Magma V2.19-8 Fri Sep 13 2013 01:04:04 on localhost [Seed = 2616939816] Type ? for help. Type -D to quit. Loading file "m202__sl3_c3.magma" ==TRIANGULATION=BEGINS== % Triangulation m202 geometric_solution 4.05976643 oriented_manifold CS_known 0.0000000000000002 2 0 torus 0.000000000000 0.000000000000 torus 0.000000000000 0.000000000000 4 1 1 2 1 0132 1230 0132 2031 0 0 1 0 0 1 0 -1 -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 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 0.500000000000 0.866025403784 0 0 0 3 0132 1302 3012 0132 0 0 0 1 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 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 0.500000000000 0.866025403784 3 3 3 0 0213 0321 2310 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 1 -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 0.500000000000 0.866025403784 2 2 1 2 0213 3201 0132 0321 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 -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 0.500000000000 0.866025403784 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1020_2' : d['c_1002_0'], 'c_1020_3' : d['c_1002_0'], 'c_1020_0' : d['c_0012_1'], 'c_1020_1' : d['c_0021_3'] * d['u'] ** 1, 'c_0201_0' : d['c_0021_2'], 'c_0201_1' : d['c_0012_0'], 'c_0201_2' : d['c_0021_3'] * d['u'] ** 1, 'c_0201_3' : d['c_0021_2'], 'c_2100_0' : d['c_0021_3'] * d['u'] ** 1, 'c_2100_1' : d['c_1002_0'], 'c_2100_2' : d['c_0021_3'], 'c_2100_3' : d['c_1002_0'], 'c_2010_2' : d['c_1002_2'], 'c_2010_3' : d['c_1002_2'], 'c_2010_0' : d['c_0012_0'], 'c_2010_1' : d['c_0012_3'] * d['u'] ** 2, 'c_0102_0' : d['c_0012_2'], 'c_0102_1' : d['c_0012_1'], 'c_0102_2' : d['c_0012_3'] * d['u'] ** 2, 'c_0102_3' : d['c_0012_2'], 'c_1101_0' : d['c_1101_0'], 'c_1101_1' : d['c_1011_0'], 'c_1101_2' : d['c_1011_3'], 'c_1101_3' : d['c_1101_3'], 'c_1200_2' : d['c_0012_3'], 'c_1200_3' : d['c_1002_2'], 'c_1200_0' : d['c_0012_3'] * d['u'] ** 2, 'c_1200_1' : d['c_1002_2'], 'c_1110_2' : d['c_1101_0'] * d['u'] ** 2, 'c_1110_3' : negation(d['c_1011_2']), 'c_1110_0' : negation(d['c_1011_1']), 'c_1110_1' : d['c_1101_3'], 'c_0120_0' : d['c_0012_1'], 'c_0120_1' : d['c_0012_2'], 'c_0120_2' : d['c_0012_2'] * d['u'] ** 2, 'c_0120_3' : d['c_0021_2'], 'c_2001_0' : d['c_1002_2'], 'c_2001_1' : d['c_0012_0'], 'c_2001_2' : d['c_1002_0'], 'c_2001_3' : d['c_0012_3'] * d['u'] ** 2, 'c_0012_2' : d['c_0012_2'], 'c_0012_3' : d['c_0012_3'], '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']), 'c_0111_2' : d['c_0111_2'], 'c_0111_3' : negation(d['c_0111_2']) * d['u'] ** 1, 'c_0210_2' : d['c_0021_2'] * d['u'] ** 1, 'c_0210_3' : d['c_0012_2'], 'c_0210_0' : d['c_0012_0'], 'c_0210_1' : d['c_0021_2'], 'c_1002_2' : d['c_1002_2'], 'c_1002_3' : d['c_0021_3'] * d['u'] ** 1, 'c_1002_0' : d['c_1002_0'], 'c_1002_1' : d['c_0012_1'], 'c_1011_2' : d['c_1011_2'], 'c_1011_3' : d['c_1011_3'], '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_0021_2'], 'c_0021_3' : d['c_0021_3']}), 'non_trivial_generalized_obstruction_class' : True} PY=EVAL=SECTION=ENDS=HERE