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BindGlobal( "ClearGreen",
function( latt )
local lev, class, vert, sel;
sel := Selected( latt );
for lev in Levels( latt ) do
for class in Classes( latt, lev ) do
for vert in Vertices( latt, lev, class ) do
if not( vert in sel ) then
Recolor( latt, vert, COLORS.black );
fi;
od;
od;
od;
end );
InstallMethod(
ChooseShape,
"NRIs",
true,
[IsGraphicPosetRep and IsGraphicIdealLattice,IsRecord],
0,
function( latt, data )
local ideal;
ideal := data.ideal;
if HasIsNearRingIdeal( ideal ) and
IsNearRingIdeal( ideal ) then
return "circle"; # two-sided ideal
elif HasIsNearRingLeftIdeal( ideal ) and
IsNearRingLeftIdeal( ideal ) then
return "diamond"; # left ideal
else
return "rectangle";
fi;
end );
InstallMethod(
ChooseLevel,
"NRIs",
true,
[IsGraphicPosetRep and IsGraphicIdealLattice, IsRecord],
0,
function( latt, data )
return Size( data.ideal );
end );
InstallMethod(
GraphicIdealLattice,
true,
[IsNearRing,IsString],
0,
function ( nr, which )
local latt, v, levels, vertices, i, j, union,
ups, newups, n, newvertex, ideals, I, funcclose;
latt := GraphicPoset( "", 800, 600 );
SetFilterObj( latt, IsGraphicIdealLattice );
# which ideals should be shown ?
ideals := [];
if 'r' in which then
SetTitle( latt, "Computing right ideals ..." );
ideals := NearRingRightIdeals( nr );
fi;
if 'l' in which then
SetTitle( latt, "Computing left ideals ..." );
ideals := Union( ideals, NearRingLeftIdeals( nr ) );
fi;
if 'i' in which and not( 'l' in which or 'r' in which ) then
SetTitle( latt, "Computing two-sided ideals ..." );
ideals := NearRingIdeals( nr );
fi;
if ideals=[] then
Error( "no ideal type selected, select 'l', 'r' or 'i'" );
fi;
SetTitle( latt, "Computing covers ..." );
n := Length(ideals);
ups := List( [1..n], i -> Filtered( [1..n], j ->
RemInt( Size(ideals[j]), Size(ideals[i]) ) = 0 and
j<>i and
IsSubset( ideals[j], ideals[i] ) ) );
for i in [1..n] do
union := [];
for j in ups[i] do
union := Union( union, ups[j] );
ups[i] := Difference( ups[i], union );
od;
od;
if HasName( nr ) then
SetTitle( latt,
Concatenation( "Ideal lattice of ", Name(nr) ) );
else
SetTitle( latt,
"Ideal lattice of nearring" );
fi;
i := 0; vertices := [];
for I in ideals do
i := i+1;
CreateLevel( latt, Size(I) );
Add( vertices, Vertex( latt, rec( ideal := I ),
rec( label := String( i )
) ) );
od;
for i in [1..n] do
for j in ups[i] do
Edge( latt, vertices[i], vertices[j] );
od;
od;
Menu( latt, "Ideals",
[
"Intersection",
"Closure",
"Commutator",
"Covers",
"Subcovers",
"Ideal type",
],
[
"forsubset",
"forsubset",
"forsubset",
"forone",
"forone",
"forsubset"
],
[
# Intersection
function(arg)
local sel, C, latt;
latt := arg[1];
sel := Selected( latt );
C := Intersection( List( sel, I -> I!.data.ideal ) );
C := WhichVertex( latt, C,
function( N, R ) return R.ideal = N; end );
ClearGreen( latt );
Recolor( latt, C, COLORS.green );
end,
# Closure
function(arg)
local sel, I, C, latt;
latt := arg[1];
sel := Selected( latt );
sel := List( sel, I -> I!.data.ideal );
C := sel[1];
for I in sel{[2..Length(sel)]} do
C := ClosureNearRingIdeal( C, I );
od;
C := WhichVertex( latt, C,
function( N, R ) return R.ideal = N; end );
ClearGreen( latt );
Recolor( latt, C, COLORS.green );
end,
# Commutator
function(arg)
local sel, I, J, C, latt;
latt := arg[1];
sel := Selected( latt );
if Length( sel )=1 then
I := sel[1]; J := sel[1];
elif Length( sel )=2 then
I := sel[1]; J := sel[2];
else
return;
fi;
C := NearRingCommutator(I!.data.ideal,J!.data.ideal);
C := WhichVertex( latt, C,
function( N, R ) return R.ideal = N; end );
ClearGreen( latt );
Recolor( latt, C, COLORS.green );
end,
# Covers
function(arg)
local V, I, Cs, latt;
latt := arg[1];
I := Selected(latt)[1];
Cs := MaximalIn( latt, I );
ClearGreen( latt );
for V in Cs do
Recolor( latt, V, COLORS.green );
od;
end,
# Subcovers
function(arg)
local V, I, Cs, latt;
latt := arg[1];
I := Selected(latt)[1];
Cs := Maximals( latt, I );
ClearGreen( latt );
for V in Cs do
Recolor( latt, V, COLORS.green );
od;
end,
# Ideal type
function(arg)
local latt, sel, vert;
latt := arg[1];
sel := Selected( latt );
for vert in sel do
if IsNearRingIdeal( vert!.data.ideal ) then
Reshape( latt, vert, "circle" );
fi;
od;
end
] );
# close text selector
funcclose := function( sel, bt )
Close(sel);
return true;
end;
InstallPopup( latt,
function( sheet, vert, x, y )
local id, text;
# text := Concatenation( "LibraryNearRing( ",Name(id[1]),", ",String(id[2])," )");
sheet!.infobox := TextSelector(
Concatenation( "Information on near ring ideal ",vert!.label ),
[
"Size : ",
function(x,y)
Relabel( x, 1, Concatenation( "Size : ", String(Size(vert!.data.ideal)) ) );
return Size(vert!.data.ideal);
end,
"twosided ideal : ",
function(x,y)
Relabel( x, 2, Concatenation( "twosided ideal : ",
String( IsNearRingIdeal( vert!.data.ideal ) ) ) );
if IsNearRingIdeal( vert!.data.ideal ) then
Reshape( latt, vert, "circle" );
fi;
return IsNearRingIdeal( vert!.data.ideal );
end,
"Factor isomorphic to",
function(x,y)
local factor, id;
factor := FactorNearRing( Parent(vert!.data.ideal),
vert!.data.ideal );
if Size(factor) > 15 then
return factor;
else
id := IdLibraryNearRing( factor );
Relabel( x, 3, Concatenation( "Factor isomorphic to ",
"LibraryNearRing( ",Name(id[1]),", ",String(id[2])," )") );
return factor;
fi;
end,
"Export ideal to GAP",
function(x,y) return vert!.data.ideal; end
],
[ "close", funcclose ] );
end
);
return latt;
end);
InstallMethod(
CompareLevels,
true,
[ IsGraphicPosetRep and IsGraphicIdealLattice, IsInt, IsInt ],
0,
function( poset, a, b )
if a < b then
return 1;
elif a > b then
return -1;
else
return 0;
fi;
end);
[ Dauer der Verarbeitung: 0.36 Sekunden
(vorverarbeitet)
]
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