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

# f is a polynomial or a rational function in x and y.
# Output: the corresponding homogeneous rational function or polynomial
`algcurves/homogeneous`:=proc(ff,x::name,y::name,z::name,what)
local i,j,n,f;
option `Copyright (c) 1996 Waterloo Maple Inc. All rights reserved. Author: M. van Hoeij`;
	if nargs>4 and what='ratfunction' then
		f:=evala(Normal(ff,'expanded'),'independent');
		i,j:=numer(f),denom(f);
		n:=degree(i,{x,y})-degree(j,{x,y});
		if n<0 then i:=i*z^(-n) elif n>0 then j:=j*z^n fi;
		return procname(i,x,y,z,polynom)/procname(j,x,y,z,polynom)
	fi;
	f:=collect(ff,{x,y},'distributed');
	n:=degree(f,{x,y});
	add(add(coeff(coeff(f,x,i),y,j)*x^i*y^j*z^(n-i-j)
	,i=0..n-j),j=0..n)
end:

#savelib ('`algcurves/homogeneous`'):