Function: nfroots
Section: number_fields
C-Name: nfroots
Prototype: DGG
Help: nfroots({nf},x): roots of polynomial x belonging to nf (Q if
 omitted) without multiplicity.
Doc: roots of the polynomial $x$ in the
 number field $\var{nf}$ given by \kbd{nfinit} without multiplicity (in $\Q$
 if $\var{nf}$ is omitted). $x$ has coefficients in the number field (scalar,
 polmod, polynomial, column vector). The main variable of $\var{nf}$ must be
 of lower priority than that of $x$ (see \secref{se:priority}). However if the
 coefficients of the number field occur explicitly (as polmods) as
 coefficients of $x$, the variable of these polmods \emph{must} be the same as
 the main variable of $t$ (see \kbd{nffactor}).

 It is possible to input a defining polynomial for \var{nf}
 instead, but this is in general less efficient since parts of an \kbd{nf}
 structure will be computed internally. This is useful in two situations: when
 you don't need the \kbd{nf}, or when you can't compute its discriminant due
 to integer factorization difficulties. In the latter case, \tet{addprimes} is
 a possibility but a dangerous one: roots will probably be missed if the
 (true) field discriminant and an \kbd{addprimes} entry are strictly divisible
 by some prime. If you have such an unsafe \var{nf}, it is safer to input
 \kbd{nf.pol}.
Variant: See also \fun{GEN}{nfrootsQ}{GEN x},
 corresponding to $\kbd{nf} = \kbd{NULL}$.

