# $Source: /u/maple/research/lib/DEtools/src/RCS/eigenring,v $
# $Notify: mvanhoei@daisy.uwaterloo.ca $

macro(
	DF=`DEtools/diffop/DF`,
	x=`DEtools/diffop/x`,
	eigenring=`DEtools/diffop/eigenring`,
	endomorphism_charpoly=`DEtools/diffop/endomorphism_charpoly`
):

# Input a differential operator L
# Output: the eigenring
`DEtools/eigenring`:=proc(L,domain)
local d,v;
	option `Copyright (c) 1997 Waterloo Maple Inc. All rights reserved. Author: M. van Hoeij`;
	d:=[args];
	v := indets(d,{radical,nonreal});
	if v<>{} then
		v := radfield(v);
		return eval(subs(v[2],procname(op(eval(subs(v[1],d))))))
	fi;
	d:=`if`(nargs>1 and type(domain,list),domain,_Envdiffopdomain);
	if nops(d)<>2 then
		error "differential algebra not specified"
	fi;
	_Envdiffopdomain:=d; # for the userinfo's in diffop.
	# call the eigenring code
	map(sort,subs(DF=d[1],x=d[2],
		eigenring(subs(d[1]=DF,d[2]=x,L),args[2..nargs])),d[1])
end:

# Input a differential operator L and a differential operator r: V(L) -> V(L)
# Output: the characteristic polynomial of this map r.
`DEtools/endomorphism_charpoly`:=proc(L,r,domain)
local d,v;
	option `Copyright (c) 1997 Waterloo Maple Inc. All rights reserved. Author: M. van Hoeij`;
	d:=[args];
	v := indets(d,{radical,nonreal});
	if v<>{} then
		v := radfield(v);
		return eval(subs(v[2],procname(op(eval(subs(v[1],d))))))
	fi;
	d:=`if`(nargs>2,domain,_Envdiffopdomain);
	if nops(d)<>2 then
		error "differential algebra not specified"
	fi;
	# call the endomorphism_charpoly code
	subs(DF=d[1],x=d[2],
		endomorphism_charpoly(op(subs(d[1]=DF,d[2]=x,[L,r]))))
end:



#savelib('`DEtools/eigenring`','`DEtools/endomorphism_charpoly`'):