Does Fractions remove common factors the way it should? If it does and you want to find the closest fraction with a smaller denominator i think tou'll need some number theory and continued fractions.
RJB On Nov 18, 8:26 pm, Steven D'Aprano <st...@remove-this- cybersource.com.au> wrote: > On Thu, 18 Nov 2010 20:08:00 +0100, Stefan Sonnenberg-Carstens wrote: > > If you need it really *precise*, cast your Fractions into type Decimal: > > It's actually the opposite. Decimal has many advantages, but being > "really precise" is not one of them. It suffers the exact same issues re > precision and round-off as binary floating point. > > It is easy to demonstrate that there are numbers which cannot be > represented precisely as Decimals no matter how many decimal places you > use, but can be represented exactly as Fractions. Fraction can exactly > represent every Decimal, but Decimal cannot represent exactly every > Fraction. > > We're not talking about weird edge cases either, but simple numbers that > you're likely to come across every day: > > >>> from decimal import Decimal > >>> one_ninth = Decimal(1)/Decimal(9) > >>> two_thirds = Decimal(2)/Decimal(3) > >>> one_ninth*6 == two_thirds > > False > > >>> from fractions import Fraction > >>> one_ninth = Fraction(1, 9) > >>> two_thirds = Fraction(2, 3) > >>> one_ninth*6 == two_thirds > > True > > Still not convinced? > > >>> f = Fraction(1) + Fraction(1, 10**100000) > >>> f != 1 > > True > > (which is virtually instantaneous, by the way) > > compared to the *much* slower: > > >>> d = Decimal(1) + Decimal(1)/Decimal(10**100000) > >>> d != 1 > > False > > Yes, I could try to set the Decimal context to 100,000 decimal places -- > and just as easily defeat it again by adding one more to the exponent. > > In my opinion, the Fraction module is one of the least appreciated and > underused modules in the standard library -- and I include myself in > that. It really is a joy, and I don't use it anywhere near enough. > > -- > Steven -- http://mail.python.org/mailman/listinfo/python-list
