Magma V2.19-8 Tue Aug 20 2013 18:03:29 on localhost [Seed = 4038149485] Type ? for help. Type -D to quit. Loading file "9^2_41__sl2_c0.magma" ==TRIANGULATION=BEGINS== % Triangulation 9^2_41 geometric_solution 12.95742943 oriented_manifold CS_known 0.0000000000000001 2 0 torus 0.000000000000 0.000000000000 torus 0.000000000000 0.000000000000 13 1 1 2 3 0132 1302 0132 0132 0 0 0 1 0 1 -1 0 -1 0 0 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 0 1 1 0 0 -1 1 0 0 -1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.475462749345 0.654550381370 0 4 5 0 0132 0132 0132 2031 0 0 1 0 0 1 -1 0 1 0 0 -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 -1 0 0 1 -1 1 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.745530833546 0.930319993120 6 6 7 0 0132 1230 0132 0132 0 0 1 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 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 0.693364380565 0.860062577615 7 8 0 9 1023 0132 0132 0132 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 0 -1 1 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 0.649134488168 0.790014934727 10 1 10 7 0132 0132 3012 3120 0 0 0 1 0 -1 1 0 1 0 -1 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 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.431883587321 0.704702577707 7 11 12 1 2031 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.379115258934 0.755634197731 2 11 2 10 0132 2031 3012 0132 0 0 0 1 0 0 -1 1 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 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 0.431883587321 0.704702577707 4 3 5 2 3120 1023 1302 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 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.714310112921 0.564890135645 11 3 11 12 2103 0132 0132 1302 0 1 0 0 0 0 0 0 1 0 -1 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 -1 0 2 -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 0.579660513369 0.916047098374 10 12 3 12 3120 0132 0132 1230 0 0 1 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 -1 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 0.579660513369 0.916047098374 4 4 6 9 0132 1230 0132 3120 0 0 1 0 0 1 -1 0 -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 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.693364380565 0.860062577615 6 5 8 8 1302 0132 2103 0132 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 0 0 0 0 0 0 0 0 0 1 0 1 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.413790193192 0.901774203627 9 9 8 5 3012 0132 2031 0132 0 0 0 1 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 -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 0.413790193192 0.901774203627 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_11' : negation(d['c_0011_3']), 'c_1001_10' : d['c_0011_11'], 'c_1001_12' : d['c_0101_12'], 'c_1001_5' : d['c_1001_5'], 'c_1001_4' : d['c_0011_0'], 'c_1001_7' : d['c_0101_1'], 'c_1001_6' : negation(d['c_0011_2']), 'c_1001_1' : negation(d['c_0011_3']), 'c_1001_0' : d['c_0101_0'], 'c_1001_3' : d['c_1001_3'], 'c_1001_2' : d['c_0101_9'], 'c_1001_9' : d['c_1001_5'], 'c_1001_8' : d['c_1001_5'], 'c_1010_12' : d['c_1001_5'], 'c_1010_11' : d['c_1001_5'], 'c_1010_10' : d['c_0011_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_2'], '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' : 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' : 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' : negation(d['c_0011_0']), 'c_0011_12' : d['c_0011_12'], 'c_1100_5' : negation(d['c_1001_3']), 'c_1100_4' : negation(d['c_0011_11']), 'c_1100_7' : d['c_0101_5'], 'c_1100_6' : negation(d['c_0101_9']), 'c_1100_1' : negation(d['c_1001_3']), 'c_1100_0' : d['c_0101_5'], 'c_1100_3' : d['c_0101_5'], 'c_1100_2' : d['c_0101_5'], 's_3_11' : d['1'], 'c_1100_9' : d['c_0101_5'], 'c_1100_11' : d['c_0101_12'], 'c_1100_10' : negation(d['c_0101_9']), 's_3_10' : d['1'], 'c_1010_7' : d['c_0101_9'], 'c_1010_6' : d['c_0011_11'], 'c_1010_5' : negation(d['c_0011_3']), 'c_1010_4' : negation(d['c_0011_3']), 'c_1010_3' : d['c_1001_5'], 'c_1010_2' : d['c_0101_0'], 'c_1010_1' : d['c_0011_0'], 'c_1010_0' : d['c_1001_3'], 'c_1010_9' : d['c_0101_12'], 'c_1010_8' : d['c_1001_3'], 'c_1100_8' : d['c_0101_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' : d['1'], 'c_1100_12' : negation(d['c_1001_3']), '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_12']), 