/* return the characteristic polynomial of alpha over nf, where alpha is an element of the algebra nf[X]/(T) given as a polynomial in X */ GEN rnfcharpoly(GEN nf, GEN T, GEN alpha, long v) { long vnf, vT, lT; pari_sp av = avma; GEN p1; nf=checknf(nf); vnf = varn(nf[1]); if (v<0) v = 0; T = fix_relative_pol(nf,T,1); if (typ(alpha) == t_POLMOD) alpha = lift_to_pol(alpha); lT = lg(T); if (typ(alpha) != t_POL || varn(alpha) == vnf) return gerepileupto(av, gpowgs(gsub(pol_x[v], alpha), lT - 3)); vT = varn(T); if (varn(alpha) != vT || varncmp(v, vnf)>=0) pari_err(talker,"incorrect variables in rnfcharpoly"); if (lg(alpha) >= lT) alpha = RgX_rem(alpha, T); if (lT <= 4) return gerepileupto(av, gsub(pol_x[v], alpha)); p1 = caract2(T, unifpol(nf,alpha, t_POLMOD), v); return gerepileupto(av, unifpol(nf, p1, t_POLMOD)); }
/* x polynomial in t_VECSMALL form, T t_POL return x mod T */ static GEN u_red(GEN x, GEN T) { return RgX_rem(smallpolrev(x), T); }