{ "Index":73, "Name":"9_38", "RolfsenName":"9_38", "DTname":"9a_30", "TunnelNumber":2, "BridgeNumber":"Not implemented", "Hyperbolic":true, "Diagram":{ "Scode":"{13, 9, 15, 3, 17, 5, 1, 11, 7}", "Acode":"{7, 5, 8, 2, 9, 3, 1, 6, 4}", "PDcode":[ "{2, 14, 3, 13}", "{4, 10, 5, 9}", "{6, 16, 7, 15}", "{8, 4, 9, 3}", "{10, 18, 11, 17}", "{12, 6, 13, 5}", "{14, 2, 15, 1}", "{16, 12, 17, 11}", "{18, 8, 1, 7}" ], "CBtype":"{3, 0}", "ParabolicReps":{ "SolvingSeq":[ "{5, 9, 3}", [], [ "{5, 9, 6, 1}", "{6, 3, 7, 1}", "{3, 5, 2, 2}", "{2, 7, 1, 2}", "{5, 2, 4, 2}", "{9, 6, 8, 2}" ], "{3, 9}", "{7}", 7 ], "SolvingSeqIdx":1, "Comps":{ "u":{ "CheckEq":[ "-1 + a + a*b + b^2 + a*u^2 - b*u^2 + a*u^4", "b + b^2 + a*u^2 - b*u^2 + 2*a*u^4 - b*u^4 + a*u^6", "-a - 2*b - a*b^2 + b^3 + a*b^4 - u + 2*a*b*u + 2*b^2*u - a^2*b^2*u - 2*a*b^3*u - b^4*u + a*u^2 + b*u^2 + 2*a^2*b*u^2 - 2*a^2*b^3*u^2 - a^3*u^4 - a^2*b*u^4 + a^3*b^2*u^4", "-b - b^3 + b^5 + u + b^2*u - a*b^3*u - b^4*u - b*u^2 + 2*a*b^2*u^2 + 2*b^3*u^2 - 2*a*b^4*u^2 + a*u^4 + b*u^4 - a^2*b*u^4 - 2*a*b^2*u^4 + a^2*b^3*u^4" ], "TimingForPrimaryIdeals":0.102896 }, "v":{ "CheckEq":[ "b + b^2", "-b - b^3 + b^5 + b^4*v", "-a - 2*b - a*b^2 + b^3 + a*b^4 + v - b^2*v + a*b^3*v + b^4*v", "-1 + a + a*b + b^2 - b*v^2" ], "TimingForPrimaryIdeals":9.6919e-2 }, "PrimaryIdeals":[ { "IdealName":"J9_38_0", "Generators":[ "1 + 4*b - 4*u - 13*u^2 - 16*u^3 - 23*u^4 - 20*u^5 - 14*u^6 - 11*u^7 - 5*u^8 - 2*u^9 - u^10", "-9 + 8*a - 4*u - 7*u^2 + 15*u^4 + 12*u^5 + 10*u^6 + 11*u^7 + 5*u^8 + 2*u^9 + u^10", "1 + 3*u + 3*u^2 + 9*u^3 + 9*u^4 + 11*u^5 + 10*u^6 + 7*u^7 + 6*u^8 + 3*u^9 + u^10 + u^11" ], "VariableOrder":[ "b", "a", "u" ], "Characteristic":0, "KnownGroebner":[], "Status":[ "vCompNormalize" ], "MonomialOrder":"lex", "IsHomogeneous":false, "IsZeroDim":true, "IdealDimension":0, "Timings":{ "TimingGroebner":5.5193000000000006e-2, "TimingZeroDimVars":4.9710000000000004e-2, "TimingmagmaVCompNormalize":5.0929e-2, "TimingNumberOfSols":0.112361, "TimingIsRadical":5.674e-3, "TimingArcColoring":5.3083e-2, "TimingObstruction":1.6838e-2, "TimingComplexVolumeN":9.57031, "TimingaCuspShapeN":4.5441e-2, "TiminguValues":0.608494, "TiminguPolysN":1.1072e-2, "TiminguPolys":0.744235, "TimingaCuspShape":0.106753, "TimingRepresentationsN":0.104103, "TiminguValues_ij":0.141374, "TiminguPoly_ij":1.18339, "TiminguPolys_ij_N":1.7456e-2 }, "ZeroDimensionalVars":[ "b", "a", "u" ], "NumberOfSols":11, "IsRadical":true, "ArcColoring":[ [ "(15 + 28*u + 41*u^2 + 48*u^3 + 39*u^4 + 28*u^5 + 18*u^6 + 11*u^7 + 5*u^8 + 2*u^9 + u^10)\/16", "(-1 + 12*u + 25*u^2 + 32*u^3 + 31*u^4 + 28*u^5 + 18*u^6 + 11*u^7 + 5*u^8 + 2*u^9 + u^10)\/8" ], [ "(7 + 12*u + 33*u^2 + 32*u^3 + 31*u^4 + 28*u^5 + 18*u^6 + 11*u^7 + 5*u^8 + 2*u^9 + u^10)\/8", "(-1 + 4*u + 13*u^2 + 16*u^3 + 23*u^4 + 20*u^5 + 14*u^6 + 11*u^7 + 5*u^8 + 2*u^9 + u^10)\/4" ], [ "(9 + 4*u + 7*u^2 - 15*u^4 - 12*u^5 - 10*u^6 - 11*u^7 - 5*u^8 - 2*u^9 - u^10)\/8", "(-1 + 4*u + 13*u^2 + 16*u^3 + 23*u^4 + 20*u^5 + 14*u^6 + 11*u^7 + 5*u^8 + 2*u^9 + u^10)\/4" ], [ "(13 + 20*u + 43*u^2 + 48*u^3 + 53*u^4 + 52*u^5 + 38*u^6 + 25*u^7 + 15*u^8 + 6*u^9 + 3*u^10)\/8", "(-1 + 4*u + 21*u^2 + 24*u^3 + 39*u^4 + 36*u^5 + 30*u^6 + 27*u^7 + 13*u^8 + 6*u^9 + 5*u^10)\/4" ], "{1, 0}", [ 1, "u^2" ], [ "(1 - 28*u - 25*u^2 - 32*u^3 - 39*u^4 - 28*u^5 - 18*u^6 - 11*u^7 - 5*u^8 - 2*u^9 - u^10)\/16", "(1 - 4*u - 9*u^2 - 24*u^3 - 23*u^4 - 20*u^5 - 18*u^6 - 11*u^7 - 5*u^8 - 2*u^9 - u^10)\/8" ], [ "u", "u + u^3" ], [ 0, "u" ] ], "Obstruction":-1, "ComplexVolumeN":[ "0.53843 + 4.57539*I", "0.53843 - 4.57539*I", "-3.44203 - 0.72668*I", "-3.44203 + 0.72668*I", "-1.48009 - 1.36667*I", "-1.48009 + 1.36667*I", "6.41512 - 6.3068*I", "6.41512 + 6.3068*I", "3.25113 - 12.9329*I", "3.25113 + 12.9329*I", -0.69551 ], "uPolysN":[ "1 + 3*u + 3*u^2 + 9*u^3 + 9*u^4 + 11*u^5 + 10*u^6 + 7*u^7 + 6*u^8 + 3*u^9 + u^10 + u^11", "4 + 9*u - 16*u^2 - 5*u^3 + 10*u^4 - u^5 - 2*u^6 + 4*u^7 + u^8 - 3*u^9 + u^11", "8 - 6*u - u^2 + 35*u^3 - 38*u^4 + 42*u^5 - 39*u^6 + 25*u^7 - 13*u^8 + 6*u^9 - 3*u^10 + u^11", "4 + 9*u - 16*u^2 - 5*u^3 + 10*u^4 - u^5 - 