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Re: Sqrt of complex number
*To*: mathgroup at smc.vnet.net
*Subject*: [mg126672] Re: Sqrt of complex number
*From*: Richard Fateman <fateman at cs.berkeley.edu>
*Date*: Wed, 30 May 2012 04:10:44 -0400 (EDT)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*References*: <201205270842.EAA17817@smc.vnet.net> <jpvfh3$q6g$1@smc.vnet.net> <jq25u1$6gl$1@smc.vnet.net>
On 5/29/2012 2:46 AM, David Bailey wrote:
.....
>>
>
> In addition to what others have said, it is maybe worth pointing out
> that in general, the Sqrt expression would be embedded in a larger
> expression, such as a+Sqrt[3-4 I]+42 - so what should Mathematica do? If
> it returns a list of all possible answers, that might not be acceptable
> to something that was expecting a single value,
That suggests to me that whatever was expecting a single value has a bug
in it. Ideally if the mathematics dictates "there are multiple answers"
then a good program should be able to deal with it. Otherwise it is
not doing mathematics.
and anyway, expressions
> such as ArcSin[.2] would have an infinite number of answers!
There are several possible notations for infinite sets.
Here's one: Table[f[x],x,1, Inf]
>
> The only possible alternative strategy would be not to evaluate at all,
No, see above.
> as is the case with Sqrt[x^2] (since the answer can by x or -x).
Root[x^2,n] works for me, if n is an integer. We could have all even
n choose one sign and odd n choose the other.
These suggestions may not fit into today's Mathematica very well, but that
does not mean that a better system could not be constructed.
RJF
>
> David Bailey
> http://www.dbaileyconsultancy.co.uk
>
>
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