PRIMARY_DECOMPOSITION_TIME: 3.840 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_0012_2, c_0012_3, c_0021_2, c_0021_3, c_0111_0, c_0111_2, c_1002_0, c_1002_2, c_1011_0, c_1011_1, c_1011_2, c_1011_3, c_1101_0, c_1101_3, u Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 8 Groebner basis: [ t + 10067597380167911/14816080438*c_1101_3^3*u + 2160257887059209/29632160876*c_1101_3^3 - 37117222588067799/14816080438*c_1101_3^2*u + 13286095675755192/7408040219*c_1101_3^2 - 65025359628846501/7408040219*c_1101_3*u + 4106467819622851/14816080438*c_1101_3 - 47532968364104525/14816080438*u - 111292222160489311/29632160876, c_0012_0 - 1, c_0012_1 - 1, c_0012_2 - 1, c_0012_3 + 54587/621011*c_1101_3^3*u + 7220/621011*c_1101_3^3 - 502307/1863033*c_1101_3^2*u + 352133/1863033*c_1101_3^2 - 2572427/1863033*c_1101_3*u + 22007/1863033*c_1101_3 + 132878/1863033*u - 67217/1863033, c_0021_2 - 39203/621011*c_1101_3^3*u + 45680/621011*c_1101_3^3 - 26619/621011*c_1101_3^2*u - 367759/621011*c_1101_3^2 + 259918/621011*c_1101_3*u - 1176053/621011*c_1101_3 - 34743/621011*u - 309037/621011, c_0021_3 - 1687/621011*c_1101_3^3*u + 30296/621011*c_1101_3^3 - 248837/1863033*c_1101_3^2*u - 521113/1863033*c_1101_3^2 - 933725/1863033*c_1101_3*u - 1735486/1863033*c_1101_3 + 735827/1863033*u + 907273/1863033, c_0111_0 - 1, c_0111_2 - 140156/1863033*c_1101_3^3*u - 25441/1863033*c_1101_3^3 + 926099/1863033*c_1101_3^2*u - 267575/1863033*c_1101_3^2 + 187098/621011*c_1101_3*u + 235635/621011*c_1101_3 + 125039/1863033*u + 118462/1863033, c_1002_0 - 9379/621011*c_1101_3^3*u + 3846/621011*c_1101_3^3 + 42245/1863033*c_1101_3^2*u - 145541/1863033*c_1101_3^2 + 19024/39639*c_1101_3*u + 17590/1863033*c_1101_3 - 210014/1863033*u - 458596/1863033, c_1002_2 - 9379/621011*c_1101_3^3*u + 3846/621011*c_1101_3^3 + 42245/1863033*c_1101_3^2*u - 145541/1863033*c_1101_3^2 + 19024/39639*c_1101_3*u + 17590/1863033*c_1101_3 - 210014/1863033*u - 458596/1863033, c_1011_0 - 31983/621011*c_1101_3^3*u - 1687/621011*c_1101_3^3 + 272276/1863033*c_1101_3^2*u - 248837/1863033*c_1101_3^2 + 801761/1863033*c_1101_3*u + 929308/1863033*c_1101_3 - 171446/1863033*u - 1127206/1863033, c_1011_1 - 31983/621011*c_1101_3^3*u - 1687/621011*c_1101_3^3 + 272276/1863033*c_1101_3^2*u - 248837/1863033*c_1101_3^2 + 801761/1863033*c_1101_3*u + 929308/1863033*c_1101_3 - 171446/1863033*u + 735827/1863033, c_1011_2 + 9379/621011*c_1101_3^3*u - 3846/621011*c_1101_3^3 - 42245/1863033*c_1101_3^2*u + 145541/1863033*c_1101_3^2 - 19024/39639*c_1101_3*u - 17590/1863033*c_1101_3 + 210014/1863033*u + 458596/1863033, c_1011_3 + 7220/621011*c_1101_3^3*u - 47367/621011*c_1101_3^3 + 352133/1863033*c_1101_3^2*u + 854440/1863033*c_1101_3^2 + 22007/1863033*c_1101_3*u + 731401/1863033*c_1101_3 - 67217/1863033*u - 200095/1863033, c_1101_0 - 22604/621011*c_1101_3^3*u - 5533/621011*c_1101_3^3 + 76677/621011*c_1101_3^2*u - 34432/621011*c_1101_3^2 - 30789/621011*c_1101_3*u + 303906/621011*c_1101_3 + 12856/621011*u - 222870/621011, c_1101_3^4 - 258/79*c_1101_3^3*u - 544/79*c_1101_3^3 - 