[Cuis-dev] Documentation for the different kinds of divisions

[Andres Valloud]

https://en.wikipedia.org/wiki/Euclidean_division

Looks like it's called centered division, and that just as div:mod: 
define truncation, these two define rounding.  Well, then how about 
centeredDiv: and centeredMod:?  They are a tad long, centerDiv: and 
centerMod: perhaps?

On 5/25/20 13:44, Luciano Notarfrancesco via Cuis-dev wrote:
> On Tue, May 26, 2020 at 4:04 AM Nicolas Cellier via Cuis-dev 
> <cuis-dev at lists.cuis.st <mailto:cuis-dev at lists.cuis.st>> wrote:
> 
>     The integer division makes sense for specialized applications.
>     I used it 30 years back for polynomial factorization, if I remember,
>     because it leads to smaller LargeIntegers in p-adic methods.
> 
> 
> Oh, now I see. The remainder of this division is also called balanced or 
> centered remainder, I think, and I guess the division must be balanced 
> or centered division? When dividing by m it gives a remainder between 
> -m/2 and m/2, and it makes sense to use it when working with p-adics, in 
> particular I use this when doing Hensel lifting when factoring 
> polynomials with Zassenhauss algorithm, probably the same thing you did 
> 30 years ago :)
> I think I always used the remainder and never the quotient of this 
> division, but it is also an Euclidean division for the integers, and it 
> has the property that the remainder is of minimal absolute value, right? 
> I didn't know the quotient was important for floating point. Personally 
> I'm not very convinced of the message names #ratio: and #residue: but I 
> can't think anything better right now.
>