About Simplify

About Simplify

Post by Pelti » Wed, 17 Aug 2005 18:46:18


The recent threads about Simplify made me wonder why the user is not allowed
to choose which transformation rules apply to the expression passed to it.
Of course Simplify and FullSimplify are no longer (if they ever were)
written in Mathematica code, but is it at all impossible to rewrite its
interface in order to let the user interact with the builtin code?

I do not know the way the code is structured for these procedures, but I can
guess that at a certain point it will try to apply certain sets of rules
having to do with trigonometric functions, Bessel functions, Hypergeometric
functions and many other more or less *** special functions.
Is there no way at all to put switches to disable certain sets of rules?
(A question for developers, of course - I do not think that Mathemaitca
users can interact with the code).

The user could pass a list of exclusion rules, such as

Simplify[ expr, BesselFunctions->False, AiryFunctions->False,
ErfFunctions->False]

when the results he gets contain certain special functions he does not want
to involve. The overhead for multiple switches will be minimal (the
procedure will have to modify a table which will be looked up by the
internal C code) and the user will be able to build custom simplify
solutions (one that uses only algebraic and trigonometric functions, one
that uses the orthogonal polynomials, one tht does not use hypergeometric
functions and so on).

I can imagine that the built-in code is not a sequence of transormation
rules to apply in chain one after the other, but perhaps many special
functions rules could be switched on and off at will without afffecting the
remaining code.
Or is it completely unthinkable?

just wondering,
Peltio
Invalid address in reply-to. Crafty demunging required to mail me.
 
 
 

About Simplify

Post by Andrzej Ko » Thu, 18 Aug 2005 17:02:22

It may be of some interest to note here that one can actually "take a
peak" at some of the transformations Mathematica uses in Simplify and
FullSimplify as follows:



ls = {};


FullSimplify[Cos[Arg[z]] - Re[z]/Abs[z], ComplexityFunction ->
((AppendTo[ls, #1]; LeafCount[#1]) & )]


0

Now evaluate

ls

Andrzej Kozlowski

 
 
 

About Simplify

Post by alber » Thu, 18 Aug 2005 17:05:30


Hi Peltio,


Maybe I have not thought enough about your posting, but I think there is a
switch to do exactly that. Are you aware of the option
TransformationFunctions that both Simplify and FullSimplify understand? It
does not work exactly as you suggested, but could be used to achieve
something quite close by defining corresponding lists of
TransformationFunctions to pass to either of the Simplify. There have been
some nice applications of this options posted to this newsgroup, in case
you need more information than what is in the helpbrowser...

Albert

PS: FullSimplify understands another option ExcludedForms which you might
want to look at...
 
 
 

About Simplify

Post by Curtis Ost » Thu, 18 Aug 2005 17:06:29

Hi, Peltio,

I tried a direct response, but my demunging wasn't crafty enough for
your email's reply-to.

The documentation for TransformationFunctions (with which I haven't
played, but wish I knew about far, far earlier) indicates that if the
user includes a list of transformations to try, only those are used. It
seems that it gets at the problem of strange outputs from just the other
direction of what you're suggesting.

I would guess that if a user knows exactly the form she wants, and can
express this correctly in a function, the built-in
TransformationFunctions would be more appropriate. However, as you say,
often the form the user wants isn't predetermined, but the user
certainly knows which forms he or she don't want, especially after
seeing them returned by Simplify.

My final thought is that in its implementation, your method would have
to include some transformations of the form that TransformationFunctions
requires; otherwise, Mathematica would just have a restricted set of
transformations from what it usually tries, and will, almost always,
return the original expression, unevaluated. Of course, I don't know the
code's true structure, and so can't be sure.

Regards,
C.O.




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About Simplify

Post by David Bail » Fri, 19 Aug 2005 13:24:22

urtis Osterhoudt wrote:
Hi,

In fact, if you look at the documentation for the
TransformationFunctions option (at least at 5.1), you can include the
default transformations as well by adding the Automatic option to the list.

The other thing to consider here is writing a function to try exactly
the operations you require - possibly calling Simplify internally to
finish the process off.

David Bailey
http://www.dbaileyconsultancy.co.uk

 
 
 

About Simplify

Post by Pelti » Sun, 21 Aug 2005 16:35:33

Thanks to everybody for their replies. I use this post to comment on them.

"Curtis Osterhoudt" wrote


I'm sorry for that. But munging is the best defense I've tried so far
against spamming. This year I received only 2 spam messages. At any rate,
"mynick @ despammed . com" (without spaces and quotes) would do - I will
prolly revise my tagline.


Being used to work chiefly on version 3, I was not aware of this particular
improvement (which I will soon investigate - especially Andrzej's 'take a
peek' code- so thanks to you and the other posters for the tips).
But, as you said, it approaches the solution the other way round and the
user might want to just skip a particular simplification that comes out in
the output of Mathematica. It would be nice to be able to exclude, for
example, the hypergeometric functions from a simplification.

I will experiment a little with TransformationFunctions and ExcludedForms
options of Simplfy and FullSimplify in the future, but from what I've
read in the documentation there is no easy way to exclude certain rules
from the simplification process.
The only way I can think of would be to build a simplification routine from
scratch, by adding tons of simplification rules and by excluding those for
the hypergeometric functions.

cheers,
Peltio
Invalid address in reply-to. Use peltio (at) despammed (dot) com to e-mail
me.