Re: [boost] Math tools polynomial enhancements

Subject: Re: [boost] Math tools polynomial enhancements
From: Jeremy Murphy (jeremy.william.murphy_at_[hidden])
Date: 2015-10-29 17:50:42

On 30/10/2015 2:24 AM, "Marc Glisse" <marc.glisse_at_[hidden]> wrote:
>
> On Fri, 30 Oct 2015, Jeremy Murphy wrote:
>
>>> Division is interesting because it's not actually clear to me what the
>>> result should be - is it a polynomial (plus remainder) or is it a
rational
>>> function (suitable reduced by the greatest common divisor).
>>
>>
>> Yes, I was initially troubled by this question but resolved, admittedly
>> more through intuition than proof, that polynomial division is Euclidean
>> (integer) division: the / operator gives you the quotient, and % gives
you
>> the remainder. Someone with a deeper understanding of abstract algebra
>> could presumably validate or discredit this claim. However, if one
accepts
>> this, then everything falls neatly into place, for example the /=
operator
>> makes sense, which it obviously wouldn't otherwise.
>
>
> This looks like a sensible choice. The situation is pretty similar to
integers. 10 / 4 could return a rational type, but the choice was made to
stay in the original type and use the Euclidean domain structure instead.

Thanks. Out of curiosity, which choice are you referring to? I presume it
must be early in computing history.

>
> You might want to provide a div-like function for people who want both
the quotient and the remainder without duplicating too much computation.

Yes, that's exactly what I've done.

Cheers.

>
> --
> Marc Glisse
>
>
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