why_define_Zi.txt

Q: Why define Zi, rather than using Python's built in complex numbers?

A: We want to exactly represent arbitrarily large Gaussian integers. Python's built-in complex type uses two floating point numbers, and Python floats are limited in size, whereas its integers are not.

Consider the following calculation, where x & x1 are ints, and y & y1 are floats:

In [1]: x = 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
   ...: 111111111111111111111111111111111111111111111111111111111111111111111

In [2]: y = 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
   ...: 111111111111111111111111111111111111111111111111111111111111111111111.0

In [3]: x1 = x + 1

In [4]: y1 = y + 1

In [5]: x1 - x
Out[5]: 1

In [6]: y1 - y
Out[6]: 0.0