Pickle FpGroups

[kiryph]

I miss the possibility to store a larger list of FpGroups to a file.
As far as I know, only permutation and matrix groups are implemented:

io/gap/pickle.gi

Lines 1155 to 1209 in a911c88

	InstallMethod( IO_Pickle, "for a permutation group",
	[ IsFile, IsPermGroup ],
	function( f, g )
	if IO_Write(f,"PRMG") = fail then return IO_Error; fi;
	if IO_Pickle(f,GeneratorsOfGroup(g)) = IO_Error then return IO_Error; fi;
	if HasSize(g) then
	if IO_Pickle(f,Size(g)) = IO_Error then return IO_Error; fi;
	else
	if IO_Pickle(f,fail) = IO_Error then return IO_Error; fi;
	fi;
	if HasStabChainImmutable(g) then
	if IO_Pickle(f,BaseStabChain(StabChainImmutable(g))) = IO_Error then
	return IO_Error;
	fi;
	elif HasStabChainMutable(g) then
	if IO_Pickle(f,BaseStabChain(StabChainMutable(g))) = IO_Error then
	return IO_Error;
	fi;
	else
	if IO_Pickle(f,fail) = IO_Error then return IO_Error; fi;
	fi;
	return IO_OK;
	end );
	IO_Unpicklers.PRMG :=
	function(f)
	local base,g,gens,size;
	gens := IO_Unpickle(f); if gens = IO_Error then return IO_Error; fi;
	g := GroupWithGenerators(gens);
	size := IO_Unpickle(f); if size = IO_Error then return IO_Error; fi;
	if size <> fail then SetSize(g,size); fi;
	base := IO_Unpickle(f); if base = IO_Error then return IO_Error; fi;
	if base <> fail then
	StabChain(g,rec(knownBase := base));
	fi;
	return g;
	end;
	InstallMethod( IO_Pickle, "for a matrix group",
	[ IsFile, IsMatrixGroup ],
	function( f, g )
	return IO_GenericObjectPickler(f,"MATG",[GeneratorsOfGroup(g)],g,
	[Name,Size,DimensionOfMatrixGroup,FieldOfMatrixGroup],[],[]);
	end );
	IO_Unpicklers.MATG :=
	function(f)
	local g,gens;
	gens := IO_Unpickle(f); if gens = IO_Error then return IO_Error; fi;
	g := GroupWithGenerators(gens);
	return
	IO_GenericObjectUnpickler(f,g,
	[Name,Size,DimensionOfMatrixGroup,FieldOfMatrixGroup],[]);
	return g;
	end;

For example:

