Lie wrote: > On Feb 18, 1:25 pm, Carl Banks <[EMAIL PROTECTED]> wrote: >> On Feb 17, 1:45 pm, Lie <[EMAIL PROTECTED]> wrote: >> >>>> Any iteration with repeated divisions and additions can thus run the >>>> denominators up. This sort of calculation is pretty common (examples: >>>> compound interest, numerical integration). >>> Wrong. Addition and subtraction would only grow the denominator up to >>> a certain limit >> I said repeated additions and divisions. > > Repeated Addition and subtraction can't make fractions grow > infinitely, only multiplication and division could. > On what basis is this claim made?
(n1/d1) + (n2/d2) = ((n1*d2) + (n2*d1)) / (d1*d2) If d1 and d2 are mutually prime (have no common factors) then it is impossible to reduce the resulting fraction further in the general case (where n1 = n2 = 1, for example). >> Anyways, addition and subtraction can increase the denominator a lot >> if for some reason you are inputing numbers with many different >> denominators. > > Up to a certain limit. After you reached the limit, the fraction would > always be simplifyable. > Where does this magical "limit" appear from? > If the input numerator and denominator have a defined limit, repeated > addition and subtraction to another fraction will also have a defined > limit. Well I suppose is you limit the input denominators to n then you have a guarantee that the output denominators won't exceed n!, but that seems like a pretty poor guarantee to me. Am I wrong here? You seem to be putting out unsupportable assertions. Please justify them or stop making them. regards Steve -- Steve Holden +1 571 484 6266 +1 800 494 3119 Holden Web LLC http://www.holdenweb.com/ -- http://mail.python.org/mailman/listinfo/python-list
