Magma V2.19-8 Tue Aug 20 2013 23:58:25 on localhost [Seed = 3330321991] Type ? for help. Type -D to quit. Loading file "K13n1180__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation K13n1180 geometric_solution 12.11532358 oriented_manifold CS_known -0.0000000000000003 1 0 torus 0.000000000000 0.000000000000 13 1 2 3 2 0132 0132 0132 0213 0 0 0 0 0 0 0 0 -1 0 1 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 12 0 -12 0 11 -11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.980611825502 1.259077396841 0 4 6 5 0132 0132 0132 0132 0 0 0 0 0 0 0 0 1 0 0 -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 0 0 0 -12 0 1 11 0 0 0 0 -11 0 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.501964668179 0.234868494217 7 0 8 0 0132 0132 0132 0213 0 0 0 0 0 0 0 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 1 -1 -12 0 12 0 0 0 0 0 0 11 -11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.980611825502 1.259077396841 5 9 10 0 0132 0132 0132 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 -1 0 1 0 0 -12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.471948648501 0.595659037780 5 1 8 11 3201 0132 1302 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 -11 0 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.728962291440 0.952844344771 3 7 1 4 0132 1302 0132 2310 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 -11 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.602573547337 0.724649833763 9 11 7 1 3012 0132 2310 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 0 0 0 1 0 0 -1 11 0 0 -11 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.980368945099 0.749899215649 2 6 10 5 0132 3201 2310 2031 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 -1 1 0 12 0 -12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.380969566889 0.833066392899 4 12 12 2 2031 0132 0321 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 1 0 -1 0 0 12 -12 -11 0 0 11 0 -12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.652321221097 0.800364935521 11 3 10 6 3120 0132 0321 1230 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 1 0 -1 11 0 0 -11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.237445970771 1.774841985248 12 7 9 3 0321 3201 0321 0132 0 0 0 0 0 0 0 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 -12 0 0 12 1 -1 0 0 -12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.636022008612 0.733638358514 12 6 4 9 3201 0132 0132 3120 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 11 0 0 -11 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.722113506651 0.697714694233 10 8 8 11 0321 0132 0321 2310 0 0 0 0 0 0 0 0 -1 0 1 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 -1 0 1 12 0 -12 0 -1 12 0 -11 12 0 -12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.652321221097 0.800364935521 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_11' : d['c_1001_1'], 'c_1001_10' : d['c_0101_1'], 'c_1001_12' : d['c_1001_12'], 'c_1001_5' : d['c_0101_2'], 'c_1001_4' : d['c_0101_2'], 'c_1001_7' : negation(d['c_0101_6']), 'c_1001_6' : d['c_0011_3'], 'c_1001_1' : d['c_1001_1'], 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : d['c_0101_6'], 'c_1001_2' : d['c_1001_12'], 'c_1001_9' : d['c_1001_0'], 'c_1001_8' : d['c_0011_11'], 'c_1010_12' : d['c_0011_11'], 'c_1010_11' : d['c_0011_3'], 'c_1010_10' : d['c_0101_6'], '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_10'], '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_1100_9' : d['c_0101_1'], 