P1 = x^4-5; P2 = x^4-x^3-7*x^2+2*x+9; P3 = x^4-x^3-3*x^2+x-1; polgalois(P1) polgalois(P2) polgalois(P3) 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) 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+23); bnf.cyc bnr = bnrinit(bnf,1); bnr.mod R = rnfkummer(bnr) [cond,bnr,subg] = rnfconductor(bnf,R); cond subg bnf = bnfinit(a^2+3); bnr = bnrinit(bnf,6); [deg,r1,D] = bnrdisc(bnr); deg r1 D [degrel,r1rel,Drel] = bnrdisc(bnr,,,1); degrel r1rel Drel R = rnfkummer(bnr) P = rnfequation(bnf,R) nf = nfinit(P); nf.disc nf.sign id31 = idealprimedec(bnf,31)[1]; bnrisprincipal(bnr,id31,0) ispower(Mod(2,31),3) r = lfun([bnr,[1]],0,1) R2 = algdep(exp(r),3) P2 = rnfequation(bnf,R2); nfisisom(P2,nf)!=0 bnf=bnfinit(a^2-217); bnf.cyc bnrinit(bnf,1).cyc bnrinit(bnf,[1,[1,1]]).cyc 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]