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]
        [0,1,1]~,-4;[2,-1,1]~,2],Mat([-1,1])]
id = idealprimedec(bnf,2);
bnfunits(bnf,id)[1]
       [[2,1,0]~,-1;[-2,1,0]~,1;[-1,1,0]~,2;
        [0,1,1]~,-4;[2,-1,1]~,2],Mat([-1,1])]

quadclassunit(1-2^127)
*** Bach constant: 1.3340686047266399061
Time factor base: 1
Time subFBquad = Vecsmall([2,11,13,17,23,31,37,41,61,67,73,79,83]): 0
Time powsubFBquad: 1
KC = 642, need 647 relations
Time random rel [#rel/#test = 647/450475]: 7681
#### Tentative class number: 5737275303524805875
Time be honest: 340

quadclassunit(1-2^127)
*** Bach constant: 1.3340686047266399061
Time factor base: 2
Time subFBquad = Vecsmall([2,11,13,17,23,31,37,41,61,67,73,79,83]): 0
Time powsubFBquad: 1
KC = 642, need 645 relations
Time MPQS rel [#rel = 645]: 33
Time hnfadd: 1808
#### Tentative class number: 5737275303524805875
Time be honest: 0
     [Qfb(10151,8649,4190256710187893599933191402717932)],1]?

\g1bnf
bnf = bnfinit(x^3+nextprime(2^72));
 PREC = 256
 Time nfinit & nfrootsof1: 2
 Floating point bnf: R1 = 1, R2 = 1
 D = 602120120360326824825289510212630173284571067
 LIMC2 = 16275
 Time computing Bach constant: 7
 Time computing inverse of hR: 0
 *** Bach constant: 1.5308321954873111981

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

R = bnrclassfield(bnf)[1]
  + (-12*a + 6)*x^4 - 30*x^3 + (18*a - 9)*x^2
  + 18*x + (-2*a + 1)

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

R2 = bnrclassfield(bnf,,2)
  + 244113*x^10 - 19818*x^8 - 3170*x^6
  + 17427*x^4 - 3258*x^2 + 199

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

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

bnrclassfield(bnr)
 + (-294*a-3273)*x^4 + (-3*a-3852)*x^2 - 3,
 x^9 - 24*x^7 + (2*a-1)*x^6 + 495*x^5
 + (-12*a+6)*x^4 - 30*x^3 + (18*a-9)*x^2
 + 18*x + (-2*a+1)]

bnrclassfield(bnr,,1)

bnr = bnrinit(bnf,7)
bnr.cyc
bnrclassfield(bnr,3) \\elementary 3-subextension
 x^3 + (-1008*a - 651)*x + (-1103067*a - 8072813)]

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,[102709,43512;0,1],,3);
bnr.cyc;
bnrclassfield(bnr)

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