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

macro(
	RAD={radical,nonreal},
	DF=`DEtools/diffop/DF`,
	x=`DEtools/diffop/x`,
	DFactorLCLM=`DEtools/diffop/DFactorLCLM`,
	DFactor=`DEtools/diffop/DFactor`
):
# Input a differential operator L
# Output: a factorization
`DEtools/DFactor`:=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,RAD);
	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.
	_Envdiffopwarnings:=true; # if message really urgent then give it.
	# call the DFactor code
	map(sort,subs(DF=d[1],x=d[2],
		DFactor(subs(d[1]=DF,d[2]=x,L),args[2..nargs])),d[1])
end:

#savelib('`DEtools/DFactor`'):

# Input a differential operator L
# Output: an LCLM factorization
`DEtools/DFactorLCLM`:=proc(L,domain)
local d,v;
	option `Copyright (c) 1999 Waterloo Maple Inc. All rights reserved. Author: M. van Hoeij`;
	d:=[args];

	v := indets(d,RAD);
if v<>{} then
	v := radfield(v);
	v := eval(subs(v[2],procname(op(eval(subs(v[1],d))))))
else
	v:=indets(d,RootOf);
	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.
	v:=map(sort,subs(DF=d[1],x=d[2],map(`DEtools/diffop/index_them`,
	  DFactorLCLM(subs(d[1]=DF,d[2]=x,L),v),v)),d[1])
fi;
	if not has([args],RootOf) then
		v:=convert(v,radical)
	fi;
	v
end:

# Replace the RootOf's that don't occur in A by indexed RootOf's.
`DEtools/diffop/index_them`:=proc(i,A)
	local j,v,k;
	option `Copyright (c) 1999 Waterloo Maple Inc. All rights reserved.`;
	v:=indets(i,RootOf) minus indets(A,RootOf);
	v:={seq(`if`(has(j,index),NULL,j),j=v)};
if v={} then
	i
else
	v:=v minus indets(map(op,v),RootOf);
	v:=v[1];
	seq(procname(subs(v=RootOf(op(v),index=j),i),A)
	,j=1..degree(`DEtools/diffop/subs_Z`(op(1,v),k),k))
fi
end:

#savelib('`DEtools/DFactorLCLM`','`DEtools/diffop/index_them`'):