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#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Thomas Breuer.
##
## 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 methods for additive cosets.
##
#############################################################################
##
#R IsAdditiveCosetDefaultRep
##
## The default additive coset is represented as a list object that stores
## at first position the additively acting domain, and at second position
## a representative.
## (Of course this representative need not be normalized.)
##
DeclareRepresentation( "IsAdditiveCosetDefaultRep",
IsPositionalObjectRep,
[ 1, 2 ] );
#############################################################################
##
#M AdditiveCoset( <A>, <a> ) . . . . . . . . for add. group and add. element
##
## The default method constructs an additive coset
## in `IsAdditiveCosetDefaultRep'.
##
InstallMethod( AdditiveCoset,
"for additive group and additive element",
IsCollsElms,
[ IsAdditiveGroup, IsAdditiveElement ], 0,
function( A, a )
return Objectify( NewType( FamilyObj( A ),
IsAdditiveCoset
and IsAdditiveCosetDefaultRep ),
[ A, a ] );
end );
#############################################################################
##
#M AdditivelyActingDomain( <A> ) . . . . . for add. coset in default repres.
##
InstallMethod( AdditivelyActingDomain,
"for additive coset in default repres.",
true,
[ IsAdditiveCoset and IsAdditiveCosetDefaultRep ], SUM_FLAGS,
A -> A![1] );
#############################################################################
##
#M Representative( <A> ) . . . . . . . . . for add. coset in default repres.
##
InstallMethod( Representative,
"for additive coset in default repres.",
true,
[ IsAdditiveCoset and IsAdditiveCosetDefaultRep ], SUM_FLAGS,
A -> A![2] );
#############################################################################
##
#M \+( <A>, <a> ) . . . . . . . . . for additive group and additive element
#M \+( <a>, <A> ) . . . . . . . . . for additive element and additive group
##
InstallOtherMethod( \+,
"for additive group and additive element",
IsCollsElms,
[ IsAdditiveGroup, IsAdditiveElement ], 0,
function( A, a )
return AdditiveCoset( A, a );
end );
InstallOtherMethod( \+,
"for additive element and additive group",
IsElmsColls,
[ IsAdditiveElement, IsAdditiveGroup ], 0,
function( a, A )
return AdditiveCoset( A, a );
end );
#############################################################################
##
#M \+( <C>, <a> ) . . . . . . . . . for additive coset and additive element
#M \+( <a>, <C> ) . . . . . . . . . for additive element and additive coset
##
InstallMethod( \+,
"for additive coset and additive element",
IsCollsElms,
[ IsAdditiveCoset, IsAdditiveElement ], 0,
function( C, a )
return AdditiveCoset( AdditivelyActingDomain( C ),
a + Representative( C ) );
end );
InstallMethod( \+,
"for additive element and additive coset",
IsElmsColls,
[ IsAdditiveElement, IsAdditiveCoset ], 0,
function( a, C )
return AdditiveCoset( AdditivelyActingDomain( C ),
a + Representative( C ) );
end );
#############################################################################
##
#M Enumerator( <A> ) . . . . . . . . . . . . . . . . . . for additive cosets
##
InstallMethod( Enumerator,
"for an additive coset",
true,
[ IsAdditiveCoset ], 0,
function( A )
local rep;
rep:= Representative( A );
return List( AsList( AdditivelyActingDomain( A ) ), a -> rep + a );
end );
#############################################################################
##
#M IsFinite( <A> ) . . . . . . . . . . . . . . . . . . . for additive cosets
##
InstallMethod( IsFinite,
"for an additive coset",
true,
[ IsAdditiveCoset ], 0,
A -> IsFinite( AdditivelyActingDomain( A ) ) );
#############################################################################
##
#M Random( <A> ) . . . . . . . . . . . . . . . . . . . . for additive cosets
##
InstallMethodWithRandomSource( Random,
"for a random source and an additive coset",
true,
[ IsRandomSource, IsAdditiveCoset ], 0,
{rs, A} -> Representative( A ) + Random( rs, AdditivelyActingDomain( A ) ) );
#############################################################################
##
#M Size( <A> ) . . . . . . . . . . . . . . . . . . . . . for additive cosets
##
InstallMethod( Size,
"for an additive coset",
true,
[ IsAdditiveCoset ], 0,
A -> Size( AdditivelyActingDomain( A ) ) );
#############################################################################
##
#M \=( <A1>, <A2> ) . . . . . . . . . . . . . . . . for two additive cosets
##
InstallMethod( \=,
"for two additive cosets",
IsIdenticalObj,
[ IsAdditiveCoset, IsAdditiveCoset ], 0,
function( A1, A2 )
local D;
D:= AdditivelyActingDomain( A1 );
return D = AdditivelyActingDomain( A2 )
and Representative( A1 ) - Representative( A2 ) in D;
end );
#T #############################################################################
#T ##
#T #M \=( <A1>, <A2> ) . . . . . . for two additive cosets with canon. repres.
