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Re: Re: A Problem with Simplify

• To: mathgroup at smc.vnet.net
• Subject: [mg87503] Re: [mg87456] Re: A Problem with Simplify
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Fri, 11 Apr 2008 05:58:55 -0400 (EDT)
• References: <ftkb7f$a9m$1@smc.vnet.net> <200804110542.BAA04641@smc.vnet.net>

On 11 Apr 2008, at 14:42, Alexey Popkov wrote:
> Recently I also have found another strange bug in Simplfy (not so
> dangerous):
> FullSimplify[Sin[x]*Cos[x]]
> gives Sin[x]*Cos[x] instead Sin[2*x]/2. The workaround is
> FullSimplify[2*Sin[x]*Cos[x]]/2


This is not a bug!

In[7]:= LeafCount[Sin[x]*Cos[x]]
Out[7]= 5

In[8]:= LeafCount[Sin[2*x]/2]
Out[8]= 8

In other words, Sin[x] Cos[x] is considered simpler by Simplify than  
Sin[2*x]/2, that's all. Indeed:

In[9]:= Simplify[Sin[2*x]/2]
Out[9]= Cos[x]*Sin[x]

If you want Simplify to return Sin[2*x]/2 use a different complexity  
functions:

  Simplify[Sin[x]*Cos[x], ComplexityFunction ->
      (LeafCount[#1] + 10*Count[#1, _Cos,
               Infinity] & )]
  (1/2)*Sin[2*x]

And, by the way, your "other bug" is also not a bug.

A basic principle worth remembering: just because something seems  
wrong to you does not mean it is wrong.

Andrzej Kozlowski

• References:
  • Re: A Problem with Simplify
    • From: Alexey Popkov <popkov@gmail.com>