x^2+1 = 0 has no real roots. The same way, log and exp as real functions
are one-to-one and thus invertible.
I'm not sure where this is leading to and how it relates to Maxima in
any way. You want everything to be in terms of complex numbers all the
time, fine. In reality, though, we use different sets according to our
needs. In introductory calculus, we teach that exp(x) is a one-to-one
function.
Whether or not we should teach calculus mixed with complex numbers and
never talk about functions of real numbers seem irrelevant to my current
concerns with Maxima.
Maybe we should solve x^2+1 is some Galois ring? Right? Then what?
There is nothing special about the complex numbers. It just so happen
that most scientist use the real numbers or the integers more often than
not. Then some people (like myself) work with complex numbers... other
work with other rings and so on...
If you want a full discussion on the solutions of
x^2+1
for all possible rings, you better have a lot of time on your hands!!!
Most scientists don't have that much time!
> Daniel Lemire wrote:
>
>
>>
>> I specifically said that I was assuming all my variables and constants
>> to be real. I said it several times, even repeating it quite clearly
>> in the message you are answering to.
>
>
>
> Yes, I know you said it several times. Do you also teach your students
> that the quadratic equation x^2+1=0 has no roots, since all your variables
> and constants are real? If so, that seems to be unfortunate.
>
> I am reminded of an old joke,
> "How many legs does a sheep have if you call its tail a leg?"
>
> Answer:
>
> Four. Calling its tail a leg does not make it a leg.
>
> Cheers.
>
>
>
>
--
Daniel Lemire, Ph.D.
http://www.ondelette.com