#T ##
#T InstallMethod( \=,
#T "for two additive cosets with canon. repres.",
#T IsIdenticalObj,
#T [ IsAdditiveCoset and HasCanonicalRepresentative,
#T IsAdditiveCoset and HasCanonicalRepresentative ], 0,
#T function( A1, A2 )
#T return AdditivelyActingDomain( A1 ) = AdditivelyActingDomain( A2 )
#T and CanonicalRepresentative( A1 ) = CanonicalRepresentative( A2 );
#T end );
#############################################################################
##
#M \=( <C>, <A> ) . . . . . . . . . . for additive coset and additive group
##
InstallMethod( \=,
"for additive coset and additive group",
IsIdenticalObj,
[ IsAdditiveCoset, IsAdditiveGroup ], 0,
function( C, A )
return AdditivelyActingDomain( C ) = A
and Representative( C ) in A;
end );
#############################################################################
##
#M \=( <A>, <C> ) . . . . . . . . . . for additive group and additive coset
##
InstallMethod( \=,
"for additive group and additive coset",
IsIdenticalObj,
[ IsAdditiveGroup, IsAdditiveCoset ], 0,
function( A, C )
return AdditivelyActingDomain( C ) = A
and Representative( C ) in A;
end );
#############################################################################
##
#M \in( <a>, <A> ) . . . . . . . . . for additive element and additive coset
##
InstallMethod( \in,
"for additive element and additive coset",
IsElmsColls,
[ IsAdditiveElement, IsAdditiveCoset ], 0,
function( a, A )
return a - Representative( A ) in AdditivelyActingDomain( A );
end );
#############################################################################
##
#M Intersection2( <C1>, <C2> ) . . . . . . . . . . . for two additive cosets
##
InstallMethod( Intersection2,
"for two additive cosets",
IsIdenticalObj,
[ IsAdditiveCoset, IsAdditiveCoset ], 0,
function( C1, C2 )
if AdditivelyActingDomain( C1 ) = AdditivelyActingDomain( C2 ) then
if Representative( C1 ) in C2 then
return C1;
else
return [];
fi;
else
TryNextMethod();
fi;
end );
#############################################################################
##
#M PrintObj( <A> ) . . . . . . . . . . . . . . . . . . for an additive coset
##
InstallMethod( PrintObj,
"for an additive coset",
true,
[ IsAdditiveCoset ], 0,
function( A )
Print( "( ", Representative( A ), " + ",
AdditivelyActingDomain( A ), " )" );
end );
#############################################################################
##
#M ViewObj( <A> ) . . . . . . . . . . . . . . . . . . for an additive coset
##
InstallMethod( ViewObj,
"for an additive coset",
true,
[ IsAdditiveCoset ], 0,
function( A )
Print( "<add. coset of " );
View( AdditivelyActingDomain( A ) );
Print( ">" );
end );
#T #############################################################################
#T ##
#T #F SpaceCosetOps.\*( <s>, <C> )
#T ##
#T SpaceCosetOps.\* := function( scalar, C )
#T if not IsInt( scalar )
#T and not scalar in C.factorDen.field then
#T Error( "only scalar multiplication" );
#T fi;
#T return SpaceCoset( C.factorDen, scalar * C.representative );
#T end;
[ Dauer der Verarbeitung: 0.6 Sekunden
(vorverarbeitet)
]
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