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From Phil Steitz <phil.ste...@gmail.com>
Subject Re: [math] Support for Abelian Groups and Rings?
Date Wed, 05 Oct 2011 02:02:55 GMT
On 10/4/11 5:42 PM, Greg Sterijevski wrote:
> Pardon my ignorance of Abelian Fields, but what would be a use of this set
> of classes? Do they simplify some calculation or make some code faster? The
> question is, "are they numerical?"

We can all look at Sebastien's use cases to assess general
usefulness.  They are not likely going to be "numerical" in the
sense of having lots of direct applications to numerical analysis,
but that is just one of the applied areas that [math] touches.  We
have both discrete and continuous components and even in dealing
with computations involving fields and real or complex function
spaces, it might be useful to have classes representing rings and
groups.  Where they might be useful is in modelling things such as
automorphism groups that have only a group (or ring, as the case may
be) structure.  I don't personally have examples where I need this
stuff, but it could be that Sebastien does.  I am open to adding
these algebraic constructs as and when the practical applications
arise that need them, or that can be expressed more simply or
naturally using them.

Phil
>
> On Tue, Oct 4, 2011 at 2:33 PM, Luc Maisonobe <Luc.Maisonobe@free.fr> wrote:
>
>> Le 03/10/2011 19:50, Mikkel Meyer Andersen a écrit :
>>
>>  2011/10/3 Sébastien Brisard<sebastien.brisard@m4x.**org<sebastien.brisard@m4x.org>
>>>> :
>>>> I would be curious to see how such a class would actually help you.  I
>>>>> have
>>>>> to admit that a big part of my curiosity is due to the fact that I don't
>>>>> understand how it really would help.  It could be, as you say, beautiful
>>>>> but
>>>>> useful is sometimes are more difficult goal with these things.
>>>>>
>>>>> I would also like to see if you are able to express enough interesting
>>>>> structure in the Java type system so as to be useful.
>>>>>
>>>>> So please do create a prototype.  It will be very interesting to see
it.
>>>>>
>>>>>  I had nothing fancy in mind. I wanted merely to build a Group and a
>>>> Ring following what has been done in CM with Field/FieldElement.
>>>> I already had the opportunity to mention this library, but Jean-Marie
>>>> Dautelle's JScience is a good example of implementation of all these
>>>> mathematical structures (http://jscience.org/). However, I tend to
>>>> prefer the way Fields are implemented in CM (there are slight
>>>> differences, most notably getZero() and getOne() which are missing in
>>>> JScience).
>>>> If you are still interested, I'll post (not commit, I got the
>>>> message!!!) tentative interfaces once I've written them.
>>>> Sébastien
>>>>
>>> Me, too.
>>>
>> I'm on the fence on this. I would also like to look at some examples about
>> what you have in mind.
>>
>> Luc
>>
>>
>>
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