Symbolic Computation
A finite field is a set equipped with two operations, addition and multiplication, satisfying the field axioms, where both operations are closed, associative, commutative, and distributive, and every non-zero element has a multiplicative inverse. Finite fields have a finite number of elements, denoted as $q$, where $q = p^n$ for some prime number $p$ and positive integer $n$. They play a critical role in many areas such as coding theory, cryptography, and algebraic geometry.
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