%!

% x is an initial guess, /f the name of a function
% with one argument x that returns the pair [ f(x) f'(x) ]
% x /f
/newton-solve { load % now the function itself is on the stack top
  1 dict begin
  /f exch def
  /x exch def
  10 { % a somewhat arbitary number of iterations
	/x 
      x
      x f 0 get
      x f 1 get
      div
      sub
    def % x = x - f(x)/f'(x) 
  } repeat
  x 
} def

% x -> [ x^2-2 2x ]
/f2 { 1 dict begin
  /x exch def
  [ 
	x dup mul 2 sub
    2 x mul
  ]
end } def

% x -> [ x^3-2 3x^2 ]
/f3 { 1 dict begin
  /x exch def
  [ 
	x dup dup mul mul 2 sub
    x dup mul 3 mul
  ]
end } def

% ===============================================================

1 /f2 newton-solve ==

1 /f3 newton-solve ==

quit