Magma V2.19-8 Tue Aug 20 2013 23:56:15 on localhost [Seed = 38038056] Type ? for help. Type -D to quit. Loading file "K12n825__sl2_c0.magma" ==TRIANGULATION=BEGINS== % Triangulation K12n825 geometric_solution 11.90775767 oriented_manifold CS_known -0.0000000000000001 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 -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 0.857515326883 0.764478267530 0 5 7 6 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 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 1.408402326319 0.794423918713 6 0 8 4 3120 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 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 0.736386268260 0.916370988646 9 9 10 0 0132 2103 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 1 0 0 -1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.365276466841 0.780713435403 7 11 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.525340765540 0.609301206556 7 1 11 8 1023 0132 2031 2031 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0.541507228881 0.839868325657 12 11 1 2 0132 2031 0132 3120 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0.666064916299 0.463824058371 4 5 9 1 0132 1023 1230 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.494293775497 0.223261172244 10 5 10 2 0213 1302 1023 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 1 -1 0 0 0 0 -1 0 0 1 -2 -1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.242022711295 1.004604336710 3 3 12 7 0132 2103 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 0 0 0 0 0 0 -1 1 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.658383838961 1.176740920290 8 12 8 3 0213 2103 1023 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 1 0 -1 0 0 0 0 0 2 1 -3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.242022711295 1.004604336710 6 4 12 5 1302 0132 1023 1302 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.363990071922 0.477235337436 6 10 11 9 0132 2103 1023 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 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 0.692959511320 0.930311877742 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_11' : d['c_0101_12'], 'c_1001_10' : d['c_0011_10'], 'c_1001_12' : d['c_0011_10'], 'c_1001_5' : negation(d['c_0110_11']), 'c_1001_4' : d['c_1001_2'], 'c_1001_7' : d['c_0101_5'], 'c_1001_6' : negation(d['c_0110_11']), 'c_1001_1' : d['c_0011_8'], 'c_1001_0' : d['c_0101_7'], 'c_1001_3' : negation(d['c_0011_3']), 'c_1001_2' : d['c_1001_2'], 'c_1001_9' : d['c_0011_3'], 'c_1001_8' : d['c_0011_8'], 'c_1010_12' : d['c_0011_3'], 'c_1010_11' : d['c_1001_2'], 'c_1010_10' : negation(d['c_0011_3']), 's_3_11' : d['1'], 's_3_10' : 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_0011_8'], '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' : negation(d['c_0101_5']), 'c_0011_10' : d['c_0011_10'], 'c_0011_12' : d['c_0011_10'], 'c_1100_5' : negation(d['c_1001_2']), 'c_1100_4' : d['c_1100_0'], 'c_1100_7' : negation(d['c_0101_2']), 'c_1100_6' : negation(d['c_0101_2']), 'c_1100_1' : negation(d['c_0101_2']), 'c_1100_0' : d['c_1100_0'], 'c_1100_3' : d['c_1100_0'], 'c_1100_2' : negation(d['c_1100_0']), 's_0_10' : d['1'], 'c_1100_11' : d['c_0101_5'], 'c_1100_10' : d['c_1100_0'], 's_0_11' : d['1'], 'c_1010_7' : d['c_0011_8'], 'c_1010_6' : d['c_0011_0'], 'c_1010_5' : d['c_0011_8'], 'c_1010_4' : d['c_0101_12'], 'c_1010_3' : d['c_0101_7'], 'c_1010_2' : d['c_0101_7'], 'c_1010_1' : negation(d['c_0110_11']), 'c_1010_0' : d['c_1001_2'], 'c_1010_9' : negation(d['c_0101_7']), 'c_1010_8' : d['c_1001_2'], 'c_1100_8' : negation(d['c_1100_0']), '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_0101_5']), '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_3']), 'c_0011_8' : d['c_0011_8'], 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : negation(d['c_0011_0']), 'c_0011_7' : d['c_0011_0'], 'c_0011_6' : negation(d['c_0011_10']), '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' : d['c_0110_11'], 'c_0110_10' : negation(d['c_0101_2']), 'c_0110_12' : d['c_0101_0'], 'c_0101_12' : d['c_0101_12'], '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_5'], 'c_0101_4' : d['c_0101_1'], 'c_0101_3' : negation(d['c_0101_2']), 'c_0101_2' : d['c_0101_2'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : d['c_0101_0'], 'c_0101_8' : 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_0101_2']), 'c_0110_8' : d['c_0101_2'], 'c_0110_1' : d['c_0101_0'], 'c_0011_11' : d['c_0011_0'], 