1nf=nfinit(y^2+1); 2rnfidealmul(rnfinit(nf,x^4-x-1),2,3) 3rnfidealmul(rnfinit(nf,[x^4-x-1,10^3]),2,3) 4rnfidealup(rnfinit(nf,x),[;]) 5nf=nfinit(quadpoly(1129,y));ord=rnfpseudobasis(nf,quadray(1129,1));rnfsteinitz(nf,ord) 6rnflllgram(nf,x^3+2,rnfpseudobasis(nf,x^3+2)) 7nf=nfinit(y^2-y-4);T=x^11-11*x^10+31*x^9-26*x^8+36*x^7+7*x^6+15*x^5-27*x^4+26*x^3+20*x^2-33*x+42; 8rnfpseudobasis(nf,T) 9rnfpseudobasis(nf,[T,10^3]) 10rnfpseudobasis(nf,[T, [3, 79, 269, 1361, 2789]]) 11T = x^2+1009^3*(10^6+3)^2*y; 12rnfpseudobasis(nf,T) 13rnfpseudobasis(nf,[T,100]) 14rnfpseudobasis(nf,[T,1010]) 15rnfpseudobasis(nf,[T, [idealprimedec(nf,2)[1], 1009]]) 16rnfdisc(nf,T) 17rnfdisc(nf,[T,100]) 18rnfdisc(nf,[T,1010]) 19rnfpseudobasis(nf,[T, [idealprimedec(nf,2)[1], 1009]]) 20rnfpseudobasis(nf,[T, [2, 1009]]) 21Q = bnfinit(y); T=x^4+x^3-71*x^2+72*x+5184; 22rnfconductor(Q,T) 23rnfconductor(Q,[T,10^3]) 24rnfconductor(Q,[T, [2,3,7,41]]) 25rnfconductor(Q,galoissubcyclo(117,116))[1] 26K=bnfinit(quadpoly(1596,y),1); rnfbasis(K,rnfsteinitz(K,rnfpseudobasis(K,quadray(K,1)))); 27 28\\ oo loop after bnrmod commit 2b72fbfbf 29rnfconductor(bnfinit(a^3-a^2-6*a+7),x^3-a*x^2+(5*a^2-35)*x+(8*a^2+6*a-35))[3] 30 31K = nfinit(x^2-x+2); M = [1, 0, x; 0, x, 0; 0,0,2+x]; N = [1, 1, 1]; 32nfsnf(K, [M, N, N]) 33rnfisabelian(y,x) 34rnfisabelian(y^2+23,x^3+x^2-1) 35T = polcyclo(7, x+Mod(y, nf.pol)); 36rnfisabelian(nf.pol, T) 37rnfisabelian(nf, T) 38rnfisabelian(a^2+1,5*x^3+2) 39rnfisabelian(4*a^2+1, 9*x^2 + (12*a+3)*x + 2*a) 40rnfisabelian(y^4+2,polsubcyclo(13,6)) 41 42pol = y^3+y^2-2*y-1; 43bnf = bnfinit(pol); 44T=rnfisnorminit(bnf, x^3-y); 45do(T,u,flag=0)=liftpol(rnfisnorm(T,u,flag)); 46do(T,y) 47[a,b]=rnfisnorm(T,2,100); 48liftpol(norm(a)*b) 49[a,b]=rnfisnorm(T,2,-2*3*5*7); 50liftpol(norm(a)*b) 51 52T=rnfisnorminit(y^2+23, x^2-y); 53do(T,y) 54do(T,2,100) 55 56\\#1157 57rnfisnorminit(y,x^2-Mod(2+y,y)); 58 59\\#1778 60K = bnfinit(x^4-2*x^3-27*x^2+28*x+53); 61t = varhigher("t"); 62L = rnfisnorminit(K,t^2-310*x^3+465*x^2+11005*x-274660); 63[a,b]=rnfisnorm(L,-28124/93*x^3+14062/31*x^2+562480/93*x+166769/31); 64liftpol(norm(a)*b) 65 66\\#1255 67K = nfinit(z^3+z^2-2*z-1); rnf = rnfinit(K, x^2+Mod(-z,z^3+z^2-2*z-1)*x+1); 68a = rnfeltup(rnf,z^2) 69rnfeltdown(rnf, a) 70 71setrand(1);a=matrix(3,4,j,k,vectorv(3,l,random(21))); 72idx=idealprimedec(K,3)[1]; 73aid=[idx,1,1,1]; 74[A,U]=nfhnf(K,[a,aid],1); 75A 76U 77lift(matbasistoalg(K,a)*matbasistoalg(K,U)) 78 79a=a[,1..3]; 