Re: FullSimplify behavior
- To: mathgroup at smc.vnet.net
- Subject: [mg41726] Re: [mg41710] FullSimplify behavior
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Tue, 3 Jun 2003 07:13:08 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
On Monday, June 2, 2003, at 05:35 pm, Carlos Felippa wrote: > I would like to get an understanding for the > behavior of FullSimplify in the last two commands. > > Print[FullSimplify[Sin[Pi/4]]//InputForm]; > Print[FullSimplify[Sin[Pi/3]]//InputForm]; > Print[FullSimplify[Sin[Pi/8]]//InputForm]; > Print[FullSimplify[TrigToExp[Sin[Pi/8]]]//InputForm]; > > 1/Sqrt[2] > Sqrt[3]/2 > Sin[Pi/8] > Sqrt[2 - Sqrt[2]]/2 > > It is because FullSimplify views Sin[Pi/8] as "simpler" than > Sqrt[2 - Sqrt[2]]/2 in terms of leaf count? It seems that way > since the counts given are 6 and 17, respectively. And the > count of TrigToExp[Sin[Pi/8]] is 31. > > Counterargument(?). For the first two commands the leaf counts > before and after FullSimplify are the same: 5 -> 5, and > 10 -> 10, respectively, yet the transformation was done. > > > Actually since Sin[Pi/4] 1/Sqrt[2] Sin[Pi/3] Sqrt[3]/2 FullSimplify never gets a chance to show what it can do. Andrzej Kozlowski Yokohama, Japan http://www.mimuw.edu.pl/~akoz/ http://platon.c.u-tokyo.ac.jp/andrzej/