Magma V2.19-8 Tue Aug 20 2013 23:55:00 on localhost [Seed = 4223505315] Type ? for help. Type -D to quit. Loading file "K12n579__sl2_c0.magma" ==TRIANGULATION=BEGINS== % Triangulation K12n579 geometric_solution 11.47690083 oriented_manifold CS_known 0.0000000000000006 1 0 torus 0.000000000000 0.000000000000 13 1 2 3 2 0132 0132 0132 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 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 0.243315814753 2.153577673216 0 4 6 5 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 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 0.055913596839 0.398995753579 0 0 7 6 3201 0132 0132 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 -1 0 1 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 0.550933536575 0.546898273249 5 8 4 0 0132 0132 3201 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 0.499697692635 0.163843019120 3 1 9 10 2310 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.867368279309 0.960827368127 3 11 1 8 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 -1 1 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 0.629026307529 1.052204149254 7 7 2 1 0321 0132 2031 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 1 -1 1 0 -1 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 0.078814424872 0.712945608388 6 6 12 2 0321 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 -1 0 1 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 0.718712464590 0.519969838746 10 3 5 9 3120 0132 1230 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 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 0.503304939152 1.351355721710 8 10 11 4 3201 2031 0321 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 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.227760855282 0.723718802825 9 12 4 8 1302 0132 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.234851088448 1.397697775164 12 5 9 12 2103 0132 0321 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 1 0 -1 1 0 1 -2 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.676027961131 1.033229530584 11 10 11 7 3120 0132 2103 0132 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 2 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 0.276303792298 0.881203324248 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_0110_6' : d['c_0011_6'], 'c_1001_11' : negation(d['c_0101_8']), 'c_1001_10' : d['c_1001_1'], 'c_1001_12' : d['c_0011_11'], 'c_1001_5' : d['c_0011_10'], 'c_1001_4' : d['c_0011_10'], 'c_1001_7' : d['c_1001_1'], 'c_1001_6' : negation(d['c_0110_2']), 'c_1001_1' : d['c_1001_1'], 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : negation(d['c_0101_4']), 'c_1001_2' : negation(d['c_0110_2']), 'c_1001_9' : negation(d['c_0101_11']), 'c_1001_8' : d['c_1001_0'], 'c_1010_12' : d['c_1001_1'], 'c_1010_11' : d['c_0011_10'], 'c_1010_10' : d['c_0011_11'], 's_3_11' : 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_0101_11'], 'c_0101_10' : negation(d['c_0011_9']), '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_8']), 'c_0011_10' : d['c_0011_10'], 'c_0011_12' : negation(d['c_0011_10']), 'c_1100_5' : negation(d['c_1001_0']), 'c_1100_4' : negation(d['c_0101_8']), 'c_1100_7' : d['c_0101_6'], 'c_1100_6' : negation(d['c_1001_0']), 'c_1100_1' : negation(d['c_1001_0']), 'c_1100_0' : negation(d['c_0011_0']), 'c_1100_3' : negation(d['c_0011_0']), 'c_1100_2' : d['c_0101_6'], 's_0_10' : d['1'], 'c_1100_11' : negation(d['c_0101_11']), 'c_1100_10' : negation(d['c_0101_8']), 's_3_10' : d['1'], 'c_1010_7' : negation(d['c_0110_2']), 'c_1010_6' : d['c_1001_1'], 'c_1010_5' : negation(d['c_0101_8']), '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_0011_10'], 'c_1010_0' : negation(d['c_0110_2']), 'c_1010_9' : d['c_0011_10'], 'c_1010_8' : negation(d['c_0101_4']), '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' : d['c_0101_6'], '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' : d['c_0011_9'], 'c_0011_8' : negation(d['c_0011_11']), 'c_0011_5' : negation(d['c_0011_11']), 'c_0011_4' : d['c_0011_0'], 'c_0011_7' : negation(d['c_0011_6']), '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' : d['c_0011_11'], 