Magma V2.19-8 Tue Aug 20 2013 23:40:47 on localhost [Seed = 2160518167] Type ? for help. Type -D to quit. Loading file "K12n411__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation K12n411 geometric_solution 11.55642272 oriented_manifold CS_known -0.0000000000000001 1 0 torus 0.000000000000 0.000000000000 12 1 2 3 2 0132 0132 0132 1230 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 -2 2 -1 1 0 0 0 -2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.414584929131 0.912486798906 0 4 6 5 0132 0132 0132 0132 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 3 0 -3 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.550433491585 0.575361384434 0 0 7 4 3012 0132 0132 0132 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 1 0 -1 0 -2 2 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.498080210721 0.776357903469 8 5 6 0 0132 0132 3120 0132 0 0 0 0 0 0 0 0 0 0 -1 1 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -3 2 2 0 0 -2 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.668956293410 0.946762852080 6 1 2 9 0321 0132 0132 0132 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 1 0 -1 3 -3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.829250332987 0.870294485565 9 3 1 10 0132 0132 0132 0132 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 -3 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.628215187729 0.721273889831 4 11 3 1 0321 0132 3120 0132 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 -3 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.119302927054 1.307568793652 10 11 8 2 3120 2310 0132 0132 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 -2 3 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.366614378162 0.853326901317 3 10 9 7 0132 0132 0132 0132 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 0 -2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.350893870851 0.860245075018 5 11 4 8 0132 0213 0132 0132 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 -3 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.266286315772 1.010705256814 11 8 5 7 0213 0132 0132 3120 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.633385621838 0.853326901317 10 6 9 7 0213 0132 0213 3201 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 -3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.425024223434 0.989280904327 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_0110_6' : negation(d['c_0011_0']), 'c_1001_11' : d['c_1001_1'], 'c_1001_10' : d['c_1001_10'], 'c_1001_5' : d['c_1001_0'], 'c_1001_4' : d['c_1001_0'], 'c_1001_7' : d['c_1001_10'], 'c_1001_6' : negation(d['c_1001_10']), 'c_1001_1' : d['c_1001_1'], 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : d['c_1001_10'], 'c_1001_2' : d['c_0101_2'], 'c_1001_9' : d['c_1001_1'], 'c_1001_8' : negation(d['c_0011_7']), 'c_1010_11' : negation(d['c_1001_10']), 'c_1010_10' : negation(d['c_0011_7']), 's_0_10' : d['1'], 's_3_10' : d['1'], 's_2_8' : d['1'], 's_2_9' : d['1'], 'c_0101_11' : d['c_0011_10'], 'c_0101_10' : d['c_0011_11'], 's_2_0' : d['1'], 's_2_1' : negation(d['1']), 's_2_2' : d['1'], 's_2_3' : d['1'], 