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From Sébastien Brisard <sebastien.bris...@m4x.org>
Subject Re: [math] Support for Abelian Groups and Rings?
Date Mon, 03 Oct 2011 15:18:37 GMT
2011/10/3 Phil Steitz <phil.steitz@gmail.com>:
> On 10/3/11 7:00 AM, Sébastien Brisard wrote:
>> Hello,
>> I'm using quite extensively the Field/FieldElement interfaces, but am
>> sometimes feeling the need for less stringent sets like Abelian Groups
>> (no multiplication) and Rings (no division). This would allow me to
>> carry out some calculations on different types of number simply by
>> changing the generic type.
>> I was thinking of adding some interfaces along the lines of the two
>> above mentioned
>>   - AbelianGroup<T>, AbelianGroupElement<T>,
>>   - Ring<T>, RingElement<T>.
>>
>> Do you think that would be useful?
>
> If you have practical applications, then OK; if this is just to have
> more math abstractions, we have generally been conservative about
> that (i.e., introduce the abstractions as we need them for practical
> applications).  Can you describe a little the use cases?
>
> Phil
>
Hi Phil,

The application I have in mind is the manipulation of Taylor
expansions (stored as multivariate polynomials). I'm trying to use
genericity in order to be able to work with different number
representations (exact fractions, double values, etc...).
>From this point of view, it would be useful to be able to have a
wrapper class for (for example) integers. However, this is not
possible at the moment, since Z is only a ring.

OK, I could go on, but honestly Phil, I think I won't be able to
convince you. Indeed, if this feature existed, I would use it, but I
must admit that I proposed it because I also find such a feature
"beautiful" (which is not a very good reason for adding it to CM).
What I'm going to do is implement those mathematical entities on my
side, and try and use them. If I realize they could be useful to the
core CM library, I'll raise this issue again later.

Thank you for trying to reason me...
Sébastien

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