This entry provides a type class for perfect fields. A perfect field K can be characterized by one of the following equivalent conditions:
- Any irreducible polynomial p is separable, i.e. gcd(p,p') = 1, or, equivalently, p' non-zero.
- Either the characteristic of K is 0 or p > 0 and the Frobenius endomorphism is surjective (i.e. every element of K has a p-th root).
- any field of characteristic 0 (e.g. the reals or complex numbers)
- any finite field (i.e. Fq for q=pn, n > 0 and p prime)
- any algebraically closed field (for example the formal Puiseux series over finite fields)