Magma V2.19-8 Tue Aug 20 2013 23:48:00 on localhost [Seed = 3819276702] Type ? for help. Type -D to quit. Loading file "K10n38__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation K10n38 geometric_solution 12.50668793 oriented_manifold CS_known -0.0000000000000004 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 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 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.903364433264 1.213452782753 0 5 4 6 0132 0132 0213 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 -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 0.298099253105 0.683221518439 7 0 5 4 0132 0132 0132 0213 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0.298099253105 0.683221518439 8 9 10 0 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 -1 0 1 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 0.309825762674 0.560552942661 10 1 0 2 0132 0213 0132 0213 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.605265180159 0.530231264314 11 1 12 2 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 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.257485297294 0.898075574086 8 7 1 12 2103 2310 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.688617750174 0.930973776229 2 11 9 6 0132 0132 2103 3201 0 0 0 0 0 1 0 -1 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 1 1 0 0 -1 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.688617750174 0.930973776229 3 11 6 10 0132 1302 2103 0321 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 -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 0.099587089846 1.232735664449 7 3 10 12 2103 0132 0321 3120 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 0 -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 0.099587089846 1.232735664449 4 8 9 3 0132 0321 0321 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 -1 1 -1 1 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.873019338208 0.709057992266 5 7 12 8 0132 0132 2310 2031 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 0 1 -1 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 0.759746048012 0.794978560771 9 11 6 5 3120 3201 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 0 0 0 0 0 0 0 0 -1 0 1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.759746048012 0.794978560771 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_11' : d['c_1001_11'], 'c_1001_10' : negation(d['c_0101_12']), 'c_1001_12' : negation(d['c_0101_11']), 'c_1001_5' : negation(d['c_1001_11']), 'c_1001_4' : d['c_1001_1'], 'c_1001_7' : negation(d['c_0011_3']), 'c_1001_6' : negation(d['c_1001_11']), 'c_1001_1' : d['c_1001_1'], 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : negation(d['c_0011_12']), 'c_1001_2' : d['c_1001_1'], 'c_1001_9' : d['c_1001_0'], 'c_1001_8' : d['c_0011_6'], 'c_1010_12' : negation(d['c_1001_11']), 'c_1010_11' : negation(d['c_0011_3']), 'c_1010_10' : negation(d['c_0011_12']), 's_0_10' : d['1'], 's_3_10' : negation(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_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' : negation(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' : negation(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' : d['1'], 's_0_3' : negation(d['1']), 's_0_0' : d['1'], 's_0_1' : d['1'], 'c_1100_9' : negation(d['c_0101_12']), 'c_1100_8' : negation(d['c_0101_12']), 'c_0011_12' : d['c_0011_12'], 'c_1100_5' : d['c_1010_4'], 'c_1100_4' : d['c_1001_0'], 