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MathGroup Archive 1995

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Re: Re: Re: Bug in interpretation of mma Series[] command?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg2343] Re: [mg2287] Re: [mg2268] Re: Bug in interpretation of mma Series[] command?
  • From: Richard Mercer <richard at seuss.math.wright.edu>
  • Date: Wed, 25 Oct 1995 02:13:35 -0400

Mgroupers,

A couple lines were inadvertantly omitted from my previous poston this  
subject. Following is the correct version.
In essence I agree with Dave Withoff and Paul Abbott, but my point here  
is that many users feel the other way, and not unreasonably.

Richard Mercer
---------------------------------------------------------------------
In view of Dave Withoff's response to this issue, perhaps I was a  

little hasty in my reply.

His reply was cogent as always and from a system design viewpoint is  

definitely the right approach.

However the best system design is not always the best for the user.
The ideal situation for many users is for

Exp[-a y^2] * Series[1/(1 + y^2), {y,0,5}]

to act like 


Exp[-a y^2] * Normal[Series[1/(1 + y^2), {y,0,5}]]

Reasons:
(1) Most average (nonexpert) users do not have a mental model  

corresponding to a SeriesData object; they think of the result of a  

Series command as being a polynomial and expect it to behave that way  

in calculations.
(2) The structure Series[Exp[-a y^2] * 1/(1 + y^2), {y,0,5}] is  

available and much more natural if you want the exponential converted  

to a series.

The best solution would seem to be a user-settable "switch" that would  

apply Normal to the output of all Series commands. This would  

presumably satisfy all those who expect Series objects to act like  

polynomials in this and other situations.

One possible way to do this, though far from perfect, is to use

$Post = (# /.  

Literal[SeriesData[stuff__]]:>Normal[SeriesData[stuff]])&;

(You could put this in your init.m file if you really like it.)
Two problems with this:
(1) It can potentially corrupt some things you don't want converted.
(For example, its own output! Try removing the semicolon.)
(2) More importantly, it's an expert solution to a non-expert problem.
The people who can/will do things like this are pretty much the people  

for whom it's not necessary.




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