bnrdisc

Function: bnrdisc
Section: number_fields
C-Name: bnrdisc0
Prototype: GDGDGD0,L,
Help: bnrdisc(A,{B},{C},{flag=0}): absolute or relative [N,R1,discf] of
 the field defined by A,B,C. [A,{B},{C}] is of type [bnr],
 [bnr,subgroup], [bnf, modulus] or [bnf,modulus,subgroup], where bnf is as
 output by bnfinit, bnr by bnrinit, and
 subgroup is the HNF matrix of a subgroup of the corresponding ray class
 group (if omitted, the trivial subgroup). flag is optional whose binary
 digits mean 1: give relative data; 2: return 0 if modulus is not the
 conductor.
Doc: $A$, $B$, $C$ defining a class field $L$ over a ground field $K$
 (of type \kbd{[\var{bnr}]},
 \kbd{[\var{bnr}, \var{subgroup}]},
 \kbd{[\var{bnr}, \var{character}]},
 \kbd{[\var{bnf}, \var{modulus}]} or
 \kbd{[\var{bnf}, \var{modulus}, \var{subgroup}]},
 \secref{se:CFT}), outputs data $[N,r_1,D]$ giving the discriminant and
 signature of $L$, depending on the binary digits of \fl:

 \item 1: if this bit is unset, output absolute data related to $L/\Q$:
 $N$ is the absolute degree $[L:\Q]$, $r_1$ the number of real places of $L$,
 and $D$ the discriminant of $L/\Q$. Otherwise, output relative data for $L/K$:
 $N$ is the relative degree $[L:K]$, $r_1$ is the number of real places of $K$
 unramified in $L$ (so that the number of real places of $L$ is equal to $r_1$
 times $N$), and $D$ is the relative discriminant ideal of $L/K$.

 \item 2: if this bit is set and if the modulus is not the conductor of $L$,
 only return 0.