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[540]= 1
Cos[theta]^2 + Sin[theta]^2 + L^2 Cos[theta]^2 // FullSimplify
Out[541]= 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