's_2_4' : d['1'], 's_2_5' : d['1'], 's_2_6' : d['1'], 's_2_7' : d['1'], 's_2_10' : d['1'], 's_2_11' : d['1'], 's_0_8' : d['1'], 's_0_9' : d['1'], 's_0_6' : negation(d['1']), 's_0_7' : d['1'], 's_0_4' : negation(d['1']), 's_0_5' : d['1'], 's_0_2' : d['1'], 's_0_3' : d['1'], 's_0_0' : d['1'], 's_0_1' : d['1'], 'c_0011_11' : d['c_0011_11'], 'c_0011_10' : d['c_0011_10'], 'c_1100_5' : negation(d['c_0101_3']), 'c_1100_4' : d['c_1100_2'], 'c_1100_7' : d['c_1100_2'], 'c_1100_6' : negation(d['c_0101_3']), 'c_1100_1' : negation(d['c_0101_3']), 'c_1100_0' : d['c_0101_4'], 'c_1100_3' : d['c_0101_4'], 'c_1100_2' : d['c_1100_2'], 's_3_11' : d['1'], 'c_1100_11' : negation(d['c_0011_7']), 'c_1100_10' : negation(d['c_0101_3']), 's_0_11' : d['1'], 'c_1010_7' : d['c_0101_2'], 'c_1010_6' : d['c_1001_1'], 'c_1010_5' : d['c_1001_10'], 'c_1010_4' : d['c_1001_1'], 'c_1010_3' : d['c_1001_0'], 'c_1010_2' : d['c_1001_0'], 'c_1010_1' : d['c_1001_0'], 'c_1010_0' : d['c_0101_2'], 'c_1010_9' : negation(d['c_0011_7']), 'c_1010_8' : d['c_1001_10'], 's_3_1' : d['1'], 's_3_0' : d['1'], 's_3_3' : d['1'], 's_3_2' : d['1'], 's_3_5' : d['1'], 's_3_4' : d['1'], 's_3_7' : d['1'], 's_3_6' : negation(d['1']), 's_3_9' : d['1'], 's_3_8' : d['1'], 's_1_7' : d['1'], 's_1_6' : d['1'], 's_1_5' : d['1'], 's_1_4' : negation(d['1']), 's_1_3' : d['1'], 's_1_2' : d['1'], 's_1_1' : negation(d['1']), 's_1_0' : d['1'], 's_1_9' : d['1'], 's_1_8' : d['1'], 'c_0011_9' : d['c_0011_10'], 'c_0011_8' : negation(d['c_0011_10']), 'c_0011_5' : negation(d['c_0011_10']), 'c_0011_4' : d['c_0011_0'], 'c_0011_7' : d['c_0011_7'], 'c_0011_6' : negation(d['c_0011_11']), 'c_0011_1' : negation(d['c_0011_0']), 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : d['c_0011_10'], 'c_0011_2' : negation(d['c_0011_0']), 'c_0110_11' : negation(d['c_0101_2']), 'c_0110_10' : d['c_0101_2'], 'c_0110_0' : negation(d['c_0011_0']), 'c_0101_7' : d['c_0101_3'], 'c_0101_6' : negation(d['c_0101_4']), 'c_0101_5' : d['c_0101_0'], 'c_0101_4' : d['c_0101_4'], 'c_0101_3' : d['c_0101_3'], 'c_0101_2' : d['c_0101_2'], 'c_0101_1' : negation(d['c_0011_0']), 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : d['c_0011_11'], 'c_0101_8' : d['c_0101_0'], 's_1_11' : d['1'], 's_1_10' : d['1'], 'c_0110_9' : d['c_0101_0'], 'c_0110_8' : d['c_0101_3'], 'c_0110_1' : d['c_0101_0'], 'c_1100_9' : d['c_1100_2'], 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : d['c_0101_4'], 'c_0110_5' : d['c_0011_11'], 'c_0110_4' : d['c_0011_11'], 'c_0110_7' : d['c_0101_2'], 'c_1100_8' : d['c_1100_2']})} PY=EVAL=SECTION=ENDS=HERE PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 13 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_11, c_0011_7, c_0101_0, c_0101_2, c_0101_3, c_0101_4, c_1001_0, c_1001_1, c_1001_10, c_1100_2 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 8 Groebner basis: [ t + 271525/88673*c_1100_2^7 + 1298607/177346*c_1100_2^6 + 2048361/177346*c_1100_2^5 + 4915359/177346*c_1100_2^4 + 2399544/88673*c_1100_2^3 - 2807449/177346*c_1100_2^2 + 1141132/88673*c_1100_2 - 484511/177346, c_0011_0 - 1, c_0011_10 - 295/359*c_1100_2^7 - 735/359*c_1100_2^6 - 