Magma V2.19-8 Tue Aug 20 2013 23:53:45 on localhost [Seed = 2034176758] Type ? for help. Type -D to quit. Loading file "K12n419__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation K12n419 geometric_solution 11.86452221 oriented_manifold CS_known 0.0000000000000002 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 -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 0.595234276563 0.525034821412 0 5 7 6 0132 0132 0132 0132 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 10 0 -10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.911594920654 0.970099078646 8 0 10 9 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 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 0.359709602979 0.395045644895 5 11 9 0 0132 0132 3012 0132 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 -1 0 1 0 1 -1 0 0 0 11 -11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.372381193264 0.722564241519 7 12 0 11 0132 0132 0132 3012 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1.292527510137 0.487205089378 3 1 12 10 0132 0132 3201 1230 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 -10 0 10 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 0.371503776179 1.281377140384 12 9 1 10 3201 2031 0132 3201 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 10 -10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.346087450994 0.971219426813 4 8 9 1 0132 0321 2031 0132 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 0 0 0 0 0.797350025788 0.651744006645 2 11 12 7 0132 1023 3120 0321 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 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 0.789460969166 0.538807046023 6 3 2 7 1302 1230 0132 1302 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 1 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 0 0 -0.043765329264 1.541393646356 5 6 11 2 3012 2310 0132 0132 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 0 0 -10 0 11 -1 1 0 0 -1 0 10 -10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.652803578498 0.980930747698 8 3 4 10 1023 0132 1230 0132 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 0 0 0 11 0 0 -11 1 -11 0 10 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.022669085103 1.369210326344 5 4 8 6 2310 0132 3120 2310 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0.320309612666 0.668976706159 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_11' : d['c_1001_0'], 'c_1001_10' : negation(d['c_0011_9']), 'c_1001_12' : negation(d['c_0101_11']), 'c_1001_5' : negation(d['c_0101_12']), 'c_1001_4' : negation(d['c_0110_6']), 'c_1001_7' : negation(d['c_0101_12']), 'c_1001_6' : negation(d['c_0101_12']), 'c_1001_1' : d['c_0101_10'], 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : negation(d['c_0011_9']), 'c_1001_2' : negation(d['c_0110_6']), 'c_1001_9' : d['c_1001_0'], 'c_1001_8' : d['c_0101_11'], 'c_1010_12' : negation(d['c_0110_6']), 'c_1010_11' : negation(d['c_0011_9']), 'c_1010_10' : negation(d['c_0110_6']), 's_0_10' : d['1'], 's_3_10' : 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' : negation(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' : 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' : negation(d['1']), 's_0_3' : d['1'], 's_0_0' : d['1'], 's_0_1' : d['1'], 'c_0011_11' : d['c_0011_0'], 'c_1100_8' : negation(d['c_0101_12']), 'c_0011_12' : d['c_0011_12'], 'c_1100_5' : negation(d['c_0011_12']), 'c_1100_4' : negation(d['c_1001_0']), 'c_1100_7' : negation(d['c_0011_10']), 'c_1100_6' : negation(d['c_0011_10']), 'c_1100_1' : negation(d['c_0011_10']), 'c_1100_0' : negation(d['c_1001_0']), 'c_1100_3' : negation(d['c_1001_0']), 'c_1100_2' : d['c_0101_7'], 's_3_11' : d['1'], 'c_1100_11' : d['c_0101_7'], 'c_1100_10' : d['c_0101_7'], 's_0_11' : negation(d['1']), 'c_1010_7' : d['c_0101_10'], 'c_1010_6' : d['c_0011_9'], 'c_1010_5' : d['c_0101_10'], 'c_1010_4' : negation(d['c_0101_11']), 'c_1010_3' : d['c_1001_0'], 'c_1010_2' : d['c_1001_0'], 'c_1010_1' : negation(d['c_0101_12']), 'c_1010_0' : negation(d['c_0110_6']), 'c_1010_9' : d['c_0011_10'], 'c_1010_8' : d['c_0101_10'], 's_3_1' : d['1'], 's_3_0' : d['1'], 's_3_3' : negation(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_0011_6'], 's_1_7' : d['1'], 