#############################################################################
##
#W In this file we prepare functions to loop over the 2,3 or 4 dimensional
#W crystallographic groups as matrix groups or pcp groups.
##

cryst4params:=
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  [ 7, 2, 2, 1 ], [ 7, 2, 2, 2 ], [ 7, 2, 3, 1 ], [ 7, 2, 3, 2 ],
  [ 7, 3, 1, 1 ], [ 7, 3, 1, 2 ], [ 7, 3, 1, 3 ], [ 7, 3, 2, 1 ],
  [ 7, 3, 2, 2 ], [ 7, 3, 3, 1 ], [ 7, 3, 3, 2 ], [ 7, 4, 1, 1 ],
  [ 7, 4, 1, 2 ], [ 7, 4, 2, 1 ], [ 7, 4, 2, 2 ], [ 7, 4, 3, 1 ],
  [ 7, 4, 3, 2 ], [ 7, 5, 1, 1 ], [ 7, 5, 1, 2 ], [ 7, 5, 1, 3 ],
  [ 7, 5, 1, 4 ], [ 7, 5, 2, 1 ], [ 7, 5, 2, 2 ], [ 7, 5, 2, 3 ],
  [ 7, 5, 2, 4 ], [ 7, 5, 3, 1 ], [ 7, 5, 3, 2 ] ];

cryst2params :=
[ [ 1, 1, 1, 1 ], [ 1, 2, 1, 1 ], [ 2, 1, 1, 1 ], [ 2, 1, 1, 2 ],
  [ 2, 1, 2, 1 ], [ 2, 2, 1, 1 ], [ 2, 2, 1, 2 ], [ 2, 2, 1, 3 ],
  [ 2, 2, 2, 1 ], [ 3, 1, 1, 1 ], [ 3, 2, 1, 1 ], [ 3, 2, 1, 2 ],
  [ 4, 1, 1, 1 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 4, 3, 1, 1 ],
  [ 4, 4, 1, 1 ] ];

NumberSpaceGroups := function( dim )
    if dim = 4 then return 4783; fi;
    if dim = 3 then return 219; fi;
    if dim = 2 then return 17; fi;
end;

SpaceGroup := function( dim, nr )
    local type;
    if dim = 4 then
        type := cryst4params[nr];
        return SpaceGroupBBNWZ( 4, type[1], type[2], type[3], type[4] );
    elif dim = 3 then
        type := cryst3params[nr];
        return SpaceGroupBBNWZ( 3, type[1], type[2], type[3], type[4] );
    elif dim = 2 then
        type := cryst2params[nr];
        return SpaceGroupBBNWZ( 2, type[1], type[2], type[3], type[4] );
    else
        return fail;
    fi;
end;

PointGroupByNumber := function( dim, nr )
    local type;
    if dim = 4 then
        type := cryst4params[nr];
        return MatGroupZClass( 4, type[1], type[2], type[3] );
    elif dim = 3 then
        type := cryst3params[nr];
        return MatGroupZClass( 3, type[1], type[2], type[3] );
    elif dim = 2 then
        type := cryst2params[nr];
        return MatGroupZClass( 2, type[1], type[2], type[3] );
    fi;
end;

SpaceGroupPcpGroup := function( dim, nr )
    local G, iso, H, F, n;
    G := SpaceGroup( dim, nr );
    iso := IsomorphismPcpGroup( G );
    if IsBool( iso ) then return fail; fi;
    H := Image( iso );
    n := Length( Igs(H) );
    F := Subgroup( H, Igs(H){[n-dim+1..n]} );
    SetFittingSubgroup( H, F );
    return H;
end;