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Re: Trig functions expressed as Radicals

• To: mathgroup at smc.vnet.net
• Subject: [mg60123] Re: [mg60054] Trig functions expressed as Radicals
• From: stephen layland <layland at wolfram.com>
• Date: Sat, 3 Sep 2005 02:06:14 -0400 (EDT)
• References: <200508310424.AAA21137@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

and thus spake mike_in_england2000 at yahoo.co.uk [2005.08.30 @ 23:53]:
> Is it something to do with the complexity of the result?  I know that
> FunctionExpand[Cos[Pi/23]] gives an extremely complicated result if you
> have the patience to wait for it (don't try and evaluate this unless
> you have a while) and so clearly it makes sense for mathematica to
> leave expressions like Cos[Pi/23] unevaluated unless the user explicity
> asks for it with FunctionExpand[].  If this is the case then what rules
> does Mathematica use in order to decide whether to leave the expression
> unevaluated or to give the radical form?
There's currently a finite table of well known exact results of these
functions.

All other values are returned unevaluated to both preserve exactness and 
efficiency.  I don't think actually calculating the exact result for all
arguments and making a decision based off of the complexity of the
result, wouldn't be worth it in this case.

HTH

--
/*------------------------------*\
|        stephen layland         |
|    Documentation Programmer    |
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