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