echo = 1 (on) ? nfpol=x^5-5*x^3+5*x+25 x^5 - 5*x^3 + 5*x + 25 ? qpol=y^3-y-1;un=Mod(1,qpol);w=Mod(y,qpol);p=un*(x^5-5*x+w) Mod(1, y^3 - y - 1)*x^5 + Mod(-5, y^3 - y - 1)*x + Mod(y, y^3 - y - 1) ? p2=x^5+3021*x^4-786303*x^3-6826636057*x^2-546603588746*x+3853890514072057 x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 546603588746*x + 385389051407 2057 ? fa=[11699,6;2392997,2;4987333019653,2] [11699 6] [2392997 2] [4987333019653 2] ? setrand(1);a=matrix(3,5,j,k,vectorv(5,l,random\10^8)); ? setrand(1);as=matrix(3,3,j,k,vectorv(5,l,random\10^8)); ? nf=nfinit(nfpol) [x^5 - 5*x^3 + 5*x + 25, [1, 2], 595125, 45, [[1, -2.42851749071941860689920 69565359418364, 5.8976972027301414394898806541072047941, -7.0734526715090929 269887668671457811020, 3.8085820570096366144649278594400435257; 1, 1.9647119 211288133163138753392090569931 + 0.80971492418897895128294082219556466857*I, 3.2044546745713084269203768790545260356 + 3.1817131285400005341145852263331 539899*I, -0.16163499313031744537610982231988834519 + 1.88804378620070569319 06454476483475283*I, 2.0660709538372480632698971148801090692 + 2.68989675196 23140991170523711857387388*I; 1, -0.75045317576910401286427186094108607489 + 1.3101462685358123283560773619310445915*I, -1.15330327593637914666531720610 81284327 - 1.9664068558894834311780119356739268309*I, 1.19836132888486390887 04932558927788962 + 0.64370238076256988899570325671192132449*I, -0.470361982 34206637050236104460013083212 + 0.083628266711589186119416762685933385421*I] , [1, 2, 2; -2.4285174907194186068992069565359418364, 3.92942384225762663262 77506784181139862 - 1.6194298483779579025658816443911293371*I, -1.5009063515 382080257285437218821721497 - 2.6202925370716246567121547238620891831*I; 5.8 976972027301414394898806541072047941, 6.408909349142616853840753758109052071 2 - 6.3634262570800010682291704526663079798*I, -2.30660655187275829333063441 22162568654 + 3.9328137117789668623560238713478536619*I; -7.0734526715090929 269887668671457811020, -0.32326998626063489075221964463977669038 - 3.7760875 724014113863812908952966950567*I, 2.3967226577697278177409865117855577924 - 1.2874047615251397779914065134238426489*I; 3.8085820570096366144649278594400 435257, 4.1321419076744961265397942297602181385 - 5.379793503924628198234104 7423714774776*I, -0.94072396468413274100472208920026166424 - 0.1672565334231 7837223883352537186677084*I], [5, 0.E-77, 10.0000000000000000000000000000000 00000, -5.0000000000000000000000000000000000000, 7.0000000000000000000000000 000000000000; 0.E-77, 19.488486013650707197449403270536023970, 2.07268045322 2666710 E-76, 19.488486013650707197449403270536023970, 4.1504592246706085588 902013976045703227; 10.000000000000000000000000000000000000, 2.0726804532226 66710 E-76, 85.960217420851846480305133936577594605, -36.0342682914829798382 67056239752434596, 53.576130452511107888183080361946556763; -5.0000000000000 000000000000000000000000, 19.488486013650707197449403270536023970, -36.03426 8291482979838267056239752434596, 60.916248374441986300937507618575151517, -1 8.470101750219179344070032346246890434; 7.0000000000000000000000000000000000 000, 4.1504592246706085588902013976045703227, 53.576130452511107888183080361 946556763, -18.470101750219179344070032346246890434, 37.97015289284236734089 7384258599214282], [5, 0, 10, -5, 7; 0, 10, 0, 10, -5; 10, 0, 30, -55, 20; - 5, 10, -55, 45, -39; 7, -5, 20, -39, 9], [345, 0, 340, 167, 150; 0, 345, 110 , 220, 153; 0, 0, 5, 2, 1; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [132825, -18975, - 5175, 27600, 17250; -18975, 34500, 41400, 3450, -43125; -5175, 41400, -41400 , -15525, 51750; 27600, 3450, -15525, -3450, 0; 17250, -43125, 51750, 0, -86 250], [595125, [-13800, 117300, 67275, 1725, 0]~]], [-2.42851749071941860689 92069565359418364, 1.9647119211288133163138753392090569931 + 0.8097149241889 7895128294082219556466857*I, -0.75045317576910401286427186094108607489 + 1.3 101462685358123283560773619310445915*I], [1, x, x^2, 1/3*x^3 - 1/3*x^2 - 1/3 , 1/15*x^4 + 1/3*x^2 + 1/3*x + 1/3], [1, 0, 0, 1, -5; 0, 1, 0, 0, -5; 0, 0, 1, 1, -5; 0, 0, 0, 3, 0; 0, 0, 0, 0, 15], [1, 0, 0, 0, 0, 0, 0, 1, -2, -1, 0 , 1, -5, -5, -3, 0, -2, -5, 1, -4, 0, -1, -3, -4, -3; 0, 1, 0, 0, 0, 1, 0, 0 , -2, 0, 0, 0, -5, 0, -5, 0, -2, 0, -5, 0, 0, 0, -5, 0, -4; 0, 0, 1, 0, 0, 0 , 1, 1, -2, 1, 1, 1, -5, 3, -3, 0, -2, 3, -5, 1, 0, 1, -3, 1, -2; 0, 0, 0, 1 , 0, 0, 0, 3, -1, 2, 0, 3, 0, 5, 1, 1, -1, 5, -4, 3, 0, 2, 1, 3, 1; 0, 0, 0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 15, -5, 10, 0, 5, -5, 10, -2, 1, 0, 10, -2, 7]] ? nf1=nfinit(nfpol,2) [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145 7205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.59 741050929194782733001765987770358483, 0.158944197453903762065494816710718942 89; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753 285514741525107*I, -0.22273329410580226599155701611419649154 - 0.13611876021 752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0 .13249517760521973840801462296650806543*I, -0.053650958656997725359297528357 602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.682941293594312 7761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.37035 26062130959637482576769100030014 + 6.9001775222880494773720769629846373016*I , -8.0696202866361678983472946546849540475 + 8.87676767859710424508852843013 48051602*I, -22.025821140069954155673449879997756863 - 8.4306586896999153544 710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, - 0.27676744146812072730095952834883393274 - 0.9836327531553728699950657102948 3050214*I, 3.3658825871886255523259123230159952011 - 4.100070245202145234594 8573967197204327*I; 1.1861718006377964594796293860483989860, -0.445466588211 60453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2. 7407052124261919274965153538200060029 - 13.800355044576098954744153925969274 603*I; -0.59741050929194782733001765987770358483, -0.26334891743571637597539 303075238832018 - 0.26499035521043947681602924593301613087*I, -16.1392405732 72335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.15 894419745390376206549481671071894289, -0.10730191731399545071859505671520521 623 - 0.55245273628338214076276569363136722973*I, -44.0516422801399083113468 99759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.000000000 0000000000000000000000000000, -2.0000000000000000000000000000000000000, -17. 000000000000000000000000000000000000, -44.0000000000000000000000000000000000 00; 2.0000000000000000000000000000000000000, 15.7781094086719980448363574712 83695361, 22.314643349754061651916553814602769764, 10.0513952578314782754999 32716306366248, -108.58917507620841447456569092094763671; -2.000000000000000 0000000000000000000000, 22.314643349754061651916553814602769764, 100.5239126 2388960975827806174040462368, 143.93295090847353519436673793501057176, -55.8 42564718082452641322500190813370023; -17.00000000000000000000000000000000000 0, 10.051395257831478275499932716306366248, 143.9329509084735351943667379350 1057176, 288.25823756749944693139292174819167135, 205.7984003827766237572018 0649465932302; -44.000000000000000000000000000000000000, -108.58917507620841 447456569092094763671, -55.842564718082452641322500190813370023, 205.7984003 8277662375720180649465932302, 1112.6092277946777707779250962522343036], [5, 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -1 01, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215, 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, - 296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -296700 , -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -897 00, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725, 0]~]], [-1.0891151457205048250249527946671612684, -0.1383837207340603636504 7976417441696637 + 0.49181637657768643499753285514741525107*I, 1.68294129359 43127761629561615079976005 + 2.0500351226010726172974286983598602163*I], [1, x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2*x], [1, 0, 0, 0, 0; 0, 1, 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0, 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14; 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2, -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9, - 19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1, 3 , 4, -4, 1, 2, 1, -4, -21]] ? nfinit(nfpol,3) [[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.08911514 57205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.5 9741050929194782733001765987770358483, 0.15894419745390376206549481671071894 289; 1, -0.13838372073406036365047976417441696637 + 0.4918163765776864349975 3285514741525107*I, -0.22273329410580226599155701611419649154 - 0.1361187602 1752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0.13249517760521973840801462296650806543*I, -0.05365095865699772535929752835 7602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.68294129359431 