Quelle nonsolvcoll.gi
Sprache: unbekannt
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InstallMethod( AllNonSolvableLieAlgebras,
"for a finite field and a positive integer",
true,
[ IsField and IsFinite, IsPosInt ],
0,
function( F, dim )
local R, fam, parlist;
# Construct the family of element objects of our ring.
if not ( IsField( F ) and IsFinite( F ) and dim in [ 1, 2, 3, 4, 5, 6 ]) then
Error( "Non-solvable Lie algebras are only included over finite fields and dimension at most 6." );
fi;
if dim in [1,2] then return []; fi;
if dim = 3 then
parlist := [[3]];
elif dim = 4 and Characteristic( F ) = 2 then
parlist := [[4,1],[4,2]];
elif dim = 4 and Characteristic( F ) > 2 then
parlist := [[4]];
elif dim = 5 and Characteristic( F ) = 2 then
parlist := [[5,1],[5,2,0],[5,2,1],[5,3,0],[5,3,1]];
elif dim = 5 and Characteristic( F ) in [3,5] then
parlist := [[5,1,0],[5,1,1],[5,2],[5,3]];
elif dim = 5 and Characteristic( F ) >= 7 then
parlist := [[5,1,0],[5,1,1],[5,2]];
elif dim = 6 and Characteristic( F ) = 2 then
parlist := EnumeratorByFunctions(
NewFamily( IsList ),
rec(
NumberElement :=
function( e, x )
local list1, list2, list3;
list1 := [[6,1],[6,2],[6,3,0],[6,3,1],[6,4,0],[6,4,1],[6,4,2],
[6,4,3]];
list2 := [[6,5],[6,6,1],[6,6,2]];
list3 := [[6,6,4,Zero(F)],[6,6,4,One(F)],[6,7],[6,8]];
if x in list1 then
return Position( list1, x );
elif x[1] = 6 and x[2] = 4 then
return Position( Enumerator( F ), x[3] )+7;
elif x in list2 then
return Position( list2, x ) + 7 + Size( F );
elif x[1] = 6 and x[2] = 6 and x[3] = 3 then
return Position( Enumerator( F ), x[4] ) + 10 + Size( F );
elif x in list3 then
return Position( list3, x ) + 10 + 2*Size( F );
else
return fail;
fi; end,
ElementNumber := function( e, n )
local list1, list2, list3;
list1 := [[6,1],[6,2],[6,3,0],[6,3,1],[6,4,0],[6,4,1],[6,4,2],
[6,4,3]];
list2 := [[6,5],[6,6,1],[6,6,2]];
list3 := [[6,6,4,Zero(F)],[6,6,4,One(F)],[6,7],[6,8]];
if n <= 8 then
return list1[n];
elif n>=9 and n<=7+Size( F ) then
return [6,4,Enumerator( F )[n-7]];
elif n>=8+Size( F ) and n<=10+Size( F ) then
return list2[n-7-Size( F )];
elif n>=11+Size( F ) and n<=10+2*Size( F ) then
return [6,6,3,Enumerator( F )[n-10-Size( F )]];
elif n>=11+2*Size( F ) and n <= 14+2*Size( F ) then
return list3[n-10-2*Size( F )];
fi; end,
Length := function( x )
return 14+2*Size( F ); end ));
elif dim = 6 and Characteristic( F ) = 3 then
parlist := LieAlgDBParListIteratorDimension6Characteristic3( F, dim, [6,1] );
elif dim = 6 and Characteristic( F ) = 5 then
parlist := EnumeratorByFunctions(
NewFamily( IsList ),
rec(
NumberElement :=
function( e, x )
local list1, list2;
list1 := [[6,1],[6,2],[6,3,1],[6,3,2]];
list2 := [[6,3,4,Zero(F)],[6,3,4,Z(Size(F))],[6,3,4,One(F)],
[6,4],[6,5],[6,6],[6,7],[6,8],[6,9]];
if x in list1 then
return Position( list1, x );
elif x[1] = 6 and x[2] = 3 and x[3] = 3 then
return Position( Enumerator( F ), x[4] )+4;
elif x in list2 then
return Position( list2, x ) + 4 + Size( F );
else
return fail;
fi; end,
ElementNumber := function( e, n )
local list1, list2;
list1 := [[6,1],[6,2],[6,3,1],[6,3,2]];
