Format of complex number in Python

Question

I am wondering about the way Python (3.3.0) prints complex numbers. I am looking for an explanation, not a way to change the print.

Example:

>>         


        

Answer 1

The answer lies in the Python source code itself.

I'll work with one of your examples. Let

a = complex(0,1)
b = complex(-1, 0)

When you doa*b you're calling this function:

real_part = a.real*b.real - a.imag*b.imag
imag_part = a.real*b.imag + a.imag*b.real

And if you do that in the python interpreter, you'll get

>>> real_part
-0.0
>>> imag_part
-1.0

From IEEE754, you're getting a negative zero, and since that's not +0, you get the parens and the real part when printing it.

if (v->cval.real == 0. && copysign(1.0, v->cval.real)==1.0) {
    /* Real part is +0: just output the imaginary part and do not
       include parens. */
...
else {
    /* Format imaginary part with sign, real part without. Include
       parens in the result. */
...

I guess (but I don't know for sure) that the rationale comes from the importance of that sign when calculating with elementary complex functions (there's a reference for this in the wikipedia article on signed zero).