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PowerExpand etc.

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  • Subject: PowerExpand etc.
  • From: Jack Goldberg <Jack.Goldberg at>
  • Date: Fri, 21 Oct 1994 13:03:18 -0400 (EDT)

As part of a previous posting, I remarked that I would like to see a 
generalization of one feature of PowerExpand which is it's ability to 
simplify Sqr[x^2] and Log[Exp[x] to x.  Many of you have responded 
warning me of the dangers in using inverse function simplifications 
indiscriminantly.  I take your warnings seriously not only because they 
are on the mark but because I am also a teacher.  But this is only one 
side of the issue.  There are good reasons for having such a simplifier, 
in spite of its dangers.  Mma uses a warning message when PowerExpand is 
invoked and I presumed that anyone who designes a generalization would do 
so as well.  I do not have an explicit instance at hand, but I can 
imagine Mma responding to Integrate with an answer far more complicated 
than necessary. (Integrate[Sqrt[x/(1-x)],x] is a reasonably good example. 
as I have previously remarked.) If one has a generalization of 
PowerExpand, say InverseSimplify, then one might apply InverseSimplify to 
see if the complicated integral simplifies.  If it does, one can then 
check whether the simplification makes sense (i.e.: is well defined and 
has the correct derivative.) 
	I suppose whether one wishes to use such a function depends on 
whether you are risk averse or not.  I'd take the risk!!  
	While I'm on this subject, I wonder if anyone knows a reference 
to an article which discusses the whole area of inverse functions in 
symbolic computing.  Of course the mathemtical theory is quite well 
elaborated on in many fine function theory books.  Are there any 
significant papers on the implementation of this theory for symbolic 
computing?  I think it is the most commonly confused and controversial 
topic in all the news groups on CAS.  
	Thanks to all of you for your observations and comments. They are 
welcome by me because they do exactly what they are intended to do; they 
stimulate my thinking and I hope others as well.

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