gap> L24fp;
[ Group([ g1, g2, g3, g4 ]), Group([ g1, g2, g3, g5*g4^-1 ]), Group([ g1, g2, g3, g4^-2 ]), Group([ g1, g2, g3, g4^3 ]), Group([ g1, g2, g3, g4^-1*g5^2*g4^-1 ]), 
  Group([ g1, g2, g3, g4^-4 ]), Group([ g1, g2, g4 ]), Group([ g1, g2, g4^-2, g5*g4^-1 ]), Group([ g1, g2, g5*g4^-1, g3*g5*g4^-1*g3^-1 ]), 
  Group([ g1, g2, g5*g4^-1, g3*g4^-2*g3^-1 ]), Group([ g1, g2, g5*g4^-1, g3*g4^2*g5^-1*g3^-1 ]), Group([ g1, g2, g5*g4^-1, g3*g4^3*g3^-1 ]), 
  Group([ g1, g2, g5*g4^-1, g3*g4^-2*g5*g4^-1*g3^-1 ]), Group([ g1, g2, g5*g4^-1, g3*g4^-4*g3^-1 ]), Group([ g1, g2, g5*g4, g4^3 ]), Group([ g1, g2, g5*g4, g4^-4 ]), 
  Group([ g1, g2, g5*g4, g4^5 ]), Group([ g1, g2, g5*g4, g4^-6 ]), Group([ g1, g2, g5*g4, g4^7 ]), Group([ g1, g2, g5*g4, g4^-8 ]), Group([ g1, g2, g4^-2 ]), 
  Group([ g1, g2, g3*g4^-2*g3^-1, g4^-4 ]), Group([ g1, g2, g4^-2*g5^-1*g4^-1 ]), Group([ g1, g2, g3*g4^-2*g3^-1, g4^-2*g5*g4^-1 ]), Group([ g1, g3, g4 ]), 
  Group([ g1, g3, g5*g4^-1 ]), Group([ g1, g3, g4^-2 ]), Group([ g1, g3, g4^-1*g5^2*g4^-1 ]), Group([ g1, g3, g4^3 ]), Group([ g1, g4 ]), 
  Group([ g1, g4*g2^-1, g4^-1*g2^-1 ]), Group([ g1, g4*g2^-1, g3*g4^-2*g3^-1 ]), Group([ g1, g4*g2^-1, g3*g4^3*g3^-1 ]), Group([ g1, g4*g2^-1, g3*g4^-4*g3^-1 ]), 
  Group([ g1, g4^-2, g5*g4^-1 ]), Group([ g1, g5*g4^-1, g3*g5*g4^-1*g3^-1 ]), Group([ g1, g5*g4^-1, g3*g4^-2*g3^-1 ]), Group([ g1, g5*g4, g2*g4^2 ]), 
  Group([ g1, g4^-2, g5^-2, g2*g4*g5^-1 ]), Group([ g1, g2*g4*g5^-1, g3*g4^-2*g3^-1 ]), Group([ g1, g5*g4, g4^3 ]), Group([ g1, g5*g4, g4^3*g2^-1 ]), 
  Group([ g1, g5*g4, g4^-4 ]), Group([ g1, g5*g4, g2*g4^4 ]), Group([ g1, g2*g4*g5, g2*g4^-2 ]), Group([ g1, g2*g4*g5, g2*g4^-1*g5^-1, g4^-4 ]), 
  Group([ g1, g2*g4*g5, g2*g4^-1*g5^-1, g4^-2*g5*g4^-1 ]), Group([ g1, g2*g4^2, g2*g4^-2 ]), Group([ g1, g4^-2 ]), Group([ g2, g3, g4 ]), Group([ g2, g3, g5*g4^-1 ]), 
  Group([ g2, g3, g4^-2 ]), Group([ g2, g3, g4^2*g5^-1 ]), Group([ g2, g3, g4^3 ]), Group([ g2, g3, g4^-1*g5^2*g4^-1 ]), Group([ g2, g4, g5 ]), 
  Group([ g2, g4, g5^-2, g1*g3^-1*g5^-1 ]), Group([ g2, g4, g5^-2 ]), Group([ g2, g4, g5^3 ]), Group([ g2, g4, g1*g3^-1*g5^3 ]), Group([ g2, g4, g5^-4 ]), 
  Group([ g2, g5*g4^-1, g1*g4^2 ]), Group([ g2, g5*g4^-1, g3*g5*g4^-1*g3^-1 ]), Group([ g2, g5*g4^-1, g4*g3^-1*g4^-1*g3, g4^3*g1^-1 ]), 
  Group([ g2, g5*g4^-1, g3*g4^-2*g3^-1 ]), Group([ g2, g5*g4^-1, g1*g3*g4^2*g3^-1 ]), Group([ g2, g5^-2, g1*g3*g5^-1, g4^-4 ]), Group([ g2, g4^-2, g5^-2 ]), 
  Group([ g2, g4^-2, g3*g4^2*g1^-1 ]), Group([ g2*g1^-1, g3, g4 ]), Group([ g2*g1^-1, g3, g5*g4^-1 ]), Group([ g2*g1^-1, g3, g4^-2 ]), 
  Group([ g2*g1^-1, g3, g4^-1*g5^2*g4^-1 ]), Group([ g2*g1^-1, g3, g4^3 ]), Group([ g2*g1^-1, g4 ]), Group([ g2*g1^-1, g4*g1^-1, g4^-1*g1^-1 ]), 
  Group([ g2*g1^-1, g4*g1^-1, g4^-3*g1^-1 ]), Group([ g2*g1^-1, g4*g1^-1, g4^-5*g1^-1 ]), Group([ g2*g1^-1, g4*g1^-1, g4^-7*g1^-1 ]), 
  Group([ g2*g1^-1, g4*g3^-1, g4^-1*g3 ]), Group([ g2*g1^-1, g4^-1*g3, g3*g5^2 ]), Group([ g2*g1^-1, g4^-1*g3, g4^2*g5^-1*g3^-1 ]), Group([ g2*g1^-1, g4^-2, g5*g4^-1 ]), 
  Group([ g2*g1^-1, g5*g4^-1, g3*g5*g4^-1*g3^-1 ]), Group([ g2*g1^-1, g5*g4^-1, g4*g3^-1*g4^-1*g3, g4^3*g1^-1 ]), Group([ g2*g1^-1, g5*g4^-1, g3*g4^-2*g3^-1 ]), 
  Group([ g2*g1^-1, g5*g4, g4^3 ]), Group([ g2*g1^-1, g5*g4, g4^-4 ]), Group([ g2*g1^-1, g1*g4*g5, g4^-4 ]), Group([ g2*g1^-1, g4^-2 ]), Group([ g3, g4 ]), 
  Group([ g3, g5*g4^-1 ]), Group([ g3, g4^-2 ]), Group([ g4, g5 ]), Group([ g4, g5*g2^-1, g5^-1*g2^-1 ]), Group([ g4, g5*g2^-1, g1*g3^-1*g5 ]), 
  Group([ g4, g5*g2^-1, g5^-3*g2^-1 ]), Group([ g4, g5*g2^-1, g1*g3^-1*g5^3 ]), Group([ g4, g5^-2, g1*g3^-1*g5^-1 ]), Group([ g4, g1*g3^-1*g5^-1, g5^-4 ]), 
  Group([ g4, g5^-2, g2*g3*g4^-1*g1^-1 ]), Group([ g4, g5^-2 ]), Group([ g4, g5^-4, g1*g2*g3^-1*g5^-2 ]), Group([ g4*g2^-1, g5*g2^-1, g1*g2*g4 ]), 
  Group([ g4*g2^-1, g5*g2^-1, g3*g4^-2*g3^-1 ]), Group([ g4*g2^-1, g5*g2^-1, g1*g2*g4^3 ]), Group([ g4*g2^-1, g4^-1*g2^-1, g5^-2 ]), 
  Group([ g4*g2^-1, g4^-1*g2^-1, g3*g4^2*g1^-1 ]), Group([ g4*g3^-1, g4^-1*g3, g5*g3^-1 ]), Group([ g5*g4^-1, g1*g2*g4^-1, g3*g4^-2*g3^-1 ]), 
  Group([ g5*g4^-1, g1*g4^2 ]) ]

Documentation on Extending the pickling framework can be found here:
https://gap-packages.github.io/io/doc/chap5_mj.html#X7B1C9A9C7D3C0312

[fingolfin]

Sure, something like this would be nice, also for pc groups. If anybody is interested in working on this, patches are welcome.

Note that pickling fp groups is a bit tricky, as each fp group has its own family, and one has to be very careful to handle this correctly when e.g. also pickling list of elements of fp groups.