On Thursday, January 2, 2014 9:22:14 PM UTC+1, bspi...@gmail.com wrote:
>
> What's going on here?
>

These are two different "sqrt": the first one is a sage specific function, 
the second one is from numpy. it's just that numpy's sqrt(2) produces 
something (a float64 type) which makes troubles with the part from sage 
(which is not of type "complex", but 
"sage.rings.complex_number.ComplexNumber")

here is a more isolated example:

import numpy as np
1j / np.float64(2)

which gives 0.

note:

type(1j)
<type 'sage.rings.complex_number.ComplexNumber'>

Harald

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