# $Source: /u/maple/research/lib/DEtools/src/RCS/de2diffop,v $
# $Notify: mvanhoei@daisy.uwaterloo.ca $

# This file contains conversion and type checking tools for diffop:

macro(
	x=`DEtools/diffop/x`,
	DF=`DEtools/diffop/DF`,

	to_diffop=`DEtools/diffop/to_diffop`,
	to_eqn=`DEtools/diffop/to_eqn`
):

# Only for the homogeneous case.
to_diffop:=proc(eqn,dvar)
global x,DF,subs_rad;
local d,L;
	option `Copyright (c) 1997 Waterloo Maple Inc. All rights reserved.`;

	`DEtools/diffop/l_p`();
	d:=`if`(nargs>1 and (type(dvar,list) or type(dvar,function))
	  ,dvar,_Envdiffopdomain);
	if type(d,list) then
		# input is already a differential operator
		_Envdiffopdomain:=d;	# the point of this step is that
					# this variable can be used for
					# making the output of userinfo nicer.
		subs(d[1]=DF,d[2]=x,eqn)
	elif type(d,function) then
		# input is an equation
		L:=subs(op(d)=x,`DEtools/convertAlg`(eqn,d));
		if evala(Normal(L[2]))<>0 then
			error "expecting a linear homogeneous differential equation"
		fi;
		add(evala(Normal(L[1][d]))*DF^(d-1),d=1..nops(L[1]))
	else
		error "wrong number (or type) of arguments"
	fi
end:

# In case dvar is a function y(x) then this proceduces an equation.
# If it is a list [Dx,x] then it produces an operator.
to_eqn:=proc(L,dvar)
global x,DF;
local i;
	option `Copyright (c) 1997 Waterloo Maple Inc. All rights reserved.`;
	# No options remember otherwise the following doesn't work:
	if nargs=1 then
		i:=_Envdiffopdomain;
		if type(i,list) then
			procname(L,i)
		else
			error "differential algebra not specified"
		fi
	elif type(L,list) or type(L,set) then
		map(procname,L,args[2..nargs])
	elif type(dvar,list) then
		# original input was an operator, so operator syntax
		# output
		sort(subs(DF=dvar[1],x=dvar[2],L),dvar[1])
	elif type(dvar,function) then
		subs(x=op(dvar),convert([
		 coeff(L,DF,0)*dvar,seq(coeff(L,DF,i)*diff(dvar,op(dvar)$i)
		 ,i=1..degree(L,DF))
		],`+`))
	else
		error "wrong arguments"
	fi
end:

#savelib('to_eqn','to_diffop'):

#macro(
#	to_eqn=readlib(`DEtools/diffop/to_eqn`),
#	to_diffop=readlib(`DEtools/diffop/to_diffop`)
#):

# Input: homogeneous equation, dependent variable, domain (the
# differential algebra)
# Output: differential operator.
# Options: monic -> make the output monic.
# Perhaps `convert/diffop` would also be a good name for this procedure.
`DEtools/de2diffop`:=proc(eqn,dvar,d)
global x,DF;
local L;
	option `Copyright (c) 1997 Waterloo Maple Inc. All rights reserved. Author: M. van Hoeij`;
	if nargs<3 or d='monic' then
		return procname(eqn,dvar,_Envdiffopdomain,args[3..nargs])
	fi;
	if not(type(d,list)) then
		if type(dvar,list) then
			return procname(eqn,d,dvar,args[4..nargs])
		else
		error "differential algebra not specified"
		fi
	elif not(type(dvar,function)) then
		error "dependent variable must be specified"
	fi;
	L:=traperror(to_diffop(eqn,dvar));
	if L=lasterror then
		# To make the error appear in here rather than
		# in some long procedure name.
		error L
	fi;
	L:=subs(DF=d[1],x=d[2],L);
	if nargs[nargs]='monic' then
		L:=collect(L/lcoeff(L,d[1]),d[1],evala@Normal)
	fi;
	sort(L,d[1])
end:

`DEtools/diffop2de`:=proc(L,dvar,d)
global x,DF;
local M;
	option `Copyright (c) 1997 Waterloo Maple Inc. All rights reserved. Author: M. van Hoeij`;
	if nargs<3 or d='monic' then
		return procname(L,dvar,_Envdiffopdomain,args[3..nargs])
	fi;
	if not(type(d,list)) then
		if type(dvar,list) then
			return procname(L,d,dvar,args[4..nargs])
		else
		error "differential algebra not specified"
		fi
	elif not(type(dvar,function)) then
		error "dependent variable must be specified"
	fi;
	M:=subs(d[1]=DF,d[2]=x,L);
	if args[nargs]='monic' then
		M:=collect(M/lcoeff(M,d[1]),d[1],evala@Normal)
	fi;
	to_eqn(M,dvar)
end:

#savelib('`DEtools/de2diffop`','`DEtools/diffop2de`'):