'c_1100_8' : d['c_1001_12'], 'c_0011_12' : d['c_0011_12'], 'c_1100_5' : d['c_0011_0'], 'c_1100_4' : d['c_0101_10'], 'c_1100_7' : d['c_0011_10'], 'c_1100_6' : d['c_0011_0'], 'c_1100_1' : d['c_0011_0'], 'c_1100_0' : d['c_1001_0'], 'c_1100_3' : d['c_1001_0'], 'c_1100_2' : d['c_1001_12'], 's_3_11' : d['1'], 'c_1100_11' : d['c_0101_10'], 'c_1100_10' : d['c_1001_0'], 's_3_10' : d['1'], 'c_1010_7' : negation(d['c_0011_3']), 'c_1010_6' : d['c_1001_1'], 'c_1010_5' : negation(d['c_0011_10']), 'c_1010_4' : d['c_1001_1'], 'c_1010_3' : d['c_1001_0'], 'c_1010_2' : d['c_1001_0'], 'c_1010_1' : d['c_0101_2'], 'c_1010_0' : d['c_1001_12'], 'c_1010_9' : d['c_0101_6'], 'c_1010_8' : d['c_1001_12'], 's_3_1' : d['1'], 's_3_0' : negation(d['1']), 's_3_3' : d['1'], 's_3_2' : negation(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_11'], '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' : negation(d['c_0011_3']), 'c_0011_8' : negation(d['c_0011_12']), 'c_0011_5' : negation(d['c_0011_3']), 'c_0011_4' : d['c_0011_0'], 'c_0011_7' : d['c_0011_0'], 'c_0011_6' : negation(d['c_0011_11']), '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' : negation(d['c_0011_11']), 'c_0110_10' : negation(d['c_0011_12']), 'c_0110_12' : negation(d['c_0011_10']), 'c_0101_12' : negation(d['c_0101_10']), 'c_0011_11' : d['c_0011_11'], 'c_0101_7' : negation(d['c_0101_1']), 'c_0101_6' : d['c_0101_6'], 'c_0101_5' : d['c_0101_0'], 'c_0101_4' : d['c_0011_12'], 'c_0101_3' : negation(d['c_0011_12']), 'c_0101_2' : d['c_0101_2'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : negation(d['c_0101_10']), 'c_0101_8' : d['c_0101_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' : negation(d['c_0011_11']), 'c_0110_8' : d['c_0101_2'], 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : d['c_0101_1'], 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : negation(d['c_0101_1']), 'c_0110_5' : negation(d['c_0011_12']), 'c_0110_4' : d['c_0011_10'], 'c_0110_7' : d['c_0101_2'], 'c_0110_6' : 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_12, c_0011_3, c_0101_0, c_0101_1, c_0101_10, c_0101_2, c_0101_6, c_1001_0, c_1001_1, c_1001_12 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 12 Groebner basis: [ t + 1364766361/16313316807*c_1001_12^11 - 3058466398/16313316807*c_1001_12^10 - 98849762/319868957*c_1001_12^9 + 9323753449/16313316807*c_1001_12^8 + 19602061861/16313316807*c_1001_12^7 - 7097659588/5437772269*c_1001_12^6 - 14633289992/5437772269*c_1001_12^5 + 32427884039/16313316807*c_1001_12^4 + 67445462173/16313316807*c_1001_12^3 - 2558460880/959606871*c_1001_12^2 - 52569600800/16313316807*c_1001_12 + 14488415047/5437772269, c_0011_0 - 1, c_0011_10 + 2386/3911*c_1001_12^11 - 2540/3911*c_1001_12^10 - 10724/3911*c_1001_12^9 - 209/3911*c_1001_12^8 + 29464/3911*c_1001_12^7 + 20738/3911*c_1001_12^6 - 44519/3911*c_1001_12^5 - 34896/3911*c_1001_12^4 + 24577/3911*c_1001_12^3 + 28936/3911*c_1001_12^2 + 4793/3911*c_1001_12 - 22414/3911, c_0011_11 - 3404/3911*c_1001_12^11 + 5512/3911*c_1001_12^10 + 14175/3911*c_1001_12^9 - 7196/3911*c_1001_12^8 - 47513/3911*c_1001_12^7 - 14060/3911*c_1001_12^6 + 86281/3911*c_1001_12^5 + 40448/3911*c_1001_12^4 - 57670/3911*c_1001_12^3 - 53136/3911*c_1001_12^2 + 371/3911*c_1001_12 + 42284/3911, c_0011_12 - 1966/3911*c_1001_12^11 + 3496/3911*c_1001_12^10 + 7702/3911*c_1001_12^9 - 6863/3911*c_1001_12^8 - 26474/3911*c_1001_12^7 + 