--- /dev/null
+## Copyright (C) 2002 Etienne Grossmann. All rights reserved.
+##
+## This program is free software; you can redistribute it and/or modify it
+## under the terms of the GNU General Public License as published by the
+## Free Software Foundation; either version 2, or (at your option) any
+## later version.
+##
+## This is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
+## for more details.
+
+## ex = poly_2_ex (l, f) - Extremum of a 1-var deg-2 polynomial
+##
+## l : 3 : Values of variable at which polynomial is known.
+## f : 3 : f(i) = Value of the degree-2 polynomial at l(i).
+##
+## ex : 1 : Value for which f reaches its extremum
+##
+## Assuming that f(i) = a*l(i)^2 + b*l(i) + c = P(l(i)) for some a, b, c,
+## ex is the extremum of the polynome P.
+##
+function ex = poly_2_ex (l, f)
+
+
+### This somewhat helps if solution is very close to one of the points.
+[f,i] = sort (f);
+l = l(i);
+
+
+m = (l(2) - l(1))/(l(3) - l(1));
+d = (2*(f(1)*(m-1)+f(2)-f(3)*m));
+if abs (d) < eps,
+ printf ("poly_2_ex : divisor is small (solution at infinity)\n");
+ printf ("%8.3e %8.3e %8.3e, %8.3e %8.3e\n",\
+ f(1), diff (f), diff (sort (l)));
+
+ ex = (2*(l(1)>l(2))-1)*inf;
+ ## keyboard
+else
+ ex = ((l(3) - l(1))*((f(1)*(m^2-1) + f(2) - f(3)*m^2))) / d ;
+
+## Not an improvement
+# n = ((l(2)+l(3))*(l(2)-l(3)) + 2*(l(3)-l(2))*l(1)) / (l(3)-l(1))^2 ;
+# ex = ((l(3) - l(1))*((f(1)*n + f(2) - f(3)*m^2))) / \
+# (2*(f(1)*(m-1)+f(2)-f(3)*m));
+# if ex != ex0,
+# ex - ex0
+# end
+ ex = l(1) + ex;
+end
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