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MathGroup Archive 2007

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Re: Choosing preferred functions for Trig Simplification?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg83228] Re: [mg83189] Choosing preferred functions for Trig Simplification?
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Thu, 15 Nov 2007 05:44:17 -0500 (EST)
  • References: <200711140949.EAA22550@smc.vnet.net>

On 14 Nov 2007, at 18:49, AES wrote:

> In Simplifying expressions containing multiple Trig functions, I'd  
> like
> to persuade Mathematica to limit its vocabulary to Sin, Cos and Tan,
> and avoid Sec, Csc and Cot (while continuing to put expressions  
> into the
> simplest Together form, and so on).
>
> Are there simple tricks or Assumptions or options to do this?
>
> [I appreciate that Simplification is a can of worms.]
>
> Thanks . . .
>

You can't do that at all without using HoldForm because Mathematica's  
evaluator always returns:

1/Sin[x]
Csc[x]

this is the Evaluator not Simplify that does that so there is no way  
for Simplify to override it. It is possible to use formating  
constucts (e.g. Format or MakeBoxes) to make Csc[x] appear as 1/Sin 
[x] but I don't think it is really worth the trouble.

And by the way, I could not disagree more with your comment about  
Simplify. Like Reduce it does use some fairly advanced symbolic  
algebra, but everything it uses is documented and all the algorithms  
can be found in texts on algorithmic algebra. The fact that engineers  
and programmers usually do not know much modern algebra does not make  
it "mysterious" or " a can of worms".

Andrzej Kolzowski




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