'c_1100_7' : negation(d['c_0011_6']), 'c_1100_6' : d['c_1010_4'], 'c_1100_1' : d['c_1010_4'], 'c_1100_0' : d['c_1001_0'], 'c_1100_3' : d['c_1001_0'], 'c_1100_2' : d['c_1010_4'], 's_3_11' : d['1'], 'c_1100_11' : d['c_0011_12'], 'c_1100_10' : d['c_1001_0'], 's_0_11' : d['1'], 'c_1010_7' : d['c_1001_11'], 'c_1010_6' : negation(d['c_0101_11']), 'c_1010_5' : d['c_1001_1'], 'c_1010_4' : d['c_1010_4'], 'c_1010_3' : d['c_1001_0'], 'c_1010_2' : d['c_1001_0'], 'c_1010_1' : negation(d['c_1001_11']), 'c_1010_0' : d['c_1001_1'], 'c_1010_9' : negation(d['c_0011_12']), 'c_1010_8' : negation(d['c_0011_12']), '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' : d['1'], 's_3_9' : d['1'], 's_3_8' : negation(d['1']), 'c_1100_12' : d['c_1010_4'], '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' : d['1'], 's_1_1' : d['1'], 's_1_0' : d['1'], 's_1_9' : d['1'], 's_1_8' : d['1'], 'c_0011_9' : negation(d['c_0011_3']), 'c_0011_8' : negation(d['c_0011_3']), 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : negation(d['c_0011_10']), 'c_0011_7' : d['c_0011_0'], 'c_0011_6' : d['c_0011_6'], '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_0011_6'], 'c_0110_10' : negation(d['c_0011_10']), 'c_0110_12' : d['c_0011_6'], 'c_0101_12' : d['c_0101_12'], 'c_0110_0' : negation(d['c_0011_10']), 'c_0101_7' : negation(d['c_0101_10']), 'c_0101_6' : d['c_0101_0'], 'c_0101_5' : d['c_0011_6'], 'c_0101_4' : negation(d['c_0011_10']), 'c_0101_3' : negation(d['c_0011_10']), 'c_0101_2' : d['c_0101_11'], 'c_0101_1' : negation(d['c_0011_10']), 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : negation(d['c_0101_10']), 'c_0101_8' : d['c_0101_0'], 'c_0011_10' : d['c_0011_10'], 's_1_12' : d['1'], 's_1_11' : d['1'], 's_1_10' : negation(d['1']), 'c_0110_9' : d['c_0011_6'], 'c_0110_8' : negation(d['c_0011_10']), 'c_0110_1' : d['c_0101_0'], 'c_0011_11' : negation(d['c_0011_0']), 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : negation(d['c_0101_10']), 'c_0110_5' : d['c_0101_11'], 'c_0110_4' : d['c_0101_10'], 'c_0110_7' : d['c_0101_11'], 'c_0110_6' : d['c_0101_12']})} 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_12, c_0011_3, c_0011_6, c_0101_0, c_0101_10, c_0101_11, c_0101_12, c_1001_0, c_1001_1, c_1001_11, c_1010_4 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 12 Groebner basis: [ t - 50637/2504*c_1001_11^11 + 36745/313*c_1001_11^10 - 263481/1252*c_1001_11^9 + 263199/5008*c_1001_11^8 + 755611/5008*c_1001_11^7 + 21985/1252*c_1001_11^6 - 1093139/5008*c_1001_11^5 + 178581/5008*c_1001_11^4 + 435135/5008*c_1001_11^3 + 16383/2504*c_1001_11^2 - 15187/626*c_1001_11 - 63827/5008, c_0011_0 - 1, c_0011_10 + 228/313*c_1001_11^11 - 1281/313*c_1001_11^10 + 2049/313*c_1001_11^9 + 216/313*c_1001_11^8 - 4327/626*c_1001_11^7 - 1151/313*c_1001_11^6 + 6917/626*c_1001_11^5 + 405/313*c_1001_11^4 - 2070/313*c_1001_11^3 - 1375/626*c_1001_11^2 + 1747/626*c_1001_11 + 191/313, c_0011_12 + 641/626*c_1001_11^11 - 1498/313*c_1001_11^10 + 1375/313*c_1001_11^9 + 9369/1252*c_1001_11^8 - 12051/1252*c_1001_11^7 - 2025/313*c_1001_11^6 + 12625/1252*c_1001_11^5 + 7277/1252*c_1001_11^4 - 9267/1252*c_1001_11^3 - 385/626*c_1001_11^2 + 664/313*c_1001_11 + 577/1252, c_0011_3 + 73/626*c_1001_11^11 - 133/313*c_1001_11^10 - 90/313*c_1001_11^9 + 3153/1252*c_1001_11^8 - 1557/1252*c_1001_11^7 - 1404/313*c_1001_11^6 + 4267/1252*c_1001_11^5 + 6577/1252*c_1001_11^4 - 4159/1252*c_1001_11^3 - 1302/313*c_1001_11^2 + 1601/626*c_1001_11 + 2349/1252, c_0011_6 - 325/313*c_1001_11^11 + 1896/313*c_1001_11^10 - 3139/313*c_1001_11^9 - 1423/626*c_1001_11^8 + 10079/626*c_1001_11^7 + 533/626*c_1001_11^6 - 11665/626*c_1001_11^5 - 219/313*c_1001_11^4 + 8603/626*c_1001_11^3 - 5/313*c_1001_11^2 - 2563/626*c_1001_11 - 356/313, c_0101_0 - 1497/626*c_1001_11^11 + 4018/313*c_1001_11^10 - 6078/313*c_1001_11^9 - 3413/1252*c_1001_11^8 + 27187/1252*c_1001_11^7 + 1985/626*c_1001_11^6 - 32389/1252*c_1001_11^5 - 335/1252*c_1001_11^4 + 19275/1252*c_1001_11^3 - 1015/626*c_1001_11^2 - 3015/626*c_1001_11 - 1495/1252, c_0101_10 + 1497/626*c_1001_11^11 - 4018/313*c_1001_11^10 + 6078/313*c_1001_11^9 + 3413/1252*c_1001_11^8 - 27187/1252*c_1001_11^7 - 1985/626*c_1001_11^6 + 32389/1252*c_1001_11^5 + 335/1252*c_1001_11^4 - 19275/1252*c_1001_11^3 + 1015/626*c_1001_11^2 + 3015/626*c_1001_11 + 1495/1252, c_0101_11 - c_1001_11, c_0101_12 - 73/626*c_1001_11^11 + 133/313*c_1001_11^10 + 90/313*c_1001_11^9 - 3153/1252*c_1001_11^8 + 1557/1252*c_1001_11^7 + 1404/313*c_1001_11^6 - 4267/1252*c_1001_11^5 - 6577/1252*c_1001_11^4 + 4159/1252*c_1001_11^3 + 1302/313*c_1001_11^2 - 1601/626*c_1001_11 - 2349/1252, c_1001_0 + 228/313*c_1001_11^11 - 1281/313*c_1001_11^10 + 2049/313*c_1001_11^9 + 216/313*c_1001_11^8 - 4327/626*c_1001_11^7 - 1151/313*c_1001_11^6 + 6917/626*c_1001_11^5 + 405/313*c_1001_11^4 - 2070/313*c_1001_11^3 - 1375/626*c_1001_11^2 + 1747/626*c_1001_11 + 191/313, c_1001_1 - 428/313*c_1001_11^11 + 2520/313*c_1001_11^10 - 4703/313*c_1001_11^9 + 1489/313*c_1001_11^8 + 3784/313*c_1001_11^7 - 2065/626*c_1001_11^6 - 4941/313*c_1001_11^5 + 3471/626*c_1001_11^4 + 2502/313*c_1001_11^3 - 700/313*c_1001_11^2 - 1687/626*c_1001_11 - 459/626, c_1001_11^12 - 5*c_1001_11^11 + 6*c_1001_11^10 + 9/2*c_1001_11^9 - 8*c_1001_11^8 - 13/2*c_1001_11^7 + 19/2*c_1001_11^6 + 6*c_1001_11^5 - 5*c_1001_11^4 - 7/2*c_1001_11^3 + c_1001_11^2 + 3/2*c_1001_11 + 1/2, c_1010_4 - 1 ], Ideal of Polynomial ring of rank 14 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_12, c_0011_3, c_0011_6, c_0101_0, c_0101_10, c_0101_11, c_0101_12, c_1001_0, c_1001_1, c_1001_11, c_1010_4 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 16 Groebner basis: [ t + 25992360067103723/33481140166784*c_1010_4^15 + 141293339040681343/16740570083392*c_1010_4^14 + 1749526863183305509/16740570083392*c_1010_4^13 + 16204718947010887643/16740570083392*c_1010_4^12 + 87514148191822847983/16740570083392*c_1010_4^11 + 585893197059856762481/33481140166784*c_1010_4^10 + 332964462738686105857/8370285041696*c_1010_4^9 + 16589375879164482717/261571407553*c_1010_4^8 + 38002931237097541595/523142815106*c_1010_4^7 + 500570032378161837425/8370285041696*c_1010_4^6 + 1178806561419243259217/33481140166784*c_1010_4^5 + 240349769253533665679/16740570083392*c_1010_4^4 + 64904141571472605531/16740570083392*c_1010_4^3 + 10002898708774047173/16740570083392*c_1010_4^2 + 739374128548471743/16740570083392*c_1010_4 + 4609107262078953/1762165271936, c_0011_0 - 1, c_0011_10 + 823342239/55067664748*c_1010_4^15 + 4184252877/27533832374*c_1010_4^14 + 209690676707/110135329496*c_1010_4^13 + 951933770069/55067664748*c_1010_4^12 + 9728007418209/110135329496*c_1010_4^11 + 7532777562339/27533832374*c_1010_4^10 + 62753679314331/110135329496*c_1010_4^9 + 90138147985375/110135329496*c_1010_4^8 + 92516557683243/110135329496*c_1010_4^7 + 68336511470939/110135329496*c_1010_4^6 + 37467164957937/110135329496*c_1010_4^5 + 