FullSimplify tricks

• To: mathgroup at smc.vnet.net
• Subject: [mg25474] FullSimplify tricks
• From: "Arturas Acus" <acus at itpa.lt>
• Date: Mon, 2 Oct 2000 22:26:54 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Dear Group,

Simplifying trigonometric expressions I found rather unexpected
feature of FullSimplify. In particularry FullSimplify sometimes can find nicer expressions if
some symbols we make "subscripted".  It is if we provide some fictive
"substructure" (two dimensional form) for some symbols. Below is one of simplest examples.
In[1]:=
\!\(\((1 - 2\ x\_0\%2 +
2\ \((\(-1\) + x\_0\%2)\)\ Cos[
2\ F])\)\ \((\(-\[ImaginaryI]\)\ Cos[F] + x\_0\
Sin[F])\)\^2 //
FullSimplify\)
Out[1]=
\!\(\((Cos[F] + \[ImaginaryI]\ Sin[F]\ x\_0)\)\^2\ \((\(-1\) + 2\
Cos[2\ F] +
4\ Sin[F]\^2\ x\_0\%2)\)\)
In[2]:=
\!\(ReplaceAll[\((1 - 2\ x\_0\%2 +
2\ \((\(-1\) + x\_0\%2)\)\ Cos[
2\ F])\)\ \((\(-\[ImaginaryI]\)\ Cos[F] + x\_0\
Sin[F])\)\^2, \
{Subscript[x, \(-1\)] -> xm1, Subscript[x, 1] -> xp1,
Subscript[x, 0] -> x0}] // FullSimplify\)
Out[2]=
\!\(\((1 - 2\ x\_0\%2 +
2\ \((\(-1\) + x\_0\%2)\)\ Cos[
2\ F])\)\ \((\(-\[ImaginaryI]\)\ Cos[F] + x\_0\
Sin[F])\)\^2\)
It is natural to expect this behaviour, due to some leaf count
algorithm used by FullSimplify. However it could sometimes be quite difficult to understand this effect if
one uses two dimensional notations for such symbols. For example in
this case I spend a hour when realized that symbol notation significantly affected FullSimplify rezult!

Dr. Arturas Acus
Institute of Theoretical
Physics and Astronomy
Gostauto 12, 2600,Vilnius
Lithuania

E-mail: acus at itpa.lt
Fax: 370-2-225361
Tel: 370-2-612906

```

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