bnf = bnfinit(x^3-11);
bnf.pol
bnf.cyc
bnf.reg
bnf.fu

bnf = bnfinit(x^3+1048583,1);
sizebyte(bnf.fu)
bnfunits(bnf)
sizebyte(bnfunits(bnf))
bnfsignunit(bnf)

bnf = bnfinit(x^3-17);
bnfunits(bnf)
bnfunits(bnf)[1]
id = idealprimedec(bnf,2);
bnfunits(bnf,id)[1]

quadclassunit(1-2^127)

quadclassunit(1-2^127)

\g1bnf
bnf = bnfinit(x^3+nextprime(2^52));

\g0bnf
bnf = bnfinit(a^2-a+50,1);
bnf.cyc

R = bnrclassfield(bnf)[1]

[cond,bnr,subg] = rnfconductor(bnf,R);
cond
subg

R2 = bnrclassfield(bnf,,2)

bnr = bnrinit(bnf,12); bnr.cyc

[deg,r1,D] = bnrdisc(bnr);
[deg,r1]
D

bnrclassfield(bnr)

bnrclassfield(bnr,,1)

bnr = bnrinit(bnf,7);
bnr.cyc
bnrclassfield(bnr,3) \\elementary 3-subextension

pr41 = idealprimedec(bnf,41)[1];
bnrisprincipal(bnr,pr41,0)

bnr = bnrinit(bnf,[102709,43512;0,1]);
bnr.cyc
bnrclassfield(bnr,[9,3;0,1]) \\subgroup of index 9

bnf=bnfinit(a^2-217,1);
bnf.cyc
bnrinit(bnf,1).cyc
bnrinit(bnf,[1,[1,1]]).cyc

bnr = bnrinit(bnf,271*379,,3);
bnr.cyc
bnrclassfield(bnr)

S = [s|s<-subgrouplist(bnr,,1),matdet(s)==3];
L = [bnrclassfield(bnr,s,1)|s<-S];
L == bnrclassfield(bnr,S,1)