Re: Re: Please, can someone explain this small function?

*To*: mathgroup at smc.vnet.net*Subject*: [mg50833] Re: [mg50808] Re: Please, can someone explain this small function?*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Thu, 23 Sep 2004 05:27:14 -0400 (EDT)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <cih0hn$md$1@smc.vnet.net> <200409220411.AAA18689@smc.vnet.net>*Reply-to*: murray at math.umass.edu*Sender*: owner-wri-mathgroup at wolfram.com

One reason to treat a polynomial as a list -- and that might not be the original poster's reason -- is that one definition of "polynomial" is as just such a list, the list of its "coefficients" (with some convention about an ascending or descending order). The reason for that is the conventional definition of a polynomial as "an expression of the form c0 + c1 x + c2 x^2 + ... + cn x^n" is a bit mysterious. Yes, one can write down such an expression, but just because one can write it down doesn't necessarily mean it corresponds to any fundamental mathematical reality. How can one give meaning to such an "expression" in terms of more fundamental mathematical entities. (And here we must be careful to distinguish between a polynomial, which is one thing, and a polynomial function which is quite another thing -- most particularly when the coefficient domain is not the reals or complexes.) It's a similar situation with respect to the definition of complex numbers. One can say that a "omplex number" is an "expression of the form "a + b i" where a and b are real and i is an object satisfying i^2 = -1, but that in itself doesn't really say what such an object actually is. Recall the history here: Folks used such expressions a + b i for a long time but felt very uncomfortable doing so -- until eventually the definition of a + bi as meaning the ordered pair (a, b) was offered, which expressed the new kind of object in terms of already understood objects. All that said, most folks do find it more convenient to write and manipulate polynomials in the "expression in x" form. After all, traditional mathematical notation -- with all its ambiguities and limitations -- was devised so as to make it easy to write polynomials! Paul Abbott wrote: > In article <cih0hn$md$1 at smc.vnet.net>, > Cole Turner <REMOVEcole.turner at liwest.at> wrote: > > >>input: two polynomials as lists > > > Why not input polynomials as polynomials? ... -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**Re: Please, can someone explain this small function?***From:*Paul Abbott <paul@physics.uwa.edu.au>

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**Re: Please, can someone explain this small function?**

**Re: Please, can someone explain this small function?**