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#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Heiko Theißen.
##
## 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
##
#############################################################################
##
#M Pcgs( <G> ) . . . . . . . . . . . . . . . . . . . . via nice monomorphism
##
InstallMethod( Pcgs, "via niceomorphism", true,
[ IsGroup and IsHandledByNiceMonomorphism ], 0,
function( G )
local nice, npcgs, pcgs;
nice := NiceMonomorphism( G );
npcgs := Pcgs( NiceObject( G ) );
if npcgs = fail then
return fail;
fi;
pcgs := List( npcgs, gen -> PreImagesRepresentative( nice, gen ) );
pcgs := PcgsByPcSequenceNC( ElementsFamily( FamilyObj( G ) ), pcgs );
if HasIsPrimeOrdersPcgs( npcgs ) and IsPrimeOrdersPcgs( npcgs ) then
SetIsPrimeOrdersPcgs( pcgs, true );
fi;
SetNiceMonomorphism( pcgs, nice );
SetNiceObject ( pcgs, npcgs );
SetGroupOfPcgs ( pcgs, G );
SetOneOfPcgs(pcgs,One(G));
SetFilterObj ( pcgs, IsHandledByNiceMonomorphism );
return pcgs;
end );
#############################################################################
##
#M DepthOfPcElement( <pcgs>, <g> [ , <from> ] ) . . . via nice monomorphism
##
AttributeMethodByNiceMonomorphismCollElm( DepthOfPcElement,
[ IsPcgs, IsMultiplicativeElementWithInverse ] );
InstallOtherMethod( DepthOfPcElement, true,
[ IsPcgs and IsHandledByNiceMonomorphism,
IsMultiplicativeElementWithInverse,
IsPosInt ], 0,
function( pcgs, g, depth )
return DepthOfPcElement( NiceObject( pcgs ),
ImagesRepresentative( NiceMonomorphism( pcgs ), g ),
depth );
end );
#############################################################################
##
#M LeadingExponentOfPcElement( <pcgs>, <g> ) . . . . . via nice monomorphism
##
AttributeMethodByNiceMonomorphismCollElm( LeadingExponentOfPcElement,
[ IsPcgs, IsMultiplicativeElementWithInverse ] );
#############################################################################
##
#M ExponentsOfPcElement( <pcgs>, <g> [ , <poss> ] ) . via nice monomorphism
##
AttributeMethodByNiceMonomorphismCollElm( ExponentsOfPcElement,
[ IsPcgs, IsMultiplicativeElementWithInverse ] );
InstallOtherMethod( ExponentsOfPcElement, true,
[ IsPcgs and IsHandledByNiceMonomorphism,
IsMultiplicativeElementWithInverse,
IsList and IsCyclotomicCollection ], 0,
function( pcgs, g, poss )
return ExponentsOfPcElement( NiceObject( pcgs ),
ImagesRepresentative( NiceMonomorphism( pcgs ), g ),
poss );
end );
InstallOtherMethod( ExponentsOfPcElement, "perm group with 0 positions", true,
[ IsPcgs and IsHandledByNiceMonomorphism,
IsMultiplicativeElementWithInverse,
IsList and IsEmpty ], 0,
function( pcgs, g, poss )
return [ ];
end );
#############################################################################
##
#M ExponentOfPcElement( <pcgs>, <g>, <pos> ) . . . . . via nice monomorphism
##
InstallMethod( ExponentOfPcElement, "via nicoemorphism", true,
[ IsPcgs and IsHandledByNiceMonomorphism,
IsMultiplicativeElementWithInverse,
IsPosInt ], 0,
function( pcgs, g, pos )
return ExponentOfPcElement( NiceObject( pcgs ),
ImagesRepresentative( NiceMonomorphism( pcgs ), g ),
pos );
end );
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