2*u^6 + 4*u^7 + u^8 - 3*u^9 + u^11", "1 + 3*u + 3*u^2 + 9*u^3 + 9*u^4 + 11*u^5 + 10*u^6 + 7*u^7 + 6*u^8 + 3*u^9 + u^10 + u^11", "1\/2 - (5*u^2)\/2 + 3*u^3 + (7*u^4)\/2 - 7*u^5 + u^6 + (11*u^7)\/2 - (3*u^8)\/2 + u^10\/2 + u^11", "1 + 3*u + 3*u^2 + 9*u^3 + 9*u^4 + 11*u^5 + 10*u^6 + 7*u^7 + 6*u^8 + 3*u^9 + u^10 + u^11", "1 + 3*u + 3*u^2 + 9*u^3 + 9*u^4 + 11*u^5 + 10*u^6 + 7*u^7 + 6*u^8 + 3*u^9 + u^10 + u^11", "1\/2 - (5*u^2)\/2 + 3*u^3 + (7*u^4)\/2 - 7*u^5 + u^6 + (11*u^7)\/2 - (3*u^8)\/2 + u^10\/2 + u^11" ], "uPolys":[ "1 + 3*u + 3*u^2 + 9*u^3 + 9*u^4 + 11*u^5 + 10*u^6 + 7*u^7 + 6*u^8 + 3*u^9 + u^10 + u^11", "4 + 9*u - 16*u^2 - 5*u^3 + 10*u^4 - u^5 - 2*u^6 + 4*u^7 + u^8 - 3*u^9 + u^11", "8 - 6*u - u^2 + 35*u^3 - 38*u^4 + 42*u^5 - 39*u^6 + 25*u^7 - 13*u^8 + 6*u^9 - 3*u^10 + u^11", "4 + 9*u - 16*u^2 - 5*u^3 + 10*u^4 - u^5 - 2*u^6 + 4*u^7 + u^8 - 3*u^9 + u^11", "1 + 3*u + 3*u^2 + 9*u^3 + 9*u^4 + 11*u^5 + 10*u^6 + 7*u^7 + 6*u^8 + 3*u^9 + u^10 + u^11", "2*(1 - 5*u^2 + 6*u^3 + 7*u^4 - 14*u^5 + 2*u^6 + 11*u^7 - 3*u^8 + u^10 + 2*u^11)", "1 + 3*u + 3*u^2 + 9*u^3 + 9*u^4 + 11*u^5 + 10*u^6 + 7*u^7 + 6*u^8 + 3*u^9 + u^10 + u^11", "1 + 3*u + 3*u^2 + 9*u^3 + 9*u^4 + 11*u^5 + 10*u^6 + 7*u^7 + 6*u^8 + 3*u^9 + u^10 + u^11", "2*(1 - 5*u^2 + 6*u^3 + 7*u^4 - 14*u^5 + 2*u^6 + 11*u^7 - 3*u^8 + u^10 + 2*u^11)" ], "aCuspShape":"-9 + (-37 + 124*u - 3*u^2 + 112*u^3 - 13*u^4 + 28*u^5 + 74*u^6 - 41*u^7 - 23*u^8 + 26*u^9 - 27*u^10)\/16", "RepresentationsN":[ [ "u->-0.361784 + 0.962924 I", "a->0.42885 - 1.90311 I", "b->-1.01942 + 0.904921 I" ], [ "u->-0.361784 - 0.962924 I", "a->0.42885 + 1.90311 I", "b->-1.01942 - 0.904921 I" ], [ "u->-1.18663 + 0.35521 I", "a->0.360998 + 0.003803 I", "b->0.988348 + 0.222965 I" ], [ "u->-1.18663 - 0.35521 I", "a->0.360998 - 0.003803 I", "b->0.988348 - 0.222965 I" ], [ "u->0.256965 + 0.681325 I", "a->0.56568 + 0.993565 I", "b->-1.4182 - 0.12736 I" ], [ "u->0.256965 - 0.681325 I", "a->0.56568 - 0.993565 I", "b->-1.4182 + 0.12736 I" ], [ "u->0.39161 + 1.21014 I", "a->-0.57189 + 1.31384 I", "b->0.308687 - 