{ "Index":65, "Name":"9_30", "RolfsenName":"9_30", "DTname":"9a_1", "TunnelNumber":1, "BridgeNumber":"Not implemented", "Hyperbolic":true, "Diagram":{ "Scode":"{8, -16, 18, -12, 2, -6, -10, -4, 14}", "Acode":"{5, -9, 1, -7, 2, -4, -6, -3, 8}", "PDcode":[ "{1, 9, 2, 8}", "{3, 16, 4, 17}", "{5, 1, 6, 18}", "{7, 12, 8, 13}", "{9, 3, 10, 2}", "{11, 6, 12, 7}", "{13, 10, 14, 11}", "{15, 4, 16, 5}", "{17, 15, 18, 14}" ], "CBtype":"{2, 1}", "ParabolicReps":{ "SolvingSeq":[ "{4, 7, 1}", [], [ "{4, -7, 5, 1}", "{1, 5, 2, 1}", "{4, 1, 3, 2}", "{7, -4, 6, 2}", "{7, -6, 8, 1}", "{1, 8, 9, 2}" ], "{5, 8}", "{2}", 2 ], "SolvingSeqIdx":1, "Comps":{ "u":{ "CheckEq":[ "1 + a*b - b^2 + u + a^2*u^2 - 2*a*b*u^2 - a^2*u^4", "b^2 - u - u^2 + a*b*u^2 + b^2*u^2 + 2*a*b*u^4 + a^2*u^6", "-a + u - 2*a*b*u + a^2*b^2*u + 2*a*b*u^3 + b^2*u^3 - a^2*b^2*u^3 - a*b^3*u^3 + a*u^4 - a*u^6 - b*u^6", "-b + u - b^2*u + a*b^3*u + a*u^2 - u^3 + b^2*u^3 - a*b^3*u^3 - b^4*u^3 - 2*a*u^4 - b*u^4 + a*u^6 + b*u^6" ], "TimingForPrimaryIdeals":9.933e-2 }, "v":{ "CheckEq":[ "b^2", "1 + a*b - b^2 - v", "-b - b^4*v", "-a + v + b^2*v - a*b^3*v - b*v^2" ], "TimingForPrimaryIdeals":7.5046e-2 }, "PrimaryIdeals":[ { "IdealName":"J9_30_0", "Generators":[ "-3 + 2*b - 4*u - 10*u^2 + 15*u^3 + 17*u^4 - 66*u^5 - 7*u^6 + 142*u^7 - 86*u^8 - 206*u^9 + 248*u^10 + 142*u^11 - 412*u^12 + 52*u^13 + 416*u^14 - 268*u^15 - 247*u^16 + 332*u^17 + 34*u^18 - 237*u^19 + 71*u^20 + 98*u^21 - 65*u^22 - 18*u^23 + 25*u^24 - 2*u^25 - 4*u^26 + u^27", "9 + 2*a - 4*u + 32*u^2 - 39*u^3 - 83*u^4 + 230*u^5 + 43*u^6 - 562*u^7 + 330*u^8 + 800*u^9 - 1032*u^10 - 510*u^11 + 1656*u^12 - 332*u^13 - 1596*u^14 + 1160*u^15 + 841*u^16 - 1328*u^17 - 12*u^18 + 873*u^19 - 341*u^20 - 322*u^21 + 265*u^22 + 38*u^23 - 95*u^24 + 16*u^25 + 14*u^26 - 5*u^27", "1 - u + 4*u^2 - 11*u^3 + 41*u^5 - 39*u^6 - 67*u^7 + 138*u^8 + 26*u^9 - 252*u^10 + 130*u^11 + 266*u^12 - 328*u^13 - 108*u^14 + 404*u^15 - 119*u^16 - 285*u^17 + 236*u^18 + 89*u^19 - 190*u^20 + 31*u^21 + 83*u^22 - 45*u^23 - 15*u^24 + 19*u^25 - 2*u^26 - 3*u^27 + u^28" ], "VariableOrder":[ "b", "a", "u" ], "Characteristic":0, "KnownGroebner":[], "Status":[ "vCompNormalize" ], "MonomialOrder":"lex", "IsHomogeneous":false, "IsZeroDim":true, "IdealDimension":0, "Timings":{ "TimingGroebner":5.7671e-2, "TimingZeroDimVars":7.1067e-2, "TimingmagmaVCompNormalize":7.2291e-2, "TimingNumberOfSols":0.301514, "TimingIsRadical":2.4893000000000002e-2, "TimingArcColoring":5.4467e-2, "TimingObstruction":9.216900000000001e-2, "TimingComplexVolumeN":1.9076115e1, "TimingaCuspShapeN":0.199871, "TiminguValues":0.621642, "TiminguPolysN":0.101566, "TiminguPolys":0.832984, "TimingaCuspShape":0.143089, "TimingRepresentationsN":0.283335, "TiminguValues_ij":0.154555, "TiminguPoly_ij":1.89156, "TiminguPolys_ij_N":0.16982 }, "ZeroDimensionalVars":[ "b", "a", "u" ], "NumberOfSols":28, "IsRadical":true, "ArcColoring":[ [ "(-9 + 4*u - 32*u^2 + 39*u^3 + 83*u^4 - 230*u^5 - 43*u^6 + 562*u^7 - 330*u^8 - 800*u^9 + 1032*u^10 + 510*u^11 - 1656*u^12 + 332*u^13 + 1596*u^14 - 1160*u^15 - 841*u^16 + 1328*u^17 + 12*u^18 - 873*u^19 + 341*u^20 + 322*u^21 - 265*u^22 - 38*u^23 + 95*u^24 - 16*u^25 - 14*u^26 + 5*u^27)\/2", "(3 + 4*u + 10*u^2 - 15*u^3 - 17*u^4 + 66*u^5 + 7*u^6 - 142*u^7 + 86*u^8 + 206*u^9 - 248*u^10 - 142*u^11 + 412*u^12 - 52*u^13 - 416*u^14 + 268*u^15 + 247*u^16 - 332*u^17 - 34*u^18 + 237*u^19 - 71*u^20 - 98*u^21 + 65*u^22 + 18*u^23 - 25*u^24 + 2*u^25 + 4*u^26 - u^27)\/2" ], [ "(-11 + 4*u - 34*u^2 + 59*u^3 + 77*u^4 - 294*u^5 + 