Function: rnfeltup
Section: number_fields
C-Name: rnfeltup0
Prototype: GGD0,L,
Help: rnfeltup(rnf,x,{flag=0}): expresses x (belonging to the base field) on
 the relative field. As a t_POLMOD if flag = 0 and as a t_COL on the absolute
 field integer basis if flag = 1.
Doc: $\var{rnf}$ being a relative number field extension $L/K$ as output by
 \kbd{rnfinit} and $x$ being an element of $K$, computes $x$ as an element of
 the absolute extension $L/\Q$. As a \typ{POLMOD} modulo \kbd{\var{rnf}.pol}
 if $\fl = 0$ and as a \typ{COL} on the absolute field integer basis if
 $\fl = 1$. Note that if $x$
 is in fact rational, it is returned as a rational number, ignoring \fl.
 \bprog
 ? K = nfinit(y^2+1); L = rnfinit(K, x^2-y);
 ? L.pol
 %2 = x^4 + 1
 ? rnfeltup(L, Mod(y, K.pol))
 %3 = Mod(x^2, x^4 + 1)
 ? rnfeltup(L, y)
 %4 = Mod(x^2, x^4 + 1)
 ? rnfeltup(L, [1,2]~) \\ in terms of K.zk
 %5 = Mod(2*x^2 + 1, x^4 + 1)
 ? rnfeltup(L, y, 1) \\ in terms of nfinit(L).zk
 %6 = [0, 1, 0, 0]~
 ? rnfeltup(L, [1,2]~, 1)
 %7 = [1, 2, 0, 0]~
 ? rnfeltup(L, [1,0]~) \\ rational
 %8 = 1
 @eprog
Variant: Also available is
 \fun{GEN}{rnfeltup}{GEN rnf, GEN x} ($\fl = 0$).
