Re: [Boost-users] [rational] proposed gcd and lcm for rational

Subject: Re: [Boost-users] [rational] proposed gcd and lcm for rational
From: Júlio Hoffimann (julio.hoffimann_at_[hidden])
Date: 2011-07-21 11:06:59

Hi Christopher,

This is the first time i heard about this interpretation. For me, still
makes no sense, but if people thinks is useful, ok.

Regards,
Júlio.

2011/7/21 Christopher Henrich <chenrich_at_[hidden]>

> GCD and LCM can be defined for rationals, if one takes "divisible" to mean
> "divisible with an integer quotient" and, similarly, "multiple" to mean
> "multiple by an integer." Then, for example, GCD(1/2, 1/3) = 1/6 and
> LCM(1/2, 1/3) = 1.
>
> On Jul 21, 2011, at 7:44 AM, Júlio Hoffimann wrote:
>
> Hi Thomas,
>
> Thank you for the intention, but as far as i know, GCD and LCM makes no
> sense in the rational field. Any rational number is divisible by all
> rationals. For instance, given two rationals b, r in Q, r != 0, you can
> write:
>
> b = (b * r^-1) * r
>
> and then b is divisible by r.
>
> Regards,
> Júlio.
>
> 2011/7/21 Thomas Taylor <thomas.taylor_at_[hidden]>
>
>> Dear boost users and maintainers,
>>
>> As I needed these functions myself I have added a gcd and an lcm for the
>> rational type.
>> Feel free to do with the code whatever you want, if suitable add it to
>> rational.hpp. Presumably this could be reworked as partial specialisation
>> of
>> boost::math::gcd and boost::math::lcm respectively (if there is a trait
>> like
>> is_rational).
>>
>> HTH,
>> Thomas
>>
>>
>>
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>
> Christopher Henrich
> chenrich_at_[hidden]
> mathinteract.com
>
>
>
>
>
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