Function: bnfcertify
Section: number_fields
C-Name: bnfcertify0
Prototype: lGD0,L,
Help: bnfcertify(bnf,{flag = 0}): certify the correctness (i.e. remove the GRH) of the bnf data output by bnfinit. If flag is present, only certify that the class group is a quotient of the one computed in bnf (much simpler in general).
Doc: $\var{bnf}$ being as output by
 \kbd{bnfinit}, checks whether the result is correct, i.e.~whether it is
 possible to remove the assumption of the Generalized Riemann
 Hypothesis\sidx{GRH}. It is correct if and only if the answer is 1. If it is
 incorrect, the program may output some error message, or loop indefinitely.
 You can check its progress by increasing the debug level. The \var{bnf}
 structure must contain the fundamental units:
 \bprog
 ? K = bnfinit(x^3+2^2^3+1); bnfcertify(K)
   ***   at top-level: K=bnfinit(x^3+2^2^3+1);bnfcertify(K)
   ***                                        ^-------------
   *** bnfcertify: missing units in bnf.
 ? K = bnfinit(x^3+2^2^3+1, 1); \\ include units
 ? bnfcertify(K)
 %3 = 1
 @eprog

 If flag is present, only certify that the class group is a quotient of the
 one computed in bnf (much simpler in general); likewise, the computed units
 may form a subgroup of the full unit group. In this variant, the units are
 no longer needed:
 \bprog
 ? K = bnfinit(x^3+2^2^3+1); bnfcertify(K, 1)
 %4 = 1
 @eprog

Variant: Also available is  \fun{GEN}{bnfcertify}{GEN bnf} ($\fl=0$).