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : d['c_0101_12'], 'c_0110_5' : d['c_0011_8'], 'c_0110_4' : d['c_0101_7'], 'c_0110_7' : d['c_0101_1'], 'c_0110_6' : d['c_0101_12']})} 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_3, c_0011_8, c_0101_0, c_0101_1, c_0101_12, c_0101_2, c_0101_5, c_0101_7, c_0110_11, c_1001_2, c_1100_0 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 12 Groebner basis: [ t + 2427186140882138068250395091/2477914380770885794786711572*c_1100_0^\ 11 - 4614486756634762576775898077/2477914380770885794786711572*c_11\ 00_0^10 - 176362857912073954026529116133/49558287615417715895734231\ 44*c_1100_0^9 + 48811553029441457566958682781/260833092712724820503\ 864376*c_1100_0^8 + 235602988547172336814907588549/1651942920513923\ 863191141048*c_1100_0^7 + 2832473460548317009916678897509/495582876\ 1541771589573423144*c_1100_0^6 + 1148035936267456000889535352807/70\ 7975537363110227081917592*c_1100_0^5 + 245309926850242957501042598675/183549213390435984799015672*c_1100_0\ ^4 + 1527109657062887146742586291668/619478595192721448696677893*c_\ 1100_0^3 - 1918323830772514412653896856141/495582876154177158957342\ 3144*c_1100_0^2 + 243389743009724849367307013983/825971460256961931\ 595570524*c_1100_0 - 79591040715655591928727790970/6883095502141349\ 4299630877, c_0011_0 - 1, c_0011_10 - 90911039568670582/24516950710706308827*c_1100_0^11 - 426173205814406173/196135605685650470616*c_1100_0^10 + 29678524286742761135/196135605685650470616*c_1100_0^9 - 72912501135152687633/196135605685650470616*c_1100_0^8 - 148623134895205229209/65378535228550156872*c_1100_0^7 - 719661649920631267505/196135605685650470616*c_1100_0^6 - 321543652174252794689/28019372240807210088*c_1100_0^5 - 119664134022169107551/5448211269045846406*c_1100_0^4 - 4830068578602146332535/196135605685650470616*c_1100_0^3 - 2540154668270662066763/98067802842825235308*c_1100_0^2 - 168543217572888146395/16344633807137539218*c_1100_0 - 17387771040489322402/2724105634522923203, c_0011_3 - 115519962060153937/32689267614275078436*c_1100_0^11 + 140605248810277635/21792845076183385624*c_1100_0^10 + 8457699488187663547/65378535228550156872*c_1100_0^9 - 14533120583556535867/21792845076183385624*c_1100_0^8 - 38072702123696022695/65378535228550156872*c_1100_0^7 - 130170544592608919261/65378535228550156872*c_1100_0^6 - 56105438044704318847/9339790746935736696*c_1100_0^5 - 42472391063781982291/8172316903568769609*c_1100_0^4 - 592192669399471897955/65378535228550156872*c_1100_0^3 + 147717713089895383/5448211269045846406*c_1100_0^2 - 15451330155682840484/8172316903568769609*c_1100_0 + 4151676465867127586/2724105634522923203, c_0011_8 - 20933100285226547/21792845076183385624*c_1100_0^11 - 8882440741309127/5448211269045846406*c_1100_0^10 + 440044024067014413/10896422538091692812*c_1100_0^9 - 302754742115694221/5448211269045846406*c_1100_0^8 - 2080900861673890679/2724105634522923203*c_1100_0^7 - 6962960617433344115/5448211269045846406*c_1100_0^6 - 11246322170106645135/3113263582311912232*c_1100_0^5 - 175869992065691667599/21792845076183385624*c_1100_0^4 - 204233923796672538337/21792845076183385624*c_1100_0^3 - 56903458512508228905/5448211269045846406*c_1100_0^2 - 14413826654541501623/2724105634522923203*c_1100_0 - 7249411922829773335/2724105634522923203, c_0101_0 + 384885261887097823/392271211371300941232*c_1100_0^11 + 2435900908913710829/392271211371300941232*c_1100_0^10 - 18472772251576423327/392271211371300941232*c_1100_0^9 - 44410090564477306265/392271211371300941232*c_1100_0^8 + 202145532960763087319/130757070457100313744*c_1100_0^7 + 976077113810690867467/392271211371300941232*c_1100_0^6 + 191351134474934846753/28019372240807210088*c_1100_0^5 + 757246795007751284041/43585690152366771248*c_1100_0^4 + 519042605141858410894/24516950710706308827*c_1100_0^3 + 2655364878757826585963/98067802842825235308*c_1100_0^2 + 101839333049315717966/8172316903568769609*c_1100_0 + 22629406717882217194/2724105634522923203, c_0101_1 - 992908755121687193/196135605685650470616*c_1100_0^11 + 161946365617017634/24516950710706308827*c_1100_0^10 + 4649755086359605891/24516950710706308827*c_1100_0^9 - 84208908808656003277/98067802842825235308*c_1100_0^8 - 42930506191240139509/32689267614275078436*c_1100_0^7 - 328161481501971980419/98067802842825235308*c_1100_0^6 - 288765545626391890103/28019372240807210088*c_1100_0^5 - 814038275474305975777/65378535228550156872*c_1100_0^4 - 3492475583016322379807/196135605685650470616*c_1100_0^3 - 