On computing the discriminant of an algebraic number field

Theresa P. Vaughan
1985 Mathematics of Computation  
Let/(x) be a monic irreducible polynomial in Z[x], and r a root of f(x) in C. Let K be the field Q(r) and St the ring of integers in K. Then for some k e Z, discr = k2 disc Si. In this paper we give constructive methods for (a) deciding if a prime p divides k, and (b) úp \ k, finding a polynomial g(x) e Z[x] so that g(x) * 0 (mod p) but g(r)/p e Ä.
doi:10.1090/s0025-5718-1985-0804946-1 fatcat:6kcpsvmtbrcchdqmjcr6ei3p6m