File: newton.mac

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newton(expr,guess):=block([y,prec:10^(fpprec/-2.0b0),var,dif, listconstvars : false],
       var:listofvars(expr)[1],
       dif:diff(expr,var),
       guess:bfloat(guess),
       do (y:sublis([var=guess],dif),y:expand(y),if abs(y) < prec then error("derivative at",guess,"is zero"),
	   guess:guess-sublis([var=(guess)],expr)/y,guess:rectform(expand(guess)), 
	   if abs(sublis([var=(guess)],expr)) < prec then return(guess)));