PowerExpand etc.

• To: mathgroup at christensen.cybernetics.net
• Subject: PowerExpand etc.
• From: Jack Goldberg <Jack.Goldberg at math.lsa.umich.edu>
• 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.
Jack

```

• Prev by Date: Mathematica World - WWW Service
• Next by Date: Re: Math on Sun..Help!
• Previous by thread: Mathematica World - WWW Service
• Next by thread: RE: PowerExpand etc.