>
> > Well, you could assert that there is no discussion, but you are
> apparently
> > wrong.
> > sqrt has 2 values except at zero. (in the complex plane, or on the real
> > line).
> >
> > for example, sqrt(9) is the set {-3,3} . That is how it is
> extended.
> > and sqrt(1) is {-1,1}.
> >
> > Is it true that 1 is equal to {-1,1} ?
> >
> > Now you could insist that sqrt() means only one of the roots. Etc for
> other
> > roots and for
> > other domains. But you would have to fill in what Etc means.
> >
> >
> > What do you suppose is going on at WRI,
http://www.wolframalpha.com/input/?i=solve+sqrt%28x%29+%3D+x
seems to be quite happy to tell us that the solutions are x=0 and x=1 .
Just sayin', though that may be part of their 'natural language' stuff
that usually (though not always) gives me "Using closest Wolfram|Alpha
interpretation" and something completely irrelevant.
> and with Maxima, each refusing to do
> > this?
>
> sqrt(x) (or Sqrt[x] in Mathematica) denotes the principal square root
> in every computer algebra system I can think of, even in Maxima:
>
> (%i1) sqrt(1);
> (%o1) 1
>
> Why should solve() work with a different definition of sqrt() than the
> definition the system uses for evaluation?
>
> I propose naming this context-dependently non-principal sqrt function
> of yours the "strawman square root".
>
>
Well, the problem is whether sqrt is a function or a symbolic expression,
according to my understanding of previous discussions of this point.
Apparently sqrt(1) is the (single-valued) function, but sqrt(x) is a
symbolic expression, n'est pas? We run into this all the time dealing with
Maxima, especially with the notorious radcan. For end users this is
unfortunately very distracting.
- kcrisman
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