33*u^6 + 672*u^7 - 570*u^8 - 852*u^9 + 1488*u^10 + 322*u^11 - 2184*u^12 + 876*u^13 + 1920*u^14 - 1896*u^15 - 783*u^16 + 1940*u^17 - 302*u^18 - 1169*u^19 + 655*u^20 + 374*u^21 - 433*u^22 - 8*u^23 + 145*u^24 - 36*u^25 - 20*u^26 + 9*u^27)\/2", "(9 + 2*u + 32*u^2 - 65*u^3 - 59*u^4 + 292*u^5 - 57*u^6 - 636*u^7 + 570*u^8 + 804*u^9 - 1416*u^10 - 318*u^11 + 2072*u^12 - 768*u^13 - 1848*u^14 + 1716*u^15 + 825*u^16 - 1782*u^17 + 184*u^18 + 1103*u^19 - 541*u^20 - 376*u^21 + 373*u^22 + 28*u^23 - 127*u^24 + 26*u^25 + 18*u^26 - 7*u^27)\/2" ], [ "(3 + 2*u - 4*u^2 + 11*u^3 + 11*u^4 - 32*u^5 + 9*u^6 + 76*u^7 - 62*u^8 - 88*u^9 + 164*u^10 + 34*u^11 - 232*u^12 + 96*u^13 + 204*u^14 - 200*u^15 - 81*u^16 + 204*u^17 - 32*u^18 - 121*u^19 + 69*u^20 + 38*u^21 - 45*u^22 + 15*u^24 - 4*u^25 - 2*u^26 + u^27)\/2", "(1 - 2*u - 7*u^3 - 7*u^4 + 28*u^5 - 9*u^6 - 74*u^7 + 62*u^8 + 88*u^9 - 164*u^10 - 34*u^11 + 232*u^12 - 96*u^13 - 204*u^14 + 200*u^15 + 81*u^16 - 204*u^17 + 32*u^18 + 121*u^19 - 69*u^20 - 38*u^21 + 45*u^22 - 15*u^24 + 4*u^25 + 2*u^26 - u^27)\/2" ], "{1, 0}", [ 1, "-u^2" ], [ "-u", "u" ], [ 0, "u" ], [ "u^3", "u - u^3" ], [ "-5 + 3*u - 17*u^2 + 28*u^3 + 43*u^4 - 145*u^5 + 2*u^6 + 344*u^7 - 254*u^8 - 456*u^9 + 706*u^10 + 230*u^11 - 1066*u^12 + 336*u^13 + 974*u^14 - 841*u^15 - 447*u^16 + 897*u^17 - 79*u^18 - 556*u^19 + 273*u^20 + 187*u^21 - 190*u^22 - 10*u^23 + 65*u^24 - 15*u^25 - 9*u^26 + 4*u^27", "(7 + 4*u + 26*u^2 - 51*u^3 - 53*u^4 + 224*u^5 - 13*u^6 - 492*u^7 + 366*u^8 + 650*u^9 - 968*u^10 - 346*u^11 + 1460*u^12 - 402*u^13 - 1344*u^14 + 1090*u^15 + 651*u^16 - 1184*u^17 + 62*u^18 + 749*u^19 - 339*u^20 - 260*u^21 + 245*u^22 + 20*u^23 - 85*u^24 + 18*u^25 + 12*u^26 - 5*u^27)\/2" ] ], "Obstruction":-1, "ComplexVolumeN":[ "-5.32101 - 6.23266*I", "-5.32101 + 6.23266*I", "1.85217 - 1.40144*I", "1.85217 + 1.40144*I", "-6.61232 + 2.08114*I", "-6.61232 - 2.08114*I", "1.56772 + 4.24816*I", "1.56772 - 4.24816*I", "0.967687 - 0.906276*I", "0.967687 + 0.906276*I", "-2.52313 - 1.47542*I", "-2.52313 + 1.47542*I", "-0.41268 - 5.75423*I", "-0.41268 + 5.75423*I", "2.40233 - 0.64414*I", "2.40233 + 0.64414*I", "-1.3221 + 1.34593*I", "-1.3221 - 1.34593*I", "-5.39487 + 3.62399*I", "-5.39487 - 3.62399*I", "-0.59978 + 6.77427*I", "-0.59978 - 6.77427*I", "0.65193 + 3.28147*I", "0.65193 - 3.28147*I", "-3.12706 + 11.9545*I", "-3.12706 - 11.9545*I", "-0.22315 - 1.43304*I", "-0.22315 + 1.43304*I" ], "uPolysN":[ "4 + 8*u - 3*u^2 - 19*u^3 + u^4 + 44*u^5 + 15*u^6 - 49*u^7 - 8*u^8 + 26*u^9 - 18*u^10 + 6*u^11 + 20*u^12 - 8*u^13 + 34*u^14 + 14*u^15 - 70*u^16 - 48*u^17 + 37*u^18 + 73*u^19 + 17*u^20 - 60*u^21 - 35*u^22 + 29*u^23 + 22*u^24 - 8*u^25 - 7*u^26 + u^27 + u^28", "1 + 2*u + 3*u^2 + 4*u^3 + 8*u^4 + 12*u^5 + 18*u^6 + 33*u^7 + 54*u^8 + 84*u^9 + 126*u^10 + 164*u^11 + 218*u^12 + 256*u^13 + 292*u^14 + 312*u^15 + 313*u^16 + 298*u^17 + 271*u^18 + 220*u^19 + 186*u^20 + 124*u^21 + 98*u^22 + 51*u^23 + 37*u^24 + 14*u^25 + 9*u^26 + 2*u^27 + u^28", "17 - 22*u + 7*u^2 - 68*u^3 + 76*u^4 + 104*u^5 - 42*u^6 - 191*u^7 - 90*u^8 + 202*u^9 + 474*u^10 - 380*u^11 - 522*u^12 + 232*u^13 + 448*u^14 - 78*u^15 - 177*u^16 - 88*u^17 + 43*u^18 + 58*u^19 + 40*u^20 - 24*u^21 - 26*u^22 - 7*u^23 + 15*u^24 + 4*u^25 - 3*u^26 - 2*u^27 + u^28", "1 + u + 4*u^2 + 11*u^3 - 41*u^5 - 39*u^6 + 67*u^7 + 138*u^8 - 26*u^9 - 252*u^10 - 130*u^11 + 266*u^12 + 328*u^13 - 108*u^14 - 404*u^15 - 119*u^16 + 285*u^17 + 236*u^18 - 89*u^19 - 190*u^20 - 31*u^21 + 83*u^22 + 45*u^23 - 15*u^24 - 19*u^25 - 2*u^26 + 3*u^27 + u^28", "4 + 8*u - 3*u^2 - 19*u^3 + u^4 + 44*u^5 + 15*u^6 - 49*u^7 - 8*u^8 + 26*u^9 - 18*u^10 + 6*u^11 + 20*u^12 - 8*u^13 + 34*u^14 + 14*u^15 - 70*u^16 - 48*u^17 + 37*u^18 + 73*u^19 + 17*u^20 - 60*u^21 - 35*u^22 + 29*u^23 + 22*u^24 - 8*u^25 - 7*u^26 + u^27 + u^28", "1 + u + 4*u^2 + 11*u^3 - 41*u^5 - 39*u^6 + 67*u^7 + 138*u^8 - 26*u^9 - 252*u^10 - 130*u^11 + 266*u^12 + 328*u^13 - 108*u^14 - 404*u^15 - 119*u^16 + 285*u^17 + 236*u^18 - 89*u^19 - 190*u^20 - 31*u^21 + 83*u^22 + 45*u^23 - 15*u^24 - 19*u^25 - 2*u^26 + 3*u^27 + u^28", "1 + 7*u - 6*u^2 - 117*u^3 + 732*u^4 - 2503*u^5 + 6363*u^6 - 13269*u^7 + 24014*u^8 - 38822*u^9 + 56920*u^10 - 76262*u^11 + 93946*u^12 - 107020*u^13 + 113236*u^14 - 111480*u^15 + 102025*u^16 - 86533*u^17 + 67670*u^18 - 48409*u^19 + 31322*u^20 - 18057*u^21 + 9105*u^22 - 3927*u^23 + 1409*u^24 - 405*u^25 + 88*u^26 - 13*u^27 + u^28", "1 + 2*u + 3*u^2 + 4*u^3 + 8*u^4 + 12*u^5 + 18*u^6 + 33*u^7 + 54*u^8 + 84*u^9 + 126*u^10 + 164*u^11 + 218*u^12 + 256*u^13 + 292*u^14 + 312*u^15 + 313*u^16 + 298*u^17 + 271*u^18 + 220*u^19 + 186*u^20 + 124*u^21 + 98*u^22 + 51*u^23 + 37*u^24 + 14*u^25 + 9*u^26 + 2*u^27 + u^28", "1 + 2*u + 9*u^2 + 20*u^3 + 52*u^4 + 120*u^5 + 260*u^6 + 411*u^7 + 542*u^8 + 836*u^9 + 1738*u^10 + 3484*u^11 + 5778*u^12 + 8064*u^13 + 10312*u^14 + 13256*u^15 + 17557*u^16 + 22546*u^17 + 26081*u^18 + 25992*u^19 + 21850*u^20 + 15320*u^21 + 8872*u^22 + 4189*u^23 + 1581*u^24 + 462*u^25 + 99*u^26 + 14*u^27 + u^28" ], "uPolys":[ "4 + 8*u - 3*u^2 - 19*u^3 + u^4 + 44*u^5 + 15*u^6 - 49*u^7 - 8*u^8 + 26*u^9 - 18*u^10 + 6*u^11 + 20*u^12 - 8*u^13 + 34*u^14 + 14*u^15 - 70*u^16 - 48*u^17 + 37*u^18 + 73*u^19 + 17*u^20 - 60*u^21 - 35*u^22 + 29*u^23 + 22*u^24 - 8*u^25 - 7*u^26 + u^27 + u^28", "1 + 2*u + 3*u^2 + 4*u^3 + 8*u^4 + 12*u^5 + 18*u^6 + 33*u^7 + 54*u^8 + 84*u^9 + 126*u^10 + 164*u^11 + 218*u^12 + 256*u^13 + 292*u^14 + 312*u^15 + 313*u^16 + 298*u^17 + 271*u^18 + 220*u^19 + 186*u^20 + 124*u^21 + 98*u^22 + 51*u^23 + 37*u^24 + 14*u^25 + 9*u^26 + 2*u^27 + u^28", "17 - 22*u + 7*u^2 - 68*u^3 + 76*u^4 + 104*u^5 - 42*u^6 - 191*u^7 - 90*u^8 + 202*u^9 + 474*u^10 - 380*u^11 - 522*u^12 + 232*u^13 + 448*u^14 - 78*u^15 - 177*u^16 - 88*u^17 + 43*u^18 + 58*u^19 + 40*u^20 - 24*u^21 - 26*u^22 - 7*u^23 + 15*u^24 + 4*u^25 - 3*u^26 - 2*u^27 + u^28", "1 + u + 4*u^2 + 11*u^3 - 41*u^5 - 39*u^6 + 67*u^7 + 138*u^8 - 26*u^9 - 252*u^10 - 130*u^11 + 266*u^12 + 328*u^13 - 108*u^14 - 404*u^15 - 119*u^16 + 285*u^17 + 236*u^18 - 89*u^19 - 190*u^20 - 31*u^21 + 83*u^22 + 45*u^23 - 15*u^24 - 19*u^25 - 2*u^26 + 3*u^27 + u^28", "4 + 8*u - 3*u^2 - 19*u^3 + u^4 + 44*u^5 + 15*u^6 - 49*u^7 - 8*u^8 + 26*u^9 - 18*u^10 + 6*u^11 + 20*u^12 - 8*u^13 + 34*u^14 + 14*u^15 - 70*u^16 - 48*u^17 + 37*u^18 + 73*u^19 + 17*u^20 - 60*u^21 - 35*u^22 + 29*u^23 + 22*u^24 - 8*u^25 - 7*u^26 + u^27 + u^28", "1 + u + 4*u^2 + 11*u^3 - 41*u^5 - 39*u^6 + 67*u^7 + 138*u^8 - 26*u^9 - 252*u^10 - 130*u^11 + 266*u^12 + 328*u^13 - 108*u^14 - 404*u^15 - 119*u^16 + 285*u^17 + 236*u^18 - 89*u^19 - 190*u^20 - 31*u^21 + 83*u^22 + 45*u^23 - 15*u^24 - 19*u^25 - 2*u^26 + 3*u^27 + u^28", "1 + 7*u - 6*u^2 - 117*u^3 + 732*u^4 - 2503*u^5 + 6363*u^6 - 13269*u^7 + 24014*u^8 - 38822*u^9 + 56920*u^10 - 76262*u^11 + 93946*u^12 - 107020*u^13 + 113236*u^14 - 111480*u^15 + 102025*u^16 - 86533*u^17 + 67670*u^18 - 48409*u^19 + 31322*u^20 - 18057*u^21 + 9105*u^22 - 3927*u^23 + 1409*u^24 - 405*u^25 + 88*u^26 - 13*u^27 + u^28", "1 + 2*u + 3*u^2 + 4*u^3 + 8*u^4 + 12*u^5 + 18*u^6 + 33*u^7 + 54*u^8 + 84*u^9 + 126*u^10 + 164*u^11 + 218*u^12 + 256*u^13 + 292*u^14 + 312*u^15 + 313*u^16 + 298*u^17 + 271*u^18 + 220*u^19 + 186*u^20 + 124*u^21 + 98*u^22 + 51*u^23 + 37*u^24 + 14*u^25 + 9*u^26 + 2*u^27 + u^28", "1 + 2*u + 9*u^2 + 20*u^3 + 52*u^4 + 120*u^5 + 260*u^6 + 411*u^7 + 542*u^8 + 836*u^9 + 1738*u^10 + 3484*u^11 + 5778*u^12 + 8064*u^13 + 10312*u^14 + 13256*u^15 + 17557*u^16 + 22546*u^17 + 26081*u^18 + 25992*u^19 + 21850*u^20 + 15320*u^21 + 8872*u^22 + 4189*u^23 + 1581*u^24 + 462*u^25 + 99*u^26 + 14*u^27 + u^28" ], "aCuspShape":"9*u - u^2 - 29*u^3 + 30*u^4 + 53*u^5 - 93*u^6 - 38*u^7 + 182*u^8 - 40*u^9 - 212*u^10 + 176*u^11 + 142*u^12 - 242*u^13 + 6*u^14 + 190*u^15 - 92*u^16 - 69*u^17 + 81*u^18 - 3*u^19 - 24*u^20 + 13*u^21 - 5*u^22 + 6*u^24 - 3*u^25 - u^26 + u^27", "RepresentationsN":[ [ "u->0.421904 + 0.904838 I", "a->-0.038492 - 0.18997 I", "b->-1.4326 - 0.55257 I" ], [ "u->0.421904 - 0.904838 I", "a->-0.038492 + 0.18997 I", "b->-1.4326 + 0.55257 I" ], [ "u->-0.959758 + 0.402988 I", "a->-0.76677 + 1.05752 I", "b->-0.623667 - 0.562813 I" ], [ "u->-0.959758 - 0.402988 I", "a->-0.76677 - 1.05752 I", "b->-0.623667 + 0.562813 I" ], [ "u->0.619172 + 0.839658 I", "a->-0.016226 + 0.286921 I", "b->-1.01947 - 0.068324 I" ], [ "u->0.619172 - 0.839658 I", "a->-0.016226 - 0.286921 I", "b->-1.01947 + 0.068324 I" ], [ "u->0.96362 + 0.456689 I", "a->0.72093 + 1.60659 I", "b->-0.015157 - 1.39558 I" ], [ "u->0.96362 - 0.456689 I", "a->0.72093 - 1.60659 I", "b->-0.015157 + 1.39558 I" ], [ "u->0.855481 + 0.371946 I", "a->-1.18245 - 1.31391 I", "b->0.6684 + 1.28739 I" ], [ "u->0.855481 - 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22*u + 7*u^2 - 68*u^3 + 76*u^4 + 104*u^5 - 42*u^6 - 191*u^7 - 90*u^8 + 202*u^9 + 474*u^10 - 380*u^11 - 522*u^12 + 232*u^13 + 448*u^14 - 78*u^15 - 177*u^16 - 88*u^17 + 43*u^18 + 58*u^19 + 40*u^20 - 24*u^21 - 26*u^22 - 7*u^23 + 15*u^24 + 4*u^25 - 3*u^26 - 2*u^27 + u^28", "59 + 56*u - 33*u^2 + 294*u^3 + 664*u^4 - 254*u^5 + 1864*u^6 + 373*u^7 - 1364*u^8 + 7634*u^9 - 4924*u^10 - 4876*u^11 + 18582*u^12 - 18870*u^13 - 3028*u^14 + 11658*u^15 - 4567*u^16 - 17400*u^17 + 20891*u^18 - 18518*u^19 + 14792*u^20 - 6008*u^21 + 4036*u^22 - 915*u^23 + 547*u^24 - 68*u^25 + 37*u^26 - 2*u^27 + u^28", "76 + 392*u + 815*u^2 + 383*u^3 - 969*u^4 - 1428*u^5 + 55*u^6 - 491*u^7 - 998*u^8 - 3684*u^9 - 4050*u^10 - 4674*u^11 + 3748*u^12 + 3176*u^13 + 9484*u^14 + 5814*u^15 + 8782*u^16 + 3586*u^17 + 5425*u^18 + 1777*u^19 + 2361*u^20 + 752*u^21 + 725*u^22 + 219*u^23 + 152*u^24 + 38*u^25 + 19*u^26 + 3*u^27 + u^28", "1 + 2*u + 9*u^2 + 20*u^3 + 52*u^4 + 120*u^5 + 260*u^6 + 411*u^7 + 542*u^8 + 836*u^9 + 1738*u^10 + 3484*u^11 + 5778*u^12 + 8064*u^13 + 10312*u^14 + 13256*u^15 + 17557*u^16 + 22546*u^17 + 26081*u^18 + 25992*u^19 + 21850*u^20 + 15320*u^21 + 8872*u^22 + 4189*u^23 + 1581*u^24 + 462*u^25 + 99*u^26 + 14*u^27 + u^28", "701 - 40*u + 3377*u^2 - 732*u^3 + 6540*u^4 - 3846*u^5 + 10778*u^6 - 10151*u^7 + 13480*u^8 - 16350*u^9 + 18374*u^10 - 16654*u^11 + 18374*u^12 - 15228*u^13 + 13990*u^14 - 11254*u^15 + 8729*u^16 - 7014*u^17 + 4557*u^18 - 3300*u^19 + 1920*u^20 - 1038*u^21 + 568*u^22 - 209*u^23 + 95*u^24 - 32*u^25 + 15*u^26 - 4*u^27 + u^28", "4 + 8*u - 3*u^2 - 19*u^3 + u^4 + 44*u^5 + 15*u^6 - 49*u^7 - 8*u^8 + 26*u^9 - 18*u^10 + 6*u^11 + 20*u^12 - 8*u^13 + 34*u^14 + 14*u^15 - 70*u^16 - 48*u^17 + 37*u^18 + 73*u^19 + 17*u^20 - 60*u^21 - 35*u^22 + 29*u^23 + 22*u^24 - 8*u^25 - 7*u^26 + u^27 + u^28", "1357 + 3304*u + 10533*u^2 + 27388*u^3 + 33120*u^4 + 2272*u^5 - 44608*u^6 - 67795*u^7 - 32522*u^8 + 87704*u^9 + 