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Re: Generation of polynomials

  • To: mathgroup at smc.vnet.net
  • Subject: [mg113085] Re: Generation of polynomials
  • From: Richard Fateman <fateman at cs.berkeley.edu>
  • Date: Tue, 12 Oct 2010 13:50:06 -0400 (EDT)
  • References: <i915vd$inm$1@smc.vnet.net>

On 10/12/2010 1:24 AM, Andrzej Kozlowski wrote:
> "Simplest" is arguable. Performance is measurable.

Right. Here is the argument.

  Are you in a hurry to run the program, or to write the program?

(I wrote the program in about 30 seconds, correctly the first time.
I was lucky in guessing that Mathematica used the name "Normal";
it is either an example of plagiarism or incredible coincidence.)

Why is this important?

Do you want a program that can only be read and understood by someone
who is steeped in the intricacies of Mathematica mumbo-jumbo?

Or would you like an expression that can be understood more easily
(and in fact trivially transliterated into other computer algebra
systems -- even "normal"), and is, in some sense, nearly 'language' 
independent?

Expanding an expression in a Taylor series in an auxiliary variable
in order to facilitate truncation on a total degree is such a
common kind of idea that other systems have it built in to their
expansion routines for multivariate series.

  I view it as a defect in Series  (and have, I think, mentioned it) 
that total degree truncation of a multivariate series is not provided in 
Mathematica.

If it were, one could simply write

Series [Product[...],{x,y},{0,0},n]   where n is total degree.

RJF



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