Function: nfweilheight
Section: number_fields
C-Name: nfweilheight
Prototype: GGp
Help: nfweilheight(nf, v): return the absolute Weil height of the vector v seen
 as an element of the projective space over the number field nf given by nfinit.
Doc: let \var{nf} be attached to a number field $K$, let $v$ be a vector of
 elements of $K$, not all of them $0$, seen as element of the projective
 space of dimension \kbd{\#v - 1}. Return the absolute logarithmic Weil height
 of that element, which does not depend on the number field used to compute it.

 When the entries of $v$ are rational, the height is
 \kbd{log(normlp(v / content(v), oo))}.
 \bprog
 ? v = [1, 2, -3, 101]; Q = nfinit(x); Qi = nfinit(x^2 + 1);
 ? exponent(nfweilheight(Q, v) - log(101))
 %2 = -125
 ? exponent(nfweilheight(Qi, v) - log(101))
 %3 = -125
 @eprog
