Re: [boost] Math tools polynomial enhancements

Subject: Re: [boost] Math tools polynomial enhancements
From: Marc Glisse (marc.glisse_at_[hidden])
Date: 2015-10-29 11:23:34

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.

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

-- 
Marc Glisse