Uniform random choice of integer
I want to perform some statistical sampling and to do this I need to uniformly randomly choose an integer from [0, N) where $N \approx 10^{50}$. It appears that there are several plausible ways to do this in Sage:
1) randint(0, N-1)
However, the standard Python random library appears to have some non-uniformity, for example see this ticket.
2) import numpy; numpy.random.randint(0, N)
However, since N is so large, this raises
ValueError: high is out of bounds for int64
3) ZZ.random_element(0, N)
Do either of the issues that methods 1) and 2) suffer from apply to method 3)? That is, is 3) the correct way to integers uniformly at random?
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