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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 mutable bases, in the representations of
## - mutable bases that store immutable bases
## - mutable bases that use immutable bases for nicer modules
##
#############################################################################
##
#M ShallowCopy( <MB> ) . . . . . . . . . . . . . . . . . for a mutable basis
##
InstallMethod( ShallowCopy,
"generic method for mutable basis",
true,
[ IsMutableBasis ], 0,
MB -> ShallowCopy( BasisVectors( MB ) ) );
#############################################################################
##
#M NrBasisVectors( <MB> ) . . . . . . . . . . . . . . . for a mutable basis
##
## The default method constructs the basis vctors, and returns the length of
## this list.
##
## (Better methods for special representations avoid to construct the basis
## vectors.)
##
InstallMethod( NrBasisVectors,
"generic method for mutable basis",
true,
[ IsMutableBasis ], 0,
MB -> Length( BasisVectors( MB ) ) );
#############################################################################
##
#M ImmutableBasis( <MB>, <V> )
##
## This method is needed for the case that one wants to construct a basis
## of <V>, and successive closures of mutable bases are needed to get a
## mutable basis; from this one then creates the immutable basis,
## and wants the particular object <V> to be the underlying module.
##
InstallMethod( ImmutableBasis,
"for mutable basis, and free left module",
IsIdenticalObj,
[ IsMutableBasis, IsFreeLeftModule ], 0,
function( MB, V )
local B, vectors;
B:= ImmutableBasis( MB );
if not IsIdenticalObj( UnderlyingLeftModule( B ), V ) then
# If `V' does not know left module generators yet,
# we store them now.
vectors:= BasisVectors( B );
UseBasis( V, vectors );
# We cannot simply replace the module;
# for example if `B' is handled by nice/ugly vectors
# then the module is needed to construct these vectors!
B:= BasisWithReplacedLeftModule( B, V );
SetBasis( V, B );
fi;
return B;
end );
#############################################################################
##
#R IsMutableBasisByImmutableBasisRep( <B> )
##
## The default case of a mutable basis stores an immutable basis,
## and constructs a new one whenever the mutable basis is changed.
##
DeclareRepresentation( "IsMutableBasisByImmutableBasisRep",
IsComponentObjectRep,
[ "immutableBasis", "leftActingDomain" ] );
#############################################################################
##
#M MutableBasis( <R>, <vectors> )
#M MutableBasis( <R>, <vectors>, <zero> )
##
InstallMethod( MutableBasis,
"generic method for ring and collection",
true,
[ IsRing, IsCollection ], 0,
function( R, vectors )
local B;
if ForAll( vectors, IsZero ) then
return MutableBasis( R, [], vectors[1] );
fi;
B:= rec(
immutableBasis := Basis(
LeftModuleByGenerators( R, vectors ) ),
leftActingDomain := R
);
return Objectify( NewType( FamilyObj( vectors ),
IsMutableBasis
and IsMutable
and IsMutableBasisByImmutableBasisRep ),
B );
end );
InstallOtherMethod( MutableBasis,
"generic method for ring, list, and object",
true,
[ IsRing, IsList, IsObject ], 0,
function( R, vectors, zero )
local B;
B:= rec(
immutableBasis := Basis(
LeftModuleByGenerators( R, vectors,
zero ) ),
leftActingDomain := R
);
return Objectify( NewType( CollectionsFamily( FamilyObj( zero ) ),
IsMutableBasis
and IsMutable
and IsMutableBasisByImmutableBasisRep ),
B );
end );
#############################################################################
##
#M ViewObj( <MB> ) . . . . . . . . . . . . . . . . . . view a mutable basis
##
InstallMethod( ViewObj,
"for mutable basis represented by an immutable basis",
true,
[ IsMutableBasis and IsMutableBasisByImmutableBasisRep ], 0,
function( MB )
Print( "<mutable basis over " );
View( MB!.leftActingDomain );
Print( ", ", Pluralize( NrBasisVectors( MB ), "vector" ), ">" );
end );
#############################################################################
##
#M PrintObj( <MB> ) . . . . . . . . . . . . . . . . . print a mutable basis
##
InstallMethod( PrintObj,
"for mutable basis represented by an immutable basis",
true,
[ IsMutableBasis and IsMutableBasisByImmutableBasisRep ], 0,
function( MB )
if NrBasisVectors( MB ) = 0 then
Print( "MutableBasis( ", MB!.leftActingDomain, ", [], ",
Zero( UnderlyingLeftModule( MB!.immutableBasis ) ), " )" );
else
Print( "MutableBasis( ", MB!.leftActingDomain, ", ",
BasisVectors( MB!.immutableBasis ), " )" );
fi;
end );
#############################################################################
##
#M BasisVectors( <MB> )
##
InstallOtherMethod( BasisVectors,
"for mutable basis represented by an immutable basis",
true,
[ IsMutableBasis and IsMutableBasisByImmutableBasisRep ], 0,
MB -> BasisVectors( MB!.immutableBasis ) );
#############################################################################
##
#M CloseMutableBasis( <MB>, <v> )
##
InstallMethod( CloseMutableBasis,
"for mutable basis represented by an immutable basis, and vector",
IsCollsElms,
[ IsMutableBasis and IsMutable and IsMutableBasisByImmutableBasisRep,
IsVector ], 0,
function( MB, v )
local V, B, vectors;
B:= MB!.immutableBasis;
V:= UnderlyingLeftModule( B );
if not v in V then
vectors:= Concatenation( BasisVectors( B ), [ v ] );
V:= LeftModuleByGenerators( LeftActingDomain( V ), vectors );
UseBasis( V, vectors );
MB!.immutableBasis := Basis( V );
return true;