27761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.3703 526062130959637482576769100030014 + 6.9001775222880494773720769629846373016* I, -8.0696202866361678983472946546849540475 + 8.8767676785971042450885284301 348051602*I, -22.025821140069954155673449879997756863 - 8.430658689699915354 4710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, -0.27676744146812072730095952834883393274 - 0.983632753155372869995065710294 83050214*I, 3.3658825871886255523259123230159952011 - 4.10007024520214523459 48573967197204327*I; 1.1861718006377964594796293860483989860, -0.44546658821 160453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2 .7407052124261919274965153538200060029 - 13.80035504457609895474415392596927 4603*I; -0.59741050929194782733001765987770358483, -0.2633489174357163759753 9303075238832018 - 0.26499035521043947681602924593301613087*I, -16.139240573 272335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.1 5894419745390376206549481671071894289, -0.1073019173139954507185950567152052 1623 - 0.55245273628338214076276569363136722973*I, -44.051642280139908311346 899759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.00000000 00000000000000000000000000000, -2.0000000000000000000000000000000000000, -17 .000000000000000000000000000000000000, -44.000000000000000000000000000000000 000; 2.0000000000000000000000000000000000000, 15.778109408671998044836357471 283695361, 22.314643349754061651916553814602769764, 10.051395257831478275499 932716306366248, -108.58917507620841447456569092094763671; -2.00000000000000 00000000000000000000000, 22.314643349754061651916553814602769764, 100.523912 62388960975827806174040462368, 143.93295090847353519436673793501057176, -55. 842564718082452641322500190813370023; -17.0000000000000000000000000000000000 00, 10.051395257831478275499932716306366248, 143.932950908473535194366737935 01057176, 288.25823756749944693139292174819167135, 205.798400382776623757201 80649465932302; -44.000000000000000000000000000000000000, -108.5891750762084 1447456569092094763671, -55.842564718082452641322500190813370023, 205.798400 38277662375720180649465932302, 1112.6092277946777707779250962522343036], [5, 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, - 101, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215 , 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, -296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -29670 0, -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -89 700, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725 , 0]~]], [-1.0891151457205048250249527946671612684, -0.138383720734060363650 47976417441696637 + 0.49181637657768643499753285514741525107*I, 1.6829412935 943127761629561615079976005 + 2.0500351226010726172974286983598602163*I], [1 , x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2*x], [1, 0, 0, 0, 0; 0, 1, 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0 , 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0, 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14 ; 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2, -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9, -19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1, 3, 4, -4, 1, 2, 1, -4, -21]], Mod(-1/2*x^4 + 3/2*x^3 - 5/2*x^2 - 2*x + 1, x^ 5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2)] ? nfinit(nfpol,4) [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145 7205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.59 741050929194782733001765987770358483, 0.158944197453903762065494816710718942 89; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753 285514741525107*I, -0.22273329410580226599155701611419649154 - 0.13611876021 752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0 .13249517760521973840801462296650806543*I, -0.053650958656997725359297528357 602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.682941293594312 7761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.37035 26062130959637482576769100030014 + 6.9001775222880494773720769629846373016*I , -8.0696202866361678983472946546849540475 + 8.87676767859710424508852843013 48051602*I, -22.025821140069954155673449879997756863 - 8.4306586896999153544 710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, - 0.27676744146812072730095952834883393274 - 0.9836327531553728699950657102948 3050214*I, 3.3658825871886255523259123230159952011 - 4.100070245202145234594 8573967197204327*I; 1.1861718006377964594796293860483989860, -0.445466588211 60453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2. 7407052124261919274965153538200060029 - 13.800355044576098954744153925969274 603*I; -0.59741050929194782733001765987770358483, -0.26334891743571637597539 303075238832018 - 0.26499035521043947681602924593301613087*I, -16.1392405732 72335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.15 894419745390376206549481671071894289, -0.10730191731399545071859505671520521 623 - 0.55245273628338214076276569363136722973*I, -44.0516422801399083113468 99759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.000000000 0000000000000000000000000000, -2.0000000000000000000000000000000000000, -17. 000000000000000000000000000000000000, -44.0000000000000000000000000000000000 00; 2.0000000000000000000000000000000000000, 15.7781094086719980448363574712 83695361, 22.314643349754061651916553814602769764, 10.0513952578314782754999 32716306366248, -108.58917507620841447456569092094763671; -2.000000000000000 0000000000000000000000, 22.314643349754061651916553814602769764, 100.5239126 2388960975827806174040462368, 143.93295090847353519436673793501057176, -55.8 42564718082452641322500190813370023; -17.00000000000000000000000000000000000 0, 10.051395257831478275499932716306366248, 143.9329509084735351943667379350 1057176, 288.25823756749944693139292174819167135, 205.7984003827766237572018 0649465932302; -44.000000000000000000000000000000000000, -108.58917507620841 447456569092094763671, -55.842564718082452641322500190813370023, 205.7984003 8277662375720180649465932302, 1112.6092277946777707779250962522343036], [5, 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -1 01, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215, 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, - 296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -296700 , -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -897 00, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725, 0]~]], [-1.0891151457205048250249527946671612684, -0.1383837207340603636504 7976417441696637 + 0.49181637657768643499753285514741525107*I, 1.68294129359 43127761629561615079976005 + 2.0500351226010726172974286983598602163*I], [1, x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2*x], [1, 0, 0, 0, 0; 0, 1, 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0, 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14; 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2, -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9, - 19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1, 3 , 4, -4, 1, 2, 1, -4, -21]] ? nf3=nfinit(x^6+108); ? nf4=nfinit(x^3-10*x+8) [x^3 - 10*x + 8, [3, 0], 568, 2, [[1, -3.50466435358804770515010852590433205 79, 6.1413361156553641347759399165844441383; 1, 0.86464088669540302583112842 266613688800, 0.37380193147270638662350044992137561317; 1, 2.640023466892644 6793189801032381951699, 3.4848619528719294786005596334941802484], [1, 1, 1; -3.5046643535880477051501085259043320579, 0.86464088669540302583112842266613 688800, 2.6400234668926446793189801032381951699; 6.1413361156553641347759399 165844441383, 0.37380193147270638662350044992137561317, 3.484861952871929478 6005596334941802484], [3, -3.454467422037777850 E-77, 10.0000000000000000000 00000000000000000; -3.454467422037777850 E-77, 20.00000000000000000000000000 0000000000, -12.000000000000000000000000000000000000; 10.0000000000000000000 00000000000000000, -12.000000000000000000000000000000000000, 50.000000000000 000000000000000000000000], [3, 0, 10; 0, 20, -12; 10, -12, 50], [284, 168, 2 35; 0, 2, 0; 0, 0, 1], [856, -120, -200; -120, 50, 36; -200, 36, 60], [568, [-216, 90, 8]~]], [-3.5046643535880477051501085259043320579, 0.8646408866954 0302583112842266613688800, 2.6400234668926446793189801032381951699], [1, x, 1/2*x^2], [1, 0, 0; 0, 1, 0; 0, 0, 2], [1, 0, 0, 0, 0, -4, 0, -4, 0; 0, 1, 0 , 1, 0, 5, 0, 5, -2; 0, 0, 1, 0, 2, 0, 1, 0, 5]] ? setrand(1);bnf2=bnfinit(qpol);nf2=bnf2[7]; ? setrand(1);bnf=bnfinit(x^2-x-57,,[0.2,0.2]) [Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060 61300699 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468 08795106061300699 - 6.2831853071795864769252867665590057684*I], [9.927737672 2507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1. 