'c_0011_8' : negation(d['c_0011_3']), 'c_0011_5' : negation(d['c_0011_11']), 'c_0011_4' : d['c_0011_0'], 'c_0011_7' : d['c_0011_3'], 'c_0011_6' : negation(d['c_0011_2']), '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' : d['c_0011_2'], 'c_0110_11' : d['c_0011_2'], 'c_0110_10' : d['c_0011_12'], 'c_0110_12' : d['c_0101_5'], 'c_0101_12' : d['c_0101_12'], 'c_0101_7' : d['c_0011_11'], 'c_0101_6' : d['c_0101_0'], 'c_0101_5' : d['c_0101_5'], 'c_0101_4' : d['c_0011_12'], 'c_0101_3' : d['c_0101_1'], 'c_0101_2' : d['c_0101_10'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : d['c_0101_9'], 'c_0101_8' : d['c_0011_2'], 's_1_12' : d['1'], 's_1_11' : d['1'], 's_1_10' : d['1'], 'c_0110_9' : d['c_0011_12'], 'c_0110_8' : negation(d['c_0101_12']), 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : d['c_0101_1'], 'c_0110_3' : d['c_0101_9'], 'c_0110_2' : d['c_0101_0'], 'c_0110_5' : d['c_0101_1'], 'c_0110_4' : d['c_0101_10'], 'c_0110_7' : d['c_0101_10'], 'c_0110_6' : d['c_0101_10']})} 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_11, c_0011_12, c_0011_2, c_0011_3, c_0101_0, c_0101_1, c_0101_10, c_0101_12, c_0101_5, c_0101_9, c_1001_3, c_1001_5 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 12 Groebner basis: [ t - 5958459/1448384000*c_1001_5^11 + 674363/47488000*c_1001_5^10 - 182563243/1448384000*c_1001_5^9 + 17970251/47488000*c_1001_5^8 - 1015139357/724192000*c_1001_5^7 + 79576699/23744000*c_1001_5^6 - 4618634493/724192000*c_1001_5^5 + 220219751/23744000*c_1001_5^4 - 19695805611/1448384000*c_1001_5^3 + 752024127/47488000*c_1001_5^2 - 21470169851/1448384000*c_1001_5 + 276926807/47488000, c_0011_0 - 1, c_0011_11 + 33/7168*c_1001_5^11 + 29/7168*c_1001_5^10 + 869/7168*c_1001_5^9 + 745/7168*c_1001_5^8 + 3749/3584*c_1001_5^7 + 3057/3584*c_1001_5^6 + 9445/3584*c_1001_5^5 + 6313/3584*c_1001_5^4 + 29669/7168*c_1001_5^3 + 18769/7168*c_1001_5^2 + 9249/7168*c_1001_5 - 2283/7168, c_0011_12 - 11/35840*c_1001_5^11 + 7/5120*c_1001_5^10 - 187/35840*c_1001_5^9 + 179/5120*c_1001_5^8 + 57/17920*c_1001_5^7 + 731/2560*c_1001_5^6 + 7333/17920*c_1001_5^5 + 1499/2560*c_1001_5^4 + 30281/35840*c_1001_5^3 + 4403/5120*c_1001_5^2 + 62241/35840*c_1001_5 - 2937/5120, c_0011_2 + 27/35840*c_1001_5^11 - 23/35840*c_1001_5^10 + 599/35840*c_1001_5^9 - 671/35840*c_1001_5^8 + 1591/17920*c_1001_5^7 - 3419/17920*c_1001_5^6 - 5081/17920*c_1001_5^5 - 12871/17920*c_1001_5^4 - 40217/35840*c_1001_5^3 - 40387/35840*c_1001_5^2 - 81717/35840*c_1001_5 - 20067/35840, c_0011_3 + 1/448*c_1001_5^11 - 1/448*c_1001_5^10 + 103/1792*c_1001_5^9 - 103/1792*c_1001_5^8 + 213/448*c_1001_5^7 - 213/448*c_1001_5^6 + 941/896*c_1001_5^5 - 941/896*c_1001_5^4 + 25/14*c_1001_5^3 - 25/14*c_1001_5^2 + 983/1792*c_1001_5 - 983/1792, c_0101_0 - 3/4480*c_1001_5^11 - 3/4480*c_1001_5^10 - 137/8960*c_1001_5^9 - 137/8960*c_1001_5^8 - 51/560*c_1001_5^7 - 51/560*c_1001_5^6 + 573/4480*c_1001_5^5 + 573/4480*c_1001_5^4 + 2143/4480*c_1001_5^3 + 2143/4480*c_1001_5^2 + 8791/8960*c_1001_5 + 8791/8960, c_0101_1 - 1, c_0101_10 + 3/512*c_1001_5^10 + 77/512*c_1001_5^8 + 315/256*c_1001_5^6 + 649/256*c_1001_5^4 + 2087/512*c_1001_5^2 - 63/512, c_0101_12 - 297/35840*c_1001_5^11 - 37/35840*c_1001_5^10 - 7709/35840*c_1001_5^9 - 909/35840*c_1001_5^8 - 32341/17920*c_1001_5^7 - 3321/17920*c_1001_5^6 - 73749/17920*c_1001_5^5 - 2749/17920*c_1001_5^4 - 220093/35840*c_1001_5^3 + 4007/35840*c_1001_5^2 + 1207/35840*c_1001_5 + 8087/35840, c_0101_5 - 1/448*c_1001_5^11 - 1/448*c_1001_5^10 - 103/1792*c_1001_5^9 - 103/1792*c_1001_5^8 - 213/448*c_1001_5^7 - 213/448*c_1001_5^6 - 941/896*c_1001_5^5 - 941/896*c_1001_5^4 - 25/14*c_1001_5^3 - 25/14*c_1001_5^2 - 983/1792*c_1001_5 - 983/1792, c_0101_9 - 33/7168*c_1001_5^11 + 29/7168*c_1001_5^10 - 869/7168*c_1001_5^9 + 745/7168*c_1001_5^8 - 3749/3584*c_1001_5^7 + 3057/3584*c_1001_5^6 - 9445/3584*c_1001_5^5 + 6313/3584*c_1001_5^4 - 29669/7168*c_1001_5^3 + 18769/7168*c_1001_5^2 - 9249/7168*c_1001_5 - 2283/7168, c_1001_3 + 1/1792*c_1001_5^10 + 31/1792*c_1001_5^8 + 173/896*c_1001_5^6 + 783/896*c_1001_5^4 + 2725/1792*c_1001_5^2 - 701/1792, c_1001_5^12 + 26*c_1001_5^10 + 219*c_1001_5^8 + 508*c_1001_5^6 + 775*c_1001_5^4 + 10*c_1001_5^2 + 61 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 0.310 Total time: 0.520 seconds, Total memory usage: 32.09MB