Magma V2.19-8 Tue Aug 20 2013 23:51:02 on localhost [Seed = 1275733829] Type ? for help. Type -D to quit. Loading file "K12a775__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation K12a775 geometric_solution 11.75528214 oriented_manifold CS_known 0.0000000000000005 1 0 torus 0.000000000000 0.000000000000 13 1 2 3 1 0132 0132 0132 2031 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 1 -1 0 0 -1 1 0 1 0 -1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.116670112795 0.606299272682 0 0 4 2 0132 1302 0132 1302 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 -1 1 0 0 0 0 0 -1 1 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.693948502305 1.590457024594 3 0 1 5 0321 0132 2031 0132 0 0 0 0 0 0 0 0 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 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 1.066650601827 0.936644392117 2 6 5 0 0321 0132 0132 0132 0 0 0 0 0 0 0 0 0 0 1 -1 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 1 0 -1 -1 0 0 1 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.379335157334 1.847669426041 6 7 5 1 0213 0132 2103 0132 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 1 0 -1 0 0 0 0 0 -1 0 1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.117016141056 1.250293922075 4 8 2 3 2103 0132 0132 0132 0 0 0 0 0 0 0 0 0 0 1 -1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.506121407476 0.838866444372 4 3 8 7 0213 0132 0132 1302 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 0 0 0 0 0 0 0 -1 0 1 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 -0.196544930829 1.177905206885 9 4 6 10 0132 0132 2031 0132 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 -1 0 1 0 0 -1 1 0 1 0 -1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.663625481729 1.084988690069 11 5 9 6 0132 0132 1230 0132 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0.260685060784 0.840849491436 7 11 10 8 0132 0213 0132 3012 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 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 0 0 0 0 0.472804293918 0.318008525358 11 12 7 9 3120 0132 0132 0132 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 -1 1 1 0 -1 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 0.257504398061 1.427607802799 8 12 9 10 0132 1302 0213 3120 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 0 0 0 0 0 0 0 0 -1 1 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 0.877633645422 0.678400694941 12 10 12 11 2031 0132 1302 2031 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 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 0 0 0 0 0 0 0 0 0.122171346906 0.725410311194 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_11' : d['c_0110_12'], 'c_1001_10' : d['c_0011_11'], 'c_1001_12' : d['c_0110_12'], 'c_1001_5' : d['c_1001_0'], 'c_1001_4' : d['c_0011_11'], 'c_1001_7' : d['c_0101_1'], 'c_1001_6' : d['c_1001_0'], 'c_1001_1' : d['c_0101_1'], 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : