> It is just a helper tool for plotting. As mentioned in the paper, we would
> like to handle plots like y < sqrt(x).
> mpmath gives a result something like below for sqrt([-0.5,0.5])
>
> In [10]: a = iv.mpf([-0.5,0.5])
> In [11]: a**0.5
> Out[11]: ([-0.70710678118654757274, 0.70710678118654757274] +
> [-0.70710678118654757274, 0.70710678118654757274]*j)

I don't get this. How is interval arithmetics defined over the complex numbers?

Are you saying that there is a bug in mpmath's interval arithmetics?

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