The a b/c key

[Joe Horn]

(03-08-2017 08:14 PM)math7 Wrote:  Thanks Joe, Oh I understand now, this is interesting. How do you know all that the CAS uses continuous fractions and the START MODE uses the PDQ algorithm (I do not know what it means)? Those things I have not seen in the manual !!!

You are correct that the information I posted above is not in the Prime documentation. The algorithms used by the [a b/c] button in Home and CAS can be deduced by the outputs. CAS only returns principle convergents of the continued fraction expansion of the input, whereas Home returns the best fraction which is sometimes an intermediate convergent. Therefore CAS must use the simple continued fraction algorithm (which misses all intermediate convergents), and Home must use PDQ (which never misses any intermediate convergents).

(03-08-2017 09:34 PM)Han Wrote:  You can read about it here: https://en.wikipedia.org/wiki/Continued_fraction (as for the name PDQ, that is likely "p divided by q").

That's right. "PDQ" was chosen not only because the literature about continued fractions often uses "p/q" but also because PDQ in English means Pretty Darn Quick, which the PDQ Algorithm is. For its complete history, search comp.sys.hp48 for "PDQ".