|
#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Alexander Hulpke.
##
## 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 rotines that enable simplified display and turn on
## some naive routines, which are primarily of interest in a teaching
## context. It is made part of the general system to ensure it will be
## always installed with GAP.
##
## FFE Display
InstallMethod(ViewObj,true,[IsFFE],100,
function(x)
local p,d;
if TEACHMODE<>true then
TryNextMethod();
fi;
d:=DegreeFFE(x);
p:=Characteristic(x);
if d=1 then
Print("ZmodnZObj(",Int(x),",",p,")");
else
Print("Z(",p^d,")^",LogFFE(x,Z(p^d)));
fi;
end);
InstallMethod(String,true,[IsFFE],100,
function(x)
local p,d;
if TEACHMODE<>true then
TryNextMethod();
fi;
d:=DegreeFFE(x);
p:=Characteristic(x);
if d=1 then
return Concatenation("ZmodnZObj(",String(Int(x)),",",String(p),")");
else
return Concatenation("Z(",String(p^d),")^",String(LogFFE(x,Z(p^d))));
fi;
end);
InstallMethod( ZmodnZObj, "for prime residues convert to GF(p)",
[ IsInt, IsPosInt ],100,
function( residue, n )
if TEACHMODE<>true then
TryNextMethod();
fi;
if not IsPrimeInt(n) then
return ZmodnZObj( ElementsFamily( FamilyObj( ZmodnZ( n ) )), residue );
else
return residue*Z(n)^0;
fi;
end );
## Cyclotomics display
## Careful, this can affect the rationals!
InstallMethod(ViewObj,true,[IsCyc],100,
function(x)
local a;
if IsRat(x) or TEACHMODE<>true or Conductor(x)=4 then
TryNextMethod();
fi;
a:=Quadratic(x,true);
if a=fail then
TryNextMethod();
fi;
Print(a.display);
end);
# basic constructors -- if teaching mode they will default to fp groups
#############################################################################
##
#F AbelianGroup( [<filt>, ]<ints> ) . . . . . . . . . . . . . abelian group
##
BindGlobal( "AbelianGroup", function ( arg )
if Length(arg) = 1 then
if ForAny(arg[1],x->x=0) or TEACHMODE=true then
return AbelianGroupCons( IsFpGroup, arg[1] );
else
return AbelianGroupCons( IsPcGroup, arg[1] );
fi;
elif IsOperation(arg[1]) then
if Length(arg) = 2 then
return AbelianGroupCons( arg[1], arg[2] );
elif Length(arg) = 3 then
return AbelianGroupCons( arg[1], arg[2], arg[3] );
fi;
fi;
Error( "usage: AbelianGroup( [<filter>, ]<ints> )" );
end );
#############################################################################
##
#F CyclicGroup( [<filt>, ]<n> ) . . . . . . . . . . . . . . . cyclic group
##
BindGlobal( "CyclicGroup", function ( arg )
if Length(arg) = 1 then
if arg[1]=infinity or TEACHMODE=true then
return CyclicGroupCons(IsFpGroup,arg[1]);
fi;
return CyclicGroupCons( IsPcGroup, arg[1] );
elif IsOperation(arg[1]) then
if Length(arg) = 2 then
return CyclicGroupCons( arg[1], arg[2] );
elif Length(arg) = 3 then
return CyclicGroupCons( arg[1], arg[2], arg[3] );
fi;
fi;
Error( "usage: CyclicGroup( [<filter>, ]<size> )" );
end );
#############################################################################
##
#F DihedralGroup( [<filt>, ]<n> ) . . . . . . . dihedral group of order <n>
##
BindGlobal( "DihedralGroup", function ( arg )
if Length(arg) = 1 then
if TEACHMODE=true then
return DihedralGroupCons( IsFpGroup, arg[1] );
else
return DihedralGroupCons( IsPcGroup, arg[1] );
fi;
elif IsOperation(arg[1]) then
if Length(arg) = 2 then
return DihedralGroupCons( arg[1], arg[2] );
elif Length(arg) = 3 then
return DihedralGroupCons( arg[1], arg[2], arg[3] );
fi;
fi;
Error( "usage: DihedralGroup( [<filter>, ]<size> )" );
end );
#############################################################################
##
#F ElementaryAbelianGroup( [<filt>, ]<n> ) . . . . elementary abelian group
##
BindGlobal( "ElementaryAbelianGroup", function ( arg )
if Length(arg) = 1 then
if TEACHMODE=true then
return ElementaryAbelianGroupCons( IsFpGroup, arg[1] );
else
return ElementaryAbelianGroupCons( IsPcGroup, arg[1] );
fi;
elif IsOperation(arg[1]) then
if Length(arg) = 2 then
return ElementaryAbelianGroupCons( arg[1], arg[2] );
elif Length(arg) = 3 then
return ElementaryAbelianGroupCons( arg[1], arg[2], arg[3] );
fi;
fi;
Error( "usage: ElementaryAbelianGroup( [<filter>, ]<size> )" );
end );
[ zur Elbe Produktseite wechseln0.30Quellennavigators
Analyse erneut starten
]
|
