Magma V2.19-8 Wed Aug 21 2013 00:02:40 on localhost [Seed = 1713377183] Type ? for help. Type -D to quit. Loading file "K13n1691__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation K13n1691 geometric_solution 11.65570050 oriented_manifold CS_known 0.0000000000000003 1 0 torus 0.000000000000 0.000000000000 13 1 2 3 4 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 -1 1 0 0 0 0 0 -1 0 0 1 3 0 -3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.756424606954 0.933888523901 0 3 6 5 0132 1230 0132 0132 0 0 0 0 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 -1 1 0 0 0 0 0 -3 -1 0 4 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.436177338858 1.241127699592 5 0 8 7 0132 0132 0132 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 1 -1 0 0 0 3 -3 -4 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.808760937435 0.615914975147 7 9 1 0 0132 0132 3012 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 0 1 -1 -1 0 1 0 0 -3 0 3 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.261493798729 1.002589196925 10 7 0 9 0132 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 0 0 0 0 0 0 0 4 -4 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.261493798729 1.002589196925 2 6 1 11 0132 1023 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 0 0 0 0 4 0 -4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.394946544299 0.594374425495 5 9 11 1 1023 1302 0132 0132 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.394946544299 0.594374425495 3 4 2 12 0132 0132 0132 0132 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 1 0 3 -4 1 -1 0 0 0 4 -4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.756424606954 0.933888523901 10 12 9 2 1302 0132 1302 0132 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 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 0.313819296590 0.466004812136 8 3 4 6 2031 0132 0132 2031 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 -3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.217413081586 0.595982051178 4 8 12 11 0132 2031 2031 2031 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 0 0 0 0 -4 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.594172600858 0.820911987761 12 10 5 6 0132 1302 0132 0132 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 -1.489957341116 0.089319354504 11 8 7 10 0132 0132 0132 1302 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 4 -4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.483938816857 0.978916595923 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_11' : d['c_0101_1'], 'c_1001_10' : negation(d['c_0101_11']), 'c_1001_12' : d['c_1001_12'], 'c_1001_5' : d['c_0101_12'], 'c_1001_4' : d['c_1001_12'], 'c_1001_7' : d['c_1001_0'], 'c_1001_6' : d['c_0110_9'], 'c_1001_1' : d['c_1001_1'], 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : d['c_0011_0'], 'c_1001_2' : d['c_1001_12'], 'c_1001_9' : d['c_1001_0'], 'c_1001_8' : d['c_0110_9'], 'c_1010_12' : d['c_0110_9'], 'c_1010_11' : d['c_0110_9'], 'c_1010_10' : d['c_0011_11'], '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'], 'c_0101_12' : d['c_0101_12'], 'c_0101_11' : d['c_0101_11'], 'c_0101_10' : d['c_0101_10'], 's_2_0' : 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' : negation(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' : negation(d['1']), 's_0_2' : negation(d['1']), 's_0_3' : d['1'], 's_0_0' : negation(d['1']), 's_0_1' : negation(d['1']), 'c_1100_9' : negation(d['c_1001_1']), 'c_1100_8' : d['c_0101_10'], 