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From Phil Steitz <>
Subject Re: [math] Questions on Field
Date Sat, 25 Apr 2009 01:02:37 GMT wrote:
> ----- "Bill Barker" <> 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 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.

> Luc
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