'c_0011_2' : negation(d['c_0011_0']), 'c_0110_11' : negation(d['c_0101_6']), 'c_0110_10' : d['c_0101_11'], 'c_0110_12' : negation(d['c_0101_6']), 'c_0101_12' : d['c_0101_11'], 'c_0110_0' : d['c_0011_6'], 'c_0101_7' : negation(d['c_0101_6']), 'c_0101_6' : d['c_0101_6'], 'c_0101_5' : d['c_0101_0'], 'c_0101_4' : d['c_0101_4'], 'c_0101_3' : d['c_0011_9'], 'c_0101_2' : negation(d['c_0011_6']), 'c_0101_1' : d['c_0011_6'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : negation(d['c_0101_11']), 'c_0101_8' : d['c_0101_8'], 's_1_12' : d['1'], 's_1_11' : d['1'], 's_1_10' : d['1'], 'c_0110_9' : d['c_0101_4'], 'c_0110_8' : d['c_0101_11'], 'c_0110_1' : d['c_0101_0'], 'c_0011_11' : d['c_0011_11'], 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : d['c_0110_2'], 'c_0110_5' : d['c_0011_9'], 'c_0110_4' : negation(d['c_0011_9']), 'c_0110_7' : negation(d['c_0011_6']), 'c_1100_8' : d['c_0011_9']})} 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_6, c_0011_9, c_0101_0, c_0101_11, c_0101_4, c_0101_6, c_0101_8, c_0110_2, c_1001_0, c_1001_1 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 16 Groebner basis: [ t + 24462410907960231520274369164474741730286420476194410160381/2139361\ 1020259839207797963396089489258866655049125*c_1001_1^15 + 102522391183419454762412954417429380636484066212042722876933/213936\ 11020259839207797963396089489258866655049125*c_1001_1^14 + 129193260076202066350916048718981085914350657486404610324562/213936\ 11020259839207797963396089489258866655049125*c_1001_1^13 - 2612109907464576034211162702410918693783215585782215837082/42787222\ 04051967841559592679217897851773331009825*c_1001_1^12 - 23881623732115073595765730394288360073933734255766217117128/4278722\ 204051967841559592679217897851773331009825*c_1001_1^11 - 3572842447344540493595889573445372538646185084177643532968/21393611\ 020259839207797963396089489258866655049125*c_1001_1^10 + 12972438203520997638145474274600018355728015199946863050442/4278722\ 204051967841559592679217897851773331009825*c_1001_1^9 - 29916655446396041196787217533851436421108444092362941845364/2139361\ 1020259839207797963396089489258866655049125*c_1001_1^8 - 26831880851692795118157445975493050387230494711466670643582/2139361\ 1020259839207797963396089489258866655049125*c_1001_1^7 + 29026361912318048076281418459345687949082221624575646576598/2139361\ 1020259839207797963396089489258866655049125*c_1001_1^6 + 420531198188214056800895589355242502440651464402382643337/213936110\ 20259839207797963396089489258866655049125*c_1001_1^5 - 8691355168091259318818969527974260736782719217030466144214/21393611\ 020259839207797963396089489258866655049125*c_1001_1^4 + 3451800745650752942913445868048105112556868402438319713587/21393611\ 020259839207797963396089489258866655049125*c_1001_1^3 - 466760060908255204407682103348946995642086411613643029488/213936110\ 20259839207797963396089489258866655049125*c_1001_1^2 - 153418240915271043892714710852520922655057360102958188/427872220405\ 1967841559592679217897851773331009825*c_1001_1 + 5022418608886664456449444750862964087431941282947716899/21393611020\ 259839207797963396089489258866655049125, c_0011_0 - 1, c_0011_10 - 4129927295041311895234298328846/224356535949381884242069187\ 5*c_1001_1^15 - 15594670789346615839221847947908/224356535949381884\ 2420691875*c_1001_1^14 - 14643352011831444171122872180272/224356535\ 9493818842420691875*c_1001_1^13 + 2264243829308899912896208805662/4\ 48713071898763768484138375*c_1001_1^12 + 3959592774740496654908625097933/448713071898763768484138375*c_1001_\ 1^11 - 6603563493600939765590032788912/2243565359493818842420691875\ *c_1001_1^10 - 2069013275692701049237079553149/44871307189876376848\ 4138375*c_1001_1^9 + 9500695463279862970272938211469/22435653594938\ 18842420691875*c_1001_1^8 + 2196705608123959862205481823417/2243565\ 359493818842420691875*c_1001_1^7 - 6631963712863373964536423565993/2243565359493818842420691875*c_1001\ _1^6 + 1954427542493407008351179202993/2243565359493818842420691875\ *c_1001_1^5 + 1350817384407665427007102179269/224356535949381884242\ 0691875*c_1001_1^4 - 1162843657617436745448363329687/22435653594938\ 18842420691875*c_1001_1^3 + 353571641806838371333388191038/22435653\ 59493818842420691875*c_1001_1^2 - 9225023228983008170057633431/4487\ 13071898763768484138375*c_1001_1 + 1097972356594434695827005931/2243565359493818842420691875, c_0011_11 + 4895427627715951362670902617797/224356535949381884242069187\ 5*c_1001_1^15 + 21242606048874304582678343458196/224356535949381884\ 2420691875*c_1001_1^14 + 28917463353228171118142049731094/224356535\ 9493818842420691875*c_1001_1^13 + 274451511759379366693840172251/44\ 8713071898763768484138375*c_1001_1^12 - 4769701016157407890091945549456/448713071898763768484138375*c_1001_\ 1^11 - 3749213838077982299794509784466/2243565359493818842420691875\ *c_1001_1^10 + 2574215388163909253545909378804/44871307189876376848\ 4138375*c_1001_1^9 - 4528698205870501271327518987368/22435653594938\ 18842420691875*c_1001_1^8 - 6408610180251681275621850163834/2243565\ 359493818842420691875*c_1001_1^7 + 5210191341759440491796366495051/2243565359493818842420691875*c_1001\ _1^6 + 896946966922345513185450941944/2243565359493818842420691875*\ c_1001_1^5 - 1855004913446828125027900794743/2243565359493818842420\ 691875*c_1001_1^4 + 507906197966371339919769475069/2243565359493818\ 842420691875*c_1001_1^3 + 40228925370126000826946958269/22435653594\ 93818842420691875*c_1001_1^2 - 7980023614575500483875525486/4487130\ 71898763768484138375*c_1001_1 + 6080588118839952789902726038/224356\ 5359493818842420691875, c_0011_6 - 488186746081278808494411430022/89742614379752753696827675*c_\ 1001_1^15 - 9602874862122258716479983685191/44871307189876376848413\ 8375*c_1001_1^14 - 10363005229158760261098343096196/448713071898763\ 768484138375*c_1001_1^13 + 831862120351437356202905206116/897426143\ 79752753696827675*c_1001_1^12 + 87069550522121793845696615303/35897\ 04575190110147873107*c_1001_1^11 - 581204082803516173608542846971/89742614379752753696827675*c_1001_1^\ 10 - 6136963870920646266663931782622/448713071898763768484138375*c_\ 1001_1^9 + 4845028788445410590638376765774/448713071898763768484138\ 375*c_1001_1^8 + 1733923041570008071278485037061/448713071898763768\ 484138375*c_1001_1^7 - 706599762991144641052676636589/8974261437975\ 2753696827675*c_1001_1^6 + 824628504462731564184331179822/448713071\ 898763768484138375*c_1001_1^5 + 810250326496331314872395300509/4487\ 13071898763768484138375*c_1001_1^4 - 593388678971284181205749614799/448713071898763768484138375*c_1001_1\ ^3 + 156239587006999502198792979266/448713071898763768484138375*c_1\ 001_1^2 - 17368673535303142354797045469/448713071898763768484138375\ *c_1001_1 + 604742790635642786223991063/448713071898763768484138375\ , c_0011_9 - 4532376967647067660522695530274/2243565359493818842420691875\ *c_1001_1^15 - 17579346427434849496519177596862/2243565359493818842\ 420691875*c_1001_1^14 - 18668396143142946681420356273353/2243565359\ 493818842420691875*c_1001_1^13 + 1381697610643027557360088544463/44\ 8713071898763768484138375*c_1001_1^12 + 3410338472411756152747464477402/448713071898763768484138375*c_1001_\ 1^11 - 6948962997039436734006053178578/2243565359493818842420691875\ *c_1001_1^10 - 367061590742749653218641227172/897426143797527536968\ 27675*c_1001_1^9 + 9916538047055019722446737192776/2243565359493818\ 842420691875*c_1001_1^8 + 1529441228445950218138157339133/224356535\ 9493818842420691875*c_1001_1^7 - 6329497265151048840056021848742/22\ 43565359493818842420691875*c_1001_1^6 + 2512627550986011887302038653187/2243565359493818842420691875*c_1001\ _1^5 + 945136318822850346136334418576/2243565359493818842420691875*\ c_1001_1^4 - 1253242095710295038787490145968/2243565359493818842420\ 691875*c_1001_1^3 + 521858351580750376441770863832/2243565359493818\ 842420691875*c_1001_1^2 - 21219610091945940010445112872/44871307189\ 8763768484138375*c_1001_1 + 8857280877038391970852949119/2243565359\ 493818842420691875, c_0101_0 - 2859419931880828350514224942341/2243565359493818842420691875\ *c_1001_1^15 - 14256244494014702014447856683213/2243565359493818842\ 420691875*c_1001_1^14 - 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