How about adding rational fraction to Python?

[Steven D'Aprano]

On Sun, 24 Feb 2008 10:09:37 -0800, Lie wrote:

> On Feb 25, 12:46 am, Steve Holden <st... at holdenweb.com> wrote:
>> Lie wrote:
>> > On Feb 18, 1:25 pm, Carl Banks <pavlovevide... at gmail.com> wrote:
>> >> On Feb 17, 1:45 pm, Lie <Lie.1... at gmail.com> 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.
>>
>>
> Well, I do a test on my own fraction class. I found out that if we set a
> limit to the numerators and denominators, the resulting output fraction
> would have limit too. I can't grow my fraction any more than this limit
> no matter how many iteration I do on them. I do the test is by something
> like this (I don't have the source code with me right now, it's quite
> long if it includes the fraction class, but I think you could use any
> fraction class that automatically simplify itself, might post the real
> code some time later):
> 
> while True:
>     a = randomly do (a + b) or (a - b)
>     b = random fraction between [0-100]/[0-100] print a
> 
> And this limit is much lower than n!. I think it's sum(primes(n)), but
> I've got no proof for this one yet.


*jaw drops*


Please stop trying to "help" convince people that rational classes are 
safe to use. That's the sort of "help" that we don't need.


For the record, it is a perfectly good strategy to *artificially* limit 
the denominator of fractions to some maximum value. (That's more or less 
the equivalent of setting your floating point values to a maximum number 
of decimal places.) But without that artificial limit, repeated addition 
of fractions risks having the denominator increase without limit.


-- 
Steven