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#############################################################################
##
#A wygraph.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
##
## Routines for the determination and the display of a Wyckoff graph
##
#############################################################################
##
#M CompareLevels( param1, param2 ) . . . . . . . . . . . . . . CompareLevels
##
InstallMethod( CompareLevels, true,
[ IsGraphicPosetRep and IsWyckoffGraph, IsList, IsList ], 0,
function( graph, level1, level2 )
# a smaller dimension is higher
if level1[1] < level2[1] then
return -1;
elif level1[1] > level2[1] then
return 1;
else
# for equal dimension, the bigger size is higher
if level1[2] > level2[2] then
return -1;
elif level1[2] > level2[2] then
return 1;
else
return 0;
fi;
fi;
end );
#############################################################################
##
#F WyckoffPosRelations( <W> ) . . . incidence relations of Wyckoff positions
##
WyckoffPosRelations := function( W )
local S, T, d, len, gens, G, L, m, O, o, i, j, k, Si, Sj, index, lst;
S := WyckoffSpaceGroup( W[1] );
T := TranslationBasis( S );
d := DimensionOfMatrixGroup( S ) - 1;
len := Length( W );
gens := GeneratorsOfGroup( S );
gens := Filtered( gens, g -> g{[1..d]}{[1..d]} <> IdentityMat( d ) );
if IsAffineCrystGroupOnLeft( S ) then
gens := List( gens, TransposedMat );
fi;
G := GroupByGenerators( gens, One( S ) );
L := List( W, w -> rec( translation := WyckoffTranslation( w ),
basis := WyckoffBasis( w ),
spaceGroup := S ) );
m := NullMat( len, len );
for i in [1..len] do
O := Orbit( G, L[i], ImageAffineSubspaceLattice );
for j in [1..len] do
Sj := WyckoffStabilizer( W[j] );
Si := WyckoffStabilizer( W[i] );
index := Size(Sj) / Size(Si);
if Length(L[j].basis) < Length(L[i].basis) and IsInt(index) then
lst := Filtered(O,o->IsSubspaceAffineSubspaceLattice(o,L[j]));
m[j][i] := Length( lst );
fi;
od;
od;
for i in Reversed([1..Length(W)]) do
for j in Reversed([1..i-1]) do
if m[j][i]<>0 then
for k in [1..j-1] do
if m[k][j]<>0 then m[k][i]:=0; fi;
od;
fi;
od;
od;
return m;
end;
#############################################################################
##
#F WyckoffGraphRecord( <lst> ) . . . . . . . Create record for Wyckoff graph
##
WyckoffGraphRecord := function( lst )
local L, m, R, i, level, j;
L := List( lst, w -> rec( wypos := w,
dim := Length( WyckoffBasis(w) ),
size := Size( WyckoffStabilizer(w) ),
class := w!.class ) );
Sort( L, function(a,b) return a.size > b.size; end );
m := WyckoffPosRelations( List( L, x -> x.wypos ) );
R := rec( levels := [],
classes := [],
vertices := [],
edges := [] );
for i in [1..Length(L)] do
level := [ L[i].dim, L[i].size ];
AddSet( R.levels, level );
AddSet( R.classes, [ L[i].class, level ] );
Add( R.vertices, [ L[i].wypos, level, L[i].class ] );
for j in [1..i-1] do
if m[j][i]<>0 then Add( R.edges, [ i, j, m[j][i] ] ); fi;
od;
od;
return R;
end;
#############################################################################
##
#M WyckoffGraphFun( W, def ) . . . . . . . . . . . . display a Wyckoff graph
##
InstallGlobalFunction( WyckoffGraphFun, function( W, def )
local S, defaults, R, wygr, x, vertices, i, v, info, data, v1, v2;
# set up defaults
S := WyckoffSpaceGroup( W[1] );
defaults := rec(width := 800,
height := 600,
title := "WyckoffGraph");
if HasName(S) then
defaults.title := Concatenation( defaults.title, " of ", Name(S) );
fi;
if IsBound(def.width) then defaults.width := def.width; fi;
if IsBound(def.height) then defaults.height := def.height; fi;
if IsBound(def.title) then defaults.title := def.title; fi;
R := WyckoffGraphRecord( W );
# open a graphic poset and make it a Wyckoff graph
wygr := GraphicPoset( defaults.title, defaults.width, defaults.height );
SetFilterObj( wygr, IsWyckoffGraph );
# create levels
for x in R.levels do
CreateLevel( wygr, x, String( x ) );
od;
# create classes
for x in R.classes do
CreateClass( wygr, x[2], x[1] );
od;
# create vertices
vertices := [];
for i in [1..Length(R.vertices)] do
v := R.vertices[i];
info := rec( label := String(i),
levelparam := v[2],
classparam := v[3] );
data := rec( wypos := v[1], info := rec() );
Add( vertices, Vertex( wygr, data, info ) );
od;
# create edges
for x in R.edges do
v1 := vertices[ x[1] ];
v2 := vertices[ x[2] ];
Edge( wygr, v1, v2, rec( label := String( x[3]) ) );
od;
# Install the info method
wygr!.selector := false;
wygr!.infodisplays := WyckoffInfoDisplays;
InstallPopup( wygr, GGLRightClickPopup );
return wygr;
end );
[ Dauer der Verarbeitung: 0.31 Sekunden
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