default(timer, 0); default(echo, 0); print("? polk = quadpoly(69, y)") polk = quadpoly(69, y) system("pause"); print("? bnfk = bnfinit(polk, 1);") bnfk = bnfinit(polk, 1); system("pause"); print("? bnr_for_Kp = bnrinit(bnfk, 3, 1);") bnr_for_Kp = bnrinit(bnfk, 3, 1); system("pause"); print("? bnr_for_Kp.clgp") bnr_for_Kp.clgp system("pause"); print("? ??bnrstark") ??bnrstark system("pause"); print("? polKp = bnrstark(bnr_for_Kp, 0, 2)") polKp = bnrstark(bnr_for_Kp, 0, 2) system("pause"); print("? polK = polcompositum(polKp, x^2+x+1)[1]") polK = polcompositum(polKp, x^2+x+1)[1] system("pause"); print("? polK = polredabs(polK)") polK = polredabs(polK) system("pause"); print("? bnfK = bnfinit(polK, 1);") bnfK = bnfinit(polK, 1); system("pause"); print("? rpol = nffactor(bnfk, polK)[1,1]") rpol = nffactor(bnfk, polK)[1,1] system("pause"); print("? cond = rnfconductor(bnfk, rpol)") cond = rnfconductor(bnfk, rpol) system("pause"); print("? bnr_for_K = bnrinit(bnfk, %[1], 1);") bnr_for_K = bnrinit(bnfk, %[1], 1); system("pause"); print("? bnr_for_K.clgp") bnr_for_K.clgp system("pause"); print("? rnfKk = rnfinit(bnfk, rpol);") rnfKk = rnfinit(bnfk, rpol); system("beep"); system("pause"); print("? ??bnrL1") ??bnrL1 system("pause"); print("? L1 = bnrL1(bnr_for_K, 0, 6)") L1 = bnrL1(bnr_for_K, 0, 6) system("beep"); system("pause"); print("? z6 = exp(2*I*Pi/6);") z6 = exp(2*I*Pi/6); system("pause"); print("? id1 = (1/6)*conj([1, z6, z6^2, z6^3, z6^4, z6^5]);") id1 = (1/6)*conj([1, z6, z6^2, z6^3, z6^4, z6^5]); system("pause"); print("? id5 = (1/6)*conj([1, z6^5, z6^10, z6^15, z6^20, z6^25]);") id5 = (1/6)*conj([1, z6^5, z6^10, z6^15, z6^20, z6^25]); system("pause"); print("? wK = bnfK.tu[1]") wK = bnfK.tu[1] system("pause"); print("? br = wK*4*(id1 + id5)") br = wK*4*(id1 + id5) system("pause"); print("? br = round(real(br))") br = round(real(br)) system("beep"); system("pause"); print("? cnj = nfgaloisconj(bnfK);") cnj = nfgaloisconj(bnfK); system("pause"); print("? length(cnj)") length(cnj) system("pause"); print("? bnr_for_K.clgp") bnr_for_K.clgp system("pause"); print("? pr = idealhnf(bnfk, bnr_for_K.clgp[3][1])") pr = idealhnf(bnfk, bnr_for_K.clgp[3][1]) system("pause"); print("? factor(bnfK.index)") factor(bnfK.index) system("pause"); print("? ??rnfidealup") ??rnfidealup system("pause"); print("? idealfactor(bnfK, mathnf(Mat(nfalgtobasis(bnfK, rnfidealup(rnfKk, pr)))))") idealfactor(bnfK, mathnf(Mat(nfalgtobasis(bnfK, rnfidealup(rnfKk, pr))))) system("pause"); print("? Pr = %[1,1]") Pr = %[1,1] system("pause"); print("? delta = rnfeltup(rnfKk, y);") delta = rnfeltup(rnfKk, y); system("pause"); print("? subst(polk, y, delta)") subst(polk, y, delta) system("pause"); print("? for (j = 1, 12, if (delta == nfgaloisapply(bnfK, cnj[j], delta) && idealval(bnfK, x^17 - nfgaloisapply(bnfK, cnj[j], x), Pr) > 0, sig = cnj[j])); sig") for (j = 1, 12, if (delta == nfgaloisapply(bnfK, cnj[j], delta) && idealval(bnfK, x^17 - nfgaloisapply(bnfK, cnj[j], x), Pr) > 0, sig = cnj[j])); sig system("pause"); print("? bnfK.clgp") bnfK.clgp system("pause"); print("? ida = bnfK.clgp[3][1];") ida = bnfK.clgp[3][1]; system("pause"); print("? gida = idealpow(bnfK, ida, br[1]);") gida = idealpow(bnfK, ida, br[1]); system("pause"); print("? gida = idealmul(bnfK, gida, idealpow(bnfK, nfgaloisapply(bnfK, sig, ida), br[2]));") gida = idealmul(bnfK, gida, idealpow(bnfK, nfgaloisapply(bnfK, sig, ida), br[2])); system("pause"); print("? p1 = nfgaloisapply(bnfK, sig, sig);") p1 = nfgaloisapply(bnfK, sig, sig); system("pause"); print("? gida = idealmul(bnfK, gida, idealpow(bnfK, nfgaloisapply(bnfK, p1, ida), br[3]));") gida = idealmul(bnfK, gida, idealpow(bnfK, nfgaloisapply(bnfK, p1, ida), br[3])); system("pause"); print("? p1 = nfgaloisapply(bnfK, p1, sig);") p1 = nfgaloisapply(bnfK, p1, sig); system("pause"); print("? gida = idealmul(bnfK, gida, idealpow(bnfK, nfgaloisapply(bnfK, p1, ida), br[4]));") gida = idealmul(bnfK, gida, idealpow(bnfK, nfgaloisapply(bnfK, p1, ida), br[4])); system("pause"); print("? p1 = nfgaloisapply(bnfK, p1, sig);") p1 = nfgaloisapply(bnfK, p1, sig); system("pause"); print("? gida = idealmul(bnfK, gida, idealpow(bnfK, nfgaloisapply(bnfK, p1, ida), br[5]));") gida = idealmul(bnfK, gida, idealpow(bnfK, nfgaloisapply(bnfK, p1, ida), br[5])); system("pause"); print("? p1 = nfgaloisapply(bnfK, p1, sig);") p1 = nfgaloisapply(bnfK, p1, sig); system("pause"); print("? gida = idealmul(bnfK, gida, idealpow(bnfK, nfgaloisapply(bnfK, p1, ida), br[6]));") gida = idealmul(bnfK, gida, idealpow(bnfK, nfgaloisapply(bnfK, p1, ida), br[6])); system("pause"); print("? bnfisprincipal(bnfK, gida)") bnfisprincipal(bnfK, gida) system("pause"); print("? alpha = %[2];") alpha = %[2]; system("pause"); print("? alpha = nfbasistoalg(bnfK, alpha);") alpha = nfbasistoalg(bnfK, alpha); system("pause"); print("? abs(conjvec(alpha))") abs(conjvec(alpha)) system("beep"); system("pause"); print("? N = 1;") N = 1; system("pause"); print("? zt = bnfK.tu[2];"); zt = bnfK.tu[2]; system("pause"); print("? while (nfgaloisapply(bnfK, sig, zt) != zt^N, N++); N") while (nfgaloisapply(bnfK, sig, zt) != zt^N, N++); N system("pause"); print("? beta = nfeltdiv(bnfK, nfbasistoalg(bnfK,nfeltpow(bnfK, alpha, 5)), nfgaloisapply(bnfK, sig, alpha));") beta = nfeltdiv(bnfK, nfbasistoalg(bnfK,nfeltpow(bnfK, alpha, 5)), nfgaloisapply(bnfK, sig, alpha)); system("pause"); print("? polbeta6 = subst(charpoly(nfbasistoalg(bnfK, beta)), x, x^6);") polbeta6 = subst(charpoly(nfbasistoalg(bnfK, beta)), x, x^6); system("pause"); print("? factor(polbeta6)") factor(polbeta6) system("pause");