then
G := ACDim3Funcs[g](param[1], param[2], param[3], param[4]);
elif Length(param) = 2 then
G := ACDim3Funcs[g](param[1], param[2] );
elif Length(param) = 1 then
G := ACDim3Funcs[g](param[1]);
fi;
# set some information
info := rec( dim := 3, type := g, param := param );
SetAlmostCrystallographicInfo( G, info );
SetIsAlmostCrystallographic( G, true );
SetDimensionOfMatrixGroup( G, 4 );
SetFieldOfMatrixGroup( G, Rationals );
SetSize( G, infinity );
return G;
end );
#############################################################################
##
#F AlmostCrystallographicDim4( type, param )
##
InstallGlobalFunction( AlmostCrystallographicDim4,
function( type, param )
local g, G, info;
# type is integer or string
if IsString( type ) then
g := Position( ACDim4Types, type );
elif IsInt( type ) then
g := type;
else
g := false;
fi;
if not g in [1..95] then
Error("type does not define a valid ac-group type");
fi;
# check parameters
if IsBool( param ) then
param := List( [1..ACDim4Param[g]], x -> Random(Integers) );
if param[1] = 0 then param[1] := Random(Integers)^2 + 1; fi;
elif IsInt( param ) then
param := List( [1..ACDim4Param[g]], x -> param );
elif Length( param ) <> ACDim4Param[g] then
Error("parameter should be a list of length ", ACDim4Param[g] );
fi;
# get group
if Length(param) = 7 then
G := ACDim4Funcs[g]( param[1], param[2], param[3], param[4],
param[5], param[6], param[7]);
elif Length(param) = 6 then
G := ACDim4Funcs[g]( param[1], param[2], param[3], param[4],
param[5], param[6]);
elif Length(param) = 5 then
G := ACDim4Funcs[g]( param[1], param[2], param[3], param[4],
param[5]);
elif Length(param) = 4 then
G := ACDim4Funcs[g]( param[1], param[2], param[3], param[4]);
elif Length(param) = 3 then
G := ACDim4Funcs[g]( param[1], param[2], param[3]);
fi;
# set some information
info := rec( dim := 4, type := g, param := param );
SetAlmostCrystallographicInfo( G, info );
SetIsAlmostCrystallographic( G, true );
SetDimensionOfMatrixGroup( G, 5 );
SetFieldOfMatrixGroup( G, Rationals );
SetSize( G, infinity );
return G;
end );
#############################################################################
##
#F AlmostCrystallographicGroup( dim, type, param )
##
InstallGlobalFunction( AlmostCrystallographicGroup,
function( dim, type, param )
if dim = 3 then
return AlmostCrystallographicDim3( type, param );
elif dim = 4 then
return AlmostCrystallographicDim4( type, param );
else
Error("dimension must be 3 or 4");
fi;
end );
#############################################################################
##
#F IsAlmostCrystallographic( <G> )
##
InstallMethod( IsAlmostCrystallographic, "for groups", true,
[IsGroup ], 0,
function( G )
if HasAlmostCrystallographicInfo( G ) then
return true;
else
Print("sorry - cannot check this property \n");
return fail;
fi;
end );
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