1155/359*c_1100_2^5 - 2733/359*c_1100_2^4 - 2730/359*c_1100_2^3 + 1575/359*c_1100_2^2 - 807/359*c_1100_2 + 105/359, c_0011_11 - 95/359*c_1100_2^7 - 474/359*c_1100_2^6 - 950/359*c_1100_2^5 - 1805/359*c_1100_2^4 - 3094/359*c_1100_2^3 - 1805/359*c_1100_2^2 + 665/359*c_1100_2 - 958/359, c_0011_7 - 63/359*c_1100_2^7 - 303/359*c_1100_2^6 - 630/359*c_1100_2^5 - 1197/359*c_1100_2^4 - 1946/359*c_1100_2^3 - 1197/359*c_1100_2^2 + 441/359*c_1100_2 - 367/359, c_0101_0 + 63/359*c_1100_2^7 + 303/359*c_1100_2^6 + 630/359*c_1100_2^5 + 1197/359*c_1100_2^4 + 1946/359*c_1100_2^3 + 1197/359*c_1100_2^2 - 441/359*c_1100_2 + 367/359, c_0101_2 - 232/359*c_1100_2^7 - 432/359*c_1100_2^6 - 525/359*c_1100_2^5 - 1536/359*c_1100_2^4 - 784/359*c_1100_2^3 + 2772/359*c_1100_2^2 - 1248/359*c_1100_2 + 472/359, c_0101_3 - 95/359*c_1100_2^7 - 474/359*c_1100_2^6 - 950/359*c_1100_2^5 - 1805/359*c_1100_2^4 - 3094/359*c_1100_2^3 - 1805/359*c_1100_2^2 + 1024/359*c_1100_2 - 958/359, c_0101_4 - 2/359*c_1100_2^7 + 281/359*c_1100_2^6 + 698/359*c_1100_2^5 + 1039/359*c_1100_2^4 + 2531/359*c_1100_2^3 + 2475/359*c_1100_2^2 - 1781/359*c_1100_2 + 883/359, c_1001_0 + 240/359*c_1100_2^7 + 744/359*c_1100_2^6 + 1323/359*c_1100_2^5 + 2765/359*c_1100_2^4 + 3584/359*c_1100_2^3 + 252/359*c_1100_2^2 - 244/359*c_1100_2 + 304/359, c_1001_1 - 105/359*c_1100_2^7 - 505/359*c_1100_2^6 - 1050/359*c_1100_2^5 - 1995/359*c_1100_2^4 - 3363/359*c_1100_2^3 - 1995/359*c_1100_2^2 + 376/359*c_1100_2 - 851/359, c_1001_10 - 105/359*c_1100_2^7 - 505/359*c_1100_2^6 - 1050/359*c_1100_2^5 - 1995/359*c_1100_2^4 - 3363/359*c_1100_2^3 - 1995/359*c_1100_2^2 + 735/359*c_1100_2 - 851/359, c_1100_2^8 + 2*c_1100_2^7 + 3*c_1100_2^6 + 8*c_1100_2^5 + 6*c_1100_2^4 - 7*c_1100_2^3 + 8*c_1100_2^2 - 3*c_1100_2 + 1 ], Ideal of Polynomial ring of rank 13 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_11, c_0011_7, c_0101_0, c_0101_2, c_0101_3, c_0101_4, c_1001_0, c_1001_1, c_1001_10, c_1100_2 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 13 Groebner basis: [ t + 9577555348798152591065/2658410166237323156*c_1100_2^12 + 19805130227545600599377/3987615249355984734*c_1100_2^11 + 275919464225369742917537/7975230498711969468*c_1100_2^10 + 290684567414820786560305/3987615249355984734*c_1100_2^9 + 40941522685866687837721/257265499958450628*c_1100_2^8 + 390817137885625495459521/1329205083118661578*c_1100_2^7 + 391471973773870513882911/664602541559330789*c_1100_2^6 + 1110149623486173033965669/2658410166237323156*c_1100_2^5 + 5860482089981983689990113/7975230498711969468*c_1100_2^4 + 2000671226449454573611493/3987615249355984734*c_1100_2^3 + 2813213315009785154551387/7975230498711969468*c_1100_2^2 + 550372137804977376661273/7975230498711969468*c_1100_2 + 8376203070825672827185/1993807624677992367, c_0011_0 - 1, c_0011_10 - 2793609191306457/1864242753322106*c_1100_2^12 - 2089787227305699/932121376661053*c_1100_2^11 - 27245858535204915/1864242753322106*c_1100_2^10 - 29813062933809456/932121376661053*c_1100_2^9 - 129729036550628363/1864242753322106*c_1100_2^8 - 120898721701277246/932121376661053*c_1100_2^7 - 241042875572383759/932121376661053*c_1100_2^6 - 