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 | | http://members.wri.com/layland | \*------------------------------*/