On Sep 17, 5:14 am, Francois Maltey <[email protected]> wrote:
> kcrisman wrote :> On Sep 16, 4:04 pm, Francois Maltey <[email protected]>
> 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
>
> > Well, there is a unique exp, but not a unique square root (or in
> > general other power, since they may be defined using log).
>
> But is XXX^(1/2) are unique and not multivariate : sage remains
> (a^2)^(1/2) and (a^b)^c.
> Neither automatic convert (a^2)^(1/2) to a nor (a^b)^c to a^(b*c)
>
> I used both Axiom with only multivariate functions asin sin a = a and
> (a^2)^(1/2)=a
> 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)
> in ]-pi,pi].
> This logarithm is MONO-variate, but we can't write ln (u v) = ln u + ln
> v in complex domain.
>
> > sage: (-1)^(1/3)
> > (-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.
Dear Francois,
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
to email sage-devel about this issue, or look for the Pynac
development list. I am quite certain that the people who have
implemented symbolics in Sage are very, very aware of such issues, as
you will see if you browse threads about such things on this list and
on sage-devel.
- kcrisman
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