Function: rnfdisc
Section: number_fields
C-Name: rnfdiscf
Prototype: GG
Help: rnfdisc(nf,T): given a polynomial T with coefficients in nf, gives a
2-component vector [D,d], where D is the relative ideal discriminant, and d
is the relative discriminant in nf^*/nf*^2.
Doc: given an \var{nf} structure attached to a number field $K$, as output
by \kbd{nfinit}, and a monic irreducible polynomial $T\in K[x]$ defining a
relative extension $L = K[x]/(T)$, compute the relative discriminant of $L$.
This is a vector $[D,d]$, where $D$ is the relative ideal discriminant and
$d$ is the relative discriminant considered as an element of $K^*/{K^*}^2$.
The main variable of $\var{nf}$ \emph{must} be of lower priority than that of
$T$, see \secref{se:priority}.
\misctitle{Huge discriminants, helping rnfdisc} the format $[T,B]$ is
also accepted instead of $T$ and computes an order which is maximal at all
$p < B$, see \kbd{??rnfinit}: the valuation of $D$ is then correct at all
prime ideals $\goth{p}$ above a rational prime $p < B$ but may be incorrect
at other primes.