15329005366771/110135329496*c_1010_4^4 + 647731957028/13766916187*c_1010_4^3 + 1571821951253/110135329496*c_1010_4^2 + 220813083031/55067664748*c_1010_4 - 14364508473/110135329496, c_0011_12 + 47315070885/3524330543872*c_1010_4^15 + 235635068649/1762165271936*c_1010_4^14 + 2938883852883/1762165271936*c_1010_4^13 + 26481445899117/1762165271936*c_1010_4^12 + 130989200030249/1762165271936*c_1010_4^11 + 750362085288751/3524330543872*c_1010_4^10 + 330824425256175/881082635968*c_1010_4^9 + 4955068647049/13766916187*c_1010_4^8 + 2101021939527/55067664748*c_1010_4^7 - 353966831965457/881082635968*c_1010_4^6 - 2106210411132897/3524330543872*c_1010_4^5 - 814355189278167/1762165271936*c_1010_4^4 - 379718307411923/1762165271936*c_1010_4^3 - 102799518448397/1762165271936*c_1010_4^2 - 13731367204311/1762165271936*c_1010_4 + 197084931349/3524330543872, c_0011_3 + 1002571101381/7048661087744*c_1010_4^15 + 5462422685927/3524330543872*c_1010_4^14 + 67624323606305/3524330543872*c_1010_4^13 + 626780234553443/3524330543872*c_1010_4^12 + 3391843569923695/3524330543872*c_1010_4^11 + 22779150855136731/7048661087744*c_1010_4^10 + 12996719710348761/1762165271936*c_1010_4^9 + 155403169452631/13150487104*c_1010_4^8 + 11993458544314851/881082635968*c_1010_4^7 + 19855487398645465/1762165271936*c_1010_4^6 + 46879257258206887/7048661087744*c_1010_4^5 + 9498769753353775/3524330543872*c_1010_4^4 + 2502951802759987/3524330543872*c_1010_4^3 + 366881675660521/3524330543872*c_1010_4^2 + 27386705005559/3524330543872*c_1010_4 + 698101577073/7048661087744, c_0011_6 + 1398024526015/3524330543872*c_1010_4^15 + 7560442649963/1762165271936*c_1010_4^14 + 93657456313673/1762165271936*c_1010_4^13 + 866138478080183/1762165271936*c_1010_4^12 + 4656015287617867/1762165271936*c_1010_4^11 + 30945263834797501/3524330543872*c_1010_4^10 + 17415005859455341/881082635968*c_1010_4^9 + 1711476359057869/55067664748*c_1010_4^8 + 480579666749687/13766916187*c_1010_4^7 + 24600486417488461/881082635968*c_1010_4^6 + 55503751134409485/3524330543872*c_1010_4^5 + 10587770510124363/1762165271936*c_1010_4^4 + 2585030312389719/1762165271936*c_1010_4^3 + 337983293633353/1762165271936*c_1010_4^2 + 25368644355947/1762165271936*c_1010_4 + 4746686997647/3524330543872, c_0101_0 + 1740265221261/7048661087744*c_1010_4^15 + 9377582370423/3524330543872*c_1010_4^14 + 116231673260737/3524330543872*c_1010_4^13 + 1073789778523443/3524330543872*c_1010_4^12 + 5755675083142751/3524330543872*c_1010_4^11 + 38102251790225347/7048661087744*c_1010_4^10 + 21348994923910633/1762165271936*c_1010_4^9 + 16702302506903265/881082635968*c_1010_4^8 + 18671414117661127/881082635968*c_1010_4^7 + 29760743089741865/1762165271936*c_1010_4^6 + 67165587471023199/7048661087744*c_1010_4^5 + 12917764816601631/3524330543872*c_1010_4^4 + 3234416810076163/3524330543872*c_1010_4^3 + 448773958586793/3524330543872*c_1010_4^2 + 37248683378631/3524330543872*c_1010_4 + 5737454908297/7048661087744, c_0101_10 + 3443660303631/7048661087744*c_1010_4^15 + 18380355914721/3524330543872*c_1010_4^14 + 228180409533423/3524330543872*c_1010_4^13 + 2102072955127557/3524330543872*c_1010_4^12 + 11181747262810697/3524330543872*c_1010_4^11 + 73241801808168137/7048661087744*c_1010_4^10 + 40535293536391663/1762165271936*c_1010_4^9 + 31214528446176833/881082635968*c_1010_4^8 + 34209623494427575/881082635968*c_1010_4^7 + 53061145824822895/1762165271936*c_1010_4^6 + 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