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