d['c_1001_3'], 'c_1001_2' : negation(d['c_0011_0']), 'c_1001_9' : d['c_0110_12'], 'c_1001_8' : d['c_1001_3'], 'c_1010_12' : d['c_0011_11'], 'c_1010_11' : negation(d['c_0011_10']), 'c_1010_10' : d['c_0110_12'], 's_0_10' : d['1'], 's_0_11' : d['1'], 's_0_12' : d['1'], 's_3_12' : d['1'], 's_2_8' : d['1'], 's_2_9' : d['1'], 'c_0101_11' : d['c_0011_4'], 'c_0101_10' : d['c_0101_10'], 's_2_0' : negation(d['1']), 's_2_1' : 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_12' : 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' : d['1'], 's_0_7' : d['1'], 's_0_4' : d['1'], 's_0_5' : d['1'], 's_0_2' : negation(d['1']), 's_0_3' : negation(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_0011_12' : negation(d['c_0011_10']), 'c_1100_5' : negation(d['c_1010_1']), 'c_1100_4' : d['c_0101_2'], 'c_1100_7' : negation(d['c_1001_3']), 'c_1100_6' : d['c_0101_7'], 'c_1100_1' : d['c_0101_2'], 'c_1100_0' : negation(d['c_1010_1']), 'c_1100_3' : negation(d['c_1010_1']), 'c_1100_2' : negation(d['c_1010_1']), 's_3_11' : d['1'], 'c_1100_11' : negation(d['c_0101_10']), 'c_1100_10' : negation(d['c_1001_3']), 's_3_10' : d['1'], 'c_1010_7' : d['c_0011_11'], 'c_1010_6' : d['c_1001_3'], 'c_1010_5' : d['c_1001_3'], 'c_1010_4' : d['c_0101_1'], 'c_1010_3' : d['c_1001_0'], 'c_1010_2' : d['c_1001_0'], 'c_1010_1' : d['c_1010_1'], 'c_1010_0' : negation(d['c_0011_0']), 'c_1010_9' : negation(d['c_0101_10']), 'c_1010_8' : d['c_1001_0'], 'c_1100_8' : d['c_0101_7'], 's_3_1' : d['1'], 's_3_0' : d['1'], 's_3_3' : negation(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' : d['1'], 's_3_9' : d['1'], 's_3_8' : d['1'], 'c_1100_12' : d['c_0011_10'], 's_1_7' : d['1'], 's_1_6' : d['1'], 's_1_5' : d['1'], 's_1_4' : d['1'], 's_1_3' : d['1'], 's_1_2' : negation(d['1']), 's_1_1' : d['1'], 's_1_0' : negation(d['1']), 's_1_9' : d['1'], 's_1_8' : d['1'], 'c_0011_9' : d['c_0011_4'], 'c_0011_8' : negation(d['c_0011_11']), 'c_0011_5' : d['c_0011_11'], 'c_0011_4' : d['c_0011_4'], 'c_0011_7' : negation(d['c_0011_4']), 'c_0011_6' : negation(d['c_0011_3']), 'c_0011_1' : negation(d['c_0011_0']), 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : d['c_0011_3'], 'c_0011_2' : negation(d['c_0011_0']), 'c_0110_11' : d['c_0101_10'], 'c_0110_10' : d['c_0101_10'], 'c_0110_12' : d['c_0110_12'], 'c_0101_12' : d['c_0011_10'], 'c_0110_0' : d['c_0101_1'], 'c_0101_7' : d['c_0101_7'], 'c_0101_6' : d['c_0011_4'], 'c_0101_5' : negation(d['c_0011_3']), 'c_0101_4' : negation(d['c_0011_3']), 'c_0101_3' : negation(d['c_0101_2']), 'c_0101_2' : d['c_0101_2'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0011_0'], 'c_0101_9' : d['c_0101_10'], 'c_0101_8' : d['c_0101_10'], 's_1_12' : d['1'], 's_1_11' : d['1'], 's_1_10' : d['1'], 'c_0110_9' : d['c_0101_7'], 'c_0110_8' : d['c_0011_4'], 'c_0110_1' : d['c_0011_0'], 'c_1100_9' : negation(d['c_1001_3']), 'c_0110_3' : d['c_0011_0'], 'c_0110_2' : negation(d['c_0011_3']), 