374890267705583313/1864242753322106*c_1100_2^5 - 602653512647413245/1864242753322106*c_1100_2^4 - 226073960412659706/932121376661053*c_1100_2^3 - 313912245555991129/1864242753322106*c_1100_2^2 - 81127587087310191/1864242753322106*c_1100_2 - 2931941013978961/932121376661053, c_0011_11 - 6721183744794201/1864242753322106*c_1100_2^12 - 10398469859136863/1864242753322106*c_1100_2^11 - 65950848007750211/1864242753322106*c_1100_2^10 - 146664277489017299/1864242753322106*c_1100_2^9 - 318331130615008741/1864242753322106*c_1100_2^8 - 595467434553914535/1864242753322106*c_1100_2^7 - 592297304523011277/932121376661053*c_1100_2^6 - 951808750089587381/1864242753322106*c_1100_2^5 - 738742336749728770/932121376661053*c_1100_2^4 - 1150154261099999427/1864242753322106*c_1100_2^3 - 786081345672846063/1864242753322106*c_1100_2^2 - 110552887242265006/932121376661053*c_1100_2 - 18202497835727731/1864242753322106, c_0011_7 - 2245166326779066/932121376661053*c_1100_2^12 - 3375678247309644/932121376661053*c_1100_2^11 - 21892309050151574/932121376661053*c_1100_2^10 - 48058287694962849/932121376661053*c_1100_2^9 - 104337021868252606/932121376661053*c_1100_2^8 - 194621992637068547/932121376661053*c_1100_2^7 - 387768702158475945/932121376661053*c_1100_2^6 - 302091910684039004/932121376661053*c_1100_2^5 - 482328579840069354/932121376661053*c_1100_2^4 - 365207765850341235/932121376661053*c_1100_2^3 - 248856185234361925/932121376661053*c_1100_2^2 - 64842307009075996/932121376661053*c_1100_2 - 4480951759710036/932121376661053, c_0101_0 + 4433641247938215/1864242753322106*c_1100_2^12 + 3384567843001492/932121376661053*c_1100_2^11 + 43432570096932873/1864242753322106*c_1100_2^10 + 47962529290784142/932121376661053*c_1100_2^9 + 208622738147491621/1864242753322106*c_1100_2^8 + 194797909045419785/932121376661053*c_1100_2^7 + 387877290793552338/932121376661053*c_1100_2^6 + 616036886978469583/1864242753322106*c_1100_2^5 + 970095721412074859/1864242753322106*c_1100_2^4 + 370722121759515672/932121376661053*c_1100_2^3 + 511926256668563721/1864242753322106*c_1100_2^2 + 137293159370086925/1864242753322106*c_1100_2 + 4938417743545247/932121376661053, c_0101_2 + 2793609191306457/1864242753322106*c_1100_2^12 + 2089787227305699/932121376661053*c_1100_2^11 + 27245858535204915/1864242753322106*c_1100_2^10 + 29813062933809456/932121376661053*c_1100_2^9 + 129729036550628363/1864242753322106*c_1100_2^8 + 120898721701277246/932121376661053*c_1100_2^7 + 241042875572383759/932121376661053*c_1100_2^6 + 374890267705583313/1864242753322106*c_1100_2^5 + 602653512647413245/1864242753322106*c_1100_2^4 + 226073960412659706/932121376661053*c_1100_2^3 + 313912245555991129/1864242753322106*c_1100_2^2 + 81127587087310191/1864242753322106*c_1100_2 + 2931941013978961/932121376661053, c_0101_3 - 6924265342898469/1864242753322106*c_1100_2^12 - 5319975800860961/932121376661053*c_1100_2^11 - 67880236619054429/1864242753322106*c_1100_2^10 - 75235970325486084/932121376661053*c_1100_2^9 - 326848359806862073/1864242753322106*c_1100_2^8 - 305604177198571387/932121376661053*c_1100_2^7 - 608189585495954340/932121376661053*c_1100_2^6 - 