1402/3911*c_1001_12^6 + 56126/3911*c_1001_12^5 + 7910/3911*c_1001_12^4 - 51824/3911*c_1001_12^3 - 25698/3911*c_1001_12^2 + 12570/3911*c_1001_12 + 30690/3911, c_0011_3 + 4408/3911*c_1001_12^11 - 6430/3911*c_1001_12^10 - 17786/3911*c_1001_12^9 + 6754/3911*c_1001_12^8 + 55033/3911*c_1001_12^7 + 18377/3911*c_1001_12^6 - 97533/3911*c_1001_12^5 - 40668/3911*c_1001_12^4 + 69900/3911*c_1001_12^3 + 54805/3911*c_1001_12^2 - 4419/3911*c_1001_12 - 52522/3911, c_0101_0 + 167/3911*c_1001_12^11 - 1594/3911*c_1001_12^10 - 885/3911*c_1001_12^9 + 5606/3911*c_1001_12^8 + 9104/3911*c_1001_12^7 - 6282/3911*c_1001_12^6 - 23125/3911*c_1001_12^5 - 3262/3911*c_1001_12^4 + 20631/3911*c_1001_12^3 + 10916/3911*c_1001_12^2 - 6049/3911*c_1001_12 - 5388/3911, c_0101_1 - 167/3911*c_1001_12^11 + 1594/3911*c_1001_12^10 + 885/3911*c_1001_12^9 - 5606/3911*c_1001_12^8 - 9104/3911*c_1001_12^7 + 6282/3911*c_1001_12^6 + 23125/3911*c_1001_12^5 + 3262/3911*c_1001_12^4 - 20631/3911*c_1001_12^3 - 14827/3911*c_1001_12^2 + 6049/3911*c_1001_12 + 13210/3911, c_0101_10 - 2734/3911*c_1001_12^11 + 3871/3911*c_1001_12^10 + 12334/3911*c_1001_12^9 - 3206/3911*c_1001_12^8 - 38646/3911*c_1001_12^7 - 20645/3911*c_1001_12^6 + 62614/3911*c_1001_12^5 + 46752/3911*c_1001_12^4 - 31948/3911*c_1001_12^3 - 42011/3911*c_1001_12^2 - 11134/3911*c_1001_12 + 27178/3911, c_0101_2 - c_1001_12^2, c_0101_6 - 1398/3911*c_1001_12^11 + 2852/3911*c_1001_12^10 + 5254/3911*c_1001_12^9 - 5290/3911*c_1001_12^8 - 20568/3911*c_1001_12^7 - 503/3911*c_1001_12^6 + 41876/3911*c_1001_12^5 + 12834/3911*c_1001_12^4 - 31162/3911*c_1001_12^3 - 25081/3911*c_1001_12^2 + 3050/3911*c_1001_12 + 23184/3911, c_1001_0 - 547/3911*c_1001_12^11 + 1474/3911*c_1001_12^10 + 2688/3911*c_1001_12^9 - 3491/3911*c_1001_12^8 - 11623/3911*c_1001_12^7 - 899/3911*c_1001_12^6 + 23239/3911*c_1001_12^5 + 10544/3911*c_1001_12^4 - 14789/3911*c_1001_12^3 - 15708/3911*c_1001_12^2 - 3887/3911*c_1001_12 + 12613/3911, c_1001_1 - 167/3911*c_1001_12^11 + 1594/3911*c_1001_12^10 + 885/3911*c_1001_12^9 - 5606/3911*c_1001_12^8 - 9104/3911*c_1001_12^7 + 6282/3911*c_1001_12^6 + 23125/3911*c_1001_12^5 + 3262/3911*c_1001_12^4 - 20631/3911*c_1001_12^3 - 10916/3911*c_1001_12^2 + 6049/3911*c_1001_12 + 13210/3911, c_1001_12^12 - 3*c_1001_12^11 - 2*c_1001_12^10 + 8*c_1001_12^9 + 11*c_1001_12^8 - 15*c_1001_12^7 - 31*c_1001_12^6 + 23*c_1001_12^5 + 33*c_1001_12^4 - 9*c_1001_12^3 - 20*c_1001_12^2 - 12*c_1001_12 + 17 ], 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_12, c_0011_3, c_0101_0, c_0101_1, c_0101_10, c_0101_2, c_0101_6, c_1001_0, c_1001_1, c_1001_12 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 16 Groebner basis: [ t - 3087292978305812/46276801945*c_1001_12^15 + 27178272757024/46276801945*c_1001_12^14 + 8936466911508498/46276801945*c_1001_12^13 - 13802142679600949/92553603890*c_1001_12^12 - 29618046721013/221420105*c_1001_12^11 + 6170918246903528/46276801945*c_1001_12^10 + 122349782904762499/740428831120*c_1001_12^9 - 342056029852303/67311711920*c_1001_12^8 - 3944111459234793/33655855960*c_1001_12^7 - 32260773240591843/370214415560*c_1001_12^6 + 5530414957268191/370214415560*c_1001_12^5 + 16385170228793133/370214415560*c_1001_12^4 + 7164262823158071/370214415560*c_1001_12^3 - 238866756339593/92553603890*c_1001_12^2 - 4185326593285087/740428831120*c_1001_12 - 1286615142509581/740428831120, c_0011_0 - 1, c_0011_10 + 13091730632/44284021*c_1001_12^15 + 6232254656/44284021*c_1001_12^14 - 