Magma V2.19-8 Tue Aug 20 2013 16:16:10 on localhost [Seed = 829468149] Type ? for help. Type -D to quit. ==TRIANGULATION=BEGINS== % Triangulation v0427 geometric_solution 4.48180508 oriented_manifold CS_known -0.0000000000000003 1 0 torus 0.000000000000 0.000000000000 7 1 0 1 0 0132 2310 2310 3201 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 0 1 0 -1 0 1 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.654504235545 0.093638297875 0 0 2 2 0132 3201 2310 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 1 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 2.195808774841 0.641426757177 3 1 1 3 0132 3201 0132 1023 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 1 -1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.221107585191 0.629667676940 2 4 5 2 0132 0132 0132 1023 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 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.261278761800 0.268679520134 5 3 5 6 2310 0132 3201 0132 0 0 0 0 0 0 1 -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 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 -0.196001827427 1.269026531269 4 6 4 3 2310 1023 3201 0132 0 0 0 0 0 0 0 0 0 0 0 0 -1 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 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.196001827427 1.269026531269 5 6 4 6 1023 1302 0132 2031 0 0 0 0 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 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 0.380070218537 0.623550335398 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 's_3_1' : d['1'], 's_3_3' : d['1'], 's_3_2' : d['1'], 's_3_5' : d['1'], 's_3_4' : d['1'], 's_3_0' : d['1'], '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_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_0_6' : 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_6' : negation(d['c_0011_5']), 'c_1100_5' : negation(d['c_0011_2']), 'c_1100_4' : negation(d['c_0011_5']), 's_3_6' : d['1'], 'c_1100_1' : d['c_0011_2'], 'c_1100_0' : negation(d['c_0011_0']), 'c_1100_3' : negation(d['c_0011_2']), 'c_1100_2' : d['c_0011_2'], 'c_0101_6' : d['c_0101_3'], 'c_0101_5' : negation(d['c_0101_3']), 'c_0101_4' : negation(d['c_0101_3']), 'c_0101_3' : d['c_0101_3'], 'c_0101_2' : d['c_0101_0'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0011_5' : d['c_0011_5'], 'c_0011_4' : d['c_0011_2'], 'c_0011_6' : d['c_0011_5'], 'c_0011_1' : negation(d['c_0011_0']), 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : negation(d['c_0011_2']), 'c_0011_2' : d['c_0011_2'], 'c_1001_5' : d['c_0101_3'], 'c_1001_4' : d['c_0101_3'], 'c_1001_6' : d['c_0110_6'], 'c_1001_1' : negation(d['c_0101_0']), 'c_1001_0' : d['c_0101_1'], 'c_1001_3' : d['c_0110_6'], 'c_1001_2' : negation(d['c_0101_1']), 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : d['c_0101_1'], 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : d['c_0101_3'], 'c_0110_5' : d['c_0101_3'], 'c_0110_4' : d['c_0101_3'], 'c_0110_6' : d['c_0110_6'], 'c_1010_6' : d['c_0011_5'], 'c_1010_5' : d['c_0110_6'], 'c_1010_4' : d['c_0110_6'], 'c_1010_3' : d['c_0101_3'], 'c_1010_2' : d['c_0101_0'], 'c_1010_1' : negation(d['c_0101_1']), 'c_1010_0' : negation(d['c_0101_1'])})} PY=EVAL=SECTION=ENDS=HERE PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 8 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_2, c_0011_5, c_0101_0, c_0101_1, c_0101_3, c_0110_6 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 23 Groebner basis: [ t + 1051886879920756827327052266609287808312/27331865933011126258622648\ 7749122285*c_0110_6^22 - 163790977431104360150621574772761904417/54\ 663731866022252517245297549824457*c_0110_6^21 - 17484045584502790296489368312256517963012/2733186593301112625862264\ 87749122285*c_0110_6^20 - 26645082399847873522747832060281895617316\ /273318659330111262586226487749122285*c_0110_6^19 + 303267440233606534548697769207014263177878/273318659330111262586226\ 487749122285*c_0110_6^18 + 1820245434560933622455686382956039418264\ 0/54663731866022252517245297549824457*c_0110_6^17 - 1898481536389631068749596195336455712048926/27331865933011126258622\ 6487749122285*c_0110_6^16 - 754503663359000290380895950871731438208\ 691/273318659330111262586226487749122285*c_0110_6^15 + 8588342348975607397431994487222264919237343/27331865933011126258622\ 6487749122285*c_0110_6^14 + 216154744518945404932679208610231389136\ 9108/273318659330111262586226487749122285*c_0110_6^13 - 24313186151386197880362855327112437027420996/2733186593301112625862\ 26487749122285*c_0110_6^12 - 40008849886490238079586447683968660836\ 