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
CĂ©sar Lozada