850843309028218571069/98067802842825235308*c_1100_0^2 - 26715128027741713057/5448211269045846406*c_1100_0 - 110458597027789189/2724105634522923203, c_0101_12 - 949160480268170399/392271211371300941232*c_1100_0^11 + 1566052505190029063/392271211371300941232*c_1100_0^10 + 34498669484458058615/392271211371300941232*c_1100_0^9 - 172711003455176116103/392271211371300941232*c_1100_0^8 - 55290716682374560927/130757070457100313744*c_1100_0^7 - 641157289280905724819/392271211371300941232*c_1100_0^6 - 139462230945383600917/28019372240807210088*c_1100_0^5 - 223740509539549029973/43585690152366771248*c_1100_0^4 - 970058143559167997639/98067802842825235308*c_1100_0^3 - 281367644637907334033/49033901421412617654*c_1100_0^2 - 40876165388385689563/8172316903568769609*c_1100_0 - 5069645247747370266/2724105634522923203, c_0101_2 + 156161485227866491/21792845076183385624*c_1100_0^11 - 337096249368799201/32689267614275078436*c_1100_0^10 - 8760438437643019997/32689267614275078436*c_1100_0^9 + 20508530991872155601/16344633807137539218*c_1100_0^8 + 28140411223202976337/16344633807137539218*c_1100_0^7 + 11628323824929846529/2724105634522923203*c_1100_0^6 + 132248105786569819849/9339790746935736696*c_1100_0^5 + 1022890831734784794391/65378535228550156872*c_1100_0^4 + 481232519791217336007/21792845076183385624*c_1100_0^3 + 351829633055969067143/32689267614275078436*c_1100_0^2 + 46504753771921858015/8172316903568769609*c_1100_0 + 2239293294179790322/2724105634522923203, c_0101_5 + 2753232730410846079/392271211371300941232*c_1100_0^11 - 4598604042846995173/392271211371300941232*c_1100_0^10 - 101239774530405890461/392271211371300941232*c_1100_0^9 + 505031574628563483841/392271211371300941232*c_1100_0^8 + 172910376372733161209/130757070457100313744*c_1100_0^7 + 1619406269947608163549/392271211371300941232*c_1100_0^6 + 190249355704264069873/14009686120403605044*c_1100_0^5 + 579252099556387673421/43585690152366771248*c_1100_0^4 + 4389669817999463057177/196135605685650470616*c_1100_0^3 + 1031946809425434212225/98067802842825235308*c_1100_0^2 + 143206847499418630789/16344633807137539218*c_1100_0 + 6067118255938594343/2724105634522923203, c_0101_7 - 2197424105069653933/392271211371300941232*c_1100_0^11 + 2837474882103851023/392271211371300941232*c_1100_0^10 + 82495642343430468115/392271211371300941232*c_1100_0^9 - 372442300400820682519/392271211371300941232*c_1100_0^8 - 192986250308180704135/130757070457100313744*c_1100_0^7 - 1412659848202784983651/392271211371300941232*c_1100_0^6 - 81833258207094451667/7004843060201802522*c_1100_0^5 - 1843121210401403364377/130757070457100313744*c_1100_0^4 - 3854887849394229172523/196135605685650470616*c_1100_0^3 - 579654650439696603733/49033901421412617654*c_1100_0^2 - 18988883695198777310/2724105634522923203*c_1100_0 - 5699758612931517896/2724105634522923203, c_0110_11 - 112754515633917230/24516950710706308827*c_1100_0^11 + 1516275768828483055/196135605685650470616*c_1100_0^10 + 33370552522973915923/196135605685650470616*c_1100_0^9 - 166160285586693683869/196135605685650470616*c_1100_0^8 - 58809829845179300141/65378535228550156872*c_1100_0^7 - 489124490333351219365/196135605685650470616*c_1100_0^6 - 241036480463144538829/28019372240807210088*c_1100_0^5 - 44438948752104830431/5448211269045846406*c_1100_0^4 - 2449553530881127061899/196135605685650470616*c_1100_0^3 - 469211520149619544159/98067802842825235308*c_1100_0^2 - 61454516722647251663/16344633807137539218*c_1100_0 - 3721578642714147280/2724105634522923203, c_1001_2 + 600942514496150149/196135605685650470616*c_1100_0^11 - 203619352294762781/98067802842825235308*c_1100_0^10 - 2910672796023441536/24516950710706308827*c_1100_0^9 + 44291862500659426307/98067802842825235308*c_1100_0^8 + 38321126595252501313/32689267614275078436*c_1100_0^7 + 215791467309302688695/98067802842825235308*c_1100_0^6 + 209195671264277375659/28019372240807210088*c_1100_0^5 + 245487510819184607137/21792845076183385624*c_1100_0^4 + 2676722409274686489289/196135605685650470616*c_1100_0^3 + 614453921682418375325/49033901421412617654*c_1100_0^2 + 99347083387867586597/16344633807137539218*c_1100_0 + 9378246619981774468/2724105634522923203, c_1100_0^12 - c_1100_0^11 - 37*c_1100_0^10 + 157*c_1100_0^9 + 279*c_1100_0^8 + 889*c_1100_0^7 + 2446*c_1100_0^6 + 3639*c_1100_0^5 + 5980*c_1100_0^4 + 4748*c_1100_0^3 + 4440*c_1100_0^2 + 1584*c_1100_0 + 864 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 6.150 Total time: 6.360 seconds, Total memory usage: 85.56MB