Magma V2.19-8 Fri Sep 13 2013 01:01:04 on localhost [Seed = 3315927970] Type ? for help. Type -D to quit. Loading file "m125__sl3_c4.magma" ==TRIANGULATION=BEGINS== % Triangulation m125 geometric_solution 3.66386238 oriented_manifold CS_known -0.0000000000000000 2 0 torus 0.000000000000 0.000000000000 torus 0.000000000000 0.000000000000 4 1 2 2 3 0132 0132 2031 0132 0 0 1 0 0 1 0 -1 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 -1 1 0 0 0 0 1 0 0 -1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.500000000000 0.500000000000 0 3 2 3 0132 2103 2103 1023 0 0 0 1 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 1 -1 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.000000000000 1.000000000000 1 0 3 0 2103 0132 2103 1302 0 0 0 1 0 -1 0 1 1 0 -1 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 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.000000000000 1.000000000000 2 1 0 1 2103 2103 0132 1023 0 0 0 1 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 1 -1 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 1.000000000000 1.000000000000 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1020_2' : d['c_0210_2'], 'c_1020_3' : d['c_0102_0'], 'c_1020_0' : d['c_0012_1'], 'c_1020_1' : d['c_0120_3'] * d['u'] ** 2, 'c_0201_0' : d['c_0120_3'] * d['u'] ** 2, 'c_0201_1' : d['c_0201_1'], 'c_0201_2' : d['c_0201_1'], 'c_0201_3' : d['c_0201_1'], 'c_2100_0' : d['c_0210_2'] * d['u'] ** 1, 'c_2100_1' : d['c_0120_2'], 'c_2100_2' : d['c_0120_3'], 'c_2100_3' : d['c_0210_2'] * d['u'] ** 2, 'c_2010_2' : d['c_0120_2'], 'c_2010_3' : d['c_0120_3'] * d['u'] ** 2, 'c_2010_0' : d['c_0012_0'], 'c_2010_1' : d['c_0102_0'], 'c_0102_0' : d['c_0102_0'], 'c_0102_1' : d['c_0102_1'], 'c_0102_2' : d['c_0102_1'], 'c_0102_3' : d['c_0102_1'], 'c_1101_0' : d['c_1101_0'], 'c_1101_1' : negation(d['c_0111_2']), 'c_1101_2' : negation(d['c_0111_3']), 'c_1101_3' : d['c_1101_3'], 'c_1200_2' : d['c_0102_0'] * d['u'] ** 2, 'c_1200_3' : d['c_0120_2'] * d['u'] ** 1, 'c_1200_0' : d['c_0120_2'] * d['u'] ** 2, 'c_1200_1' : d['c_0210_2'], 'c_1110_2' : d['c_1101_0'] * d['u'] ** 2, 'c_1110_3' : negation(d['c_1110_1']), 'c_1110_0' : d['c_1101_3'] * d['u'] ** 2, 'c_1110_1' : d['c_1110_1'], 'c_0120_0' : d['c_0102_1'] * d['u'] ** 2, 'c_0120_1' : d['c_0102_0'] * d['u'] ** 1, 'c_0120_2' : d['c_0120_2'], 'c_0120_3' : d['c_0120_3'], 'c_2001_0' : d['c_0120_2'], 'c_2001_1' : d['c_0012_0'], 'c_2001_2' : d['c_0012_0'], 'c_2001_3' : d['c_0012_0'], 'c_0012_2' : d['c_0012_1'], 'c_0012_3' : d['c_0012_1'], 'c_0012_0' : d['c_0012_0'], 'c_0012_1' : d['c_0012_1'], 'c_0111_0' : d['c_0111_0'], 'c_0111_1' : negation(d['c_0111_0']) * d['u'] ** 1, 'c_0111_2' : d['c_0111_2'], 'c_0111_3' : d['c_0111_3'], 'c_0210_2' : d['c_0210_2'], 'c_0210_3' : d['c_0102_0'] * d['u'] ** 2, 'c_0210_0' : d['c_0201_1'] * d['u'] ** 1, 'c_0210_1' : d['c_0120_3'] * d['u'] ** 1, 'c_1002_2' : d['c_0012_1'], 'c_1002_3' : d['c_0012_1'], 'c_1002_0' : d['c_0210_2'], 'c_1002_1' : d['c_0012_1'], 'c_1011_2' : negation(d['c_1011_0']), 'c_1011_3' : negation(d['c_1011_1']), 'c_1011_0' : d['c_1011_0'], 'c_1011_1' : d['c_1011_1'], 'c_0021_0' : d['c_0012_1'], 'c_0021_1' : d['c_0012_0'], 'c_0021_2' : d['c_0012_0'], 'c_0021_3' : d['c_0012_0']}), 'non_trivial_generalized_obstruction_class' : True} PY=EVAL=SECTION=ENDS=HERE PRIMARY_DECOMPOSITION_TIME: 1.760 PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 18 over Rational Field Order: Lexicographical Variables: