On Sep 16, 4:04 pm, Francois Maltey <fmal...@nerim.fr> wrote:
> Hi,
>
> 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
Well, there is a unique exp, but not a unique square root (or in
general other power, since they may be defined using log). Are you
suggesting that exp(a)^(1/2) always return exp(a)^(1/2), or that it
return something about branches? I suppose that is possible. For
instance,
sage: (-1)^(1/3)
(-1)^(1/3)
Here I believe the simplification is done by Pynac (Ginac), and I'm
sure someone more informed will be able to describe its algorithms.
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
Hope this helps,
- kcrisman
>
> 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
> mathematics.
>
> Theses sage rules are right only for positive real numbers, and in
> mathematics we quickly get complex numbers.
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