'c_0110_5' : negation(d['c_0101_2']), 'c_0110_4' : d['c_0101_1'], 'c_0110_7' : d['c_0101_10'], 'c_0110_6' : negation(d['c_0101_1'])})} PY=EVAL=SECTION=ENDS=HERE PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 14 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_11, c_0011_3, c_0011_4, c_0101_1, c_0101_10, c_0101_2, c_0101_7, c_0110_12, c_1001_0, c_1001_3, c_1010_1 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 43 Groebner basis: [ t - 79690242491622933/91382838550400*c_1010_1^42 + 258243677293276103/9138283855040*c_1010_1^41 - 42631187949342954299/91382838550400*c_1010_1^40 + 95015524032487246359/18276567710080*c_1010_1^39 - 200082366438139809461/4569141927520*c_1010_1^38 + 6767738959273995594937/22845709637600*c_1010_1^37 - 15270875615256591725431/9138283855040*c_1010_1^36 + 736724336841145465213897/91382838550400*c_1010_1^35 - 309497143965584986336793/9138283855040*c_1010_1^34 + 5737107881774166366371831/45691419275200*c_1010_1^33 - 9481321217467467911974467/22845709637600*c_1010_1^32 + 112645811333279629502679341/91382838550400*c_1010_1^31 - 81637256630430856162371/24658078400*c_1010_1^30 + 9716429052411145105180709/1202405770400*c_1010_1^29 - 51387998860628179374835533/2855713704700*c_1010_1^28 + 837862206548422740194555167/22845709637600*c_1010_1^27 - 3133480410230322322916810317/45691419275200*c_1010_1^26 + 2693111757361367756718186419/22845709637600*c_1010_1^25 - 8523038747086285781500199087/45691419275200*c_1010_1^24 + 12427772905058635466030901477/45691419275200*c_1010_1^23 - 2088637254653015530428606491/5711427409400*c_1010_1^22 + 2590038752798376189274858993/5711427409400*c_1010_1^21 - 11848858900444479448699567311/22845709637600*c_1010_1^20 + 2939784317966850549910908837/5375461091200*c_1010_1^19 - 48554549082230260190374477983/91382838550400*c_1010_1^18 + 2713945073258436545909453159/5711427409400*c_1010_1^17 - 7140312167338004812879350879/18276567710080*c_1010_1^16 + 2694186934244562425807235027/9138283855040*c_1010_1^15 - 4656003680380537359979473763/22845709637600*c_1010_1^14 + 2941029088417773119215864801/22845709637600*c_1010_1^13 - 846249414063694678416465013/11422854818800*c_1010_1^12 + 1768271038178750346728704291/45691419275200*c_1010_1^11 - 834763905045520659136303253/45691419275200*c_1010_1^10 + 177084616197284584896802871/22845709637600*c_1010_1^9 - 7059055999707176265921503/2404811540800*c_1010_1^8 + 22469878361648620771622171/22845709637600*c_1010_1^7 - 658610325410524847935389/2284570963760*c_1010_1^6 + 1663108768952445149162399/22845709637600*c_1010_1^5 - 88537499375774056689679/5711427409400*c_1010_1^4 + 246410770049456244930609/91382838550400*c_1010_1^3 - 6647972656634217518113/18276567710080*c_1010_1^2 + 393910774917387907899/11422854818800*c_1010_1 - 163546663632032463517/91382838550400, c_0011_0 - 1, c_0011_10 - c_1010_1^27 + 20*c_1010_1^26 - 207*c_1010_1^25 + 1453*c_1010_1^24 - 7698*c_1010_1^23 + 32568*c_1010_1^22 - 