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#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Andrew Solomon.
##
## Copyright of GAP belongs to its developers, whose names are too numerous
## to list here. Please refer to the COPYRIGHT file for details.
##
## SPDX-License-Identifier: GPL-2.0-or-later
##
## This file contains generic methods for magma ideals
##
#############################################################################
##
#M PrintObj( <S> )
## print a [left, right, two-sided] MagmaIdeal
##
## left
InstallMethod( PrintObj,
"for a left magma ideal",
true,
[ IsLeftMagmaIdeal ], 0,
function( S )
Print( "LeftMagmaIdeal( ... )" );
end );
InstallMethod( PrintObj,
"for a left magma ideal with known generators",
true,
[ IsLeftMagmaIdeal and HasGeneratorsOfLeftMagmaIdeal ], 0,
function( S )
Print( "LeftMagmaIdeal( ", GeneratorsOfLeftMagmaIdeal( S ), " )" );
end );
## right
InstallMethod( PrintObj,
"for a right magma ideal",
true,
[ IsRightMagmaIdeal ], 0,
function( S )
Print( "RightMagmaIdeal( ... )" );
end );
InstallMethod( PrintObj,
"for a right magma ideal with known generators",
true,
[ IsRightMagmaIdeal and HasGeneratorsOfRightMagmaIdeal ], 0,
function( S )
Print( "RightMagmaIdeal( ", GeneratorsOfRightMagmaIdeal( S ), " )" );
end );
## two sided
InstallMethod( PrintObj,
"for a magma ideal",
true,
[ IsMagmaIdeal ], 0,
function( S )
Print( "MagmaIdeal( ... )" );
end );
InstallMethod( PrintObj,
"for a magma ideal with known generators",
true,
[ IsMagmaIdeal and HasGeneratorsOfMagmaIdeal ], 0,
function( S )
Print( "MagmaIdeal( ", GeneratorsOfMagmaIdeal( S ), " )" );
end );
#############################################################################
##
#M ViewObj( <S> )
## view a [left,right,two-sided] magma ideal
##
## left
InstallMethod( ViewObj,
"for a LeftMagmaIdeal",
true,
[ IsLeftMagmaIdeal ], 0,
function( S )
Print( "<LeftMagmaIdeal>" );
end );
InstallMethod( ViewObj,
"for a LeftMagmaIdeal with generators",
true,
[ IsLeftMagmaIdeal and HasGeneratorsOfLeftMagmaIdeal ], 0,
function( S )
Print( "<LeftMagmaIdeal with ",
Pluralize( Length( GeneratorsOfLeftMagmaIdeal( S ) ), "generator" ),
">" );
end );
## right
InstallMethod( ViewObj,
"for a RightMagmaIdeal",
true,
[ IsRightMagmaIdeal ], 0,
function( S )
Print( "<RightMagmaIdeal>" );
end );
InstallMethod( ViewObj,
"for a RightMagmaIdeal with generators",
true,
[ IsRightMagmaIdeal and HasGeneratorsOfRightMagmaIdeal ], 0,
function( S )
Print( "<RightMagmaIdeal with ",
Pluralize( Length( GeneratorsOfRightMagmaIdeal( S ) ), "generator" ),
">" );
end );
## two sided
InstallMethod( ViewObj,
"for a MagmaIdeal",
true,
[ IsMagmaIdeal ], 0,
function( S )
Print( "<MagmaIdeal>" );
end );
InstallMethod( ViewObj,
"for a MagmaIdeal with generators",
true,
[ IsMagmaIdeal and HasGeneratorsOfMagmaIdeal ], 0,
function( S )
Print( "<MagmaIdeal with ",
Pluralize( Length( GeneratorsOfMagmaIdeal( S ) ), "generator" ),
">" );
end );
#############################################################################
##
#M LeftMagmaIdealByGenerators( <D>, <gens> )
#M RightMagmaIdealByGenerators( <D>, <gens> )
#M MagmaIdealByGenerators( <D>, <gens> )
##
## ASSUMES that <gens> are a subset of <D>
##
InstallMethod( LeftMagmaIdealByGenerators,
"for a collection of magma elements",
IsIdenticalObj,
[ IsMagma, IsCollection ], 0,
function( M, gens )
local S;
S:= Objectify( NewType( FamilyObj( gens ),
IsLeftMagmaIdeal and IsAttributeStoringRep ),
rec() );
SetGeneratorsOfLeftMagmaIdeal( S, AsList( gens ) );
SetParent(S, M);
SetLeftActingDomain(S, M);
