[Maxima-bugs] [ maxima-Bugs-1285104 ] trigsimp and trigreduce & square roots

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Bugs item #1285104, was opened at 2005-09-08 12:53
Message generated for change (Comment added) made by rtoy
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Category: None
Group: None
Status: Open
Resolution: None
Priority: 5
Submitted By: Barton Willis (willisbl)
Assigned to: Nobody/Anonymous (nobody)
Summary: trigsimp and trigreduce & square roots

Initial Comment:
Sometimes trigsimp and trigreduce seem to make
assumptions of the sign of variables.  Consider:

(%i1) sqrt(r^2 * cos(x)^2 + r^2 * sin(x)^2);
(%o1) sqrt(r^2*sin(x)^2+r^2*cos(x)^2)
(%i2) trigsimp(%o1);
(%o2) r                          <--- should be |r|

(%i3) trigreduce(%o1);
(%o3) r                          <--- should be |r|

(%i4) trigreduce(sqrt(r^2));
(%o4) abs(r)                   <---- OK here

(%i5) trigsimp(sqrt(r^2));
(%o5) abs(r)                   <--- OK here too

And oh my! Using z instead of r makes the problem
go away.

(%i9) sqrt(z^2 * cos(x)^2 + z^2 * sin(x)^2);
(%o9) sqrt(sin(x)^2*z^2+cos(x)^2*z^2)
(%i10) trigsimp(%);
(%o10) abs(z)             <--- OK here as well!

(%i6) build_info();
Maxima version: 5.9.1.1cvs
Maxima build date: 14:5 8/30/2005
host type: i686-pc-mingw32
lisp-implementation-type: GNU Common Lisp (GCL)
lisp-implementation-version: GCL 2.6.7

Barton

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>Comment By: Raymond Toy (rtoy)
Date: 2005-10-05 09:41

Message:
Logged In: YES 
user_id=28849

Neat.  

It appears to be a bug in radcan. 
radcan(sqrt(r^2*cos(x)^2+r^2*sin(x)^2)) returns just
r*stuff, but with r replaced with z, it returns
abs(z)*stuff.  Tracing radcan and friends, I see that fr1
returns something different for the r version.

I don't know why.


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Comment By: Barton Willis (willisbl)
Date: 2005-09-10 05:35

Message:
Logged In: YES 
user_id=895922

A possible fix:

(defun sp1expt (b e)
  (cond ((mexptp b)  (power b e))
;;(sp1expt (cadr b) (m* e (caddr b))))  <---  (sp1expt x^2
1/2) --> x

The old code calls sp1expt after it does (a^b)^c --> a^(bc). 
I'm not sure if that second call to sp1expt ever makes a 
difference.

Barton
	

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