'c_0011_12' : negation(d['c_0011_11']), 'c_1100_5' : d['c_1100_1'], 'c_1100_4' : negation(d['c_1001_1']), 'c_1100_7' : d['c_0101_10'], 'c_1100_6' : d['c_1100_1'], 'c_1100_1' : d['c_1100_1'], 'c_1100_0' : negation(d['c_1001_1']), 'c_1100_3' : negation(d['c_1001_1']), 'c_1100_2' : d['c_0101_10'], 's_3_11' : d['1'], 'c_1100_11' : d['c_1100_1'], 'c_1100_10' : negation(d['c_0110_9']), 's_3_10' : d['1'], 'c_1010_7' : d['c_1001_12'], 'c_1010_6' : d['c_1001_1'], 'c_1010_5' : d['c_0101_1'], 'c_1010_4' : d['c_1001_0'], 'c_1010_3' : d['c_1001_0'], 'c_1010_2' : d['c_1001_0'], 'c_1010_1' : d['c_0101_12'], 'c_1010_0' : d['c_1001_12'], 'c_1010_9' : d['c_0011_0'], 'c_1010_8' : d['c_1001_12'], 's_3_1' : negation(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' : d['1'], 's_3_9' : d['1'], 's_3_8' : d['1'], 'c_1100_12' : d['c_0101_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_10'], 'c_0011_8' : d['c_0011_11'], 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : negation(d['c_0011_10']), 'c_0011_7' : d['c_0011_10'], 'c_0011_6' : d['c_0011_0'], 'c_0011_1' : negation(d['c_0011_0']), 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : negation(d['c_0011_10']), 'c_0011_2' : negation(d['c_0011_0']), 'c_0110_11' : d['c_0101_12'], 'c_0110_10' : d['c_0101_1'], 'c_0110_12' : d['c_0101_11'], 'c_0011_11' : d['c_0011_11'], 'c_0101_7' : d['c_0101_0'], 'c_0101_6' : d['c_0101_12'], 'c_0101_5' : d['c_0101_0'], 'c_0101_4' : d['c_0101_1'], 'c_0101_3' : d['c_0101_12'], 'c_0101_2' : d['c_0101_11'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : d['c_0101_10'], 'c_0101_8' : negation(d['c_0011_10']), 'c_0011_10' : d['c_0011_10'], 's_1_12' : d['1'], 's_1_11' : d['1'], 's_1_10' : d['1'], 'c_0110_9' : d['c_0110_9'], 'c_0110_8' : d['c_0101_11'], 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : d['c_0101_1'], 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : d['c_0101_0'], 'c_0110_5' : d['c_0101_11'], 'c_0110_4' : d['c_0101_10'], 'c_0110_7' : d['c_0101_12'], 'c_0110_6' : d['c_0101_1'], 's_2_9' : d['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_0101_0, c_0101_1, c_0101_10, c_0101_11, c_0101_12, c_0110_9, c_1001_0, c_1001_1, c_1001_12, c_1100_1 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 12 Groebner basis: [ t + 197627782/1079955*c_1100_1^5 + 1029713633/1079955*c_1100_1^4 - 3933629416/1079955*c_1100_1^3 - 44748288/23999*c_1100_1^2 + 5901381416/1079955*c_1100_1 - 103533244/119995, c_0011_0 - 1, c_0011_10 - c_1001_12 + 1, c_0011_11 + 28/5*c_1100_1^5 + 436/15*c_1100_1^4 - 112*c_1100_1^3 - 273/5*c_1100_1^2 + 2512/15*c_1100_1 - 461/15, c_0101_0 - 172/15*c_1001_12*c_1100_1^5 - 893/15*c_1001_12*c_1100_1^4 + 688/3*c_1001_12*c_1100_1^3 + 1687/15*c_1001_12*c_1100_1^2 - 5176/15*c_1001_12*c_1100_1 + 923/15*c_1001_12 + 88/15*c_1100_1^5 + 457/15*c_1100_1^4 - 352/3*c_1100_1^3 - 868/15*c_1100_1^2 + 888/5*c_1100_1 - 159/5, c_0101_1 + 119/15*c_1001_12*c_1100_1^5 + 616/15*c_1001_12*c_1100_1^4 - 478/3*c_1001_12*c_1100_1^3 - 378/5*c_1001_12*c_1100_1^2 + 3607/15*c_1001_12*c_1100_1 - 222/5*c_1001_12 - 88/15*c_1100_1^5 - 457/15*c_1100_1^4 + 352/3*c_1100_1^3 + 868/15*c_1100_1^2 - 888/5*c_1100_1 + 159/5, c_0101_10 + 4/15*c_1100_1^5 + 7/5*c_1100_1^4 - 16/3*c_1100_1^3 - 49/15*c_1100_1^2 + 152/15*c_1100_1 - 31/15, c_0101_11 - 86/15*c_1001_12*c_1100_1^5 - 148/5*c_1001_12*c_1100_1^4 + 347/3*c_1001_12*c_1100_1^3 + 806/15*c_1001_12*c_1100_1^2 - 2638/15*c_1001_12*c_1100_1 + 494/15*c_1001_12 + 31/15*c_1100_1^5 + 53/5*c_1100_1^4 - 42*c_1100_1^3 - 266/15*c_1100_1^2 + 943/15*c_1100_1 - 63/5, c_0101_12 - 119/15*c_1001_12*c_1100_1^5 - 616/15*c_1001_12*c_1100_1^4 + 478/3*c_1001_12*c_1100_1^3 + 378/5*c_1001_12*c_1100_1^2 - 3607/15*c_1001_12*c_1100_1 + 222/5*c_1001_12 + 31/15*c_1100_1^5 + 53/5*c_1100_1^4 - 42*c_1100_1^3 - 266/15*c_1100_1^2 + 943/15*c_1100_1 - 63/5, c_0110_9 + 86/15*c_1001_12*c_1100_1^5 + 148/5*c_1001_12*c_1100_1^4 - 347/3*c_1001_12*c_1100_1^3 - 806/15*c_1001_12*c_1100_1^2 + 2638/15*c_1001_12*c_1100_1 - 494/15*c_1001_12 - 11/3*c_1100_1^5 - 19*c_1100_1^4 + 221/3*c_1100_1^3 + 36*c_1100_1^2 - 113*c_1100_1 + 61/3, c_1001_0 + 47/15*c_1100_1^5 + 81/5*c_1100_1^4 - 63*c_1100_1^3 - 442/15*c_1100_1^2 + 1406/15*c_1100_1 - 81/5, c_1001_1 - 172/15*c_1001_12*c_1100_1^5 - 893/15*c_1001_12*c_1100_1^4 + 688/3*c_1001_12*c_1100_1^3 + 1687/15*c_1001_12*c_1100_1^2 - 5176/15*c_1001_12*c_1100_1 + 923/15*c_1001_12 + 28/5*c_1100_1^5 + 436/15*c_1100_1^4 - 112*c_1100_1^3 - 273/5*c_1100_1^2 + 2512/15*c_1100_1 - 446/15, c_1001_12^2 - c_1001_12 + 9/5*c_1100_1^5 + 46/5*c_1100_1^4 - 110/3*c_1100_1^3 - 217/15*c_1100_1^2 + 776/15*c_1100_1 - 128/15, c_1100_1^6 + 5*c_1100_1^5 - 21*c_1100_1^4 - 6*c_1100_1^3 + 32*c_1100_1^2 - 11*c_1100_1 + 1 ], Ideal of Polynomial ring of rank 14 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_11, c_0101_0, c_0101_1, c_0101_10, c_0101_11, c_0101_12, c_0110_9, c_1001_0, c_1001_1, c_1001_12, c_1100_1 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 19 Groebner basis: [ t - 9152759701440019711003262/96443496587846657066741*c_1100_1^18 - 1051862770428594782928336133/867991469290619913600669*c_1100_1^17 - 14341986974037597572903950307/1735982938581239827201338*c_1100_1^16 - 3678588782741794507128876420/96443496587846657066741*c_1100_1^15 - 115345239938829448510418239403/867991469290619913600669*c_1100_1^14 - 320096362923563241717248514878/867991469290619913600669*c_1100_1^\ 13 - 244082513809822309773813422093/289330489763539971200223*c_1100\ _1^12 - 469934823251902093338740708416/289330489763539971200223*c_1\ 100_1^11 - 330148986979780908842213412356/123998781327231416228667*\ c_1100_1^10 - 3239574109672062884835057268444/867991469290619913600\ 669*c_1100_1^9 - 3870286756816171692447692793088/867991469290619913\ 600669*c_1100_1^8 - 3902589859137134615659440188219/867991469290619\ 913600669*c_1100_1^7 - 6506767818177178859295738943769/173598293858\ 1239827201338*c_1100_1^6 - 4331145792126067923719312652803/17359829\ 38581239827201338*c_1100_1^5 - 32608844258819483337397656994/263027\ 71796685451927293*c_1100_1^4 - 99150832741865235533302320575/247997\ 562654462832457334*c_1100_1^3 - 17675262760672719873577348369/24799\ 7562654462832457334*c_1100_1^2 - 6872441455789039156908672988/28933\ 0489763539971200223*c_1100_1 - 7840654446867297421529740147/1928869\ 93175693314133482, c_0011_0 - 1, c_0011_10 + 343748689265269769185/52605543593370903854586*c_1100_1^18 + 654572105906038082666/8767590598895150642431*c_1100_1^17 + 528636449867018510837/1143598773768932692491*c_1100_1^16 + 51120160811934336558976/26302771796685451927293*c_1100_1^15 + 109027517326837510287021/17535181197790301284862*c_1100_1^14 + 419822261776217688265058/26302771796685451927293*c_1100_1^13 + 298752274418712819268525/8767590598895150642431*c_1100_1^12 + 1623666495836337927594112/26302771796685451927293*c_1100_1^11 + 720921753580418912867867/7515077656195843407798*c_1100_1^10 + 2253237338507898828205579/17535181197790301284862*c_1100_1^9 + 