35520645172/44284021*c_1001_12^13 + 14444560393/44284021*c_1001_12^12 + 35913440818/44284021*c_1001_12^11 - 15980580544/44284021*c_1001_12^10 - 302359811215/354272168*c_1001_12^9 - 95868895943/354272168*c_1001_12^8 + 67506518599/177136084*c_1001_12^7 + 78520142843/177136084*c_1001_12^6 + 12963095301/177136084*c_1001_12^5 - 24000172213/177136084*c_1001_12^4 - 15932804743/177136084*c_1001_12^3 - 311748968/44284021*c_1001_12^2 + 5767212739/354272168*c_1001_12 + 2051237729/354272168, c_0011_11 - 2662730840/44284021*c_1001_12^15 - 1837871168/44284021*c_1001_12^14 + 7751624220/44284021*c_1001_12^13 - 1145360731/44284021*c_1001_12^12 - 9929066262/44284021*c_1001_12^11 + 2917598544/44284021*c_1001_12^10 + 78927523437/354272168*c_1001_12^9 + 26275082965/354272168*c_1001_12^8 - 19768073869/177136084*c_1001_12^7 - 20947858257/177136084*c_1001_12^6 - 3115826247/177136084*c_1001_12^5 + 7594369567/177136084*c_1001_12^4 + 5199446913/177136084*c_1001_12^3 + 99640844/44284021*c_1001_12^2 - 2145260161/354272168*c_1001_12 - 832105411/354272168, c_0011_12 - 4933660092/44284021*c_1001_12^15 - 4075044880/44284021*c_1001_12^14 + 13152122406/44284021*c_1001_12^13 - 2142787631/88568042*c_1001_12^12 - 16808299461/44284021*c_1001_12^11 + 3547886042/44284021*c_1001_12^10 + 255518765321/708544336*c_1001_12^9 + 135393893141/708544336*c_1001_12^8 - 39898293457/354272168*c_1001_12^7 - 76900492433/354272168*c_1001_12^6 - 26051128367/354272168*c_1001_12^5 + 16371081071/354272168*c_1001_12^4 + 16256488817/354272168*c_1001_12^3 + 979076695/88568042*c_1001_12^2 - 4210263525/708544336*c_1001_12 - 2595205507/708544336, c_0011_3 + 10360713740/44284021*c_1001_12^15 + 1634921936/44284021*c_1001_12^14 - 28848699438/44284021*c_1001_12^13 + 40166366275/88568042*c_1001_12^12 + 21917710465/44284021*c_1001_12^11 - 19089291138/44284021*c_1001_12^10 - 378736103317/708544336*c_1001_12^9 - 50470273649/708544336*c_1001_12^8 + 112267918957/354272168*c_1001_12^7 + 103424981981/354272168*c_1001_12^6 - 212423861/354272168*c_1001_12^5 - 40361498723/354272168*c_1001_12^4 - 20213263141/354272168*c_1001_12^3 + 14679507/88568042*c_1001_12^2 + 9603004497/708544336*c_1001_12 + 3117399047/708544336, c_0101_0 - 169242632/44284021*c_1001_12^15 - 992986208/44284021*c_1001_12^14 - 533034892/44284021*c_1001_12^13 + 1752005183/44284021*c_1001_12^12 - 420011494/44284021*c_1001_12^11 - 2530349876/44284021*c_1001_12^10 + 3575418439/354272168*c_1001_12^9 + 21510003179/354272168*c_1001_12^8 + 6617205401/177136084*c_1001_12^7 - 624102011/177136084*c_1001_12^6 - 4390073205/177136084*c_1001_12^5 - 2634553779/177136084*c_1001_12^4 + 298618071/177136084*c_1001_12^3 + 84235988/44284021*c_1001_12^2 + 354211509/354272168*c_1001_12 - 97435509/354272168, c_0101_1 - 169242632/44284021*c_1001_12^15 - 992986208/44284021*c_1001_12^14 - 533034892/44284021*c_1001_12^13 + 1752005183/44284021*c_1001_12^12 - 420011494/44284021*c_1001_12^11 - 2530349876/44284021*c_1001_12^10 + 3575418439/354272168*c_1001_12^9 + 21510003179/354272168*c_1001_12^8 + 6617205401/177136084*c_1001_12^7 - 624102011/177136084*c_1001_12^6 - 4390073205/177136084*c_1001_12^5 - 2634553779/177136084*c_1001_12^4 + 298618071/177136084*c_1001_12^3 + 84235988/44284021*c_1001_12^2 + 354211509/354272168*c_1001_12 + 256836659/354272168, c_0101_10 + 1213510652/44284021*c_1001_12^15 + 875037232/44284021*c_1001_12^14 - 3549919142/44284021*c_1001_12^13 - 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