80[A,U,V]=nfsnf(K,[a, aid[1..3], [1,1,1]],1); 81A 82U 83V 84lift(matbasistoalg(K,U)*matbasistoalg(K,a)*matbasistoalg(K,V)) 85 86nf=nfinit(y); A = [[1,1/2;0,1],[1,1]]; 87nfhnfmod(nf, A, nfdetint(nf,A)) 88 89K=bnfinit(y^2-40); 90bnfisnorm(K,2, 0) 91bnfisnorm(K,6, 0) 92 93K=bnfinit(y^3-21); 94bnfisnorm(K,2) 95bnfisnorm(K,6) 96L=rnfinit(K,x^2-y); 97 98v = [2,1/2,x+y,Mod(1,K.pol),Mod(1/2,K.pol),Mod(y,K.pol),Mod(1,L.polabs),Mod(1/2,L.polabs),Mod(x,L.polabs),Mod(x+y/2,L.pol),y,z,Mod(y+1/2,y^2+1),[1]~,[1,2]~,[1,y]~,[1,I]~, y+I,x^2]; 99f=[rnfalgtobasis,rnfbasistoalg,rnfeltabstorel,rnfeltreltoabs,rnfeltup,rnfeltdown,rnfelttrace,rnfeltnorm]; 100 101test(L,v) = 102{ 103 for (i=1,#v, 104 for (j=1,#f, print([i,j], ": ", iferr(f[j](L,v[i]), E,E))) 105 ); 106 my (K = L.nf); 107 for (i=1,#v, 108 print(i, ": ", iferr(rnfcharpoly(K,x^2-y,v[i]),E,E)) 109 ); 110} 111test(L,v); 112KQ = nfinit(y+1); 113LQ = rnfinit(KQ, x^2-y); 114vQ = [2,1/2,x+y, Mod(1/2,KQ.pol), y, Mod(Mod(x/2+1,KQ.pol),LQ.pol), Mod(x,LQ.pol), Mod(x,LQ.polabs), Mod(x+y/2,x^2-y), x, [1]~,[1,2]~,[y]~]; 115test(LQ, vQ); 116 117nf = nfinit(y); 118rnf = rnfinit(nf,x^2-2); 119rel = Mod(Mod(1,y)+0*y,x^2-2); 120a = rnfeltreltoabs(rnf,rel) 121variable(lift(a)) 122 123Labs = nfinit(L); 124idL = idealhnf(Labs, x^3+x^2+10); 125idK = idealhnf(K, y^2+10*y+5); 126id = rnfidealabstorel(L,Labs.zk*idL) 127rnfidealnormabs(L,id) == idealnorm(Labs, idL) 128m = rnfidealreltoabs(L, id) 129mathnf(matalgtobasis(Labs,m)) == idL 130 131P3 = idealprimedec(K,3); 132\\ pr[5] depends on 32/64-bit arch 133strip5(pr)=pr[1..4]; 134apply(strip5, rnfidealprimedec(L, P3[1])) 135my(v=rnfidealprimedec(L,7)); [apply(strip5, v[1]), apply(strip5, v[2][1])] 136 137k=nfinit(y^3-y^2+1); rnfidealprimedec(rnfinit(k,x),idealprimedec(k,89)[1]) 138 139rnffa(rnf,id)=my(fa=rnfidealfactor(rnf,id)); fa[,1] = apply(strip5,fa[,1]); fa; 140rnffa(L,7) 141rnffa(L,x) 142rnffa(L,y) 143rnfidealfactor(L,id) == rnfidealfactor(L,idL) 144 145m = rnfidealup(L, idK) 146mabs = rnfidealup(L, idK, 1); 147mathnf( Mat(apply(x->nfalgtobasis(Labs,x), m)) ) == mabs 148rnfidealdown(L, m) == idK 149rnfidealdown(L, mabs) == idK 150m = rnfidealdown(L, Labs.zk*idL) 151M=rnfidealup(L, m) 152mathnf(matalgtobasis(Labs,M)) == rnfidealup(L, m, 1) 153\\ 154V=concat(v, [[;], [], 0, [[;],[]], idealprimedec(K,2)[1], idK, idL, Labs.zk*idL, id]); 155f=[rnfidealhnf,rnfidealreltoabs,rnfidealabstorel,rnfidealdown,rnfidealup,rnfidealnormrel,rnfidealnormabs,rnfidealtwoelt]; 156{ 