2897619530652735025030086072395031017 + 0.E-57*I, -2.01097980249891575621226 34098917610612 + 3.1415926535897932384626433832795028842*I, 24.4121877466590 95772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.3376 98160660239595315877930058147543 + 9.4247779607693797153879301498385086526*I , -20.610866187462450639586440264933189691 + 9.42477796076937971538793014983 85086526*I, 29.258282452818196217527894893424939793 + 9.42477796076937971538 79301498385086526*I, -0.34328764427702709438988786673341921876 + 3.141592653 5897932384626433832795028842*I, -14.550628376291080203941433635329724736 + 0 .E-56*I, 24.478366048541841504313284087778334822 + 3.14159265358979323846264 33832795028842*I; -9.9277376722507613003718504524486100858 + 6.2831853071795 864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.424 7779607693797153879301498385086526*I, 2.010979802498915756212263409891761061 2 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.14159265358979323 84626433832795028842*I, -30.337698160660239595315877930058147543 + 3.1415926 535897932384626433832795028842*I, 20.610866187462450639586440264933189691 + 3.1415926535897932384626433832795028842*I, -29.25828245281819621752789489342 4939793 + 6.2831853071795864769252867665590057684*I, 0.343287644277027094389 88786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.14 15926535897932384626433832795028842*I, -24.478366048541841504313284087778334 822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0, 1 ]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~ , 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1 ]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.0663729752107779635959310 246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.0663729 752107779635959310246705326058, 8.0663729752107779635959310246705326058], [2 , 1.0000000000000000000000000000000000000; 1.0000000000000000000000000000000 000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.066372975210777963595931024 6705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.7124653051843439746 808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [Mat(1), [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.14159265358979323846 26433832795028842*I, -9.9277376722507613003718504524486100858 + 6.2831853071 795864769252867665590057684*I]]], 0] ? setrand(1);bnfinit(x^2-x-100000,1) [Mat(5), Mat([3, 2, 1, 2, 0, 3, 2, 3, 0, 0, 1, 4, 3, 2, 2, 3, 3, 2]), [-129. 82045011403975460991182396195022419 - 6.283185307179586476925286766559005768 4*I; 129.82045011403975460991182396195022419 - 12.56637061435917295385057353 3118011536*I], [-41.811264589129943393339502258694361489 + 8.121413879410077 514 E-115*I, 9.2399004147902289816376260438840931575 + 3.1415926535897932384 626433832795028842*I, -11.874609881075406725097315997431161032 + 9.424777960 7693797153879301498385086526*I, 389.46135034211926382973547188585067257 + 12 .566370614359172953850573533118011536*I, -440.512515346039436204712600188429 12722 + 0.E-113*I, -324.55112528509938652477955990487556047 + 6.283185307179 5864769252867665590057684*I, 229.70424552002497255158146166263724792 + 3.141 5926535897932384626433832795028842*I, -785.660451862534215720251179722755983 25 + 6.2831853071795864769252867665590057684*I, -554.35531386699327377220656 215544062014 + 6.2831853071795864769252867665590057684*I, -47.66831907156823 3997332918482707687879 + 9.4247779607693797153879301498385086526*I, 177.4887 6918560798860724474244465791207 + 6.497131103528062011 E-114*I, -875.6123693 7168080069763246690606885226 + 2.598852441411224804 E-113*I, 54.878404098312 329644822020875673145627 + 9.4247779607693797153879301498385086526*I, -404.4 4153844676787690336623107514389175 + 0.E-113*I, 232.809823743598178900114904 85449930607 + 6.2831853071795864769252867665590057684*I, -668.80899963671483 856204802764462926790 + 9.4247779607693797153879301498385086526*I, 367.35683 481950538594888487746203445802 + 12.566370614359172953850573533118011536*I, -1214.0716092619656173892944003952818868 + 9.4247779607693797153879301498385 086526*I, -125.94415646756187210316334148291471657 + 6.283185307179586476925 2867665590057684*I; 41.811264589129943393339502258694361489 + 6.283185307179 5864769252867665590057684*I, -9.2399004147902289816376260438840931575 + 12.5 66370614359172953850573533118011536*I, 11.8746098810754067250973159974311610 32 + 8.121413879410077514 E-115*I, -389.46135034211926382973547188585067257 + 6.2831853071795864769252867665590057684*I, 440.512515346039436204712600188 42912722 + 3.1415926535897932384626433832795028842*I, 324.551125285099386524 77955990487556047 + 9.4247779607693797153879301498385086526*I, -229.70424552 002497255158146166263724792 + 6.2831853071795864769252867665590057684*I, 785 .66045186253421572025117972275598325 + 9.42477796076937971538793014983850865 26*I, 554.35531386699327377220656215544062014 + 3.14159265358979323846264338 32795028842*I, 47.668319071568233997332918482707687878 + 3.14159265358979323 84626433832795028842*I, -177.48876918560798860724474244465791207 + 6.2831853 071795864769252867665590057684*I, 875.61236937168080069763246690606885226 + 6.497131103528062011 E-114*I, -54.878404098312329644822020875673145627 + 9.4 247779607693797153879301498385086526*I, 404.44153844676787690336623107514389 175 + 9.4247779607693797153879301498385086526*I, -232.8098237435981789001149 0485449930607 + 3.1415926535897932384626433832795028842*I, 668.8089996367148 3856204802764462926790 + 6.2831853071795864769252867665590057684*I, -367.356 83481950538594888487746203445803 + 3.1415926535897932384626433832795028842*I , 1214.0716092619656173892944003952818868 + 3.141592653589793238462643383279 5028842*I, 125.94415646756187210316334148291471657 + 6.283185307179586476925 2867665590057684*I], [[2, [1, 1]~, 1, 1, [0, 1]~], [2, [2, 1]~, 1, 1, [1, 1] ~], [5, [4, 1]~, 1, 1, [0, 1]~], [5, [5, 1]~, 1, 1, [-1, 1]~], [7, [3, 1]~, 2, 1, [3, 1]~], [13, [-6, 1]~, 1, 1, [5, 1]~], [13, [5, 1]~, 1, 1, [-6, 1]~] , [17, [14, 1]~, 1, 1, [2, 1]~], [17, [19, 1]~, 1, 1, [-3, 1]~], [23, [-7, 1 ]~, 1, 1, [6, 1]~], [23, [6, 1]~, 1, 1, [-7, 1]~], [29, [-14, 1]~, 1, 1, [13 , 1]~], [29, [13, 1]~, 1, 1, [-14, 1]~], [31, [23, 1]~, 1, 1, [7, 1]~], [31, [38, 1]~, 1, 1, [-8, 1]~], [41, [-7, 1]~, 1, 1, [6, 1]~], [41, [6, 1]~, 1, 1, [-7, 1]~], [43, [-16, 1]~, 1, 1, [15, 1]~], [43, [15, 1]~, 1, 1, [-16, 1] ~]]~, [1, 3, 6, 2, 4, 5, 7, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 18], [ x^2 - x - 100000, [2, 0], 400001, 1, [[1, -315.72816130129840161392089489603 747004; 1, 316.72816130129840161392089489603747004], [1, 1; -315.72816130129 840161392089489603747004, 316.72816130129840161392089489603747004], [2, 1.00 00000000000000000000000000000000000; 1.0000000000000000000000000000000000000 , 200001.00000000000000000000000000000000], [2, 1; 1, 200001], [400001, 2000 00; 0, 1], [200001, -1; -1, 2], [400001, [200000, 1]~]], [-315.7281613012984 0161392089489603747004, 316.72816130129840161392089489603747004], [1, x], [1 , 0; 0, 1], [1, 0, 0, 100000; 0, 1, 1, 1]], [[5, [5], [[2, 1; 0, 1]]], 129.8 2045011403975460991182396195022419, 0.9876536979069047239, [2, -1], [3795548 84019013781006303254896369154068336082609238336*x + 119836165644250789990462 835950022871665178127611316131167], 186], [Mat(1), [[0, 0]], [[-41.811264589 129943393339502258694361489 + 8.121413879410077514 E-115*I, 41.8112645891299 43393339502258694361489 + 6.2831853071795864769252867665590057684*I]]], 0] ? \p19 realprecision = 19 significant digits ? setrand(1);sbnf=bnfinit(x^3-x^2-14*x-1,3) [x^3 - x^2 - 14*x - 1, 3, 10889, [1, x, x^2], [-3.233732695981516673, -0.071 82350902743636344, 4.305556205008953036], [10889, 5698, 3794; 0, 1, 0; 0, 0, 1], Mat(2), Mat([0, 1, 1, 1, 1, 0, 1, 1]), [9, 15, 16, 17, 10, 69, 33, 39, 57], [2, [-1, 0, 0]~], [[0, 1, 0]~, [-4, 2, 1]~], [-4, 3, -1, 2, 3, 11, 1, - 1, -7; 1, 1, 1, 1, 0, 2, 1, -4, -2; 0, 0, 0, 0, 0, -1, 0, -1, 0]] ? \p38 realprecision = 38 significant digits ? bnrinit(bnf,[[5,3;0,1],[1,0]],1) [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746 808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767 22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1 .2897619530652735025030086072395031017 + 0.E-57*I, -2.0109798024989157562122 634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659 095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337 698160660239595315877930058147543 + 9.4247779607693797153879301498385086526* I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498 385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153 879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265 35897932384626433832795028842*I, -14.550628376291080203941433635329724736 + 0.E-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626 433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179 5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42 47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106 12 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.1415926535897932 