       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)

```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

```

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