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