384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592 6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 + 3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934 24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438 988786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.1 415926535897932384626433832795028842*I, -24.47836604854184150431328408777833 4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1] ~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1 , 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7 , 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931 0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372 9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [ 2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000 0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114 ; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102 46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974 6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [Mat(1), [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384 626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307 1795864769252867665590057684*I]]], [0, [Mat([[5, 1]~, 1])]]], [[[5, 3; 0, 1] , [1, 0]], [8, [4, 2], [[2, 0]~, [-1, 1]~]], Mat([[5, [-2, 1]~, 1, 1, [1, 1] ~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], [[-1, 1]~] , Mat(1)]], [1, 0; 0, 1]], [1], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[ 3, 2; 0, 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]] ? bnr=bnrclass(bnf,[[5,3;0,1],[1,0]],2) [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746 808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767 22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1 .2897619530652735025030086072395031017 + 0.E-57*I, -2.0109798024989157562122 634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659 095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337 698160660239595315877930058147543 + 9.4247779607693797153879301498385086526* I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498 385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153 879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265 35897932384626433832795028842*I, -14.550628376291080203941433635329724736 + 0.E-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626 433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179 5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42 47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106 12 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.1415926535897932 384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592 6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 + 3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934 24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438 988786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.1 415926535897932384626433832795028842*I, -24.47836604854184150431328408777833 4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1] ~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1 , 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7 , 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931 0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372 9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [ 2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000 0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114 ; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102 46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974 6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [Mat(1), [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384 626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307 1795864769252867665590057684*I]]], [0, [Mat([[5, 1]~, 1])]]], [[[5, 3; 0, 1] , [1, 0]], [8, [4, 2], [[2, 0]~, [-1, 1]~]], Mat([[5, [-2, 1]~, 1, 1, [1, 1] ~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], [[-1, 1]~] , Mat(1)]], [1, 0; 0, 1]], [1], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[ 3, 2; 0, 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]] ? rnfinit(nf2,x^5-x-2) [x^5 - x - 2, [[1, 2], [0, 5]], [[49744, 0, 0; 0, 49744, 0; 0, 0, 49744], [3 109, 0, 0]~], [1, 0, 0; 0, 1, 0; 0, 0, 1], [[[1, 1.2671683045421243172528914 279776896412, 1.6057155120361619195949075151301679393, 2.0347118029638523119 874445717108994866, 2.5783223055935536544757871909285592749; 1, 0.2609638803 8645528500256735072673484811 + 1.1772261533941944394700286585617926513*I, -1 .3177592693689352747870763902256347904 + 0.614427010164338838041906608641467 31824*I, -1.0672071180669977537495893497477340535 - 1.3909574189920019216524 673160314582604*I, 1.3589689411882615753626439480614001936 - 1.6193337759893 970298359887428575174472*I; 1, -0.89454803265751744362901306471557966872 + 0 .53414854617473272670874609150394379949*I, 0.5149015133508543149896226326605 5082078 - 0.95564306225496055080453352211847466685*I, 0.04985121658507159775 5867063892284310224 + 1.1299025160425089918993024639913611785*I, -0.64813009 398503840260053754352567983115 - 0.98412411795664774269323431620030610541*I] , [1, 1.2671683045421243172528914279776896412 + 0.E-38*I, 1.6057155120361619 195949075151301679393 + 0.E-38*I, 2.0347118029638523119874445717108994866 + 0.E-37*I, 2.5783223055935536544757871909285592749 + 0.E-37*I; 1, 0.260963880 38645528500256735072673484811 - 1.1772261533941944394700286585617926513*I, - 1.3177592693689352747870763902256347904 - 0.61442701016433883804190660864146 731824*I, -1.0672071180669977537495893497477340535 + 1.390957418992001921652 4673160314582604*I, 1.3589689411882615753626439480614001936 + 1.619333775989 3970298359887428575174472*I; 1, 0.26096388038645528500256735072673484811 + 1 .1772261533941944394700286585617926513*I, -1.3177592693689352747870763902256 347904 + 0.61442701016433883804190660864146731824*I, -1.06720711806699775374 95893497477340535 - 1.3909574189920019216524673160314582604*I, 1.35896894118 82615753626439480614001936 - 1.6193337759893970298359887428575174472*I; 1, - 0.89454803265751744362901306471557966872 - 0.5341485461747327267087460915039 4379949*I, 0.51490151335085431498962263266055082078 + 0.95564306225496055080 453352211847466685*I, 0.049851216585071597755867063892284310224 - 1.12990251 60425089918993024639913611785*I, -0.64813009398503840260053754352567983115 + 0.98412411795664774269323431620030610541*I; 1, -0.8945480326575174436290130 6471557966872 + 0.53414854617473272670874609150394379949*I, 0.51490151335085 431498962263266055082078 - 0.95564306225496055080453352211847466685*I, 0.049 851216585071597755867063892284310224 + 1.12990251604250899189930246399136117 85*I, -0.64813009398503840260053754352567983115 - 0.984124117956647742693234 31620030610541*I]], [[1, 2, 2; 1.2671683045421243172528914279776896412, 0.52 192776077291057000513470145346969622 - 2.35445230678838887894005731712358530 26*I, -1.7890960653150348872580261294311593374 - 1.0682970923494654534174921 830078875989*I; 1.6057155120361619195949075151301679393, -2.6355185387378705 495741527804512695809 - 1.2288540203286776760838132172829346364*I, 1.0298030 267017086299792452653211016415 + 1.9112861245099211016090670442369493337*I; 2.0347118029638523119874445717108994866, -2.13441423613399550749917869949546 81070 + 2.7819148379840038433049346320629165208*I, 0.09970243317014319551173 4127784568620449 - 2.2598050320850179837986049279827223571*I; 2.578322305593 5536544757871909285592749, 2.7179378823765231507252878961228003872 + 3.23866 75519787940596719774857150348944*I, -1.2962601879700768052010750870513596623 + 1.9682482359132954853864686324006122108*I], [1, 1, 1, 1, 1; 1.26716830454 21243172528914279776896412 + 0.E-38*I, 0.26096388038645528500256735072673484 811 + 1.1772261533941944394700286585617926513*I, 0.2609638803864552850025673 5072673484811 - 1.1772261533941944394700286585617926513*I, -0.89454803265751 744362901306471557966872 + 0.53414854617473272670874609150394379949*I, -0.89 454803265751744362901306471557966872 - 0.53414854617473272670874609150394379 949*I; 1.6057155120361619195949075151301679393 + 0.E-38*I, -1.31775926936893 52747870763902256347904 + 0.61442701016433883804190660864146731824*I, -1.317 7592693689352747870763902256347904 - 0.6144270101643388380419066086414673182 4*I, 0.51490151335085431498962263266055082078 - 0.95564306225496055080453352 211847466685*I, 0.51490151335085431498962263266055082078 + 0.955643062254960 55080453352211847466685*I; 2.0347118029638523119874445717108994866 + 0.E-37* I, -1.0672071180669977537495893497477340535 - 1.3909574189920019216524673160 314582604*I, -1.0672071180669977537495893497477340535 + 1.390957418992001921 6524673160314582604*I, 0.049851216585071597755867063892284310224 + 1.1299025 160425089918993024639913611785*I, 0.049851216585071597755867063892284310224 - 1.1299025160425089918993024639913611785*I; 2.57832230559355365447578719092 