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MathGroup Archive 2006

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Re: RE: FullSimplify and HypergeometricPFQ

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72072] Re: [mg72050] RE: [mg72035] FullSimplify and HypergeometricPFQ
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Mon, 11 Dec 2006 04:54:41 -0500 (EST)
  • References: <200612100948.EAA17354@smc.vnet.net>

On 10 Dec 2006, at 18:48, David Park wrote:

> I doubt if you will ever get a full description of how Simplify and
> FullSimplify work.

I can't agree with the above. If you search through the archives for  
posts by Adam Strzebonski with the word Simplify with them you wil  
find that he has provided almost complete information about them. In  
particular, he has posted the default ComplexityFucntion, the  
complete lists of default transformation functions used by Simplify  
and FullSimplify and other information, which means that in fact we  
already have a more complete description of how these functions work  
than is the case with almost any other Mathematica functions.  
(Actually, in the particular case the original poster referred to,  
the key work is done by FunctionExpand, about which we, or at least  
I, do not know all that much, but it does not change the fact that  
Simplify and FullSimplify themselves have been described very fully).
>
> I consider Simplify and FullSimplify as 'gifts from heaven'. When  
> they do
> what I want, which they often do, great. When they don't, then I  
> don't try
> to mess around with ComplexityFunction because that isn't very  
> precise but
> only tends to push the result one way or the other. Rather, I  
> resort to
> 'microsurgery' on the expression, using rules, replacements of  
> specific
> parts and things like that.

Of course you are right, but the point is that Simplify and  
FullSimplify were never intended to get you from expression A to some  
user specified expression B (although many users try to use or rather  
misuse, them, to do just that.) There are other functions for this  
purpose. Simplify and FullSimplify have two main purposes. in my  
opinion, by far the most important one is showing that two different  
symbolic expressions are equal. In this respect these functions are  
unique; there is nothing in Mathematica that can replace them at this  
task and this is also the most subtle aspect of what they do (and it  
also has been described by Adam Strzebonski). The other important use  
is to try to find a simpler form of a complicated expression in  
situations when it is too hard to do this by hand. As there obviously  
is no objective definition of "the simplest form" the user has a lot  
of control of the direction he can  "push the result in", but of  
course this cannot be "precise" because in such situations  there is  
no "precise target".

>
> My experience is, that with a little practice, it is possible to  
> manipulate
> expressions and simplify them in a way that a reader could  
> understand and
> follow. Sometimes one does have to directly employ specific  
> mathematical
> theorems or identities to carry out a derivation. But it still can  
> be done
> within Mathematica.

Of course you are right. But the point of it all is simply that  
Simplify and FullSimplify are not intended as tools for "manipulating  
expressions". They can sometimes be used for this, but it usually  
difficult to do precisely (as you have pointed out) and moreover,  
even when it works it is almost always the most inefficient way of  
achieving the result.

Andrzej Kozlowski


>
> David Park
> djmp at earthlink.net
> http://home.earthlink.net/~djmp/
>
> From: guy.verhofstadt at gmail.com [mailto:guy.verhofstadt at gmail.com]
>
> Hi,
> I have a question regarding something that Mathematica can do via the
> command FullSimplify.
> I use it to prove an identity between HypergeometricPFQ's. However it
> would be helpful to me to see how Mathematica proves it. How can I get
> access to the intermediate expressions and the transformations  
> applied?
> Also, is there a definite list of all the things FullSimplify will try
> in Automatic setting?
> Thank you very much
>
>


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