else
# The basis was not extended.
return false;
fi;
end );
#############################################################################
##
#M IsContainedInSpan( <MB>, <v> )
##
InstallMethod( IsContainedInSpan,
"for mutable basis represented by an immutable basis, and vector",
IsCollsElms,
[ IsMutableBasis and IsMutableBasisByImmutableBasisRep, IsVector ], 0,
function( MB, v )
return v in UnderlyingLeftModule( MB!.immutableBasis );
end );
#############################################################################
##
#M ImmutableBasis( <MB> )
##
InstallMethod( ImmutableBasis,
"for mutable basis represented by an immutable basis",
true,
[ IsMutableBasis and IsMutableBasisByImmutableBasisRep ], 0,
MB -> MB!.immutableBasis );
#############################################################################
##
#R IsMutableBasisViaNiceMutableBasisRep( <B> )
##
DeclareRepresentation( "IsMutableBasisViaNiceMutableBasisRep",
IsComponentObjectRep,
[ "leftModule", "niceMutableBasis", "zero" ] );
#############################################################################
##
#F MutableBasisViaNiceMutableBasisMethod2( <R>, <vectors> )
##
## *Note* that <vectors> must be a collection.
## (This must be guaranteed by the installations of this function as
## method of `MutableBasis'.)
##
InstallGlobalFunction( MutableBasisViaNiceMutableBasisMethod2,
function( R, vectors )
local M, nice, B;
if ForAll( vectors, IsZero ) then
return MutableBasisViaNiceMutableBasisMethod3( R, [], vectors[1] );
fi;
M:= LeftModuleByGenerators( R, vectors );
if not IsHandledByNiceBasis( M ) then
Error( "<M> is not handled via nice bases" );
fi;
nice:= MutableBasis( R, List( vectors, v -> NiceVector( M, v ) ) );
B:= rec(
niceMutableBasis := nice,
leftModule := M
);
return Objectify( NewType( FamilyObj( vectors ),
IsMutableBasis
and IsMutable
and IsMutableBasisViaNiceMutableBasisRep ),
B );
end );
#############################################################################
##
#F MutableBasisViaNiceMutableBasisMethod3( <R>, <vectors>, <zero> )
##
InstallGlobalFunction( MutableBasisViaNiceMutableBasisMethod3,
function( R, vectors, zero )
local M, B;
M:= LeftModuleByGenerators( R, vectors, zero );
B:= rec( leftModule:= M );