85592749 + 0.E-37*I, 1.3589689411882615753626439480614001936 - 1.61933377598 93970298359887428575174472*I, 1.3589689411882615753626439480614001936 + 1.61 93337759893970298359887428575174472*I, -0.6481300939850384026005375435256798 3115 - 0.98412411795664774269323431620030610541*I, -0.6481300939850384026005 3754352567983115 + 0.98412411795664774269323431620030610541*I]], [[5, -5.877 471754111437539 E-39 + 3.4227493991378543323575495001314729016*I, 2.35098870 1644575015 E-38 - 0.68243210418124342552525382695401469720*I, -2.35098870164 4575015 E-38 - 0.52210980589898585950632970408019416371*I, 3.999999999999999 9999999999999999999999 - 5.2069157878920895450584461181156471052*I; -5.87747 1754111437539 E-39 - 3.4227493991378543323575495001314729016*I, 6.6847043424 634879841147654217963674264 - 5.877471754111437539 E-39*I, 0.851456773407213 76574333983502938573598 + 4.5829573180978430291541592600601794652*I, -0.1357 4266252716976137461193821267520737 - 0.2880510854402577236173893646768205039 1*I, 0.27203784387468568916539788233281013320 - 1.59171472799429477189656508 59986677247*I; 2.350988701644575015 E-38 + 0.6824321041812434255252538269540 1469720*I, 0.85145677340721376574333983502938573598 - 4.58295731809784302915 41592600601794652*I, 9.1630968530221077951281598310681467898 + 0.E-38*I, 2.2 622987652095629453403849736225691490 + 6.23619279135585067657240470631807068 69*I, -0.21796409886496632254445901043974770643 + 0.345593689310632156861589 39748833975810*I; -2.350988701644575015 E-38 + 0.522109805898985859506329704 08019416371*I, -0.13574266252716976137461193821267520737 + 0.288051085440257 72361738936467682050392*I, 2.2622987652095629453403849736225691490 - 6.23619 27913558506765724047063180706869*I, 12.845768948832335511882696939380696155 + 1.175494350822287507 E-38*I, 4.5618400502378124720913214622468855074 + 8.6 033930051068500425218923146793019614*I; 3.9999999999999999999999999999999999 999 + 5.2069157878920895450584461181156471052*I, 0.2720378438746856891653978 8233281013320 + 1.5917147279942947718965650859986677247*I, -0.21796409886496 632254445901043974770643 - 0.34559368931063215686158939748833975810*I, 4.561 8400502378124720913214622468855074 - 8.6033930051068500425218923146793019615 *I, 18.362968630416114402425299186062892646 + 5.877471754111437539 E-39*I], [5, -1.175494350822287507 E-38 + 0.E-38*I, 2.350988701644575015 E-38 + 0.E-3 8*I, -1.763241526233431261 E-38 + 0.E-38*I, 3.999999999999999999999999999999 9999998 + 0.E-38*I; -1.175494350822287507 E-38 + 0.E-38*I, 6.684704342463487 9841147654217963674264 - 5.877471754111437539 E-39*I, 0.85145677340721376574 333983502938573597 + 5.877471754111437539 E-39*I, -0.13574266252716976137461 193821267520737 + 5.877471754111437539 E-39*I, 0.272037843874685689165397882 33281013314 - 5.877471754111437539 E-39*I; 2.350988701644575015 E-38 + 0.E-3 8*I, 0.85145677340721376574333983502938573597 + 5.877471754111437539 E-39*I, 9.1630968530221077951281598310681467898 + 0.E-38*I, 2.262298765209562945340 3849736225691490 + 2.350988701644575015 E-38*I, -0.2179640988649663225444590 1043974770651 + 0.E-38*I; -1.763241526233431261 E-38 + 0.E-38*I, -0.13574266 252716976137461193821267520737 + 5.877471754111437539 E-39*I, 2.262298765209 5629453403849736225691490 + 2.350988701644575015 E-38*I, 12.8457689488323355 11882696939380696155 + 0.E-37*I, 4.5618400502378124720913214622468855073 - 3 .526483052466862523 E-38*I; 3.9999999999999999999999999999999999998 + 0.E-38 *I, 0.27203784387468568916539788233281013314 - 5.877471754111437539 E-39*I, -0.21796409886496632254445901043974770651 + 0.E-38*I, 4.56184005023781247209 13214622468855073 - 3.526483052466862523 E-38*I, 18.362968630416114402425299 186062892646 + 0.E-37*I]], [Mod(5, y^3 - y - 1), 0, 0, 0, Mod(4, y^3 - y - 1 ); 0, 0, 0, Mod(4, y^3 - y - 1), Mod(10, y^3 - y - 1); 0, 0, Mod(4, y^3 - y - 1), Mod(10, y^3 - y - 1), 0; 0, Mod(4, y^3 - y - 1), Mod(10, y^3 - y - 1), 0, 0; Mod(4, y^3 - y - 1), Mod(10, y^3 - y - 1), 0, 0, Mod(4, y^3 - y - 1)] , [;], [;], [;]], [[1.2671683045421243172528914279776896412, 0.2609638803864 5528500256735072673484811 + 1.1772261533941944394700286585617926513*I, -0.89 454803265751744362901306471557966872 + 0.53414854617473272670874609150394379 949*I], [1.2671683045421243172528914279776896412 + 0.E-38*I, 0.2609638803864 5528500256735072673484811 - 1.1772261533941944394700286585617926513*I, 0.260 96388038645528500256735072673484811 + 1.177226153394194439470028658561792651 3*I, -0.89454803265751744362901306471557966872 - 0.5341485461747327267087460 9150394379949*I, -0.89454803265751744362901306471557966872 + 0.5341485461747 3272670874609150394379949*I]~], [[Mod(1, y^3 - y - 1), Mod(1, y^3 - y - 1)*x , Mod(1, y^3 - y - 1)*x^2, Mod(1, y^3 - y - 1)*x^3, Mod(1, y^3 - y - 1)*x^4] , [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1]]], [M od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1), 0, 0, 0; 0, 0, Mod(1 , y^3 - y - 1), 0, 0; 0, 0, 0, Mod(1, y^3 - y - 1), 0; 0, 0, 0, 0, Mod(1, y^ 3 - y - 1)], [], [y^3 - y - 1, [1, 1], -23, 1, [[1, 1.3247179572447460259609 088544780973407, 1.7548776662466927600495088963585286918; 1, -0.662358978622 37301298045442723904867036 + 0.56227951206230124389918214490937306149*I, 0.1 2256116687665361997524555182073565405 - 0.7448617666197442365931704286043923 6724*I], [1, 2; 1.3247179572447460259609088544780973407, -1.3247179572447460 259609088544780973407 - 1.1245590241246024877983642898187461229*I; 1.7548776 662466927600495088963585286918, 0.24512233375330723995049110364147130810 + 1 .4897235332394884731863408572087847344*I], [3, 0.E-96, 2.0000000000000000000 000000000000000000; 0.E-96, 3.2646329987400782801485266890755860756, 1.32471 79572447460259609088544780973407; 2.0000000000000000000000000000000000000, 1 .3247179572447460259609088544780973407, 4.2192762054875453178332176670757633 303], [3, 0, 2; 0, 2, 3; 2, 3, 2], [23, 13, 15; 0, 1, 0; 0, 0, 1], [-5, 6, - 4; 6, 2, -9; -4, -9, 6], [23, [7, 10, 1]~]], [1.3247179572447460259609088544 780973407, -0.66235897862237301298045442723904867036 + 0.5622795120623012438 9918214490937306149*I], [1, y, y^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0, 0, 0, 1, 0, 1, 0; 0, 1, 0, 1, 0, 1, 0, 1, 1; 0, 0, 1, 0, 1, 0, 1, 0, 1]], [x ^15 - 5*x^13 + 5*x^12 + 7*x^11 - 26*x^10 - 5*x^9 + 45*x^8 + 158*x^7 - 98*x^6 + 110*x^5 - 190*x^4 + 189*x^3 + 144*x^2 + 25*x + 1, Mod(39516536165538345/8 3718587879473471*x^14 - 6500512476832995/83718587879473471*x^13 - 1962154720 46117185/83718587879473471*x^12 + 229902227480108910/83718587879473471*x^11 + 237380704030959181/83718587879473471*x^10 - 1064931988160773805/8371858787 9473471*x^9 - 20657086671714300/83718587879473471*x^8 + 1772885205999206010/ 83718587879473471*x^7 + 5952033217241102348/83718587879473471*x^6 - 48388401 87320655696/83718587879473471*x^5 + 5180390720553188700/83718587879473471*x^ 4 - 8374015687535120430/83718587879473471*x^3 + 8907744727915040221/83718587 879473471*x^2 + 4155976664123434381/83718587879473471*x + 318920215718580450 /83718587879473471, x^15 - 5*x^13 + 5*x^12 + 7*x^11 - 26*x^10 - 5*x^9 + 45*x ^8 + 158*x^7 - 98*x^6 + 110*x^5 - 190*x^4 + 189*x^3 + 144*x^2 + 25*x + 1), - 1, [1, x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, x^10, x^11, x^12, x^13, 1/ 83718587879473471*x^14 - 20528463024680133/83718587879473471*x^13 - 47423929 48888610/83718587879473471*x^12 - 9983523646123358/83718587879473471*x^11 + 40898955597139011/83718587879473471*x^10 + 29412692423971937/837185878794734 71*x^9 - 5017479463612351/83718587879473471*x^8 + 41014993230075066/83718587 879473471*x^7 - 2712810874903165/83718587879473471*x^6 + 20152905879672878/8 3718587879473471*x^5 + 9591643151927789/83718587879473471*x^4 - 847190574595 7397/83718587879473471*x^3 - 13395753879413605/83718587879473471*x^2 + 27623 037732247492/83718587879473471*x + 26306699661480593/83718587879473471], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26306699661480593; 0, 1, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, -27623037732247492; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13395753879413605; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 847 1905745957397; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9591643151927789; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -20152905879672878; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2712810874903165; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -41014993230075066; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 50 17479463612351; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -29412692423971937 ; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -40898955597139011; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 9983523646123358; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 1, 0, 4742392948888610; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 