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From Phil Steitz <phil.ste...@gmail.com>
Subject Re: [math] Questions on Field
Date Sat, 25 Apr 2009 14:39:56 GMT
luc.maisonobe@free.fr wrote:
> ----- "Bill Barker" <billwbarker@verizon.net> a écrit :
>
>   
>> ----- Original Message ----- 
>> From: "Phil Steitz" <phil.steitz@gmail.com>
>> To: "Commons Developers List" <dev@commons.apache.org>
>> Sent: Friday, April 24, 2009 6:02 PM
>> Subject: Re: [math] Questions on Field
>>
>>
>>     
>>> luc.maisonobe@free.fr wrote:
>>>       
>>>> ----- "Bill Barker" <wbarker@wilshire.com> a écrit :
>>>>
>>>>
>>>>         
>>>>> I've been looking over the Field<T> implementations, and it looks
>>>>>           
>> like
>>     
>>>>> it's mostly done except for FieldPolynomial<T>.  I'm not really
>>>>>           
>> sure 
>>     
>>>>> which
>>>>>
>>>>>           
>>>> SparseFieldMatrix and SparseFieldVector are also missing for now.
>>>>
>>>>
>>>>         
>>>>> package this should go in, since o.a.c.m.analysis.polynomial seems
>>>>>           
>> to
>>     
>>>>> be about Real polynomials.  Any hints would be appreciated.
>>>>>
>>>>>           
>>>> I'm not sure either.
>>>> I wonder if an algebra package would make sense or not. If so, it
>>>>         
>> could 
>>     
>>>> contain the Field top interfaces as well as field polynomials,
>>>>         
>> Z/pZ, 
>>     
>>>> rational functions and BigReal. If such an algebra were created I
>>>>         
>> think 
>>     
>>>> polynomials should be moved there.
>>>> Polynomials (and rational functions) are at the boundary between
>>>>         
>> algebra 
>>     
>>>> and analysis, at least when using double coefficients only. When
>>>>         
>> using 
>>     
>>>> Field coefficients, they are more algebra-tainted to me.
>>>> What do other people think about this ?
>>>>
>>>>         
>>> I agree that we could go in this direction and certainly polynomials
>>>       
>> over 
>>     
>>> arbitrary fields are algebraic objects, so an algebra package would
>>>       
>> make 
>>     
>>> sense if we do this.  Building all of this out, however,  is sort of
>>>       
>> a 
>>     
>>> slippery slope that leads away from an applications-driven applied
>>>       
>> math 
>>     
>>> library into a more abstract framework.  I have always maintained
>>>       
>> that we 
>>     
>>> should introduce mathematical abstractions as we need them, with
>>>       
>> "need" 
>>     
>>> driven by applied math problems that we and our users have to solve.
>>>       
>>  So 
>>     
>>> here I would ask, what applied problems are we trying to solve and
>>>       
>> what 
>>     
>>> additional algebraic structure do we need to solve them?  I am not
>>>       
>> pushing 
>>     
>>> back here, just wanting to understand what applications people have
>>>       
>> in 
>>     
>>> mind.
>>>       
>> I, personally, have no use for it.  The main use case I could see is
>> for 
>> somebody that wants to use c-m to implement elliptic curve crypto (or
>> higher 
>> dimension variants).  And this would only be for Z/pZ or finite
>> extentions 
>> of it.  So I'm happy with waiting until there is a Jira issue
>> requesting 
>> this.
>>     
>
> OK. So we wait before adding new fields.
> I created the first implementations to address some problems I have with ODE: I need
to solve linear systems involving only rational numbers to compute some coefficients very
accurately. I also wanted to replace the old BigMatrix with something more consistent with
the new linear package. So I think it is interesting to finish this work on linear algebra
and add the SparseFieldMatrix and SparseFieldVector classes.
> Do you agree with this and would Bill accept to give an hand on this work ?
>   
+1 - like I said not pushing back and I understand why you did what you 
with Field and that is consistent with what I meant.

Phil
> Luc
>
>   
>>>>> I could provide implementations for SimplePrimeFieldElement
>>>>> (representing Z/pZ), and even SimplePadicFieldElement (with a 
>>>>> representation similar
>>>>> to double).  Not certain that it is useful for 2.0 without
>>>>>           
>> greatly
>>     
>>>>> delaying the release.  Most algebraist want to use finite
>>>>>           
>> extensions as 
>>     
>>>>> well.
>>>>>           
>>>> I would really like to see 2.0 be published as soon as possible,
>>>>         
>> but even 
>>     
>>>> my own tasks keep being delayed (ODE for stiff equations,
>>>>         
>> MATH-172). I 
>>     
>>>> would like to target a release near end of May.
>>>>
>>>>         
>>> +1 - I would really like to get 2.0 out.  I should have my stuff
>>>       
>> wrapped 
>>     
>>> up in the next couple of weeks.
>>>
>>> Phil
>>>       
>>>> Luc
>>>>
>>>>
>>>>         
>>>>>
>>>>>           
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>>>>>           
>>>>         
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>>>>
>>>>         
>>>
>>>       
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>>     
>
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