7791367079489120372575543/52605543593370903854586*c_1100_1^8 + 3845655783951175827646402/26302771796685451927293*c_1100_1^7 + 46467381872179784376582/381199591256310897497*c_1100_1^6 + 4433367545863275611789627/52605543593370903854586*c_1100_1^5 + 1226872819789220159094776/26302771796685451927293*c_1100_1^4 + 73307684211433145222342/3757538828097921703899*c_1100_1^3 + 21952344149760861457844/3757538828097921703899*c_1100_1^2 + 14363977122203833112119/17535181197790301284862*c_1100_1 + 13128028226491409180707/17535181197790301284862, c_0011_11 - 48886487019323598028/26302771796685451927293*c_1100_1^18 - 437494155870237185359/26302771796685451927293*c_1100_1^17 - 28059895710797961351/381199591256310897497*c_1100_1^16 - 4521339147427106930129/26302771796685451927293*c_1100_1^15 - 2298974832833865211994/26302771796685451927293*c_1100_1^14 + 8772388800206825174806/8767590598895150642431*c_1100_1^13 + 41535679807388099235998/8767590598895150642431*c_1100_1^12 + 345848105060449295825161/26302771796685451927293*c_1100_1^11 + 102538046259761733300506/3757538828097921703899*c_1100_1^10 + 1188993268004249746874312/26302771796685451927293*c_1100_1^9 + 1613926872918951015800230/26302771796685451927293*c_1100_1^8 + 1792792898352471758154464/26302771796685451927293*c_1100_1^7 + 70236588341476975757791/1143598773768932692491*c_1100_1^6 + 384782373939627579522071/8767590598895150642431*c_1100_1^5 + 624310121772480011779394/26302771796685451927293*c_1100_1^4 + 38775258489003827850334/3757538828097921703899*c_1100_1^3 + 5108453938964337416199/1252512942699307234633*c_1100_1^2 + 31382079740425650651570/8767590598895150642431*c_1100_1 + 10953273406808108410656/8767590598895150642431, c_0101_0 - 8565959946429660001/7515077656195843407798*c_1100_1^18 - 14244379039947049708/1252512942699307234633*c_1100_1^17 - 9716131446369185957/163371253395561813213*c_1100_1^16 - 754331948617989907891/3757538828097921703899*c_1100_1^15 - 1207139189574541215203/2505025885398614469266*c_1100_1^14 - 3108108055288244864003/3757538828097921703899*c_1100_1^13 - 1131473680569549431020/1252512942699307234633*c_1100_1^12 - 444839425992608996644/3757538828097921703899*c_1100_1^11 + 16136821548085127909479/7515077656195843407798*c_1100_1^10 + 14760626379859352630143/2505025885398614469266*c_1100_1^9 + 75773010084206415260177/7515077656195843407798*c_1100_1^8 + 47841393918062363679170/3757538828097921703899*c_1100_1^7 + 668622584394021594141/54457084465187271071*c_1100_1^6 + 65913527519626318976521/7515077656195843407798*c_1100_1^5 + 15854110679680279664488/3757538828097921703899*c_1100_1^4 + 5582078594791803684715/3757538828097921703899*c_1100_1^3 + 1437459921514046577568/3757538828097921703899*c_1100_1^2 + 2968442589099784214817/2505025885398614469266*c_1100_1 + 1090601497219708913633/2505025885398614469266, c_0101_1 + 78509952610139529681/17535181197790301284862*c_1100_1^18 + 1413825200217924702524/26302771796685451927293*c_1100_1^17 + 387118579676963091592/1143598773768932692491*c_1100_1^16 + 12485667394686861089033/8767590598895150642431*c_1100_1^15 + 235254584539068477544415/52605543593370903854586*c_1100_1^14 + 291820454679925108643575/26302771796685451927293*c_1100_1^13 + 197415285861993832828140/8767590598895150642431*c_1100_1^12 + 334359510643762542686130/8767590598895150642431*c_1100_1^11 + 407830047869464576209047/7515077656195843407798*c_1100_1^10 + 3396996357783580814879509/52605543593370903854586*c_1100_1^9 + 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