let rec optimalRoot low high count =
            let mid = (((high-low)/2.)+low)
            if count>10 then
                mid
            elif (sturmSeq sturm low mid) > 0 then
                optimalRoot low mid (count+1)
            elif (sturmSeq sturm mid high) > 0 then
                optimalRoot mid high (count+1)
            else
                infinity


let rec NRap (t : float) rep oldFx =
            if rep > 50 then
                None
            else
               let fx = solveMap t poly
               if abs(fx)<1e-6 then
                   Some(t)
               else
                   NRap (t-(fx/(solveMap t diffMap))) (rep+1) fx