list2 := [[6,3,4,Zero(F)],[6,3,4,Z(Size(F))],[6,3,4,One(F)],
[6,4],[6,5],[6,6],[6,7],[6,8],[6,9]];
if n <= 4 then
return list1[n];
elif n>=5 and n<=4+Size( F ) then
return [6,3,3,Enumerator( F )[n-4]];
elif n>=5+Size( F ) and n<=13+Size( F ) then
return list2[n-4-Size( F )];
fi; end,
Length := function( x )
return 13+Size( F ); end ));
elif dim = 6 and Characteristic( F ) >= 7 then
parlist := EnumeratorByFunctions(
NewFamily( IsList ),
rec(
NumberElement :=
function( e, x )
local list1, list2;
list1 := [[6,1],[6,2],[6,3,1],[6,3,2]];
list2 := [[6,3,4,Zero(F)],[6,3,4,Z(Size(F))],[6,3,4,One(F)],
[6,4],[6,5],[6,6],[6,7]];
if x in list1 then
return Position( list1, x );
elif x[1] = 6 and x[2] = 3 and x[3] = 3 then
return Position( Enumerator( F ), x[4] )+4;
elif x in list2 then
return Position( list2, x ) + 4 + Size( F );
else
return fail;
fi; end,
ElementNumber := function( e, n )
local list1, list2;
list1 := [[6,1],[6,2],[6,3,1],[6,3,2]];
list2 := [[6,3,4,Zero(F)],[6,3,4,Z(Size(F))],[6,3,4,One(F)],
[6,4],[6,5],[6,6],[6,7]];
if n <= 4 then
return list1[n];
elif n>=5 and n<=4+Size( F ) then
return [6,3,3,Enumerator( F )[n-4]];
elif n>=5+Size( F ) and n<=11+Size( F ) then
return list2[n-4-Size( F )];
fi; end,
Length := function( x )
return 11+Size( F ); end ));
fi;
# Make the domain.
R := rec( field := F,
dim := dim,
type := "NonSolvable",
parlist := parlist );
fam := NewFamily( IsLieAlgDBCollection_NonSolvable );
R := Objectify( NewType( fam, IsLieAlgDBCollection_NonSolvable ), R );
return R;
end );
InstallMethod( AsList,
"method for LieAlgDBCollections",
[ IsLieAlgDBCollection_NonSolvable ],
function( R )
local i, l, list;
if IsEnumeratorByFunctions( Enumerator( R )) then
TryNextMethod();
fi;
i := Iterator( R );
list := [];
for l in i do
Add( list, l );
od;
return list;
end);
InstallMethod( Enumerator,
"method for LieAlgDBCollections",
[ IsLieAlgDBCollection_NonSolvable ],
function( R )
if not IsEnumeratorByFunctions( R!.parlist ) and not
IsList( R!.parlist ) then
return fail;
else
return EnumeratorByFunctions( NewFamily(
CategoryCollections( IsLieAlgebra )),
rec(
ElementNumber := function( e, n )
return NonSolvableLieAlgebra( R!.field, R!.parlist[n] );
end,
NumberElement := function( e, x )
return Position( R!.parlist, x!.arg );
end,
Length := function( x ) return Length( R!.parlist ); end ));
fi;
end );
InstallMethod( Iterator,
"method for LieAlgDBCollections",
[ IsLieAlgDBCollection_NonSolvable ],
function( R )
if IsEnumeratorByFunctions( R!.parlist ) or IsList( R!.parlist ) then
TryNextMethod();
elif IsIterator( R!.parlist ) then
R!.parlist := LieAlgDBParListIteratorDimension6Characteristic3( R!.field, R!.dim, [6,1] );
return
IteratorByFunctions( rec(
NextIterator := function( iter )
return NonSolvableLieAlgebra( R!.field,
NextIterator( R!.parlist ));
end,
IsDoneIterator := function( iter )
return IsDoneIterator( R!.parlist );
end,
ShallowCopy := function( iter )
return fail;
end ));
fi;
end );
[ Dauer der Verarbeitung: 0.8 Sekunden
(vorverarbeitet)
]
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2026-04-02
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