20 528463024680133; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83718587879473471 ]]] ? bnfcertify(bnf) 1 ? setrand(1);bnfclassunit(x^4-7,2,[0.2,0.2]) [x^4 - 7] [[2, 1]] [[-87808, 1]] [[1, x, x^2, x^3]] [[2, [2], [[3, 1, 2, 1; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]] [14.229975145405511722395637833443108790] [1.121117107152756229] ? setrand(1);bnfclassunit(x^2-x-100000) *** Warning: insufficient precision for fundamental units, not given. [x^2 - x - 100000] [[2, 0]] [[400001, 1]] [[1, x]] [[5, [5], [[2, 1; 0, 1]]]] [129.82045011403975460991182396195022419] [0.9876536979069047239] [[2, -1]] [[;]] [0] ? setrand(1);bnfclassunit(x^2-x-100000,1) [x^2 - x - 100000] [[2, 0]] [[400001, 1]] [[1, x]] [[5, [5], [[2, 1; 0, 1]]]] [129.82045011403975460991182396195022419] [0.9876536979069047239] [[2, -1]] [[379554884019013781006303254896369154068336082609238336*x + 119836165644250 789990462835950022871665178127611316131167]] [186] ? setrand(1);bnfclassunit(x^4+24*x^2+585*x+1791,,[0.1,0.1]) [x^4 + 24*x^2 + 585*x + 1791] [[0, 2]] [[18981, 3087]] [[1, x, 1/3*x^2, 1/1029*x^3 + 33/343*x^2 - 155/343*x - 58/343]] [[4, [4], [[7, 6, 2, 4; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]] [3.7941269688216589341408274220859400302] [0.8826018286655581306] [[6, -10/1029*x^3 + 13/343*x^2 - 165/343*x - 1135/343]] [[1/147*x^3 + 1/147*x^2 - 8/49*x - 9/49]] [182] ? setrand(1);bnfclgp(17) [1, [], []] ? setrand(1);bnfclgp(-31) [3, [3], [Qfb(2, 1, 4)]] ? setrand(1);bnfclgp(x^4+24*x^2+585*x+1791) [4, [4], [[7, 5, 1, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]] ? bnrconductor(bnf,[[25,13;0,1],[1,1]]) [[5, 3; 0, 1], [1, 0]] ? bnrconductorofchar(bnr,[2]) [[5, 3; 0, 1], [0, 0]] ? bnfisprincipal(bnf,[5,1;0,1],0) [1]~ ? bnfisprincipal(bnf,[5,1;0,1]) [[1]~, [-2, -1/3]~, 181] ? bnfisunit(bnf,Mod(3405*x-27466,x^2-x-57)) [-4, Mod(1, 2)]~ ? \p19 realprecision = 19 significant digits ? bnfmake(sbnf) [Mat(2), Mat([0, 1, 1, 1, 1, 0, 1, 1]), [1.173637103435061715 + 3.1415926535 89793238*I, -4.562279014988837901 + 3.141592653589793238*I; -2.6335434327389 76049 + 3.141592653589793238*I, 1.420330600779487357 + 3.141592653589793238* I; 1.459906329303914334, 3.141948414209350543], [1.246346989334819161 + 3.14 1592653589793238*I, -1.990056445584799713 + 3.141592653589793238*I, 0.540400 6376129469727 + 3.141592653589793238*I, -0.6926391142471042845 + 3.141592653 589793238*I, 0.E-96, 0.3677262014027817705 + 3.141592653589793238*I, 0.00437 5616572659815402 + 3.141592653589793238*I, -0.8305625946607188639, -1.977791 147836553953 + 3.141592653589793238*I; 0.6716827432867392935 + 3.14159265358 9793238*I, 0.5379005671092853266, -0.8333219883742404172 + 3.141592653589793 238*I, -0.2461086674077943078, 0.E-96, 0.9729063188316092378, -0.87383180430 71131265, -1.552661549868775853 + 3.141592653589793238*I, 0.5774919091398324 092 + 3.141592653589793238*I; -1.918029732621558454, 1.452155878475514386, 0 .2929213507612934444, 0.9387477816548985923, 0.E-96, -1.340632520234391008, 0.8694561877344533111, 2.383224144529494717 + 3.141592653589793238*I, 1.4002 99238696721544 + 3.141592653589793238*I], [[3, [-1, 1, 0]~, 1, 1, [1, 0, 1]~ ], [5, [3, 1, 0]~, 1, 1, [-2, 1, 1]~], [5, [-1, 1, 0]~, 1, 1, [1, 0, 1]~], [ 5, [2, 1, 0]~, 1, 1, [2, 2, 1]~], [3, [1, 0, 1]~, 1, 2, [-1, 1, 0]~], [23, [ -10, 1, 0]~, 1, 1, [7, 9, 1]~], [11, [1, 1, 0]~, 1, 1, [-1, -2, 1]~], [13, [ 19, 1, 0]~, 1, 1, [2, 6, 1]~], [19, [-6, 1, 0]~, 1, 1, [-3, 5, 1]~]]~, [1, 2 , 3, 4, 5, 6, 7, 8, 9]~, [x^3 - x^2 - 14*x - 1, [3, 0], 10889, 1, [[1, -3.23 3732695981516673, 10.45702714905988813; 1, -0.07182350902743636344, 0.005158 616449014232794; 1, 4.305556205008953036, 18.53781423449109762], [1, 1, 1; - 3.233732695981516673, -0.07182350902743636344, 4.305556205008953036; 10.4570 2714905988813, 0.005158616449014232794, 18.53781423449109762], [3, 1.0000000 00000000000, 29.00000000000000000; 1.000000000000000000, 29.0000000000000000 0, 46.00000000000000000; 29.00000000000000000, 46.00000000000000000, 453.000 0000000000000], [3, 1, 29; 1, 29, 46; 29, 46, 453], [10889, 5698, 3794; 0, 1 , 0; 0, 0, 1], [11021, 881, -795; 881, 518, -109; -795, -109, 86], [10889, [ 1890, 5190, 1]~]], [-3.233732695981516673, -0.07182350902743636344, 4.305556 205008953036], [1, x, x^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0, 0, 0, 1, 0, 1, 1; 0, 1, 0, 1, 0, 14, 0, 14, 15; 0, 0, 1, 0, 1, 1, 1, 1, 15]], [[2, [2 ], [[3, 2, 2; 0, 1, 0; 0, 0, 1]]], 10.34800724602767998, 1.00000000000000000 0, [2, -1], [x, x^2 + 2*x - 4], 1000], [Mat(1), [[0, 0, 0]], [[1.24634698933 4819161 + 3.141592653589793238*I, 0.6716827432867392935 + 3.1415926535897932 38*I, -1.918029732621558454]]], [-4, 3, -1, 2, 3, 11, 1, -1, -7; 1, 1, 1, 1, 0, 2, 1, -4, -2; 0, 0, 0, 0, 0, -1, 0, -1, 0]] ? \p38 realprecision = 38 significant digits ? bnfnarrow(bnf) [3, [3], [[3, 2; 0, 1]]] ? bnfreg(x^2-x-57) 2.7124653051843439746808795106061300699 ? bnfsignunit(bnf) [-1] [1] ? bnfunit(bnf) [[x + 7], 185] ? bnrclass(bnf,[[5,3;0,1],[1,0]]) [12, [12], [[3, 2; 0, 1]]] ? bnr2=bnrclass(bnf,[[25,13;0,1],[1,1]],2) [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746 808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767 22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1 .2897619530652735025030086072395031017 + 0.E-57*I, -2.0109798024989157562122 634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659 095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337 698160660239595315877930058147543 + 9.4247779607693797153879301498385086526* I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498 385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153 879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265 35897932384626433832795028842*I, -14.550628376291080203941433635329724736 + 0.E-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626 433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179 5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42 47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106 12 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.1415926535897932 384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592 6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 + 3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934 24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438 988786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.1 415926535897932384626433832795028842*I, -24.47836604854184150431328408777833 4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1] ~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1 , 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7 , 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931 0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372 9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [ 2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000 0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114 ; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102 46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974 6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [Mat(1), [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384 626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307 1795864769252867665590057684*I]]], [0, [Mat([[5, 1]~, 1])]]], [[[25, 13; 0, 1], [1, 1]], [80, [20, 2, 2], [[2, 0]~, [0, -2]~, [2, 2]~]], Mat([[5, [-2, 1 ]~, 1, 1, [1, 1]~], 2]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2), Mod(0, 2 )]~], 1], [[5], [[6, 0]~], [[6, 0]~], [[Mod(0, 2), Mod(0, 2)]~], Mat([1/5, - 13/5])]], [[2, 2], [[0, -2]~, [2, 2]~], [0, 1; 1, 0]]], [1, -12, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]], [1], [1, -3, 0, -6; 0, 0, 1, 0; 0, 0, 0, 1; 0, 1, 0, 0] , [12, [12], [[3, 2; 0, 1]]], [[1, 9, -18; -1/2, -5, 10], [-2, 0; 0, 10]]] ? bnrclassno(bnf,[[5,3;0,1],[1,0]]) 12 ? lu=ideallist(bnf,55,3); ? bnrclassnolist(bnf,lu) [[3], [], [3, 3], [3], [6, 6], [], [], [], [3, 3, 3], [], [3, 3], [3, 3], [] , [], [12, 6, 6, 12], [3], [3, 3], [], [9, 9], [6, 6], [], [], [], [], [6, 1 2, 6], [], [3, 3, 3, 3], [], [], [], [], [], [3, 6, 6, 3], [], [], [9, 3, 9] , [6, 6], [], [], [], [], [], [3, 3], [3, 3], [12, 12, 6, 6, 12, 12], [], [] , [6, 6], [9], [], [3, 3, 3, 3], [], [3, 3], [], [6, 12, 12, 6]] ? bnrdisc(bnr,Mat(6)) [12, 12, 18026977100265125] ? bnrdisc(bnr) [24, 12, 40621487921685401825918161408203125] ? bnrdisc(bnr2,,,2) 0 ? bnrdisc(bnr,Mat(6),,1) [6, 2, [125, 13; 0, 1]] ? bnrdisc(bnr,,,1) [12, 1, [1953125, 1160888; 0, 1]] ? bnrdisc(bnr2,,,3) 0 ? bnrdisclist(bnf,lu) [[[6, 6, Mat([229, 3])]], [], [[], []], [[]], [[12, 12, [5, 3; 229, 6]], [12 , 12, [5, 3; 229, 6]]], [], [], [], [[], [], []], [], [[], []], [[], []], [] , [], [[24, 24, [3, 6; 5, 9; 229, 12]], [], [], [24, 24, [3, 6; 5, 9; 229, 1 2]]], [[]], [[], []], [], [[18, 18, [19, 6; 229, 9]], [18, 18, [19, 6; 229, 