I have studied a random method to generate an irreducible polynomial of degree $d$ over $\Bbb{F}_p$. Now I am reading a paper in which they study a deterministic method to find such an irreducible polynomial.
With deterministic it is meant that it will always output the same polynomial (not random), and we won't try a bunch of polynomials in a certain order until we find one that is irreducible.
Now I am wondering, why are mathematicians interested in a deterministic method? Is it faster ? Are there certain benefits of the result not being random ? Another reason ?
Any random method can be made deterministic in the sense that it always produces the same output by choosing a specific pseudorandom number generator and seeding it in a consistent manner.
However, determinism has another property: it always finishes in a bounded finite time. With a probabilistic method you can theoretically get unlucky and take an incredibly long time to find the answer.