bnrclassno

Function: bnrclassno
Section: number_fields
C-Name: bnrclassno0
Prototype: GDGDG
Help: bnrclassno(A,{B},{C}): relative degree of the class field defined by
 A,B,C. [A,{B},{C}] is of type [bnr], [bnr,subgroup], [bnf,modulus],
 or [bnf,modulus,subgroup].
 Faster than bnrinit if only the ray class number is wanted.
Doc:
  let $A$, $B$, $C$ define a class field $L$ over a ground field $K$
 (of type \kbd{[\var{bnr}]},
 \kbd{[\var{bnr}, \var{subgroup}]},
 or \kbd{[\var{bnf}, \var{modulus}]},
 or \kbd{[\var{bnf}, \var{modulus},\var{subgroup}]},
 \secref{se:CFT}); this function returns the relative degree $[L:K]$.

 In particular if $A$ is a \var{bnf} (with units), and $B$ a modulus,
 this function returns the corresponding ray class number modulo $B$.
 One can input the attached \var{bid} (with generators if the subgroup
 $C$ is non trivial) for $B$ instead of the module itself, saving some time.

 This function is faster than \kbd{bnrinit} and should be used if only the
 ray class number is desired. See \tet{bnrclassnolist} if you need ray class
 numbers for all moduli less than some bound.

Variant: Also available is
 \fun{GEN}{bnrclassno}{GEN bnf,GEN f} to compute the ray class number
 modulo~$f$.