Should numpy.sqrt(-1) return 1j rather than nan?

Alan G Isaac aisaac at american.edu
Thu Oct 12 09:53:12 CDT 2006


On Thu, 12 Oct 2006, Stefan van der Walt apparently wrote: 
> I tried to explain the argument at 
> http://www.scipy.org/NegativeSquareRoot 

Helpful.  But you start off by saying:
        In mathematics, the above assumption is true -- that 
        the square root of -1 is 1j.

Since square root is (here) a function, and part of the 
function definition is the domain and codomain, this 
statement is not correct.  If the codomain is real numbers, 
the domain must correspondingly be (a subset of) the 
nonnegative reals.  The nan output is the result of an 
**invalid** input.

So the question is really: "Why is a negative real number an 
invalid input in this implementation", or "Why in this 
implementation is the type of the output restricted by the 
type of the input?" You get a good start on answering that.

Cheers,
Alan Isaac


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