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FullSimplify behavior

  • To: mathgroup at smc.vnet.net
  • Subject: [mg41710] FullSimplify behavior
  • From: carlos at colorado.edu (Carlos Felippa)
  • Date: Mon, 2 Jun 2003 04:35:19 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

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.


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