default(new_galois_format,1); P1 = x^4-5; polgalois(P1) P2 = x^4-x^3-7*x^2+2*x+9; polgalois(P2) P3 = x^4-x^3-3*x^2+x-1; polgalois(P3) nflist([4,3],2000) nflist([4,4],[1,10000]) nflist([4,5],[1,5000],0) Q1 = nfsplitting(P1) Q2 = nfsplitting(P2) Q3 = nfsplitting(P3) Q3 = polredbest(Q3) gal = galoisinit(Q3); gal.gen ord = gal.orders prod(i=1,#ord,ord[i]) galoisidentify(gal) galoisgetname(24,12) L = galoissubgroups(gal); #L R1 = galoisfixedfield(gal,L[25])[1]; polgalois(R1) R2 = galoisfixedfield(gal,L[28])[1]; polgalois(R2) nf = nfinit(Q3); factor(nf.disc) dec3 = idealprimedec(nf,3); pr3 = dec3[1]; [#dec3, pr3.f, pr3.e] ram3 = idealramgroups(nf,gal,pr3); #ram3 galoisidentify(ram3[1]) galoisisabelian(ram3[1]) galoisidentify(ram3[2]) galoisidentify(ram3[3]) dec11 = idealprimedec(nf,11); pr11 = dec11[1]; [#dec11, pr11.f, pr11.e] ram11 = idealramgroups(nf,gal,pr11); #ram11 galoisidentify(ram11[1]) galoisidentify(ram11[2]) dec2 = idealprimedec(nf,2); pr2 = dec2[1]; [#dec2, pr2.f, pr2.e] frob2 = idealfrobenius(nf,gal,pr2); permorder(frob2) N = 7*13*19; L1 = polsubcyclo(N,3); L2 = [P | P <- L1, #factor(nfinit(P).disc)[,1]==3] G = znstar(N) H = mathnfmodid([1,0;-1,1;0,-1],3); pol = galoissubcyclo(G,H) factor(nfinit(pol).disc) bnf = bnfinit(a^2-a+50); 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) \\3-sous-ext. élémentaire pr41 = idealprimedec(bnf,41)[1]; bnrisprincipal(bnr,pr41,0) bnr = bnrinit(bnf,[102709,43512;0,1]); bnr.cyc M = [9,3;0,1]; \\sous-groupe d'indice 9 bnrclassfield(bnr,M) bnf=bnfinit(a^2-217); bnf.cyc bnr=bnrinit(bnf,1); bnr.cyc bnrinit(bnf,[1,[1,1]]).cyc bnf = bnfinit(a^2+23); bnr = bnrinit(bnf,1); bnr.cyc r = lfun([bnr,[1]],0,1) R2 = algdep(exp(r),3) nfdisc(R2) quadhilbert(-31) lift(quadray(13,7)) bnf = bnfinit(x^2+2*3*5*7*11); bnf.cyc bnr = bnrinit(bnf,1,1); gal = galoisinit(bnf); m = bnrgaloismatrix(bnr,gal)[1] bnf=bnfinit(a^2+47); bnf.cyc P=quadhilbert(-47) [A,J] = rnfpseudobasis(bnf,P); A J [As,Js] = rnfsteinitz(bnf,[A,J]); Js bnfisprincipal(bnf, Js[#Js])