[with patch, positive review] powers of exp are over simplified

[burcin]

Francois Maltey wrote on sage-support:

var("a,b,c")
exp(a)^2 # returns exp(2a) is right
exp(a)^(1/2) # returns exp (a/2) is wrong, with a=2*i*pi we get -1=1
exp(a)^b # returns exp(a*b) is wrong

The thread is here:

​http://groups.google.com/group/sage-support/browse_thread/thread/330a015bf640a4f3/0ddfdd5a4e021579

[burcin]

This is fixed in my pynac tree, attachment:trac_6948-exp_power.patch​ is the corresponding patch for Sage. I will release a pynac spkg with some more fixes and post instructions for review.

[burcin]

New pynac package available at #6993.

[kcrisman]

Nice, but does it actually fix the examples provided?

sage: exp(a)^(1/2)
sqrt(e^a)

I guess that's okay. But

sage: exp(a)^(1/3)
e^a^(1/3)
sage: exp(a^(1/3))
e^(a^(1/3))

I think there are missing parentheses in the first example, particularly because it's not typeset. Even if that is a convention, which I'm not so sure of, the dictum is that it's better to be explicit.

I also get a doctest failure (not mentioned in the Pynac upgrade ticket) in product and quotient rule differentiation in calculus/tests.py, but it looks like that's the one in #6524, so it's properly speaking another issue, I guess.

[burcin]

This package should fix this problem:

​http://sage.math.washington.edu/home/burcin/pynac/pynac-0.1.9.p0.spkg

I'll attach a patch with some more doctests now.

[kcrisman]

Positive review!

[mvngu]

Merged both patches.

[mvngu]

There is no 4.1.2.alpha3. Sage 4.1.2.alpha3 was William Stein's release for working on making the notebook a standalone package.