nf=nfinit(y^2+1);
rnfidealmul(rnfinit(nf,x^4-x-1),2,3)
rnfidealup(rnfinit(nf,x),[;])
nf=nfinit(quadpoly(1129,y));ord=rnfpseudobasis(nf,quadray(1129,1));rnfsteinitz(nf,ord)
rnflllgram(nf,x^3+2,rnfpseudobasis(nf,x^3+2))
rnfpseudobasis(nfinit(quadpoly(17,y)),x^11-11*x^10+31*x^9-26*x^8+36*x^7+7*x^6+15*x^5-27*x^4+26*x^3+20*x^2-33*x+42)
rnfconductor(bnfinit(y),x^4+x^3-71*x^2+72*x+5184)
K=bnfinit(quadpoly(1596,y),1); rnfbasis(K,rnfsteinitz(K,rnfpseudobasis(K,quadray(K,1))));

nf = nfinit(y^2-3); P = x^3 - 2*y;
pr3 = idealprimedec(nf,3)[1];
pr2 = idealprimedec(nf,2)[1];

rnfdedekind(nf, P, pr2)
rnfdedekind(nf, P, pr3)
rnfdedekind(nf, P, pr2, 1)
rnfdedekind(nf, P, pr3, 1)
rnfdedekind(nf, P)
rnfdedekind(nf, P, [pr2,pr3])

P = (y+1)*x^4 + x^2 + x + 2;
rnfdedekind(nf, P, pr2, 1)
rnfdedekind(nf, P, pr3, 1)
rnfdedekind(nf, P)
rnfdedekind(nf, P, [pr2,pr3])

K = nfinit(x^2-x+2); M = [1, 0, x; 0, x, 0; 0,0,2+x]; N = [1, 1, 1];
nfsnf(K, [M, N, N])
rnfisabelian(y,x)
rnfisabelian(y^2+23,x^3+x^2-1)

\\#1157
rnfisnorminit(y,x^2-Mod(2+y,y));

\\#1256
K = nfinit(z^3+z^2-2*z-1); rnf = rnfinit(K, x^2+Mod(-z,z^3+z^2-2*z-1)*x+1);
a = rnfeltup(rnf,z^2)
rnfeltdown(rnf, a)