's_1_6' : d['1'], 's_1_5' : d['1'], 's_1_4' : d['1'], 's_1_3' : negation(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' : negation(d['1']), 'c_0011_9' : d['c_0011_9'], 'c_0011_8' : d['c_0011_0'], 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : negation(d['c_0011_12']), 'c_0011_7' : d['c_0011_12'], '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' : negation(d['c_0011_0']), 'c_0011_2' : negation(d['c_0011_0']), 'c_0110_11' : d['c_0101_10'], 'c_0110_10' : negation(d['c_0011_12']), 'c_0110_12' : negation(d['c_0101_0']), 'c_0110_0' : d['c_0101_1'], 'c_0101_7' : d['c_0101_7'], 'c_0101_6' : d['c_0101_0'], 'c_0101_5' : d['c_0101_0'], 'c_0101_4' : d['c_0101_1'], 'c_0101_3' : d['c_0011_10'], 'c_0101_2' : negation(d['c_0011_12']), 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : negation(d['c_0011_6']), 'c_0101_8' : negation(d['c_0011_6']), 'c_0011_10' : d['c_0011_10'], 's_1_12' : d['1'], 's_1_11' : negation(d['1']), 's_1_10' : d['1'], 'c_0110_9' : d['c_0101_12'], 'c_0110_8' : negation(d['c_0011_12']), 'c_0110_1' : d['c_0101_0'], 'c_1100_9' : d['c_0101_7'], 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : negation(d['c_0011_6']), 'c_0110_5' : d['c_0011_10'], 'c_0110_4' : d['c_0101_7'], 'c_0110_7' : d['c_0101_1'], 'c_0110_6' : d['c_0110_6'], '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_12, c_0011_6, c_0011_9, c_0101_0, c_0101_1, c_0101_10, c_0101_11, c_0101_12, c_0101_7, c_0110_6, c_1001_0 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 19 Groebner basis: [ t - 3521251608509896456393374237447803417236814518895/81030479621711045\ 911345937308649838315062502048*c_1001_0^18 - 14489126200192030047424076605718234282758813945225/8103047962171104\ 5911345937308649838315062502048*c_1001_0^17 - 12399937954603596190578582107234855277719672233237/8103047962171104\ 5911345937308649838315062502048*c_1001_0^16 + 2173963247901195554781297079811943690738560117639/81030479621711045\ 911345937308649838315062502048*c_1001_0^15 - 23690647036760249233249922468365413192958712539295/8103047962171104\ 5911345937308649838315062502048*c_1001_0^14 - 58427357522860819142767072633002140385566892100/8168395123156355434\ 6114856157913143462764619*c_1001_0^13 - 424262927384721694041498008498831641304988627277/506440497635694036\ 9459121081790614894691406378*c_1001_0^12 - 4778865921737835470607938897210450250221737706849/81030479621711045\ 911345937308649838315062502048*c_1001_0^11 - 55262914109885701362437282974842294829191400285357/8103047962171104\ 5911345937308649838315062502048*c_1001_0^10 + 15018309925976729687654719656865627923654388592063/8103047962171104\ 5911345937308649838315062502048*c_1001_0^9 - 4447119578430041238620349058363037931270147919303/20257619905427761\ 477836484327162459578765625512*c_1001_0^8 - 10967557124638648038670670728336783858025378617411/8103047962171104\ 5911345937308649838315062502048*c_1001_0^7 + 21845848648924446067057759031051505423995374902883/8103047962171104\ 5911345937308649838315062502048*c_1001_0^6 - 14152063597154127169100316064129286926288428491911/8103047962171104\ 5911345937308649838315062502048*c_1001_0^5 + 231088861583633434602010804805817119615414665921/253220248817847018\ 4729560540895307447345703189*c_1001_0^4 + 2326000483296321612942006827143264441041883881401/81030479621711045\ 911345937308649838315062502048*c_1001_0^3 - 5223299204222645830628177902804393030043627515577/81030479621711045\ 911345937308649838315062502048*c_1001_0^2 + 1119026805854614195148380454024279470884779659841/40515239810855522\ 955672968654324919157531251024*c_1001_0 - 37886844279931433872534336223304701098754600503/6752539968475920492\ 612161442387486526255208504, c_0011_0 - 1, c_0011_10 - 4035379925551759337243504260166654443/153579114779361514954\ 362734097514246*c_1001_0^18 - 2373954425366521069356214526264698543\ /76789557389680757477181367048757123*c_1001_0^17 + 1651714443006909119824940629662819714/76789557389680757477181367048\ 757123*c_1001_0^16 - 962318738423323888276948433821794124/767895573\ 89680757477181367048757123*c_1001_0^15 - 10777991171749779496675296230774675599/7678955738968075747718136704\ 8757123*c_1001_0^14 + 1363600049579034312286697692783660357/1535791\ 