# If `vectors' is empty then in general `M' will *not* be
# handled by nice bases.
if IsHandledByNiceBasis( M ) then
B.niceMutableBasis:= MutableBasis( R,
List( vectors,
v -> NiceVector( M, v ) ),
NiceVector( M, zero ) );
elif IsEmpty( vectors ) then
B.zero:= zero;
else
Error( "<M> is not handled via nice bases" );
fi;
return Objectify( NewType( CollectionsFamily( FamilyObj( zero ) ),
IsMutableBasis
and IsMutable
and IsMutableBasisViaNiceMutableBasisRep ),
B );
end );
#############################################################################
##
#M ViewObj( <MB> ) . . . . . . . . . . . . . . . . . . view a mutable basis
##
InstallMethod( ViewObj,
"for mutable basis represented by a nice mutable basis",
true,
[ IsMutableBasis and IsMutableBasisViaNiceMutableBasisRep ], 0,
function( MB )
Print( "<mutable basis over " );
View( LeftActingDomain( MB!.leftModule ) );
if IsBound( MB!.niceMutableBasis ) then
Print( ", ",
Pluralize( NrBasisVectors( MB!.niceMutableBasis ), "vector" ),
">" );
else
Print( ", 0 vectors>" );
fi;
end );
#############################################################################
##
#M PrintObj( <MB> ) . . . . . . . . . . . . . . . . . print a mutable basis
##
InstallMethod( PrintObj,
"for mutable basis represented by a nice mutable basis",
true,
[ IsMutableBasis and IsMutableBasisViaNiceMutableBasisRep ], 0,
function( MB )
if IsBound( MB!.niceMutableBasis ) then
Print( "MutableBasis( ",
LeftActingDomain( MB!.leftModule ), ", ",
BasisVectors( MB!.niceMutableBasis ), ", ",
Zero( LeftActingDomain( MB!.leftModule ) ), " )" );
else
Print( "MutableBasis( ",
LeftActingDomain( MB!.leftModule ), ", [], ",
Zero( LeftActingDomain( MB!.leftModule ) ), " )" );
fi;
end );
#############################################################################
##
#M BasisVectors( <MB> )
##
InstallOtherMethod( BasisVectors,
"for mutable basis represented by a nice mutable basis",
true,
[ IsMutableBasis and IsMutableBasisViaNiceMutableBasisRep ], 0,
function( MB )
local M;
if IsBound( MB!.niceMutableBasis ) then
M:= MB!.leftModule;
return Immutable( List( BasisVectors( MB!.niceMutableBasis ),
v -> UglyVector( M, v ) ) );
else
return Immutable( [] );
fi;
end );
#############################################################################
##
#M NrBasisVectors( <MB> ) . for a mutable basis using a nice mutable basis
##
InstallMethod( NrBasisVectors,
"for mutable basis represented by a nice mutable basis",
true,
[ IsMutableBasis and IsMutableBasisViaNiceMutableBasisRep ], 0,
function( MB )
if IsBound( MB!.niceMutableBasis ) then
return Length( BasisVectors( MB!.niceMutableBasis ) );
else
return 0;
fi;
end );
#############################################################################
##
#M CloseMutableBasis( <MB>, <v> )
##
InstallMethod( CloseMutableBasis,
"for mutable basis repres. by a nice mutable basis, and vector",
IsCollsElms,
[ IsMutableBasis and IsMutable and IsMutableBasisViaNiceMutableBasisRep,
IsVector ], 0,
function( MB, v )
local R, M;
if IsBound( MB!.niceMutableBasis ) then
return CloseMutableBasis( MB!.niceMutableBasis,
NiceVector( MB!.leftModule, v ) );
elif v <> MB!.zero then
# We have to setup the component `niceMutableBasis'.
R:= LeftActingDomain( MB!.leftModule );
M:= LeftModuleByGenerators( R, [ v ] );
if not IsHandledByNiceBasis( M ) then
Error( "<M> must be handled via nice bases" );
fi;
MB!.leftModule:= M;
MB!.niceMutableBasis:= MutableBasis( R,
[ NiceVector( M, v ) ] );
return true;
fi;
end );
#############################################################################
##
#M IsContainedInSpan( <MB>, <v> )
##
InstallMethod( IsContainedInSpan,
"for mutable basis repres. by a nice mutable basis, and vector",
IsCollsElms,
[ IsMutableBasis and IsMutableBasisViaNiceMutableBasisRep, IsVector ], 0,
function( MB, v )
if IsBound( MB!.niceMutableBasis ) then
return IsContainedInSpan( MB!.niceMutableBasis,
NiceVector( MB!.leftModule, v ) );
else
return v = MB!.zero;
fi;
end );
#############################################################################
##
#M ImmutableBasis( <MB> )
##
InstallMethod( ImmutableBasis,
"for mutable basis represented by a nice mutable basis",
true,
[ IsMutableBasis and IsMutableBasisViaNiceMutableBasisRep ], 0,
function( MB )
local M, nice, vectors, B;
M:= MB!.leftModule;
if IsBound( MB!.niceMutableBasis ) then
nice:= ImmutableBasis( MB!.niceMutableBasis );
vectors:= List( BasisVectors( nice ), v -> UglyVector( M, v ) );
if not IsEmpty( vectors ) then
M:= LeftModuleByGenerators( LeftActingDomain( M ), vectors );
SetNiceFreeLeftModule( M, UnderlyingLeftModule( nice ) );
fi;
#T use that we have the nice basis already!
#T (do not construct it twice!)
else
vectors:= [];
fi;
B:= BasisNC( M, vectors );
if HasIsSmallList( vectors ) then
SetIsSmallList( B, IsSmallList( vectors ) );
fi;
return B;
end );
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