t, c_0012_0, c_0012_1, c_0102_0, c_0102_1, c_0111_0, c_0111_2, c_0111_3, c_0120_2, c_0120_3, c_0201_1, c_0210_2, c_1011_0, c_1011_1, c_1101_0, c_1101_3, c_1110_1, u Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 16 Groebner basis: [ t + 281570946597/419549221*c_1110_1^7*u + 22349258731/419549221*c_1110_1^7 + 14372139234867/2936844547*c_1110_1^6*u + 8199086226180/2936844547*c_1110_1^6 + 2260214879862/225911119*c_1110_1^5*u + 2741698509486/225911119*c_1110_1^5 + 8461857776026/2936844547*c_1110_1^4*u + 40316868091351/2936844547*c_1110_1^4 - 16973069124675/2936844547*c_1110_1^3*u - 2381080135620/2936844547*c_1110_1^3 - 6927570874373/2936844547*c_1110_1^2*u - 4571866468518/2936844547*c_1110_1^2 - 6269792779546/2936844547*c_1110_1*u + 7089344213743/2936844547*c_1110_1 - 724253032655/2936844547*u - 2711303900796/2936844547, c_0012_0 - 1, c_0012_1 - 1, c_0102_0 - 1, c_0102_1 - 841797/8562229*c_1110_1^7*u - 6101855/8562229*c_1110_1^7 + 16952607/8562229*c_1110_1^6*u - 27202529/8562229*c_1110_1^6 + 53712020/4610431*c_1110_1^5*u - 4747560/4610431*c_1110_1^5 + 981565031/59935603*c_1110_1^4*u + 515158144/59935603*c_1110_1^4 + 139864308/59935603*c_1110_1^3*u + 369015110/59935603*c_1110_1^3 - 36844021/59935603*c_1110_1^2*u + 116146305/59935603*c_1110_1^2 + 158458836/59935603*c_1110_1*u + 340320356/59935603*c_1110_1 - 106791746/59935603*u - 48814802/59935603, c_0111_0 - 1, c_0111_2 - 4544158/59935603*c_1110_1^7*u - 43658582/59935603*c_1110_1^7 + 958844235/419549221*c_1110_1^6*u - 1167301936/419549221*c_1110_1^6 + 371841510/32273017*c_1110_1^5*u + 27535383/32273017*c_1110_1^5 + 5389089646/419549221*c_1110_1^4*u + 4141836316/419549221*c_1110_1^4 - 574635972/419549221*c_1110_1^3*u + 1964317793/419549221*c_1110_1^3 + 314694907/419549221*c_1110_1^2*u + 898282517/419549221*c_1110_1^2 + 1573220483/419549221*c_1110_1*u + 2276965053/419549221*c_1110_1 - 416738240/419549221*u - 578785269/419549221, c_0111_3 + 10132009/59935603*c_1110_1^7*u - 53087499/59935603*c_1110_1^7 + 1923723881/419549221*c_1110_1^6*u - 1076188408/419549221*c_1110_1^6 + 563932604/32273017*c_1110_1^5*u + 150143901/32273017*c_1110_1^5 + 6544699659/419549221*c_1110_1^4*u + 6165769522/419549221*c_1110_1^4 - 2602643699/419549221*c_1110_1^3*u + 521049024/419549221*c_1110_1^3 - 766436850/419549221*c_1110_1^2*u - 358198790/419549221*c_1110_1^2 + 1756421789/419549221*c_1110_1*u + 3271703325/419549221*c_1110_1 - 691686075/419549221*u - 908075436/419549221, c_0120_2 - 55667103/59935603*c_1110_1^7*u - 63961708/59935603*c_1110_1^7 - 1306366197/419549221*c_1110_1^6*u - 3249430130/419549221*c_1110_1^6 + 118555249/32273017*c_1110_1^5*u - 515413742/32273017*c_1110_1^5 + 7099483848/419549221*c_1110_1^4*u - 2234887621/419549221*c_1110_1^4 + 2320903582/419549221*c_1110_1^3*u + 2848374751/419549221*c_1110_1^3 - 541928990/419549221*c_1110_1^2*u + 288680879/419549221*c_1110_1^2 + 3096201156/419549221*c_1110_1*u + 1613700904/419549221*c_1110_1 - 766583299/419549221*u - 272425339/419549221, c_0120_3 - 16879678/59935603*c_1110_1^7*u - 31949139/59935603*c_1110_1^7 + 9633758/419549221*c_1110_1^6*u - 1195610413/419549221*c_1110_1^6 + 165789745/32273017*c_1110_1^5*u - 92158480/32273017*c_1110_1^5 + 3311029439/419549221*c_1110_1^4*u + 1712075650/419549221*c_1110_1^4 - 636663831/419549221*c_1110_1^3*u + 1673178125/419549221*c_1110_1^3 + 903551/419549221*c_1110_1^2*u + 142528226/419549221*c_1110_1^2 + 1548401160/419549221*c_1110_1*u + 1579065321/419549221*c_1110_1 - 789886781/419549221*u - 470949095/419549221, c_0201_1 - 5260058/8562229*c_1110_1^7*u + 841797/8562229*c_1110_1^7 - 