84357/273318659330111262586226487749122285*c_0110_6^11 + 47705941713282704124820123513726091418145312/2733186593301112625862\ 26487749122285*c_0110_6^10 + 82495098081575466062358433331986739988\ 531/54663731866022252517245297549824457*c_0110_6^9 - 2700504439842053218591966066641928022586179/11883419970874402721140\ 282076048795*c_0110_6^8 + 94983546289080027342433476251312868623840\ 02/273318659330111262586226487749122285*c_0110_6^7 + 48001746080487588707062034581345333751792742/2733186593301112625862\ 26487749122285*c_0110_6^6 - 113000176375608259327283172661583983135\ 91643/273318659330111262586226487749122285*c_0110_6^5 - 19474278356744355584185472674058466360837613/2733186593301112625862\ 26487749122285*c_0110_6^4 + 476668430417938488523122260201861938928\ 8366/273318659330111262586226487749122285*c_0110_6^3 + 3191154600354974452231021727692787324709748/27331865933011126258622\ 6487749122285*c_0110_6^2 - 1336111926267838458565736445704984886793\ 09/54663731866022252517245297549824457*c_0110_6 - 10288297930691643626714030100084110424572/2733186593301112625862264\ 87749122285, c_0011_0 - 1, c_0011_2 - 28466575611539951162902315462323028813/273318659330111262586\ 226487749122285*c_0110_6^22 - 1534259501378091735826271124611917166\ /54663731866022252517245297549824457*c_0110_6^21 + 460165629515787272220984885615126282583/273318659330111262586226487\ 749122285*c_0110_6^20 + 1200633491923253376063271345426042472119/27\ 3318659330111262586226487749122285*c_0110_6^19 - 6868996913268168975618553728193174239707/27331865933011126258622648\ 7749122285*c_0110_6^18 - 1886178621643519136285017581564506281865/5\ 4663731866022252517245297549824457*c_0110_6^17 + 40354587968096779227945959808930577998234/2733186593301112625862264\ 87749122285*c_0110_6^16 + 60735944750310908200498317640486275442579\ /273318659330111262586226487749122285*c_0110_6^15 - 162166791176344623218219444576597756880982/273318659330111262586226\ 487749122285*c_0110_6^14 - 2159513405973304579721274273556968065809\ 62/273318659330111262586226487749122285*c_0110_6^13 + 406174415491003709463370092013120791877024/273318659330111262586226\ 487749122285*c_0110_6^12 + 4886382160312803873209715116320461617953\ 38/273318659330111262586226487749122285*c_0110_6^11 - 717791552153531339562318083754362904883198/273318659330111262586226\ 487749122285*c_0110_6^10 - 1318837526723793065070612332159731711811\ 48/54663731866022252517245297549824457*c_0110_6^9 + 38527438591267568928057236847823390523856/1188341997087440272114028\ 2076048795*c_0110_6^8 + 524154455794680011778452903253799451678322/\ 273318659330111262586226487749122285*c_0110_6^7 - 622995897580103205730975729785876673656413/273318659330111262586226\ 487749122285*c_0110_6^6 - 21741706347597149528423215463095893471476\ 3/273318659330111262586226487749122285*c_0110_6^5 + 211547038553909980946894560224004340088342/273318659330111262586226\ 487749122285*c_0110_6^4 + 30592619477704763518480703116200963396861\ /273318659330111262586226487749122285*c_0110_6^3 - 26168334131567917960749821088038566700927/2733186593301112625862264\ 87749122285*c_0110_6^2 + 528717506606638061447585477837091262827/54\ 663731866022252517245297549824457*c_0110_6 + 31448949880649727969262101506770357308/2733186593301112625862264877\ 49122285, c_0011_5 - 4351394013780076007735061554579740194/2733186593301112625862\ 26487749122285*c_0110_6^22 - 364132022110133296033488798825603159/5\ 4663731866022252517245297549824457*c_0110_6^21 + 70111895576630664297908187733286849424/2733186593301112625862264877\ 49122285*c_0110_6^20 + 193929557016240743541036412140775880962/2733\ 18659330111262586226487749122285*c_0110_6^19 - 1021773198037961017527890517198527948951/27331865933011126258622648\ 7749122285*c_0110_6^18 - 318946836974320429995683185093654232237/54\ 663731866022252517245297549824457*c_0110_6^17 + 5942904248545365923182075892858031099302/27331865933011126258622648\ 7749122285*c_0110_6^16 + 10169568219889384840911229171152234762247/\ 273318659330111262586226487749122285*c_0110_6^15 - 23341787287369381970776540132455909294506/2733186593301112625862264\ 87749122285*c_0110_6^14 - 36498787233375049261907229525321726951361\ /273318659330111262586226487749122285*c_0110_6^13 + 56948614344339657053509355074597651142432/2733186593301112625862264\ 87749122285*c_0110_6^12 + 83166190824171965297205622536763682316229\ /273318659330111262586226487749122285*c_0110_6^11 - 98099027393869597930715393850371265447984/2733186593301112625862264\ 87749122285*c_0110_6^10 - 23060912390143850404354596577523030352765\ /54663731866022252517245297549824457*c_0110_6^9 + 5202050839612376846899004917839888667233/11883419970874402721140282\ 076048795*c_0110_6^8 + 97458798816340309769761992295805305377031/27\ 3318659330111262586226487749122285*c_0110_6^7 - 82190369648690329785237046334564384734869/2733186593301112625862264\ 87749122285*c_0110_6^6 - 44623120726729536250478673220517873248244/\ 273318659330111262586226487749122285*c_0110_6^5 + 26415013276289739959236563601887185972701/2733186593301112625862264\ 87749122285*c_0110_6^4 + 8042250603593704576073992904270096735348/2\ 73318659330111262586226487749122285*c_0110_6^3 - 2891709890940666458813270939246775256206/27331865933011126258622648\ 7749122285*c_0110_6^2 + 20013744103233454610302745818531244254/5466\ 3731866022252517245297549824457*c_0110_6 + 1345976269149151896236632784380102504/27331865933011126258622648774\ 9122285, c_0101_0 - 6797507416216757880508450942588754808/2733186593301112625862\ 26487749122285*c_0110_6^22 - 407686079401414526454358337231782500/5\ 4663731866022252517245297549824457*c_0110_6^21 + 109761207441889927678318634490831230108/273318659330111262586226487\ 749122285*c_0110_6^20 + 290034351684447306855802868077549399529/273\ 318659330111262586226487749122285*c_0110_6^19 - 1630479525640195230425052925293172052992/27331865933011126258622648\ 7749122285*c_0110_6^18 - 459859338320801648914141930605500888065/54\ 663731866022252517245297549824457*c_0110_6^17 + 9551624471083097368262179338894556638774/27331865933011126258622648\ 7749122285*c_0110_6^16 + 14778093261675411827759071594064825277274/\ 273318659330111262586226487749122285*c_0110_6^15 - 38189723690318853011573716065485586280022/2733186593301112625862264\ 87749122285*c_0110_6^14 - 52625390444523099784471875777608380845502\ /273318659330111262586226487749122285*c_0110_6^13 + 95045047856791123182328762892502398584814/2733186593301112625862264\ 87749122285*c_0110_6^12 + 11922565961422689682580252942245330649002\ 8/273318659330111262586226487749122285*c_0110_6^11 - 166923850233180284855886578297061606750358/273318659330111262586226\ 487749122285*c_0110_6^10 - 3235626848661721902894258372802636816304\ 9/54663731866022252517245297549824457*c_0110_6^9 + 8921820616556604624039573539032737747371/11883419970874402721140282\ 076048795*c_0110_6^8 + 130488168616208047143680447722839743456002/2\ 73318659330111262586226487749122285*c_0110_6^7 - 143096651396918934516229022219212117562823/273318659330111262586226\ 487749122285*c_0110_6^6 - 55657789533781061866574085268855216931538\ /273318659330111262586226487749122285*c_0110_6^5 + 47795792503905206727965958174322714497342/2733186593301112625862264\ 87749122285*c_0110_6^4 + 8521031150022125909850600803565089795536/2\ 73318659330111262586226487749122285*c_0110_6^3 - 5725486253562957305730465599156157573332/27331865933011126258622648\ 7749122285*c_0110_6^2 + 100377389633444882283609746484501019808/546\ 63731866022252517245297549824457*c_0110_6 + 5927982534682547515917826919531924158/27331865933011126258622648774\ 9122285, c_0101_1 - 17357279865466843897244941512704346393/273318659330111262586\ 226487749122285*c_0110_6^22 - 706149488153880399459662093623131872/\ 54663731866022252517245297549824457*c_0110_6^21 + 280698145221466592307957470348318829943/273318659330111262586226487\ 749122285*c_0110_6^20 + 713756064816101405499636591264393050804/273\ 318659330111262586226487749122285*c_0110_6^19 - 4233666576658089672060511288270628363657/27331865933011126258622648\ 7749122285*c_0110_6^18 - 1093958700787865219704200449477631369173/5\ 4663731866022252517245297549824457*c_0110_6^17 + 24930657649050452021467470096090806191134/2733186593301112625862264\ 87749122285*c_0110_6^16 + 35413703606586832370931366235686236552854\ /273318659330111262586226487749122285*c_0110_6^15 - 101011031400049679950792328377746296794327/273318659330111262586226\ 487749122285*c_0110_6^14 - 1251325273751670314653179766739236986413\ 12/273318659330111262586226487749122285*c_0110_6^13 + 254959274688707193016999882512575017362174/273318659330111262586226\ 487749122285*c_0110_6^12 + 2818146170836866491174465497231906727036\ 78/273318659330111262586226487749122285*c_0110_6^11 - 453716364587606099394612356514282661047638/273318659330111262586226\ 487749122285*c_0110_6^10 - 7482682210087527886448136584825334837918\ 9/54663731866022252517245297549824457*c_0110_6^9 + 24362377196874677712900648213991158121266/1188341997087440272114028\ 2076048795*c_0110_6^8 + 286996918951029203498610392198819212079047/\ 273318659330111262586226487749122285*c_0110_6^7 - 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