Re: Re: Re: Re: smallest
- To: mathgroup at smc.vnet.net
- Subject: [mg86870] Re: [mg86833] Re: [mg86828] Re: [mg86792] Re: [mg86771] smallest
- From: Carl Woll <carlw at wolfram.com>
- Date: Mon, 24 Mar 2008 01:45:16 -0500 (EST)
- References: <200803200757.CAA29500@smc.vnet.net> <200803210653.BAA18315@smc.vnet.net> <200803220554.AAA00496@smc.vnet.net> <200803230600.BAA25688@smc.vnet.net>
Artur wrote:
>If we want to find rational fraction f =p/q such that 113/355<f<106/333
>and sum p+q is minimal
>anyone procedure proposed up to now doesn't work
>good result should be
>{137563,{p->13215,q->104348}}
>but isn't
>
>
Your good result isn't so good, consider:
In[36]:= 113/355 < 219/688 < 106/333
Out[36]= True
One idea (similar to your Recognize approach) is to use Rationalize or
RootApproximant with SetPrecision:
In[71]:= Rationalize[SetPrecision[(106/333 + 113/355)/2, 6], 0]
Out[71]= 219/688
In[72]:= RootApproximant[SetPrecision[(106/333 + 113/355)/2, 6], 1]
Out[72]= 219/688
I'm not sure of the correct method to determine the precision to use. It
could be something like:
Choose largest prec such that:
IntervalMemberQ[Interval[{lo, hi}], SetPrecision[midpoint, prec]]
is still True.
Carl Woll
Wolfram Research
>ARTUR
>
>Artur pisze:
>
>
>>If value p/q is known
>>smallest Abs[p]+Abs[q ] should be
>><< NumberTheory`Recognize`
>>Recognize[p/q,1,x]
>>
>>see also
>>http://www.research.att.com/~njas/sequences/A138335
>>
>>Best wishes,
>>Artur
>>
>>Curtis Osterhoudt pisze:
>>
>>
>>
>>> I doubt this is in the spirit of the problem, but if p and q (assumed
>>>integers) aren't restricted to be _positive_, then taking them both to be
>>>very large negative numbers would both fit the p/q in I requirement, and p+q
>>>as "small" as possible.
>>>
>>> C.O.
>>>
>>>On Thursday 20 March 2008 01:57:30 masmoudi wrote:
>>>
>>>
>>>
>>>
>>>>hi
>>>>
>>>>suppose that we have an interval I belong to [0,1]
>>>>
>>>>I want to know how to calculate a fraction p/q
>>>>belong to I and p+q is the smallest possible
>>>>
>>>>
>>>>
>>>>
>>>
>>>
>>>
>>>
>>__________ NOD32 Informacje 2701 (20071204) __________
>>
>>Wiadomosc zostala sprawdzona przez System Antywirusowy NOD32
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>>
>>
>>
>>
>>
>>
- References:
- smallest fraction
- From: masmoudi <mas_atef@yahoo.fr>
- Re: smallest fraction
- From: Curtis Osterhoudt <cfo@lanl.gov>
- Re: Re: smallest fraction
- From: Artur <grafix@csl.pl>
- Re: Re: Re: smallest fraction
- From: Artur <grafix@csl.pl>
- smallest fraction