113846*c_1010_1^21 + 336233*c_1010_1^20 - 851874*c_1010_1^19 + 1871298*c_1010_1^18 - 3590642*c_1010_1^17 + 6048771*c_1010_1^16 - 8975116*c_1010_1^15 + 11750684*c_1010_1^14 - 13582204*c_1010_1^13 + 13852294*c_1010_1^12 - 12446227*c_1010_1^11 + 9826452*c_1010_1^10 - 6791829*c_1010_1^9 + 4088733*c_1010_1^8 - 2128950*c_1010_1^7 + 949556*c_1010_1^6 - 357898*c_1010_1^5 + 111778*c_1010_1^4 - 28073*c_1010_1^3 + 5396*c_1010_1^2 - 723*c_1010_1 + 53, c_0011_11 + c_1010_1^4 - 3*c_1010_1^3 + 6*c_1010_1^2 - 5*c_1010_1 + 2, c_0011_3 - c_1010_1^2 + c_1010_1 - 1, c_0011_4 + c_1010_1^3 - 2*c_1010_1^2 + 3*c_1010_1 - 1, c_0101_1 + c_1010_1^42 - 31*c_1010_1^41 + 491*c_1010_1^40 - 5260*c_1010_1^39 + 42650*c_1010_1^38 - 278015*c_1010_1^37 + 1512238*c_1010_1^36 - 7038356*c_1010_1^35 + 28535248*c_1010_1^34 - 102117169*c_1010_1^33 + 325836182*c_1010_1^32 - 934291288*c_1010_1^31 + 2422268808*c_1010_1^30 - 5706104900*c_1010_1^29 + 12260798664*c_1010_1^28 - 24104144744*c_1010_1^27 + 43461080778*c_1010_1^26 - 72001568146*c_1010_1^25 + 109749297030*c_1010_1^24 - 154056506928*c_1010_1^23 + 199255566260*c_1010_1^22 - 237505636375*c_1010_1^21 + 260860395116*c_1010_1^20 - 263884090628*c_1010_1^19 + 245670600441*c_1010_1^18 - 210258635438*c_1010_1^17 + 165194556001*c_1010_1^16 - 118932925260*c_1010_1^15 + 78292548752*c_1010_1^14 - 46999816314*c_1010_1^13 + 25646990584*c_1010_1^12 - 12672445100*c_1010_1^11 + 5643276158*c_1010_1^10 - 2251958204*c_1010_1^9 + 799591654*c_1010_1^8 - 250366668*c_1010_1^7 + 68340312*c_1010_1^6 - 16013243*c_1010_1^5 + 3152256*c_1010_1^4 - 504816*c_1010_1^3 + 62391*c_1010_1^2 - 5384*c_1010_1 + 251, c_0101_10 + c_1010_1^35 - 26*c_1010_1^34 + 347*c_1010_1^33 - 3137*c_1010_1^32 + 21456*c_1010_1^31 - 117768*c_1010_1^30 + 537856*c_1010_1^29 - 2093905*c_1010_1^28 + 7067937*c_1010_1^27 - 20944564*c_1010_1^26 + 54995491*c_1010_1^25 - 128858918*c_1010_1^24 + 270866554*c_1010_1^23 - 512866272*c_1010_1^22 + 877327078*c_1010_1^21 - 1358799229*c_1010_1^20 + 1908085384*c_1010_1^19 - 2431238682*c_1010_1^18 + 2811502340*c_1010_1^17 - 2949838827*c_1010_1^16 + 2805811764*c_1010_1^15 - 2416314124*c_1010_1^14 + 1880561236*c_1010_1^13 - 1319498837*c_1010_1^12 + 832079467*c_1010_1^11 - 469712108*c_1010_1^10 + 236165673*c_1010_1^9 - 105077888*c_1010_1^8 + 41027494*c_1010_1^7 - 13902708*c_1010_1^6 + 4027714*c_1010_1^5 - 976653*c_1010_1^4 + 192024*c_1010_1^3 - 29062*c_1010_1^2 + 3068*c_1010_1 - 175, c_0101_2 + c_1010_1^41 - 30*c_1010_1^40 + 460*c_1010_1^39 - 4771*c_1010_1^38 + 37449*c_1010_1^37 - 236255*c_1010_1^36 + 1243304*c_1010_1^35 - 5596217*c_1010_1^34 + 21931553*c_1010_1^33 - 75828419*c_1010_1^32 + 233640120*c_1010_1^31 - 646558924*c_1010_1^30 + 1616914924*c_1010_1^29 - 3672049692*c_1010_1^28 + 7602656088*c_1010_1^27 - 14394752004*c_1010_1^26 + 24985420486*c_1010_1^25 - 39832228696*c_1010_1^24 + 58406831280*c_1010_1^23 - 78851112805*c_1010_1^22 + 98070222569*c_1010_1^21 - 112400744265*c_1010_1^20 + 