       Re: Surprising FullSimplify result

• To: mathgroup at smc.vnet.net
• Subject: [mg111510] Re: Surprising FullSimplify result
• From: "David Park" <djmpark at comcast.net>
• Date: Tue, 3 Aug 2010 06:42:48 -0400 (EDT)

```Two techniques that are useful for manipulating or simplifying expressions
are:

1) Protect certain subexpressions against participating in simplifications
by using a Hold or HoldForm.

2) Operate only on a selected subset of level parts in an expression.

The following uses the first technique:

Cos[theta]^2 + Sin[theta]^2 + L^2 Cos[theta]^2;
MapAt[Hold, %, 2];
% // Simplify // ReleaseHold

1 + L^2 Cos[theta]^2

The second technique can be implemented using the MapLevelParts or
MapLevelPatterns routines in the Presentations Manipulation subsection.

Needs["Presentations`Master`"]

Cos[theta]^2 + Sin[theta]^2 + L^2 Cos[theta]^2;
% // MapLevelParts[Simplify, {{1, 3}}]

1 + L^2 Cos[theta]^2

Or using patterns and TrigExpand instead:

Cos[theta]^2 + Sin[theta]^2 + L^2 Cos[theta]^2;
% // MapLevelPatterns[TrigExpand, {{(Sin | Cos)[_]^2}}]

1 + L^2 Cos[theta]^2

David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/

From: Sam Takoy [mailto:sam.takoy at yahoo.com]

Here's what I am getting

Cos[theta]^2 + Sin[theta]^2 // FullSimplify
Out= 1

Cos[theta]^2 + Sin[theta]^2 + L^2 Cos[theta]^2 // FullSimplify
Out= 1/2 (2 + L^2 + L^2 Cos[2 theta])

I'm really surprised that the answer in the latter case is not

1+ L^2 Cos[theta]^2

Is there an explanation?

Thanks,

Sam

```

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