972482473863918133/1864242753322106*c_1100_2^5 - 1520805578569197901/1864242753322106*c_1100_2^4 - 588322866409178962/932121376661053*c_1100_2^3 - 806405695100615041/1864242753322106*c_1100_2^2 - 226965777282320487/1864242753322106*c_1100_2 - 9097758971649340/932121376661053, c_0101_4 + 6461154460242969/1864242753322106*c_1100_2^12 + 9897480117359245/1864242753322106*c_1100_2^11 + 63260375384127631/1864242753322106*c_1100_2^10 + 140067576326901465/1864242753322106*c_1100_2^9 + 304046349450385037/1864242753322106*c_1100_2^8 + 568263674374400017/1864242753322106*c_1100_2^7 + 565583354028384106/932121376661053*c_1100_2^6 + 899681767203246549/1864242753322106*c_1100_2^5 + 704981359319045294/932121376661053*c_1100_2^4 + 1088237582639506181/1864242753322106*c_1100_2^3 + 741978359931680527/1864242753322106*c_1100_2^2 + 100935097054626936/932121376661053*c_1100_2 + 14547439518807317/1864242753322106, c_1001_0 + 2937031495535481/932121376661053*c_1100_2^12 + 8825734313249483/1864242753322106*c_1100_2^11 + 28636919825842663/932121376661053*c_1100_2^10 + 125694241554778809/1864242753322106*c_1100_2^9 + 136465179945722096/932121376661053*c_1100_2^8 + 509112330593932407/1864242753322106*c_1100_2^7 + 507231318616507833/932121376661053*c_1100_2^6 + 395120792237262718/932121376661053*c_1100_2^5 + 1262787342460830339/1864242753322106*c_1100_2^4 + 956484715914559197/1864242753322106*c_1100_2^3 + 325974183027990798/932121376661053*c_1100_2^2 + 170653641938484687/1864242753322106*c_1100_2 + 11447432437379761/1864242753322106, c_1001_1 - 6924265342898469/1864242753322106*c_1100_2^12 - 5319975800860961/932121376661053*c_1100_2^11 - 67880236619054429/1864242753322106*c_1100_2^10 - 75235970325486084/932121376661053*c_1100_2^9 - 326848359806862073/1864242753322106*c_1100_2^8 - 305604177198571387/932121376661053*c_1100_2^7 - 608189585495954340/932121376661053*c_1100_2^6 - 972482473863918133/1864242753322106*c_1100_2^5 - 1520805578569197901/1864242753322106*c_1100_2^4 - 588322866409178962/932121376661053*c_1100_2^3 - 806405695100615041/1864242753322106*c_1100_2^2 - 226965777282320487/1864242753322106*c_1100_2 - 9097758971649340/932121376661053, c_1001_10 - 6858210437617605/1864242753322106*c_1100_2^12 - 5295175616443103/932121376661053*c_1100_2^11 - 67296478813071313/1864242753322106*c_1100_2^10 - 74755421455822347/932121376661053*c_1100_2^9 - 324699830374347941/1864242753322106*c_1100_2^8 - 303696934570782887/932121376661053*c_1100_2^7 - 604244394796975277/932121376661053*c_1100_2^6 - 970459517893773529/1864242753322106*c_1100_2^5 - 1510130019367040073/1864242753322106*c_1100_2^4 - 586572117326203165/932121376661053*c_1100_2^3 - 803329749312795175/1864242753322106*c_1100_2^2 - 225919527652730597/1864242753322106*c_1100_2 - 8819347514029082/932121376661053, c_1100_2^13 + 5/3*c_1100_2^12 + 10*c_1100_2^11 + 23*c_1100_2^10 + 50*c_1100_2^9 + 283/3*c_1100_2^8 + 187*c_1100_2^7 + 163*c_1100_2^6 + 712/3*c_1100_2^5 + 198*c_1100_2^4 + 138*c_1100_2^3 + 142/3*c_1100_2^2 + 20/3*c_1100_2 + 1/3 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 0.460 Total time: 0.670 seconds, Total memory usage: 32.09MB