118706690968*c_1010_1^19 - 115473249311*c_1010_1^18 + 103386745472*c_1010_1^17 - 85102890759*c_1010_1^16 + 64307956012*c_1010_1^15 - 44522062690*c_1010_1^14 + 28170811326*c_1010_1^13 - 16240295706*c_1010_1^12 + 8497584212*c_1010_1^11 - 4016487190*c_1010_1^10 + 1704876456*c_1010_1^9 - 645117902*c_1010_1^8 + 215590396*c_1010_1^7 - 62865097*c_1010_1^6 + 15738573*c_1010_1^5 - 3307677*c_1010_1^4 + 564404*c_1010_1^3 - 74059*c_1010_1^2 + 6742*c_1010_1 - 327, c_0101_7 + c_1010_1^4 - 3*c_1010_1^3 + 6*c_1010_1^2 - 5*c_1010_1 + 2, c_0110_12 - c_1010_1^11 + 8*c_1010_1^10 - 35*c_1010_1^9 + 101*c_1010_1^8 - 210*c_1010_1^7 + 324*c_1010_1^6 - 374*c_1010_1^5 + 321*c_1010_1^4 - 200*c_1010_1^3 + 90*c_1010_1^2 - 28*c_1010_1 + 5, c_1001_0 - c_1010_1^42 + 31*c_1010_1^41 - 491*c_1010_1^40 + 5260*c_1010_1^39 - 42650*c_1010_1^38 + 278015*c_1010_1^37 - 1512238*c_1010_1^36 + 7038356*c_1010_1^35 - 28535248*c_1010_1^34 + 102117169*c_1010_1^33 - 325836182*c_1010_1^32 + 934291288*c_1010_1^31 - 2422268808*c_1010_1^30 + 5706104900*c_1010_1^29 - 12260798664*c_1010_1^28 + 24104144744*c_1010_1^27 - 43461080778*c_1010_1^26 + 72001568146*c_1010_1^25 - 109749297030*c_1010_1^24 + 154056506928*c_1010_1^23 - 199255566260*c_1010_1^22 + 237505636375*c_1010_1^21 - 260860395116*c_1010_1^20 + 263884090628*c_1010_1^19 - 245670600441*c_1010_1^18 + 210258635438*c_1010_1^17 - 165194556001*c_1010_1^16 + 118932925260*c_1010_1^15 - 78292548752*c_1010_1^14 + 46999816314*c_1010_1^13 - 25646990584*c_1010_1^12 + 12672445100*c_1010_1^11 - 5643276158*c_1010_1^10 + 2251958204*c_1010_1^9 - 799591654*c_1010_1^8 + 250366668*c_1010_1^7 - 68340312*c_1010_1^6 + 16013243*c_1010_1^5 - 3152256*c_1010_1^4 + 504816*c_1010_1^3 - 62391*c_1010_1^2 + 5384*c_1010_1 - 251, c_1001_3 + c_1010_1^3 - 2*c_1010_1^2 + 3*c_1010_1 - 1, c_1010_1^43 - 32*c_1010_1^42 + 523*c_1010_1^41 - 5781*c_1010_1^40 + 48370*c_1010_1^39 - 325436*c_1010_1^38 + 1827702*c_1010_1^37 - 8786849*c_1010_1^36 + 36816908*c_1010_1^35 - 136248634*c_1010_1^34 + 449884904*c_1010_1^33 - 1335955889*c_1010_1^32 + 3590200216*c_1010_1^31 - 8774932632*c_1010_1^30 + 19583818488*c_1010_1^29 - 40036993100*c_1010_1^28 + 75167881610*c_1010_1^27 - 129857400928*c_1010_1^26 + 206736285662*c_1010_1^25 - 303638032654*c_1010_1^24 + 411718904468*c_1010_1^23 - 515612315440*c_1010_1^22 + 596436254060*c_1010_1^21 - 637145230009*c_1010_1^20 + 628261382037*c_1010_1^19 - 571402485190*c_1010_1^18 + 478839936911*c_1010_1^17 - 369230372020*c_1010_1^16 + 261533430024*c_1010_1^15 - 169814427756*c_1010_1^14 + 100817618224*c_1010_1^13 - 54559731390*c_1010_1^12 + 26813305470*c_1010_1^11 - 11911721552*c_1010_1^10 + 4756426314*c_1010_1^9 - 1695076224*c_1010_1^8 + 534297376*c_1010_1^7 - 147218652*c_1010_1^6 + 34904072*c_1010_1^5 - 6964749*c_1010_1^4 + 1131611*c_1010_1^3 - 141834*c_1010_1^2 + 12377*c_1010_1 - 578 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 0.970 Total time: 1.179 seconds, Total memory usage: 32.09MB