Function: zetakinit
Section: number_fields
C-Name: initzeta
Prototype: Gp
Help: zetakinit(bnf): compute number field information necessary to use zetak.
 bnf may also be an irreducible polynomial.
Doc: computes a number of initialization data
 concerning the number field associated to \kbd{bnf} so as to be able
 to compute the \idx{Dedekind} zeta and lambda functions, respectively
 $\kbd{zetak}(x)$ and $\kbd{zetak}(x,1)$, at the current real precision. If
 you do not need the \kbd{bnfinit} data somewhere else, you may call it
 with an irreducible polynomial instead of a \var{bnf}: it will call
 \kbd{bnfinit} itself.

 The result is a 9-component vector $v$ whose components are very technical
 and cannot really be used except through the \kbd{zetak} function.

 This function is very inefficient and should be rewritten. It needs to
 computes millions of coefficients of the corresponding Dirichlet series if
 the precision is big. Unless the discriminant is small it will not be able
 to handle more than 9 digits of relative precision. For instance,
 \kbd{zetakinit(x\pow 8 - 2)} needs 440MB of memory at default precision.