157for (i=1,#V, 158 print(i,":"); 159 for (j=1, #f, 160 print(iferr(f[j](L,V[i]),E,E)) 161 ) 162) 163} 164rnfidealmul(L, 0,1) 165rnfidealmul(L, 1,0) 166rnfidealmul(L, x,y) 167rnfidealmul(L, y,x) 168rnfidealmul(L, id,x) 169rnfidealmul(L, x,id) 170rnfdet(K,[[;],[]]) 171rnfdet(K,id) 172rnfbasis(bnfinit(y^2-1105),x^2-y) 173\\#1508 174K=nfinit(y); L=rnfinit(K,x^3-2); rnfeltdown(L,Mod(Mod(1,K.pol),L.polabs)) 175 176rnf=rnfinit(nfinit(y^2+1),x^2-2); rnfidealup(rnf, matid(2)/2) 177 178k1=bnfinit(y^3+y^2-2*y-1); 179u=x^3+y*x^2+(y-2)*x+(y^2-y-1); 180rnfconductor(k1,u) 181rnfconductor(k1,u / Mod(y,k1.pol))[^2] \\ wrong: not Abelian 182rnfconductor(k1, y*x^2+(y-2)*x+(y^2-y-1))[^2] 183 184K = bnfinit(y^4+10*y^2+17); 185rnfconductor(K, x + 1/2*y^3 - 1/2*y^2 + 9/2*y - 13/2)[1] 186 187K = nfinit(y^2+y+1); 188rnfislocalcyclo(rnfinit(K, x^3-2)) 189rnfislocalcyclo(rnfinit(K, x)) 190rnfislocalcyclo(rnfinit(K, x^3 - y)) 191rnfislocalcyclo(rnfinit(K, x^3 - y + 3^6)) 192 193nf=nfinit(y^2+9); \\ 3 divides index 194P=idealprimedec(nf,3)[1]; 195rnfdedekind(nf, (x+y/3)^3+3*y, P) 196 197nf = nfinit(y^2-3); P = x^3 - 2*y; 198pr3 = idealprimedec(nf,3)[1]; 199pr2 = idealprimedec(nf,2)[1]; 200 201rnfdedekind(nf, P, pr2) 202rnfdedekind(nf, P, pr3) 203rnfdedekind(nf, P, pr2, 1) 204rnfdedekind(nf, P, pr3, 1) 205rnfdedekind(nf, P) 206rnfdedekind(nf, P, [pr2,pr3]) 207 208P = (y+1)*x^4 + x^2 + x + 2; 209rnfdedekind(nf, P, pr3, 1) 210 211t = 't; T = polcyclo(9,t); 212pol = y^2 + Mod(t^5+t^2+t-1, T)*y + Mod(1-t, T); 213Qchi=nfinit([T,10^6]); 214rnfinit(Qchi,[pol,10^6]); \\ segv in 2.11 215 216k = nfinit(y^4 + 10*y^2 + 17); 217rnfdisc(k, x^2 - x + 1/Mod(y,k.pol)) 218rnfdisc(k, x^2 - x + 1/2) 219 220k = nfinit(y^4 - 10*y^2 + 1); 221rnfdisc(k,x^2-(y^3/2+y^2-5*y/2+1)) 222 223default(parisize,"16M"); 224pol=x^2+(-4*y^60+2*y^58-4*y^56+7*y^54-5*y^52+y^48+3*y^46-3*y^44-2*y^42+3*y^40+y^38-2*y^36-3*y^34+6*y^32-3*y^30-y^28-2*y^26+5*y^24-y^22-4*y^20+2*y^18+2*y^16-y^14-3*y^12+3*y^10+2*y^8-2*y^6-4*y^4+5*y^2+5); 225rnfdisc(nfinit(y^62-y^2-1),pol) 226 227\\ ERRORS, keep at end of file 228rnfdedekind(nf, P, pr2, 1) 229rnfdedekind(nf, P) 230rnfdedekind(nf, P, [pr2,pr3]) 231 232rnfpseudobasis(nf, x^2/2 + 1); 233rnfpseudobasis(nf, x^2 + 1/2); 234 235rnfislocalcyclo(rnfinit(K, x^6-y+1)) 236\\#1530 237L=rnfinit(nfinit(y^2-3),x^2+23); 238rnfidealtwoelt(L, [[1;0], [1/104]]) 239 240\\#2093 241nf = nfinit(y); 242rnf = rnfinit(nf,x^2+5); 243rnfidealup(rnf,Mat(3),1); 244bnfinit(rnf) 245