I play with sage, exp, sin, cos, sinh, and co...
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
But silly examples about power and asin (sin (x)) seems right.
I find that sage (but it's perhaps maxima) is not enough fine with
Theses sage rules are right only for positive real numbers, and in
mathematics we quickly get complex numbers.
I used both Axiom with only multivariate functions asin sin a = a and
and Maple/mupad with no multivariate functions (but bugs).
Mathematics for undergraduate are finest by this way.
> Are you suggesting that exp(a)^(1/2) always return exp(a)^(1/2)
It's what I prefer
> , or that it return something about branches?
In my mind log z = ln |z| + i arctan2 (Re(z),Im(z)) where arctan2 (x,y)
This logarithm is MONO-variate, but we can't write ln (u v) = ln u + ln
v in complex domain.
> sage: (-1)^(1/3)
It's right, arctan(-1,0)=pi, e^(i*pi/3) = 0.5 + 0.866... I
> But in general Sage does things over complex numbers fairly
> consistently. We constantly get complaints about
> sage: (-1.)^(1/3)
> 0.500000000000000 + 0.866025403784439*I
All right, so (exp (a))^b is a singular exception... And I prefer a
system without such exception.
> On Sep 17, 5:14 am, Francois Maltey <fmal...@nerim.fr> wrote:
> > kcrisman wrote :> On Sep 16, 4:04 pm, Francois Maltey
> > <fmal...@nerim.fr> wrote:
> > >> I play with sage, exp, sin, cos, sinh, and co...
> > >> 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
> It appears that either 1) the Pynac simplification has a bug or 2)
> there is a very good reason for this behavior. I would encourage you
This is a bug in pynac. I wrote the power method for exp during the
rush for the symbolics switch.
Here is a ticket for this issue:
It will be fixed in the next Sage release.
Thanks a lot for reporting this.