Menu
▾
▴
#779 trigsimp and trigreduce & square roots
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
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
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.
Logged In: YES
user_id=501686
Observed in 5.9.3cvs.
Logged In: YES
user_id=28849
What radcan returns seems to depend on the order of the
variables.
radcan(sqrt(c^2*cos(b)^2+c^2*sin(b)^2)) ->
sqrt(sin(b)^2+cos(b)^2)*abs(c)
radcan(sqrt(a^2*cos(b)^2+a^2*sin(b)^2)) ->
a*sqrt(sin(b)^2+cos(b)^2)
This seems to be true for any variables ordered in this way.
FR1 returns different things in these two cases. For the
first, FR1 factors c^2*cos(b)^2+c^2*sin(b)^2 to
(sin(b)^2+cos(b)^2)*c^2.
In the second, it's not factored out.
Don't know why.
Fixed in trigred.lisp revision 1.11.
The original example works now as expected.
Closing this bug report as fixed.
Dieter Kaiser