1Function: rnfeltabstorel
2Section: number_fields
3C-Name: rnfeltabstorel
4Prototype: GG
5Help: rnfeltabstorel(rnf,x): transforms the element x from absolute to
6 relative representation.
7Doc: Let $\var{rnf}$ be a relative
8 number field extension $L/K$ as output by \kbd{rnfinit} and let $x$ be an
9 element of $L$ expressed as a polynomial modulo the absolute equation
10 \kbd{\var{rnf}.pol}, or in terms of the absolute $\Z$-basis for $\Z_L$
11 if \var{rnf} contains one (as in \kbd{rnfinit(nf,pol,1)}, or after
12 a call to \kbd{nfinit(rnf)}).
13 Computes $x$ as an element of the relative extension
14 $L/K$ as a polmod with polmod coefficients.
15 \bprog
16 ? K = nfinit(y^2+1); L = rnfinit(K, x^2-y);
17 ? L.polabs
18 %2 = x^4 + 1
19 ? rnfeltabstorel(L, Mod(x, L.polabs))
20 %3 = Mod(x, x^2 + Mod(-y, y^2 + 1))
21 ? rnfeltabstorel(L, 1/3)
22 %4 = 1/3
23 ? rnfeltabstorel(L, Mod(x, x^2-y))
24 %5 = Mod(x, x^2 + Mod(-y, y^2 + 1))
25
26 ? rnfeltabstorel(L, [0,0,0,1]~) \\ Z_L not initialized yet
27  ***   at top-level: rnfeltabstorel(L,[0,
28  ***                 ^--------------------
29  *** rnfeltabstorel: incorrect type in rnfeltabstorel, apply nfinit(rnf).
30 ? nfinit(L); \\ initialize now
31 ? rnfeltabstorel(L, [0,0,0,1]~)
32 %6 = Mod(Mod(y, y^2 + 1)*x, x^2 + Mod(-y, y^2 + 1))
33 @eprog
34