Hello everybody:

Just a suggestion.

There is a strong relation between continued fractions and function FindTransientRepeat[] and this last is not referenced neither in the help of ContinuedFraction[] nor in the help of FromContinuedFraction[]. These lacks of links in the help See also sections made me to spend some time in writing my own FindTransientRepeat[] which, by pure chance, I found later into the 6800+ functions in Mathematica.

My main point is that FindTransientRepeat[] should appear in the See also sections of helps of ContinuedFraction[] and FromContinuedFraction[].

This is what I was doing: We can expand 5 + 2 Sqrt[7] and find 10.291502622129181181003231507. How can I find the first quadratic irrational expression from the given decimal expansion?. The following steps do that work for low numbers in the quadratic irrational:

xx = 10.2915026221291811810032315073; cf = ContinuedFraction[xx]; tr = FindTransientRepeat[cf, 2]; yy = FromContinuedFraction[{Flatten[tr]}]

(*output*)
5 + 2 Sqrt[7]   

QuadraticIrrationalQ[yy] True

César Lozada