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MathGroup Archive 2006

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Re: Question about trig simplify

  • To: mathgroup at smc.vnet.net
  • Subject: [mg71168] Re: [mg71099] Question about trig simplify
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Thu, 9 Nov 2006 03:40:21 -0500 (EST)
  • References: <200611081115.GAA22432@smc.vnet.net>

Compare the LeafCounts:

In[1]:=In[1]:=
LeafCount[2*Sin[a]*Cos[a]]

Out[1]=
6

In[2]:=
LeafCount[Sin[2a]]

Out[2]=
4

So the simplified expression is "simpler" according to the defaul  
ComplexityFunction (which is more or less LeafCount). On the other hand:

In[4]:=
LeafCount[-Sin[2 a]]

Out[4]=
6

In[5]:=
LeafCount[-2Cos[a]  Sin[a]]

Out[5]=
6

So there is no ground for replacing one expression by the other. You  
need to use a different ComplexityFunction. I like to use this:

VisibleSimplify[expr_, opts___] := Simplify[
     expr, opts, ComplexityFunction -> \
(StringLength[ToString[TraditionalForm[#]]] &)]

Then:

In[11]:=
VisibleSimplify[2*Sin[a]*Cos[a]]

Out[11]=
Sin[2*a]

In[12]:=
VisibleSimplify[-2*Cos[a]*Sin[a]]

Out[12]=
-Sin[2*a]

Andrzej Kozlowski
Tokyo, Japan





On 8 Nov 2006, at 20:15, Robert Pigeon wrote:

>
> Hello all,
> 	Is this a bug?
>
> 2*Sin[a]*Cos[a] // Simplify  gives Sin[2 a] as expected.
>
> But
>
> -2*Sin[a]*Cos[a] // Simplify  gives -2*Cos[a]*Sin[a]  ...... Why?
> If I do -2*(Sin[a]*Cos[a]) // Simplify I get the same answer.
>
> This comes from the rotation matrix: r = {{Cos[a],Sin[a]},{-Sin 
> [a],Cos[a]}}.
> Then I do: r.r // Simplify. That gives: {{Cos[2 a],Sin[2 a]},{-2 Cos 
> [a]
> Sin[a],Cos[2 a]}}. It does not matter if I do a FullSimplify  
> instead of
> Simplify.
>
> After if I do r.r.r // Simplify. The answer is simplified correctly.
>
> I am using Mathematica 5.2 on Windows XP Home.
>
> Any idea?
>
> Robert
>
> Robert Pigeon
> TZ = -5
>


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