if HasGeneratorsOfGroup(M) then
# Because any ideal of a group the whole group, we should set the
# generators.
SetGeneratorsOfGroup(S, GeneratorsOfGroup(M));
fi;
return S;
end );
InstallMethod( RightMagmaIdealByGenerators,
"for a collection of magma elements",
IsIdenticalObj,
[ IsMagma, IsCollection ], 0,
function( M, gens )
local S;
S:= Objectify( NewType( FamilyObj( gens ),
IsRightMagmaIdeal and IsAttributeStoringRep ),
rec() );
SetGeneratorsOfRightMagmaIdeal( S, AsList( gens ) );
SetParent(S, M);
SetRightActingDomain(S, M);
if HasGeneratorsOfGroup(M) then
# Because any ideal of a group is the whole group, we should set the
# generators.
SetGeneratorsOfGroup(S, GeneratorsOfGroup(M));
fi;
return S;
end );
InstallMethod( MagmaIdealByGenerators,
"for a collection of magma elements",
IsIdenticalObj,
[ IsMagma, IsCollection ], 0,
function( M, gens )
local S;
S:= Objectify( NewType( FamilyObj( gens ),
IsMagmaIdeal and IsAttributeStoringRep ),
rec() );
SetGeneratorsOfMagmaIdeal( S, AsList( gens ) );
SetParent(S, M);
SetActingDomain(S, M);
if HasGeneratorsOfGroup(M) then
# Because any ideal of a group is the whole group, we should set the
# generators.
SetGeneratorsOfGroup(S, GeneratorsOfGroup(M));
fi;
return S;
end );
#############################################################################
##
#F LeftMagmaIdeal( <gen>, ... )
#F RightMagmaIdeal( <gens> )
#F MagmaIdeal( <gens> )
##
## Unimplemented
##
# InstallGlobalFunction( LeftMagmaIdeal, function( arg )
# InstallGlobalFunction( RightMagmaIdeal, function( arg )
# InstallGlobalFunction( MagmaIdeal, function( arg )
#############################################################################
##
#M AsLeftMagmaIdeal( <D>, <C> )
##
## Regard the list <C> of elements as a left ideal of <D>.
## It is not checked, but assumed, that <C> are all the elements
## of the ideal and that <C> is a subset of <D>.
##
InstallMethod( AsLeftMagmaIdeal,
"generic method for a domain and a collection",
IsIdenticalObj,
[ IsDomain, IsCollection ], 0,
function( D, C )
local S;
S:= LeftMagmaIdealByGenerators( D, AsList(C));
UseIsomorphismRelation( C, S );
UseSubsetRelation( C, S );
return S;
end );
#############################################################################
##
#M Enumerator( <I> ) . . . . . . . . . . . . elements of a magma ideal
##
BindGlobal( "EnumeratorOfMagmaIdeal", function( I )
local gens, # magma generators of <I>
H, # submagma
gen, # generator of <I>
x,y, # elements of parent
M; # parent
# handle the case of an empty magma
gens:= GeneratorsOfMagmaIdeal( I );
if IsEmpty( gens ) then
return [];
fi;
M := Parent(I); # the magma whose ideal it is
# start with the empty magma and its element generators list
H:= Submagma( M, [] );
SetAsSSortedList( H, Immutable( [ ] ) );
# Add the generators one after the other.
# We use a function that maintains the elements list for the closure.
for gen in gens do
for x in AsSSortedList(M) do
for y in AsSSortedList(M) do
H:= ClosureMagmaDefault( H, x*gen*y );
od;
od;
od;
# return the list of elements
Assert( 2, HasAsSSortedList( H ) );
return AsSSortedList( H );
end );
InstallMethod( Enumerator,
"generic method for a magma ideal",
true,
[ IsMagma and IsAttributeStoringRep and IsMagmaIdeal ], 0,
EnumeratorOfMagmaIdeal );
#############################################################################
##
#M AsSSortedList( <R> ) - for a right magma ideal
#M AsSSortedList( <L> ) - for a left magma ideal
##
## Lazy methods for listing the elements of a left/right magma ideal
## assuming the object is finite. Should write enumerators some time...
##
InstallMethod( AsSSortedList,
"for a right magma ideal", true,
[IsRightMagmaIdeal and HasGeneratorsOfRightMagmaIdeal],0,
function(I)
local
g, # a generator of the ideal
x, # an element of the parent
plist, # elements of the parent
genlist, # right ideal generators
idealelts; # elements of the ideal
plist := AsSet(Parent(I));
genlist := AsSet(GeneratorsOfRightMagmaIdeal(I));
idealelts := ShallowCopy(genlist);
for g in genlist do
for x in plist do
AddSet(idealelts, g*x);
od;
od;
return idealelts;
end);
InstallMethod( AsSSortedList,
"for a left magma ideal", true,
[IsLeftMagmaIdeal and HasGeneratorsOfLeftMagmaIdeal],0,
function(I)
local
g, # a generator of the ideal
x, # an element of the parent
plist, # elements of the parent
genlist, # left ideal generators
idealelts; # elements of the ideal
plist := AsSet(Parent(I));
genlist := AsSet(GeneratorsOfLeftMagmaIdeal(I));
idealelts := ShallowCopy(genlist);
for g in genlist do
for x in plist do
AddSet(idealelts, x*g);
od;
od;
return idealelts;
end);
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