127/79*c_1101_3^2*u - 1029/79*c_1101_3^2 + 380/79*c_1101_3*u + 266/79*c_1101_3 - 125/79*u - 48/79, u^2 + u + 1 ], Ideal of Polynomial ring of rank 18 over Rational Field Order: Lexicographical Variables: t, c_0012_0, c_0012_1, c_0012_2, c_0012_3, c_0021_2, c_0021_3, c_0111_0, c_0111_2, c_1002_0, c_1002_2, c_1011_0, c_1011_1, c_1011_2, c_1011_3, c_1101_0, c_1101_3, u Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 22 Groebner basis: [ t + 53713071849134955590790565/491164555728582798633974*c_1101_3^10*u - 1328995364627250538636996225/982329111457165597267948*c_1101_3^10 + 4060657432350547912219499471/4420481001557245187705766*c_1101_3^9*u + 30427383686466698358698012039/4420481001557245187705766*c_1101_3^\ 9 + 23690456150227871577422245711/8840962003114490375411532*c_1101_\ 3^8*u - 39637416617216344221111637040/2210240500778622593852883*c_1\ 101_3^8 - 56294895361244407111149253859/3683734167964370989754805*c\ _1101_3^7*u + 2390505235913150870247739301/70389824865561229103595*\ c_1101_3^7 + 654571453065603070264368013799/14734936671857483959019\ 220*c_1101_3^6*u - 427851924404339321933994083926/11051202503893112\ 969264415*c_1101_3^6 - 3372820138295470213851653613763/442048100155\ 72451877057660*c_1101_3^5*u + 105345311090654473823957568943/442048\ 1001557245187705766*c_1101_3^5 + 3616570741204582175102363192663/44\ 204810015572451877057660*c_1101_3^4*u - 123469002500959257401415733319/44204810015572451877057660*c_1101_3^\ 4 - 15353060890496931054923116717/283364166766490076134985*c_1101_3\ ^3*u - 1752813386766034175005712753/283364166766490076134985*c_1101\ _3^3 + 347430144473971414994783799559/14734936671857483959019220*c_\ 1101_3^2*u - 61896931614267296717824108747/147349366718574839590192\ 20*c_1101_3^2 - 25436132771926352841848214205/294698733437149679180\ 3844*c_1101_3*u + 66751508117787200581704513539/1473493667185748395\ 9019220*c_1101_3 + 6459041541400344667896099803/3683734167964370989\ 754805*u - 3426116937039848637237391718/3683734167964370989754805, c_0012_0 - 1, c_0012_1 - 1, c_0012_2 - 1, c_0012_3 - 2626618802767572371600/4692654991037415273573*c_1101_3^10*u - 2592187018471460948125/1564218330345805091191*c_1101_3^10 + 58218176674037925685945/14077964973112245820719*c_1101_3^9*u + 103147002845032471099505/14077964973112245820719*c_1101_3^9 - 99299430114712332902135/14077964973112245820719*c_1101_3^8*u - 285656844396821903492935/14077964973112245820719*c_1101_3^8 + 122941511684905177888589/14077964973112245820719*c_1101_3^7*u + 592693716460829090770456/14077964973112245820719*c_1101_3^7 + 30688179248224306507565/14077964973112245820719*c_1101_3^6*u - 810801416161189644385325/14077964973112245820719*c_1101_3^6 - 27886921119174634188840/1564218330345805091191*c_1101_3^5*u + 266012375185185420430487/4692654991037415273573*c_1101_3^5 + 85691562126445738776878/4692654991037415273573*c_1101_3^4*u - 201861573217908717811352/4692654991037415273573*c_1101_3^4 - 909160299894529658581/360973460849031944121*c_1101_3^3*u + 9730797651462134237638/360973460849031944121*c_1101_3^3 - 15169686096861569426083/1564218330345805091191*c_1101_3^2*u - 38962526493725200908141/1564218330345805091191*c_1101_3^2 + 10419289545686551779733/1564218330345805091191*c_1101_3*u + 16138984886551737844651/1564218330345805091191*c_1101_3 - 3012417378597237763702/1564218330345805091191*u - 1322561889426994045532/1564218330345805091191, c_0021_2 - 15507686651946916417625/14077964973112245820719*c_1101_3^10*\ u - 16796357997668243797900/14077964973112245820719*c_1101_3^10 + 21934642368258768883070/4692654991037415273573*c_1101_3^9*u + 5690893018710765334380/1564218330345805091191*c_1101_3^9 - 139561632921365433587420/14077964973112245820719*c_1101_3^8*u - 169489485157078965454495/14077964973112245820719*c_1101_3^8 + 26756365379647668382508/1564218330345805091191*c_1101_3^7*u + 115949415752141681444893/4692654991037415273573*c_1101_3^7 - 189721515508665499231910/14077964973112245820719*c_1101_3^6*u - 471551491310619260480179/14077964973112245820719*c_1101_3^6 + 25818817959011589060905/4692654991037415273573*c_1101_3^5*u + 141711302876504989902064/4692654991037415273573*c_1101_3^5 - 10408062216829846097857/4692654991037415273573*c_1101_3^4*u - 22647434205947134108808/1564218330345805091191*c_1101_3^4 + 1710455502748714454867/360973460849031944121*c_1101_3^3*u + 333314548651578827971/360973460849031944121*c_1101_3^3 - 51034873269016753909183/4692654991037415273573*c_1101_3^2*u - 25962948824333522538560/4692654991037415273573*c_1101_3^2 - 404522496918408288077/1564218330345805091191*c_1101_3*u - 3792125618568286682971/1564218330345805091191*c_1101_3 + 1516008123489282702775/1564218330345805091191*u + 2487276383721662422962/1564218330345805091191, c_0021_3 - 19509050425411478933675/14077964973112245820719*c_1101_3^10*\ u - 8103526363183889540350/14077964973112245820719*c_1101_3^10 + 65999310349074677364485/14077964973112245820719*c_1101_3^9*u + 5975126283747513963010/14077964973112245820719*c_1101_3^9 - 20105933853132101871575/1564218330345805091191*c_1101_3^8*u - 25559966240136252523780/4692654991037415273573*c_1101_3^8 + 363524686193146907860312/14077964973112245820719*c_1101_3^7*u + 187325062313129931301442/14077964973112245820719*c_1101_3^7 - 452203614512809964246947/14077964973112245820719*c_1101_3^6*u - 338619388683746240965121/14077964973112245820719*c_1101_3^6 + 135772196916699049080262/4692654991037415273573*c_1101_3^5*u + 40751336348069938278982/1564218330345805091191*c_1101_3^5 - 87262048230667857634324/4692654991037415273573*c_1101_3^4*u - 19398838123710359230498/1564218330345805091191*c_1101_3^4 + 965077855401869614762/120324486949677314707*c_1101_3^3*u - 509725527243809368692/120324486949677314707*c_1101_3^3 - 51848506232201395892488/4692654991037415273573*c_1101_3^2*u + 7945175374336848002020/4692654991037415273573*c_1101_3^2 - 2507600701741906674639/1564218330345805091191*c_1101_3*u - 6782933128788598671086/1564218330345805091191*c_1101_3 + 3877424825765094389723/1564218330345805091191*u + 3841001365990643617003/1564218330345805091191, c_0111_0 - 1, c_0111_2 - 8382839404859753278525/14077964973112245820719*c_1101_3^10*u + 11866215904320400328725/14077964973112245820719*c_1101_3^10 + 7646949887224608209645/14077964973112245820719*c_1101_3^9*u - 64920865705334911242365/14077964973112245820719*c_1101_3^9 - 9343705135427233828150/1564218330345805091191*c_1101_3^8*u + 39210451514408121578110/4692654991037415273573*c_1101_3^8 + 24866459384498870625961/1564218330345805091191*c_1101_3^7*u - 66403838162337263092546/4692654991037415273573*c_1101_3^7 - 423798672501231283620080/14077964973112245820719*c_1101_3^6*u + 132738769334844523910507/14077964973112245820719*c_1101_3^6 + 522598865816549089062337/14077964973112245820719*c_1101_3^5*u - 18158621686934563468732/14077964973112245820719*c_1101_3^5 - 120758414195280616376177/4692654991037415273573*c_1101_3^4*u + 3771573905858966835697/4692654991037415273573*c_1101_3^4 + 2225450244316558763641/360973460849031944121*c_1101_3^3*u - 2080868874752832701129/360973460849031944121*c_1101_3^3 - 16231053828524628532217/4692654991037415273573*c_1101_3^2*u + 42201099566950813728977/4692654991037415273573*c_1101_3^2 - 9323116570850274693490/4692654991037415273573*c_1101_3*u - 14608424616117741580100/4692654991037415273573*c_1101_3 + 1378837131287886849733/1564218330345805091191*u + 60218096661599337909/1564218330345805091191, c_1002_0 + 16553265299218101530800/14077964973112245820719*c_1101_3^10*\ u + 8644131091804655799650/14077964973112245820719*c_1101_3^10 - 66054506695144551003005/14077964973112245820719*c_1101_3^9*u - 21706639809971649951025/14077964973112245820719*c_1101_3^9 + 190630116681460725529145/14077964973112245820719*c_1101_3^8*u + 115673877050166505050325/14077964973112245820719*c_1101_3^8 - 391789803963756716744521/14077964973112245820719*c_1101_3^7*u - 292562563300245859806860/14077964973112245820719*c_1101_3^7 + 171811527120370522732441/4692654991037415273573*c_1101_3^6*u + 178932209725148985555961/4692654991037415273573*c_1101_3^6 - 162697992280757937489080/4692654991037415273573*c_1101_3^5*u - 222428211963887350576658/4692654991037415273573*c_1101_3^5 + 109470391990064082852296/4692654991037415273573*c_1101_3^4*u + 56656349971281687500478/1564218330345805091191*c_1101_3^4 - 4535418879222106139036/360973460849031944121*c_1101_3^3*u - 5766676933757567800981/360973460849031944121*c_1101_3^3 + 71111127220766409601658/4692654991037415273573*c_1101_3^2*u + 42083714358498477218392/4692654991037415273573*c_1101_3^2 - 7526090455768046869015/1564218330345805091191*c_1101_3*u - 2153378001292747646478/1564218330345805091191*c_1101_3 + 115652454786819009159/1564218330345805091191*u - 1194225248455657525225/1564218330345805091191, c_1002_2 - 3626193485581458008875/4692654991037415273573*c_1101_3^10*u - 1364334412797513494300/4692654991037415273573*c_1101_3^10 + 42872239189337063344235/14077964973112245820719*c_1101_3^9*u + 8440913180345106107470/14077964973112245820719*c_1101_3^9 - 130314854678946452278375/14077964973112245820719*c_1101_3^8*u - 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