# $Source: /u/maple/research/lib/algcurves/src/RCS/homogeneous,v $
# $Notify: hoeij@sci.kun.nl $

# 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,y,z,what)
local i,j,n,f;
	option `Copyright (c) 1996 Waterloo Maple Inc. All rights reserved.`;
	f:=collect(ff,{x,y},'distributed');
	if nargs>4 and what='ratfunction' then
		i:=collect(numer(f),{x,y},'distributed');
		j:=collect(denom(f),{x,y},'distributed');
		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;
	n:=degree(f,{x,y});
	convert([seq(seq(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`','`algcurves/homogeneous.m`'):