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

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

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

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

```

• Prev by Date: Re: Documentation - what is the big secret?
• Next by Date: Re: Path, Get, etc.
• Previous by thread: Re: A Problem with Simplify
• Next by thread: Re: A Problem with Simplify