Function: nfeltembed
Section: number_fields
C-Name: nfeltembed
Prototype: GGDGp
Help: nfeltembed(nf,x,{pl}): complex embeddings of x at places given
by vector pl.
Doc: given an element $x$ in the number field \var{nf}, return
the (real or) complex embeddings of $x$ specified by optional argument
\var{pl}, at the current \kbd{realprecision}:
\item \var{pl} omitted: return the vector of embeddings at all $r_1+r_2$
places;
\item \var{pl} an integer between $1$ and $r_1+r_2$: return the
$i$-th embedding of $x$, attached to the $i$-th root of \kbd{nf.pol},
i.e. \kbd{nf.roots$[i]$};
\item \var{pl} a vector or \typ{VECSMALL}: return the vector of embeddings; the $i$-th
entry gives the embedding at the place attached to the $\var{pl}[i]$-th real
root of \kbd{nf.pol}.
\bprog
? nf = nfinit('y^3 - 2);
? nf.sign
%2 = [1, 1]
? nfeltembed(nf, 'y)
%3 = [1.25992[...], -0.62996[...] + 1.09112[...]*I]]
? nfeltembed(nf, 'y, 1)
%4 = 1.25992[...]
? nfeltembed(nf, 'y, 3) \\ there are only 2 arch. places
*** at top-level: nfeltembed(nf,'y,3)
*** ^-----------------
*** nfeltembed: domain error in nfeltembed: index > 2
@eprog