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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: [mg83204] Re: Choosing preferred functions for Trig Simplification?
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Thu, 15 Nov 2007 05:31:46 -0500 (EST)
  • Organization: The Open University, Milton Keynes, UK
  • References: <fhegov$m8b$1@smc.vnet.net>

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?

You could use the option *ComplexityFunction* and define your own 
complexity function that would penalized the usage of the unwanted 
trigonometric functions. For instance,

In[1]:= f[e_] := 100 Count[e, _Sec | _Csc | _Cot, {0, Infinity}] + 
LeafCount[e]

In[2]:= expr = (TrigExpand[Cot[x + y]] + Sec[y])

Out[2]=
                  Cos[x] Cos[y]                   Sin[x] Sin[y]
Sec[y] + ----------------------------- - -----------------------------
          Cos[y] Sin[x] + Cos[x] Sin[y]   Cos[y] Sin[x] + Cos[x] Sin[y]

In[3]:= Simplify[expr, ComplexityFunction -> #] & /@ {Automatic, f}
LeafCount /@ %

Out[3]=
  1
{- Csc[x + y] Sec[y] (Cos[x] + Cos[x + 2 y] + 2 Sin[x + y]),
  2

   -Sin[x] (-1 + Sin[y]) + Cos[x] (Cos[y] + Tan[y])
   ------------------------------------------------}
            Cos[y] Sin[x] + Cos[x] Sin[y]

Out[4]= {25, 31}

Regards,
-- 
Jean-Marc


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