9]]], [[], []], [], [], [], [], [[], [24, 24, [5, 12; 229, 12]], []], [], [[ ], [], [], []], [], [], [], [], [], [[], [12, 12, [3, 3; 11, 3; 229, 6]], [1 2, 12, [3, 3; 11, 3; 229, 6]], []], [], [], [[18, 18, [2, 12; 3, 12; 229, 9] ], [], [18, 18, [2, 12; 3, 12; 229, 9]]], [[12, 12, [37, 3; 229, 6]], [12, 1 2, [37, 3; 229, 6]]], [], [], [], [], [], [[], []], [[], []], [[], [], [], [ ], [], []], [], [], [[12, 12, [2, 12; 3, 3; 229, 6]], [12, 12, [2, 12; 3, 3; 229, 6]]], [[18, 18, [7, 12; 229, 9]]], [], [[], [], [], []], [], [[], []], [], [[], [24, 24, [5, 9; 11, 6; 229, 12]], [24, 24, [5, 9; 11, 6; 229, 12]] , []]] ? bnrdisclist(bnf,20,,1) [[[[matrix(0,2), [[6, 6, Mat([229, 3])], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]], [], [[Mat([12, 1]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [12, 0, [3, 3; 229, 6 ]]]], [Mat([13, 1]), [[0, 0, 0], [0, 0, 0], [12, 6, [-1, 1; 3, 3; 229, 6]], [0, 0, 0]]]], [[Mat([10, 1]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]] , [[Mat([20, 1]), [[12, 12, [5, 3; 229, 6]], [0, 0, 0], [0, 0, 0], [24, 0, [ 5, 9; 229, 12]]]], [Mat([21, 1]), [[12, 12, [5, 3; 229, 6]], [0, 0, 0], [24, 12, [5, 9; 229, 12]], [0, 0, 0]]]], [], [], [], [[Mat([12, 2]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[12, 1; 13, 1], [[0, 0, 0], [12, 6, [-1 , 1; 3, 6; 229, 6]], [0, 0, 0], [24, 0, [3, 12; 229, 12]]]], [Mat([13, 2]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]], [], [[Mat([44, 1]), [[0, 0, 0], [0, 0, 0], [12, 6, [-1, 1; 11, 3; 229, 6]], [0, 0, 0]]], [Mat([45, 1]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [12, 0, [11, 3; 229, 6]]]]], [[[10, 1; 12, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[10, 1; 13, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]], [], [], [[[12, 1; 20, 1], [[24, 24, [3, 6; 5, 9; 229, 12]], [0, 0, 0], [0, 0, 0], [48, 0, [3, 12; 5, 18; 229, 2 4]]]], [[13, 1; 20, 1], [[0, 0, 0], [24, 12, [3, 6; 5, 9; 229, 12]], [24, 12 , [3, 6; 5, 6; 229, 12]], [48, 0, [3, 12; 5, 18; 229, 24]]]], [[12, 1; 21, 1 ], [[0, 0, 0], [24, 12, [3, 6; 5, 9; 229, 12]], [0, 0, 0], [48, 0, [3, 12; 5 , 18; 229, 24]]]], [[13, 1; 21, 1], [[24, 24, [3, 6; 5, 9; 229, 12]], [0, 0, 0], [48, 24, [3, 12; 5, 18; 229, 24]], [0, 0, 0]]]], [[Mat([10, 2]), [[0, 0 , 0], [12, 6, [-1, 1; 2, 12; 229, 6]], [12, 6, [-1, 1; 2, 12; 229, 6]], [24, 0, [2, 36; 229, 12]]]]], [[Mat([68, 1]), [[0, 0, 0], [12, 6, [-1, 1; 17, 3; 229, 6]], [0, 0, 0], [0, 0, 0]]], [Mat([69, 1]), [[0, 0, 0], [12, 6, [-1, 1 ; 17, 3; 229, 6]], [0, 0, 0], [0, 0, 0]]]], [], [[Mat([76, 1]), [[18, 18, [1 9, 6; 229, 9]], [0, 0, 0], [0, 0, 0], [36, 0, [19, 15; 229, 18]]]], [Mat([77 , 1]), [[18, 18, [19, 6; 229, 9]], [0, 0, 0], [36, 18, [-1, 1; 19, 15; 229, 18]], [0, 0, 0]]]], [[[10, 1; 20, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[10, 1; 21, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]]] ? bnrisprincipal(bnr,idealprimedec(bnf,7)[1]) [[9]~, [-2170/6561, -931/19683]~, 256] ? dirzetak(nf4,30) [1, 2, 0, 3, 1, 0, 0, 4, 0, 2, 1, 0, 0, 0, 0, 5, 1, 0, 0, 3, 0, 2, 0, 0, 2, 0, 1, 0, 1, 0] ? factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1) [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(-t, t^3 + t^2 - 2*t - 1) 1] [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(-t^2 + 2, t^3 + t^2 - 2*t - 1) 1] [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(t^2 + t - 1, t^3 + t^2 - 2*t - 1) 1] ? vp=idealprimedec(nf,3)[1] [3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~] ? idx=idealmul(nf,matid(5),vp) [3 1 2 2 2] [0 1 0 0 0] [0 0 1 0 0] [0 0 0 1 0] [0 0 0 0 1] ? idealinv(nf,idx) [1 0 2/3 0 0] [0 1 1/3 0 0] [0 0 1/3 0 0] [0 0 0 1 0] [0 0 0 0 1] ? idy=idealred(nf,idx,[1,5,6]) [5 0 0 2 0] [0 5 0 0 0] [0 0 5 2 0] [0 0 0 1 0] [0 0 0 0 5] ? idx2=idealmul(nf,idx,idx) [9 7 5 8 2] [0 1 0 0 0] [0 0 1 0 0] [0 0 0 1 0] [0 0 0 0 1] ? idt=idealmul(nf,idx,idx,1) [2 0 0 0 1] [0 2 0 0 1] [0 0 2 0 0] [0 0 0 2 1] [0 0 0 0 1] ? idz=idealintersect(nf,idx,idy) [15 5 10 12 10] [0 5 0 0 0] [0 0 5 2 0] [0 0 0 1 0] [0 0 0 0 5] ? aid=[idx,idy,idz,matid(5),idx] [[3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1] , [5, 0, 0, 2, 0; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 5 ], [15, 5, 10, 12, 10; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 5], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0 , 0, 1], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]] ? bid=idealstar(nf2,54,1) [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0, 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[ 0, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 0] ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0 ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3 , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~, [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0, 0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7 , -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]] ? vaid=[idx,idy,matid(5)] [[3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1] , [5, 0, 0, 2, 0; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 5 ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]] ? haid=[matid(5),matid(5),matid(5)] [[1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1] , [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1 ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]] ? idealadd(nf,idx,idy) [1 0 0 0 0] [0 1 0 0 0] [0 0 1 0 0] [0 0 0 1 0] [0 0 0 0 1] ? idealaddtoone(nf,idx,idy) [[3, 0, 2, 1, 0]~, [-2, 0, -2, -1, 0]~] ? idealaddtoone(nf,[idy,idx]) [[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~] ? idealappr(nf,idy) [-2, 0, -2, 4, 0]~ ? idealappr(nf,idealfactor(nf,idy),1) [-2, 0, -2, 4, 0]~ ? idealcoprime(nf,idx,idx) [-2/3, 2/3, -1/3, 0, 0]~ ? idealdiv(nf,idy,idt) [5 5/2 5/2 7/2 0] [0 5/2 0 0 0] [0 0 5/2 1 0] [0 0 0 1/2 0] [0 0 0 0 5/2] ? idealdiv(nf,idx2,idx,1) [3 1 2 2 2] [0 1 0 0 0] [0 0 1 0 0] [0 0 0 1 0] [0 0 0 0 1] ? idf=idealfactor(nf,idz) [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~] 1] [[5, [-2, 0, 0, 0, 1]~, 1, 1, [2, 2, 1, 1, 4]~] 1] [[5, [0, 0, -1, 0, 1]~, 4, 1, [4, 5, 4, 2, 0]~] 3] ? idealhnf(nf,vp) [3 1 2 2 2] [0 1 0 0 0] [0 0 1 0 0] [0 0 0 1 0] [0 0 0 0 1] ? idealhnf(nf,vp[2],3) [3 1 2 2 2] [0 1 0 0 0] [0 0 1 0 0] [0 0 0 1 0] [0 0 0 0 1] ? ideallist(bnf,20) [[[1, 0; 0, 1]], [], [[3, 2; 0, 1], [3, 0; 0, 1]], [[2, 0; 0, 2]], [[5, 3; 0 , 1], [5, 1; 0, 1]], [], [], [], [[9, 5; 0, 1], [3, 0; 0, 3], [9, 3; 0, 1]], [], [[11, 9; 0, 1], [11, 1; 0, 1]], [[6, 4; 0, 2], [6, 0; 0, 2]], [], [], [ [15, 8; 0, 1], [15, 3; 0, 1], [15, 11; 0, 1], [15, 6; 0, 1]], [[4, 0; 0, 4]] , [[17, 14; 0, 1], [17, 2; 0, 1]], [], [[19, 18; 0, 1], [19, 0; 0, 1]], [[10 , 6; 0, 2], [10, 2; 0, 2]]] ? ideallog(nf2,w,bid) [1574, 8, 6]~ ? idealmin(nf,idx,[1,2,3]) [[-1; 0; 0; 1; 0], [2.0885812311199768913287869744681966008 + 3.141592653589 7932384626433832795028842*I, 1.5921096812520196555597562531657929785 + 4.244 7196639216499665715751642189271112*I, -0.79031915447583185468082063233076160 203 + 2.5437460822678889883600220330800078854*I]] ? idealnorm(nf,idt) 16 ? idp=idealpow(nf,idx,7) [2187 1807 2129 692 1379] [0 1 0 0 0] [0 0 1 0 0] [0 0 0 1 0] [0 0 0 0 1] ? idealpow(nf,idx,7,1) [5 0 0 2 0] [0 5 0 0 0] [0 0 5 2 0] [0 0 0 1 0] [0 0 0 0 5] ? idealprimedec(nf,2) [[2, [3, 1, 0, 0, 0]~, 1, 1, [1, 1, 0, 1, 1]~], [2, [-3, -5, -4, 3, 15]~, 1, 4, [1, 1, 0, 0, 0]~]] ? idealprimedec(nf,3) [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~], [3, [-1, 1, -1, 0, 1]~, 2, 2, [1, 2, 3, 1, 0]~]] ? idealprimedec(nf,11) [[11, [11, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]] ? idealprincipal(nf,Mod(x^3+5,nfpol)) [6] [0] [1] [3] [0] ? idealtwoelt(nf,idy) [5, [2, 0, 2, 1, 0]~] ? idealtwoelt(nf,idy,10) [-2, 0, -2, -1, 0]~ ? idealstar(nf2,54) [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0, 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[ 0, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 0] ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0 ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3 , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~, [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0, 0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7 , -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]] ? idealval(nf,idp,vp) 7 ? ideleprincipal(nf,Mod(x^3+5,nfpol)) [[6; 0; 1; 3; 0], [2.2324480827796254080981385584384939684 + 3.1415926535897 932384626433832795028842*I, 5.0387659675158716386435353106610489968 + 1.5851 760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173 - 0.0083630478144368246110910258645462996191*I]] ? ba=nfalgtobasis(nf,Mod(x^3+5,nfpol)) [6, 0, 1, 3, 0]~ ? bb=nfalgtobasis(nf,Mod(x^3+x,nfpol)) [1, 1, 1, 3, 0]~ ? bc=matalgtobasis(nf,[Mod(x^2+x,nfpol);Mod(x^2+1,nfpol)]) [[0, 1, 1, 0, 0]~] [[1, 0, 1, 0, 0]~] ? matbasistoalg(nf,bc) [Mod(x^2 + x, x^5 - 5*x^3 + 5*x + 25)] [Mod(x^2 + 1, x^5 - 5*x^3 + 5*x + 25)] ? nfbasis(x^3+4*x+5) [1, x, 1/7*x^2 - 1/7*x - 2/7] ? nfbasis(x^3+4*x+5,2) [1, x, 1/7*x^2 - 1/7*x - 2/7] ? nfbasis(x^3+4*x+12,1) [1, x, 1/2*x^2] ? nfbasistoalg(nf,ba) Mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25) ? nfbasis(p2,0,fa) [1, x, x^2, 1/11699*x^3 + 1847/11699*x^2 - 132/11699*x - 2641/11699, 1/13962 3738889203638909659*x^4 - 1552451622081122020/139623738889203638909659*x^3 + 418509858130821123141/139623738889203638909659*x^2 - 6810913798507599407313 4/139623738889203638909659*x - 13185339461968406/58346808996920447] ? da=nfdetint(nf,[a,aid]) [30 5 25 27 10] [0 5 0 0 0] [0 0 5 2 0] [0 0 0 1 0] [0 0 0 0 5] ? nfdisc(x^3+4*x+12) -1036 ? nfdisc(x^3+4*x+12,1) -1036 ? nfdisc(p2,0,fa) 136866601 ? nfeltdiv(nf,ba,bb) [755/373, -152/373, 159/373, 120/373, -264/373]~ ? nfeltdiveuc(nf,ba,bb) [2, 0, 0, 0, -1]~ ? nfeltdivrem(nf,ba,bb) [[2, 0, 0, 0, -1]~, [-12, -7, 0, 9, 5]~] ? nfeltmod(nf,ba,bb) [-12, -7, 0, 9, 5]~ ? nfeltmul(nf,ba,bb) [-25, -50, -30, 15, 90]~ ? nfeltpow(nf,bb,5) [23455, 156370, 115855, 74190, -294375]~ ? nfeltreduce(nf,ba,idx) [1, 0, 0, 0, 0]~ ? nfeltval(nf,ba,vp) 0 ? nffactor(nf2,x^3+x) [Mod(1, y^3 - y - 1)*x 1] [Mod(1, y^3 - y - 1)*x^2 + Mod(1, y^3 - y - 1) 1] ? aut=nfgaloisconj(nf3) [x, 1/12*x^4 - 1/2*x, -1/12*x^4 - 1/2*x, 1/12*x^4 + 1/2*x, -1/12*x^4 + 1/2*x , -x]~ ? nfgaloisapply(nf3,aut[5],Mod(x^5,x^6+108)) Mod(1/2*x^5 - 9*x^2, x^6 + 108) ? nfhilbert(nf,3,5) -1 ? nfhilbert(nf,3,5,idf[1,1]) -1 ? nfhnf(nf,[a,aid]) [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1 , 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0, 0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0 , 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]] ? nfhnfmod(nf,[a,aid],da) [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1 , 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0, 0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0 , 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]] ? nfisideal(bnf[7],[5,1;0,1]) 1 ? nfisincl(x^2+1,x^4+1) [-x^2, x^2] ? nfisincl(x^2+1,nfinit(x^4+1)) [-x^2, x^2] ? nfisisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1) [x, -x^2 - x + 1, x^2 - 2] ? nfisisom(x^3-2,nfinit(x^3-6*x^2-6*x-30)) [-1/25*x^2 + 13/25*x - 2/5] ? nfroots(nf2,x+2) [Mod(-2, y^3 - y - 1)] ? nfrootsof1(nf) [2, [-1, 0, 0, 0, 0]~] ? nfsnf(nf,[as,haid,vaid]) [[10951073973332888246310, 5442457637639729109215, 2693780223637146570055, 3 910837124677073032737, 3754666252923836621170; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 5], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0 ; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]] ? nfsubfields(nf) [[x^5 - 5*x^3 + 5*x + 25, x], [x, x^5 - 5*x^3 + 5*x + 25]] ? polcompositum(x^4-4*x+2,x^3-x-1) [x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x ^2 - 128*x - 5] ? polcompositum(x^4-4*x+2,x^3-x-1,1) [[x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58* x^2 - 128*x - 5, Mod(-279140305176/29063006931199*x^11 + 129916611552/290630 06931199*x^10 + 1272919322296/29063006931199*x^9 - 2813750209005/29063006931 199*x^8 - 2859411937992/29063006931199*x^7 - 414533880536/29063006931199*x^6 - 35713977492936/29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 4 9785595543672/29063006931199*x^3 + 9423768373204/29063006931199*x^2 - 427797 76146743/29063006931199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8 *x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), M od(-279140305176/29063006931199*x^11 + 129916611552/29063006931199*x^10 + 12 72919322296/29063006931199*x^9 - 2813750209005/29063006931199*x^8 - 28594119 37992/29063006931199*x^7 - 414533880536/29063006931199*x^6 - 35713977492936/ 29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 49785595543672/2906 3006931199*x^3 + 9423768373204/29063006931199*x^2 - 13716769215544/290630069 31199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12 *x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), -1]] ? polgalois(x^6-3*x^2-1) [12, 1, 1] ? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568) [x - 1, x^5 - x^4 - 6*x^3 + 6*x^2 + 13*x - 5, x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1, x^5 - x^4 + 4*x^3 - 2*x^2 + x - 1, x^5 + 4*x^3 - 4*x^2 + 8*x - 8] ? polred(x^4-28*x^3-458*x^2+9156*x-25321,3) [1 x - 1] [1/115*x^2 - 14/115*x - 327/115 x^2 - 10] [3/1495*x^3 - 63/1495*x^2 - 1607/1495*x + 13307/1495 x^4 - 32*x^2 + 216] [1/4485*x^3 - 7/1495*x^2 - 1034/4485*x + 7924/4485 x^4 - 8*x^2 + 6] ? polred(x^4+576,1) [x - 1, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1] ? polred(x^4+576,3) [1 x - 1] [1/192*x^3 + 1/8*x + 1/2 x^2 - x + 1] [-1/24*x^2 x^2 + 1] [-1/192*x^3 + 1/48*x^2 + 1/8*x x^4 - x^2 + 1] ? polred(p2,0,fa) [x - 1, x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1, x^5 - 2*x^4 - 53*x^3 - 46 *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52 *x^3 - 197*x^2 - 273*x - 127] ? polred(p2,1,fa) [x - 1, x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1, x^5 - 2*x^4 - 53*x^3 - 46 *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52 *x^3 - 197*x^2 - 273*x - 127] ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568) x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1 ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568,1) [x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1, Mod(2*x^4 - x^3 + 3*x^2 - 3*x - 1, x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1)] ? polredord(x^3-12*x+45*x-1) [x - 1, x^3 - 363*x - 2663, x^3 + 33*x - 1] ? polsubcyclo(31,5) x^5 + x^4 - 12*x^3 - 21*x^2 + x + 5 ? setrand(1);poltschirnhaus(x^5-x-1) x^5 - 15*x^4 + 88*x^3 - 278*x^2 + 452*x - 289 ? aa=rnfpseudobasis(nf2,p) [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-2, 0, 0]~, [11, 0, 0]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [2, 0, 0]~, [-8, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [1, 0, 0]~, [4, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [-2, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~ ], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1 , 0; 0, 0, 1], [1, 0, 3/5; 0, 1, 2/5; 0, 0, 1/5], [1, 0, 8/25; 0, 1, 22/25; 0, 0, 1/25]], [416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1 280, 5, 5]~] ? rnfbasis(bnf2,aa) [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [38/25, -33/25, 11/25]~ [-11, -4, 9]~] [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-14/25, 24/25, -8/25]~ [28/5, 2/5, -24/5] ~] [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [57/25, -12/25, 4/25]~ [-58/5, -47/5, 44/5 ]~] [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [9/25, 6/25, -2/25]~ [-4/5, -11/5, 2/5]~] [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [8/25, -3/25, 1/25]~ [-9/5, -6/5, 7/5]~] ? rnfdisc(nf2,p) [[416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~] ? rnfequation(nf2,p) x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1 ? rnfequation(nf2,p,1) [x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1, Mod(-x^5 + 5*x, x^15 - 1 5*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1), 0] ? rnfhnfbasis(bnf2,aa) [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/5, 2/5, -4/5]~ [11/25, 99/25, -33/25]~ ] [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [2/5, -2/5, 4/5]~ [-8/25, -72/25, 24/25]~] [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [1/5, -1/5, 2/5]~ [4/25, 36/25, -12/25]~] [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/5, -1/5, 2/5]~ [-2/25, -18/25, 6/25]~] [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/25, 9/25, -3/25]~] ? rnfisfree(bnf2,aa) 1 ? rnfsteinitz(nf2,aa) [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [38/25, -33/25, 11/25]~, [-27/125, 33/ 125, -11/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [-14/25, 24/25, -8/25]~, [6/125, -24/125, 8/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [57/25, -12/2 5, 4/25]~, [-53/125, 12/125, -4/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [ 9/25, 6/25, -2/25]~, [-11/125, -6/125, 2/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [8/25, -3/25, 1/25]~, [-7/125, 3/125, -1/125]~], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [125, 0, 108; 0, 125, 22; 0, 0, 1]], [416134375, 21294 0625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~] ? nfz=zetakinit(x^2-2); ? zetak(nfz,-3) 0.091666666666666666666666666666666666666 ? zetak(nfz,1.5+3*I) 0.88324345992059326405525724366416928890 - 0.2067536250233895222724230899142 7938845*I ? setrand(1);quadclassunit(1-10^7,,[1,1]) *** Warning: not a fundamental discriminant in quadclassunit. [2416, [1208, 2], [Qfb(277, 55, 9028), Qfb(1700, 1249, 1700)], 1, 0.99984980 75377600233] ? setrand(1);quadclassunit(10^9-3,,[0.5,0.5]) [4, [4], [Qfb(3, 1, -83333333, 0.E-57)], 2800.625251907016076486370621737074 5514, 0.9990369458964383232] ? sizebyte(%) 328 ? getheap [198, 120613] ? print("Total time spent: ",gettime); Total time spent: 4836 ? \q