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#############################################################################
##
#A spacegrp.gi Cryst library Bettina Eick
#A Franz G"ahler
#A Werner Nickel
##
#Y Copyright 1997-1999 by Bettina Eick, Franz G"ahler and Werner Nickel
##
## Extraction functions for IT space groups
##
#############################################################################
##
#M SpaceGroupSettingsIT . . . . . . . .available settings of IT space groups
##
InstallGlobalFunction( SpaceGroupSettingsIT, function( dim, nr )
if dim = 2 then
if nr in [1..17] then
return List( RecNames( SpaceGroupList2d[nr] ), x -> x[1] );
else
Error( "space group number must be in [1..17]" );
fi;
elif dim = 3 then
if nr in [1..230] then
return List( RecNames( SpaceGroupList3d[nr] ), x -> x[1] );
else
Error( "space group number must be in [1..230]" );
fi;
else
Error( "only dimensions 2 and 3 are supported" );
fi;
end );
#############################################################################
##
#M SpaceGroupDataIT . . . . . . . . . . . data extractor for IT space groups
##
InstallGlobalFunction( SpaceGroupDataIT, function( r )
local settings;
if r.dim = 2 then
if r.nr in [1..17] then
if IsBound( r.setting ) and r.setting <> '1' then
Error( "requested setting is not available" );
fi;
r.setting := '1';
return SpaceGroupList2d[r.nr].1;
else
Error( "in 2d, space group number must be in [1..17]" );
fi;
elif r.dim = 3 then
if r.nr in [1..230] then
settings := SpaceGroupSettingsIT( 3, r.nr );
if IsBound( r.setting ) then
if r.setting in settings then
return SpaceGroupList3d[r.nr].([r.setting]);
else
Error( "requested setting is not available" );
fi;
else
if 'b' in settings then
r.setting := 'b';
return SpaceGroupList3d[r.nr].b;
elif '2' in settings then
r.setting := '2';
return SpaceGroupList3d[r.nr].2;
elif 'h' in settings then
r.setting := 'h';
return SpaceGroupList3d[r.nr].h;
else
r.setting := '1';
return SpaceGroupList3d[r.nr].1;
fi;
fi;
else
Error( "space group number must be in [1..230]" );
fi;
else
Error( "only dimensions 2 and 3 are supported" );
fi;
end );
#############################################################################
##
#M SpaceGroupFunIT . . . . . . . . . constructor function for IT space group
##
InstallGlobalFunction( SpaceGroupFunIT, function( r )
local data, gens, vec, name, norm, S, P, N;
data := SpaceGroupDataIT( r );
gens := ShallowCopy( data.generators );
for vec in data.basis do
Add( gens, AugmentedMatrix( IdentityMat( r.dim ), vec ) );
od;
if r.action = LeftAction then
gens := List( gens, TransposedMat );
norm := List( data.normgens, TransposedMat );
name := "SpaceGroupOnLeftIT(";
S := AffineCrystGroupOnLeftNC( gens, IdentityMat( r.dim+1 ) );
else
norm := data.normgens;
name := "SpaceGroupOnRightIT(";
S := AffineCrystGroupOnRightNC( gens, IdentityMat( r.dim+1 ) );
fi;
AddTranslationBasis( S, data.basis );
SetName( S, Concatenation( name, String(r.dim), ",", String(r.nr),
",'", [r.setting], "')" ) );
P := PointGroup( S );
N := GroupByGenerators( norm, One(P) );
SetSize( N, data.normsize );
SetNormalizerPointGroupInGLnZ( P, N );
if data.basis = One(P) then
SetNormalizerInGLnZ( P, N );
fi;
return S;
end );
#############################################################################
##
#M SpaceGroupOnRightIT . . . . . . . .constructor for IT space group OnRight
##
InstallGlobalFunction( SpaceGroupOnRightIT, function( arg )
local r;
r := rec( dim := arg[1], nr := arg[2], action := RightAction );
if IsBound( arg[3] ) then
r.setting := arg[3];
fi;
return SpaceGroupFunIT( r );
end );
#############################################################################
##
#M SpaceGroupOnLeftIT . . . . . . . . .constructor for IT space group OnLeft
##
InstallGlobalFunction( SpaceGroupOnLeftIT, function( arg )
local r;
r := rec( dim := arg[1], nr := arg[2], action := LeftAction );
if IsBound( arg[3] ) then
r.setting := arg[3];
fi;
return SpaceGroupFunIT( r );
end );
#############################################################################
##
#M SpaceGroupIT . . . . . . . . . . . . . . . constructor for IT space group
##
InstallGlobalFunction( SpaceGroupIT, function( arg )
local r;
r := rec( dim := arg[1], nr := arg[2], action := CrystGroupDefaultAction );
if IsBound( arg[3] ) then
r.setting := arg[3];
fi;
return SpaceGroupFunIT( r );
end );
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