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

[Luciano Notarfrancesco]

On Tue, May 26, 2020 at 4:04 AM Nicolas Cellier via Cuis-dev <
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.
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