44155136/8562229*c_1110_1^6*u - 16952607/8562229*c_1110_1^6 - 58459580/4610431*c_1110_1^5*u - 53712020/4610431*c_1110_1^5 - 466406887/59935603*c_1110_1^4*u - 981565031/59935603*c_1110_1^4 + 229150802/59935603*c_1110_1^3*u - 139864308/59935603*c_1110_1^3 + 152990326/59935603*c_1110_1^2*u + 36844021/59935603*c_1110_1^2 + 181861520/59935603*c_1110_1*u - 158458836/59935603*c_1110_1 + 57976944/59935603*u + 106791746/59935603, c_0210_2 + 7569719/8562229*c_1110_1^7*u + 6958995/8562229*c_1110_1^7 + 30533523/8562229*c_1110_1^6*u + 51505274/8562229*c_1110_1^6 + 4711152/4610431*c_1110_1^5*u + 60014018/4610431*c_1110_1^5 - 375292800/59935603*c_1110_1^4*u + 380406940/59935603*c_1110_1^4 - 31224344/59935603*c_1110_1^3*u - 265032059/59935603*c_1110_1^3 + 25918000/59935603*c_1110_1^2*u - 137423088/59935603*c_1110_1^2 - 222777362/59935603*c_1110_1*u + 2480301/59935603*c_1110_1 + 75877405/59935603*u + 13180607/59935603, c_1011_0 + 22904101/59935603*c_1110_1^7*u + 12622892/59935603*c_1110_1^7 + 777660003/419549221*c_1110_1^6*u + 811369415/419549221*c_1110_1^6 + 70170599/32273017*c_1110_1^5*u + 152647949/32273017*c_1110_1^5 + 143593020/419549221*c_1110_1^4*u + 1164402027/419549221*c_1110_1^4 + 618358112/419549221*c_1110_1^3*u - 399583412/419549221*c_1110_1^3 + 401748772/419549221*c_1110_1^2*u + 110484683/419549221*c_1110_1^2 - 125074168/419549221*c_1110_1*u + 291173618/419549221*c_1110_1 + 151991275/419549221*u - 85873019/419549221, c_1011_1 - 31949139/59935603*c_1110_1^7*u - 15069461/59935603*c_1110_1^7 - 1195610413/419549221*c_1110_1^6*u - 1205244171/419549221*c_1110_1^6 - 92158480/32273017*c_1110_1^5*u - 257948225/32273017*c_1110_1^5 + 1712075650/419549221*c_1110_1^4*u - 1598953789/419549221*c_1110_1^4 + 1673178125/419549221*c_1110_1^3*u + 2309841956/419549221*c_1110_1^3 + 142528226/419549221*c_1110_1^2*u + 141624675/419549221*c_1110_1^2 + 1159516100/419549221*c_1110_1*u - 388885060/419549221*c_1110_1 - 470949095/419549221*u + 318937686/419549221, c_1101_0 - 30083932/59935603*c_1110_1^7*u - 36090073/59935603*c_1110_1^7 - 718482624/419549221*c_1110_1^6*u - 1712389011/419549221*c_1110_1^6 + 37192535/32273017*c_1110_1^5*u - 267450177/32273017*c_1110_1^5 + 2770642620/419549221*c_1110_1^4*u - 1498446553/419549221*c_1110_1^4 + 836928520/419549221*c_1110_1^3*u + 1455641001/419549221*c_1110_1^3 + 220322772/419549221*c_1110_1^2*u + 1072446299/419549221*c_1110_1^2 + 1434367366/419549221*c_1110_1*u + 273811511/419549221*c_1110_1 - 379150560/419549221*u - 178137268/419549221, c_1101_3 - 14676167/59935603*c_1110_1^7*u + 9428917/59935603*c_1110_1^7 - 964879646/419549221*c_1110_1^6*u - 91113528/419549221*c_1110_1^6 - 192091094/32273017*c_1110_1^5*u - 122608518/32273017*c_1110_1^5 - 1155610013/419549221*c_1110_1^4*u - 2023933206/419549221*c_1110_1^4 + 2028007727/419549221*c_1110_1^3*u + 1443268769/419549221*c_1110_1^3 + 1081131757/419549221*c_1110_1^2*u + 1256481307/419549221*c_1110_1^2 - 183201306/419549221*c_1110_1*u - 994738272/419549221*c_1110_1 - 144601386/419549221*u + 329290167/419549221, c_1110_1^8 - 27/7*c_1110_1^7*u + 24/7*c_1110_1^7 - 17*c_1110_1^6*u - 3*c_1110_1^6 - 16*c_1110_1^5*u - 15*c_1110_1^5 + 51/7*c_1110_1^4*u - 22/7*c_1110_1^4 + 2*c_1110_1^3*u + c_1110_1^3 - 34/7*c_1110_1^2*u - 46/7*c_1110_1^2 + 19/7*c_1110_1*u + 22/7*c_1110_1 - 3/7*u - 2/7, u^2 + u + 1 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE FREE=VARIABLES=IN=COMPONENTS=BEGINS=HERE [ [ ] ] FREE=VARIABLES=IN=COMPONENTS=ENDS=HERE CPUTIME: 1.760 Total time: 1.970 seconds, Total memory usage: 32.09MB