14779361514954362734097514246*c_1001_0^13 + 4821303938581610619066749106073277172/76789557389680757477181367048\ 757123*c_1001_0^12 - 27726810414853530285515788161873040071/1535791\ 14779361514954362734097514246*c_1001_0^11 + 9644542802348707748167046887354512998/76789557389680757477181367048\ 757123*c_1001_0^10 - 3781743370524670656540873761311333673/76789557\ 389680757477181367048757123*c_1001_0^9 - 5540498982777541903306205535369021129/15357911477936151495436273409\ 7514246*c_1001_0^8 + 16835962796961798463531704747938798949/1535791\ 14779361514954362734097514246*c_1001_0^7 - 6005283849446107304444300518257167404/76789557389680757477181367048\ 757123*c_1001_0^6 + 3782742459780959839599657279404418458/767895573\ 89680757477181367048757123*c_1001_0^5 - 11946000337040777552551800228064441/1535791147793615149543627340975\ 14246*c_1001_0^4 - 2825823787921013150248841283436000037/1535791147\ 79361514954362734097514246*c_1001_0^3 + 973764567368314501724486663961588169/767895573896807574771813670487\ 57123*c_1001_0^2 - 90321458149911371820870872390264123/139617377072\ 14683177669339463410386*c_1001_0 + 196152064280530167940136842677916720/767895573896807574771813670487\ 57123, c_0011_12 - 3097444888637659782959974276787599985/153579114779361514954\ 362734097514246*c_1001_0^18 - 2047039650679128070639122169745247145\ /76789557389680757477181367048757123*c_1001_0^17 + 724731932839815788331307134214477634/767895573896807574771813670487\ 57123*c_1001_0^16 - 1095874438469021098011128728455991133/767895573\ 89680757477181367048757123*c_1001_0^15 - 8628823185521612041325212575455158182/76789557389680757477181367048\ 757123*c_1001_0^14 - 2202708362207005267562182531769868893/15357911\ 4779361514954362734097514246*c_1001_0^13 + 2026115020383829418796587960873425290/76789557389680757477181367048\ 757123*c_1001_0^12 - 22640997341438056677100317351655398005/1535791\ 14779361514954362734097514246*c_1001_0^11 + 5161313218949653063877700259197546838/76789557389680757477181367048\ 757123*c_1001_0^10 - 4420255439224323902872105195528879156/76789557\ 389680757477181367048757123*c_1001_0^9 - 5567373580774193501467067733901540633/15357911477936151495436273409\ 7514246*c_1001_0^8 + 10067635315213157283209987166459196343/1535791\ 14779361514954362734097514246*c_1001_0^7 - 5086707647197375557132430990624288573/76789557389680757477181367048\ 757123*c_1001_0^6 + 2644140138091167243715196670998511996/767895573\ 89680757477181367048757123*c_1001_0^5 - 733470521108954988944125220054892399/153579114779361514954362734097\ 514246*c_1001_0^4 - 1944442862240322082853204149542631581/153579114\ 779361514954362734097514246*c_1001_0^3 + 757005314091317385115592536262614846/767895573896807574771813670487\ 57123*c_1001_0^2 - 75952189802583172299796369613902843/139617377072\ 14683177669339463410386*c_1001_0 + 171531442431586417814329224893713458/767895573896807574771813670487\ 57123, c_0011_6 - 3867914083087628668940382120469681347/1535791147793615149543\ 62734097514246*c_1001_0^18 - 2500799306879840512345529201680124277/\ 76789557389680757477181367048757123*c_1001_0^17 + 1060290371963472355316386747530973988/76789557389680757477181367048\ 757123*c_1001_0^16 - 1054845397857363536896164972588512974/76789557\ 389680757477181367048757123*c_1001_0^15 - 10265203397119992975736112760661330005/7678955738968075747718136704\ 8757123*c_1001_0^14 - 1457271825634218631411547641572682529/1535791\ 14779361514954362734097514246*c_1001_0^13 + 3245331887850315298411292317833734901/76789557389680757477181367048\ 757123*c_1001_0^12 - 25524173968939040210287876666881976849/1535791\ 14779361514954362734097514246*c_1001_0^11 + 8161937612408711108813691962418933850/76789557389680757477181367048\ 757123*c_1001_0^10 - 4633867781183187080339392204124061451/76789557\ 389680757477181367048757123*c_1001_0^9 - 4331421252586129166456880473478736245/15357911477936151495436273409\ 7514246*c_1001_0^8 + 14544332959488788294504295101158164323/1535791\ 14779361514954362734097514246*c_1001_0^7 - 5484232465076433418837201595943267002/76789557389680757477181367048\ 757123*c_1001_0^6 + 3582820852159186257344661765192688395/767895573\ 89680757477181367048757123*c_1001_0^5 - 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