247260*u^10 + 232342*u^11 + 29240*u^12 - 30328*u^13 + 159864*u^14 + 323052*u^15 + 298375*u^16 + 188514*u^17 + 102607*u^18 + 51948*u^19 + 22136*u^20 + 7508*u^21 + 2380*u^22 + 825*u^23 + 243*u^24 + 46*u^25 + 9*u^26 + 4*u^27 + u^28", "34228 + 154992*u + 589989*u^2 + 744393*u^3 + 351977*u^4 - 660684*u^5 + 405175*u^6 + 1787663*u^7 + 2590576*u^8 + 2528554*u^9 + 521526*u^10 - 804984*u^11 - 710696*u^12 - 304498*u^13 + 34460*u^14 + 58442*u^15 - 19818*u^16 + 12882*u^17 + 46085*u^18 + 28851*u^19 + 9987*u^20 + 4662*u^21 + 2261*u^22 + 603*u^23 + 150*u^24 + 34*u^25 - 3*u^26 + u^27 + u^28", "1 + 2*u + 3*u^2 + 8*u^3 + 30*u^4 + 146*u^5 + 364*u^6 + 873*u^7 + 2252*u^8 + 4978*u^9 + 11950*u^10 + 18334*u^11 + 31002*u^12 + 31238*u^13 + 41998*u^14 + 30318*u^15 + 33913*u^16 + 18446*u^17 + 17519*u^18 + 7426*u^19 + 6010*u^20 + 1994*u^21 + 1396*u^22 + 353*u^23 + 217*u^24 + 38*u^25 + 21*u^26 + 2*u^27 + u^28" ], "Multiplicity":1, "MinRepresentationVolume":[ "{15, 16}", 0.64414 ], "ij_list":[ [ "{4, 6}", "{4, 7}", "{5, 7}" ], [ "{4, 5}", "{6, 7}", "{6, 8}" ], [ "{7, 8}" ], [ "{1, 2}", "{4, 8}", "{5, 6}" ], [ "{3, 5}", "{5, 8}" ], [ "{3, 6}" ], [ "{3, 7}" ], [ "{3, 4}" ], [ "{2, 9}", "{3, 8}", "{3, 9}" ], [ "{1, 9}" ], [ "{1, 7}" ], [ "{1, 3}", "{1, 4}", "{2, 8}" ], [ "{5, 9}" ], [ "{1, 6}" ], [ "{1, 8}", "{2, 3}", "{8, 9}" ], [ "{6, 9}" ], [ "{1, 5}", "{2, 5}", "{2, 6}" ], [ "{4, 9}" ], [ "{7, 9}" ], [ "{2, 4}", "{2, 7}" ] ], "SortedReprnIndices":"{25, 26, 21, 22, 2, 1, 14, 13, 7, 8, 19, 20, 23, 24, 5, 6, 12, 11, 28, 27, 4, 3, 17, 18, 10, 9, 16, 15}", "aCuspShapeN":[ "-4.1497524293808488348`4.992098319115882 + 4.3007884985153339167`5.007624216878894*I", "-4.1497524293808488348`4.992098319115882 - 4.3007884985153339167`5.007624216878894*I", "4.6994694041842816671`5.122428149238373 + 1.7462963595999071255`4.692497271416257*I", "4.6994694041842816671`5.122428149238373 - 1.7462963595999071255`4.692497271416257*I", "-5.7959547953717167809`5.105299847120143 - 2.7886213145190119195`4.787564400045341*I", "-5.7959547953717167809`5.105299847120143 + 2.7886213145190119195`4.787564400045341*I", "1.8864489378082692785`4.567051824639951 - 6.9790380659192105842`5.135202337493184*I", "1.8864489378082692785`4.567051824639951 + 6.9790380659192105842`5.135202337493184*I", "-0.5976794911630401804`4.677879951099726 - 1.6709358995425343621`5.124371387241192*I", "-0.5976794911630401804`4.677879951099726 + 1.6709358995425343621`5.124371387241192*I", "-1.2934515630078849137`5.108622406620138 + 0.5966567611802440119`4.772596802977023*I", "-1.2934515630078849137`5.108622406620138 - 0.5966567611802440119`4.772596802977023*I", "0.1069786885925034938`3.4040194748925923 + 5.966546041974007971`5.150445201425338*I", "0.1069786885925034938`3.4040194748925923 - 5.966546041974007971`5.150445201425338*I", "4.3539811485479185013`5.131784273130964 - 1.3068307802239994947`4.609117083796188*I", "4.3539811485479185013`5.131784273130964 + 1.3068307802239994947`4.609117083796188*I", "-1.9193171463980586848`5.12615837415489 - 0.6612569678945374639`4.663381892403492*I", "-1.9193171463980586848`5.12615837415489 + 0.6612569678945374639`4.663381892403492*I", "-4.2087109302948953044`5.072751350086822 - 2.7618569777880510929`4.889803437224474*I", "-4.2087109302948953044`5.072751350086822 + 2.7618569777880510929`4.889803437224474*I", "1.7740637679174480548`4.677890708401278 - 4.9596214402622549843`5.124370010879412*I", "1.7740637679174480548`4.677890708401278 + 4.9596214402622549843`5.124370010879412*I", "-1.2326609558542909624`4.530074477680336 - 4.9939198931263729285`5.137672409226426*I", "-1.2326609558542909624`4.530074477680336 + 4.9939198931263729285`5.137672409226426*I", "-1.0411624408070625438`4.244422657006862 - 8.3222056746381774933`5.147142608875936*I", "-1.0411624408070625438`4.244422657006862 + 8.3222056746381774933`5.147142608875936*I", "-1.5822521947726233105`4.63199275624857 + 4.9760300417744648571`5.129600043139023*I", "-1.5822521947726233105`4.63199275624857 - 4.9760300417744648571`5.129600043139023*I" ], "Abelian":false }, { "IdealName":"J9_30_1", "Generators":[ "a + b", "1 - a + a^2", "1 + u" ], "VariableOrder":[ "b", "a", "u" ], "Characteristic":0, "KnownGroebner":[], "Status":[ "vCompNormalize" ], "MonomialOrder":"lex", "IsHomogeneous":false, "IsZeroDim":true, "IdealDimension":0, "Timings":{ "TimingGroebner":5.3756000000000005e-2, "TimingZeroDimVars":4.9580000000000006e-2, "TimingmagmaVCompNormalize":5.0962e-2, "TimingNumberOfSols":2.3411e-2, "TimingIsRadical":1.585e-3, "TimingArcColoring":4.4896000000000005e-2, "TimingObstruction":1.075e-3, "TimingComplexVolumeN":2.678524, "TimingaCuspShapeN":9.664e-3, "TiminguValues":0.568662, "TiminguPolysN":3.31e-4, "TiminguPolys":0.720172, "TimingaCuspShape":9.1067e-2, "TimingRepresentationsN":2.572e-2, "TiminguValues_ij":0.105876, "TiminguPolys_ij_N":3.06e-4 }, "ZeroDimensionalVars":[ "b", "a", "u" ], "NumberOfSols":2, "IsRadical":true, "ArcColoring":[ [ "a", "-a" ], [ "a", "-a" ], [ "a", "1 - a" ], "{1, 0}", "{1, -1}", "{1, -1}", "{0, -1}", "{-1, 0}", [ 0, "-a" ] ], "Obstruction":1, "ComplexVolumeN":[ "1.64493 - 2.02988*I", "1.64493 + 2.02988*I" ], "uPolysN":[ "u^2", "1 - u + u^2", "1 + u + u^2", "1 + 2*u + u^2", "u^2", "1 - 2*u + u^2", "1 - 2*u + u^2", "1 + u + u^2", "1 + u + u^2" ], "uPolys":[ "u^2", "1 - u + u^2", "1 + u + u^2", "(1 + u)^2", "u^2", "(-1 + u)^2", "(-1 + u)^2", "1 + u + u^2", "1 + u + u^2" ], "aCuspShape":"1 + 4*a", "RepresentationsN":[ [ "u->-1.", "a->0.5 + 0.866025 I", "b->-0.5 - 0.866025 I" ], [ "u->-1.", "a->0.5 - 0.866025 I", "b->-0.5 + 0.866025 I" ] ], "Epsilon":2.44949, "uPolys_ij_N":[ "1 + 2*u + u^2", "u^2", "1 - u + u^2", "1 + u + u^2", "1 + u + u^2", "1 - u + u^2" ], "GeometricComponent":0, "Multiplicity":1, "MinRepresentationVolume":[ "{1, 2}", 2.02988 ], "ij_list":[ [ "{3, 5}", "{3, 6}", "{4, 5}", "{4, 6}", "{4, 7}", "{5, 7}", "{5, 8}", "{6, 7}", "{6, 8}", "{7, 8}" ], [ "{1, 2}", "{1, 5}", "{1, 6}", "{2, 5}", "{2, 6}", "{4, 8}", "{5, 6}", "{7, 9}" ], [ "{1, 9}", "{2, 9}", "{3, 8}", "{3, 9}" ], [ "{3, 4}" ], [ "{1, 7}", "{1, 8}", "{2, 7}", "{2, 8}", "{3, 7}", "{4, 9}", "{5, 9}", "{6, 9}" ], [ "{1, 3}", "{1, 4}", "{2, 3}", "{2, 4}", "{8, 9}" ] ], "SortedReprnIndices":"{2, 1}", "aCuspShapeN":[ "3.`4.9665266051846935 + 3.464101615137754587`5.028995973488844*I", "3.`4.9665266051846935 - 3.464101615137754587`5.028995973488844*I" ], "Abelian":false }, { "IdealName":"abJ9_30_2", "Generators":[ "b", "-1 + a", "-1 + v" ], "VariableOrder":[ "b", "a", "v" ], "Characteristic":0, "KnownGroebner":[], "Status":[ "vCompNormalize" ], "MonomialOrder":"lex", "IsHomogeneous":false, "IsZeroDim":true, "IdealDimension":0, "Timings":{ "TimingGroebner":5.1003999999999994e-2, "TimingZeroDimVars":4.9229e-2, "TimingmagmaVCompNormalize":5.0497e-2, "TimingNumberOfSols":1.9155000000000002e-2, "TimingIsRadical":1.1970000000000001e-3, "TimingArcColoring":4.1184000000000005e-2, "TimingObstruction":3.8e-4, "TimingComplexVolumeN":0.392856, "TimingaCuspShapeN":4.247e-3, "TiminguValues":0.561011, "TiminguPolysN":6.7e-5, "TiminguPolys":0.723091, "TimingaCuspShape":9.0394e-2, "TimingRepresentationsN":2.2135e-2, "TiminguValues_ij":0.102369, "TiminguPoly_ij":0.111385, "TiminguPolys_ij_N":2.7000000000000002e-5 }, "ZeroDimensionalVars":[ "b", "a", "v" ], "NumberOfSols":1, "IsRadical":true, "ArcColoring":[ "{1, 0}", "{1, 0}", "{1, 0}", "{1, 0}", "{1, 0}", "{1, 0}", "{1, 0}", "{1, 0}", "{1, 0}" ], "Obstruction":1, "ComplexVolumeN":"{0}", "uPolysN":[ "u", "u", "u", "u", "u", "u", "u", "u", "u" ], "uPolys":[ "u", "u", "u", "u", "u", "u", "u", "u", "u" ], "aCuspShape":0, "RepresentationsN":[ [ "v->1.", "a->1.", "b->0" ] ], "Epsilon":"Infinity", "uPolys_ij":[ "u" ], "GeometricComponent":0, "uPolys_ij_N":[ "u" ], "Multiplicity":1, "ij_list":[ [ "{1, 2}", "{1, 3}", "{1, 4}", "{1, 5}", "{1, 6}", "{1, 7}", "{1, 8}", "{1, 9}", "{2, 3}", "{2, 4}", "{2, 5}", "{2, 6}", "{2, 7}", "{2, 8}", "{2, 9}", "{3, 4}", "{3, 5}", "{3, 6}", "{3, 7}", "{3, 8}", "{3, 9}", "{4, 5}", "{4, 6}", "{4, 7}", "{4, 8}", "{4, 9}", "{5, 6}", "{5, 7}", "{5, 8}", "{5, 9}", "{6, 7}", "{6, 8}", "{6, 9}", "{7, 8}", "{7, 9}", "{8, 9}" ] ], "SortedReprnIndices":"{1}", "aCuspShapeN":"{0}", "Abelian":true } ] }, "uPolyC":[ "u^2*(4 + 8*u - 3*u^2 - 19*u^3 + u^4 + 44*u^5 + 15*u^6 - 49*u^7 - 8*u^8 + 26*u^9 - 18*u^10 + 6*u^11 + 20*u^12 - 8*u^13 + 34*u^14 + 14*u^15 - 70*u^16 - 48*u^17 + 37*u^18 + 73*u^19 + 17*u^20 - 60*u^21 - 35*u^22 + 29*u^23 + 22*u^24 - 8*u^25 - 7*u^26 + u^27 + u^28)", "(1 - u + u^2)*(1 + 2*u + 3*u^2 + 4*u^3 + 8*u^4 + 12*u^5 + 18*u^6 + 33*u^7 + 54*u^8 + 84*u^9 + 126*u^10 + 164*u^11 + 218*u^12 + 256*u^13 + 292*u^14 + 312*u^15 + 313*u^16 + 298*u^17 + 271*u^18 + 220*u^19 + 186*u^20 + 124*u^21 + 98*u^22 + 51*u^23 + 37*u^24 + 14*u^25 + 9*u^26 + 2*u^27 + u^28)", "(1 + u + u^2)*(17 - 22*u + 7*u^2 - 68*u^3 + 76*u^4 + 104*u^5 - 42*u^6 - 191*u^7 - 90*u^8 + 202*u^9 + 474*u^10 - 380*u^11 - 522*u^12 + 232*u^13 + 448*u^14 - 78*u^15 - 177*u^16 - 88*u^17 + 43*u^18 + 58*u^19 + 40*u^20 - 24*u^21 - 26*u^22 - 7*u^23 + 15*u^24 + 4*u^25 - 3*u^26 - 2*u^27 + u^28)", "(1 + u)^2*(1 + u + 4*u^2 + 11*u^3 - 41*u^5 - 39*u^6 + 67*u^7 + 138*u^8 - 26*u^9 - 252*u^10 - 130*u^11 + 266*u^12 + 328*u^13 - 108*u^14 - 404*u^15 - 119*u^16 + 285*u^17 + 236*u^18 - 89*u^19 - 190*u^20 - 31*u^21 + 83*u^22 + 45*u^23 - 15*u^24 - 19*u^25 - 2*u^26 + 3*u^27 + u^28)", "u^2*(4 + 8*u - 3*u^2 - 19*u^3 + u^4 + 44*u^5 + 15*u^6 - 49*u^7 - 8*u^8 + 26*u^9 - 18*u^10 + 6*u^11 + 20*u^12 - 8*u^13 + 34*u^14 + 14*u^15 - 70*u^16 - 48*u^17 + 37*u^18 + 73*u^19 + 17*u^20 - 60*u^21 - 35*u^22 + 29*u^23 + 22*u^24 - 8*u^25 - 7*u^26 + u^27 + u^28)", "(-1 + u)^2*(1 + u + 4*u^2 + 11*u^3 - 41*u^5 - 39*u^6 + 67*u^7 + 138*u^8 - 26*u^9 - 252*u^10 - 130*u^11 + 266*u^12 + 328*u^13 - 108*u^14 - 404*u^15 - 119*u^16 + 285*u^17 + 236*u^18 - 89*u^19 - 190*u^20 - 31*u^21 + 83*u^22 + 45*u^23 - 15*u^24 - 19*u^25 - 2*u^26 + 3*u^27 + u^28)", "(-1 + u)^2*(1 + 7*u - 6*u^2 - 117*u^3 + 732*u^4 - 2503*u^5 + 6363*u^6 - 13269*u^7 + 24014*u^8 - 38822*u^9 + 56920*u^10 - 76262*u^11 + 93946*u^12 - 107020*u^13 + 113236*u^14 - 111480*u^15 + 102025*u^16 - 86533*u^17 + 67670*u^18 - 48409*u^19 + 31322*u^20 - 18057*u^21 + 9105*u^22 - 3927*u^23 + 1409*u^24 - 405*u^25 + 88*u^26 - 13*u^27 + u^28)", "(1 + u + u^2)*(1 + 2*u + 3*u^2 + 4*u^3 + 8*u^4 + 12*u^5 + 18*u^6 + 33*u^7 + 54*u^8 + 84*u^9 + 126*u^10 + 164*u^11 + 218*u^12 + 256*u^13 + 292*u^14 + 312*u^15 + 313*u^16 + 298*u^17 + 271*u^18 + 220*u^19 + 186*u^20 + 124*u^21 + 98*u^22 + 51*u^23 + 37*u^24 + 14*u^25 + 9*u^26 + 2*u^27 + u^28)", "(1 + u + u^2)*(1 + 2*u + 9*u^2 + 20*u^3 + 52*u^4 + 120*u^5 + 260*u^6 + 411*u^7 + 542*u^8 + 836*u^9 + 1738*u^10 + 3484*u^11 + 5778*u^12 + 8064*u^13 + 10312*u^14 + 13256*u^15 + 17557*u^16 + 22546*u^17 + 26081*u^18 + 25992*u^19 + 21850*u^20 + 15320*u^21 + 8872*u^22 + 4189*u^23 + 1581*u^24 + 462*u^25 + 99*u^26 + 14*u^27 + u^28)" ], "RileyPolyC":[ "y^2*(16 - 88*y + 321*y^2 - 951*y^3 + 2303*y^4 - 4280*y^5 + 5681*y^6 - 4457*y^7 + 292*y^8 + 3588*y^9 - 4522*y^10 + 6038*y^11 - 12678*y^12 + 19468*y^13 - 15952*y^14 + 2172*y^15 + 9648*y^16 - 11216*y^17 + 6921*y^18 - 4703*y^19 + 5967*y^20 - 7144*y^21 + 6059*y^22 - 3651*y^23 + 1592*y^24 - 500*y^25 + 109*y^26 - 15*y^27 + y^28)", "(1 + y + y^2)*(1 + 2*y + 9*y^2 + 20*y^3 + 52*y^4 + 120*y^5 + 260*y^6 + 411*y^7 + 542*y^8 + 836*y^9 + 1738*y^10 + 3484*y^11 + 5778*y^12 + 8064*y^13 + 10312*y^14 + 13256*y^15 + 17557*y^16 + 22546*y^17 + 26081*y^18 + 25992*y^19 + 21850*y^20 + 15320*y^21 + 8872*y^22 + 4189*y^23 + 1581*y^24 + 462*y^25 + 99*y^26 + 14*y^27 + y^28)", "(1 + y + y^2)*(289 - 246*y - 359*y^2 - 412*y^3 + 7868*y^4 - 19432*y^5 + 27452*y^6 - 32437*y^7 + 73518*y^8 - 223092*y^9 + 505014*y^10 - 797204*y^11 + 890242*y^12 - 701632*y^13 + 362136*y^14 - 77840*y^15 - 52955*y^16 + 67178*y^17 - 40731*y^18 + 18108*y^19 - 6574*y^20 + 1796*y^21 + 112*y^22 - 559*y^23 + 421*y^24 - 186*y^25 + 55*y^26 - 10*y^27 + y^28)", "(-1 + y)^2*(1 + 7*y - 6*y^2 - 117*y^3 + 732*y^4 - 2503*y^5 + 6363*y^6 - 13269*y^7 + 24014*y^8 - 38822*y^9 + 56920*y^10 - 76262*y^11 + 93946*y^12 - 107020*y^13 + 113236*y^14 - 111480*y^15 + 102025*y^16 - 86533*y^17 + 67670*y^18 - 48409*y^19 + 31322*y^20 - 18057*y^21 + 9105*y^22 - 3927*y^23 + 1409*y^24 - 405*y^25 + 88*y^26 - 13*y^27 + y^28)", "y^2*(16 - 88*y + 321*y^2 - 951*y^3 + 2303*y^4 - 4280*y^5 + 5681*y^6 - 4457*y^7 + 292*y^8 + 3588*y^9 - 4522*y^10 + 6038*y^11 - 12678*y^12 + 19468*y^13 - 15952*y^14 + 2172*y^15 + 9648*y^16 - 11216*y^17 + 6921*y^18 - 4703*y^19 + 5967*y^20 - 7144*y^21 + 6059*y^22 - 3651*y^23 + 1592*y^24 - 500*y^25 + 109*y^26 - 15*y^27 + y^28)", "(-1 + y)^2*(1 + 7*y - 6*y^2 - 117*y^3 + 732*y^4 - 2503*y^5 + 6363*y^6 - 13269*y^7 + 24014*y^8 - 38822*y^9 + 56920*y^10 - 76262*y^11 + 93946*y^12 - 107020*y^13 + 113236*y^14 - 111480*y^15 + 102025*y^16 - 86533*y^17 + 67670*y^18 - 48409*y^19 + 31322*y^20 - 18057*y^21 + 9105*y^22 - 3927*y^23 + 1409*y^24 - 405*y^25 + 88*y^26 - 13*y^27 + y^28)", "(-1 + y)^2*(1 - 61*y + 3138*y^2 + 25295*y^3 + 107560*y^4 + 314657*y^5 + 707823*y^6 + 1275843*y^7 + 1910510*y^8 + 2393482*y^9 + 2558064*y^10 + 2323754*y^11 + 1821074*y^12 + 1227228*y^13 + 734060*y^14 + 397672*y^15 + 213229*y^16 + 112323*y^17 + 58950*y^18 + 25139*y^19 + 8134*y^20 + 807*y^21 - 435*y^22 - 231*y^23 + 53*y^24 + 67*y^25 + 32*y^26 + 7*y^27 + y^28)", "(1 + y + y^2)*(1 + 2*y + 9*y^2 + 20*y^3 + 52*y^4 + 120*y^5 + 260*y^6 + 411*y^7 + 542*y^8 + 836*y^9 + 1738*y^10 + 3484*y^11 + 5778*y^12 + 8064*y^13 + 10312*y^14 + 13256*y^15 + 17557*y^16 + 22546*y^17 + 26081*y^18 + 25992*y^19 + 21850*y^20 + 15320*y^21 + 8872*y^22 + 4189*y^23 + 1581*y^24 + 462*y^25 + 99*y^26 + 14*y^27 + y^28)", "(1 + y + y^2)*(1 + 14*y + 105*y^2 + 576*y^3 + 2024*y^4 + 6088*y^5 + 20792*y^6 + 46043*y^7 + 120230*y^8 + 210660*y^9 + 344218*y^10 + 485948*y^11 + 504530*y^12 + 474304*y^13 + 379784*y^14 + 262368*y^15 + 170433*y^16 + 94954*y^17 + 52913*y^18 + 24212*y^19 + 12726*y^20 + 4384*y^21 + 2380*y^22 + 549*y^23 + 321*y^24 + 46*y^25 + 27*y^26 + 2*y^27 + y^28)" ] }, "GeometricRepresentation":[ 1.19545e1, [ "J9_30_0", 1, "{25, 26}" ] ] } }