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Re: RE: FullSimplify and HypergeometricPFQ

• To: mathgroup at smc.vnet.net
• Subject: [mg72093] Re: [mg72050] RE: [mg72035] FullSimplify and HypergeometricPFQ
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Mon, 11 Dec 2006 04:55:30 -0500 (EST)
• References: <NDBBJGNHKLMPLILOIPPOKEKOFEAA.djmp@earthlink.net> <E3FB0E44-E3F0-4FC1-88A9-98DFB9B65DAC@mimuw.edu.pl>

On 11 Dec 2006, at 09:45, Andrzej Kozlowski wrote:

>  So to really understand what they do you have to understand the  
> transformation functions themselves; particularly PolynomialReduce  
> for polynomial expressions and FunctionalExpand for special  
> functions etc.

Another thing I forgot: CylindricalDecompostion etc, is used for all  
the assumptions mechanism involving inequalities. This also works  
only with polynomial input, which is why there is only the slightest  
chance that assumptions involving inequalities will help with  
simplifying non-algebraic expressions. In such cases, since there is  
no general algorithm,  pattern matching is used, to match the  
expression to be simplified (perhaps after applying some  
transformations) with some stored rule. Because there are so many  
possible patterns the chances of such approach succeeding are pretty  
small. I also forgot to say that expressions involving polynomials in  
trigonometric functions: Sin[n x], Cos[n x] etc, with integer n can  
also be (in principle) dealt with completely since they really reduce  
to algebraic functions of Sin or Cos. However, inverse trigonometric  
functions, as in your example, are a completely different thing; in  
fact when FullSimplify works in such cases it is indeed a "gift from  
Heaven".

Andrzej Kozlowski