1.22493 I" ], [ "u->0.39161 - 1.21014 I", "a->-0.57189 - 1.31384 I", "b->0.308687 + 1.22493 I" ], [ "u->0.57851 + 1.29417 I", "a->-0.05089 - 1.59336 I", "b->1.29294 + 0.6749 I" ], [ "u->0.57851 - 1.29417 I", "a->-0.05089 + 1.59336 I", "b->1.29294 - 0.6749 I" ], [ "u->-0.357337", "a->1.0345", "b->-0.304704" ] ], "Epsilon":0.838812, "uPolys_ij":[ "1 + 3*u + 3*u^2 + 9*u^3 + 9*u^4 + 11*u^5 + 10*u^6 + 7*u^7 + 6*u^8 + 3*u^9 + u^10 + u^11", "1 + 3*u - 27*u^2 + 73*u^3 - 87*u^4 + 47*u^5 - 5*u^7 - 8*u^8 + 11*u^9 - 5*u^10 + u^11", "4 + 16*u + 29*u^2 + 45*u^3 + 20*u^4 + 85*u^6 + 165*u^7 + 129*u^8 + 52*u^9 + 11*u^10 + u^11", "64 + 52*u - 187*u^2 + 1269*u^3 - 1326*u^4 + 500*u^5 + 7*u^6 - 43*u^7 + 19*u^8 + 8*u^9 - 3*u^10 + u^11", "8 - 6*u - u^2 + 35*u^3 - 38*u^4 + 42*u^5 - 39*u^6 + 25*u^7 - 13*u^8 + 6*u^9 - 3*u^10 + u^11", "2*(7 + 56*u + 167*u^2 + 216*u^3 + 75*u^4 - 88*u^5 - 72*u^6 + 47*u^7 + 29*u^8 - 14*u^9 - 3*u^10 + 2*u^11)", "4*(28 + 125*u - 161*u^2 - 360*u^3 + 38*u^4 + 391*u^5 + 201*u^6 - 29*u^7 + 22*u^8 + 71*u^9 + 31*u^10 + 4*u^11)", "4*(1 + 10*u + 39*u^2 + 102*u^3 + 191*u^4 + 268*u^5 + 260*u^6 + 143*u^7 + 69*u^8 + 50*u^9 + u^10 + 4*u^11)", "4*(98 + 945*u + 3973*u^2 + 9618*u^3 + 14944*u^4 + 15739*u^5 + 11529*u^6 + 5899*u^7 + 2072*u^8 + 477*u^9 + 65*u^10 + 4*u^11)", "2*(1 + 8*u + 25*u^2 + 34*u^3 - 19*u^4 - 70*u^5 - 12*u^6 + 49*u^7 + 11*u^8 - 14*u^9 - u^10 + 2*u^11)", "2*(17 + 108*u + 291*u^2 + 496*u^3 + 635*u^4 + 622*u^5 + 432*u^6 + 199*u^7 + 59*u^8 + 16*u^9 + 7*u^10 + 2*u^11)", "4 + 9*u - 16*u^2 - 5*u^3 + 10*u^4 - u^5 - 2*u^6 + 4*u^7 + u^8 - 3*u^9 + u^11", "2*(1 - 5*u^2 + 6*u^3 + 7*u^4 - 14*u^5 + 2*u^6 + 11*u^7 - 3*u^8 + u^10 + 2*u^11)", "2*(1 + 22*u + 167*u^2 + 510*u^3 + 617*u^4 + 426*u^5 + 122*u^6 - 85*u^7 - 73*u^8 - 4*u^9 + 9*u^10 + 2*u^11)", "16 + 209*u + 426*u^2 + 343*u^3 + 90*u^4 - 21*u^5 - 16*u^6 + 16*u^7 + 27*u^8 + 17*u^9 + 6*u^10 + u^11" ], "GeometricComponent":"{9, 10}", "uPolys_ij_N":[ "1 + 3*u + 3*u^2 + 9*u^3 + 9*u^4 + 11*u^5 + 10*u^6 + 7*u^7 + 6*u^8 + 3*u^9 + u^10 + u^11", "1 + 3*u - 27*u^2 + 73*u^3 - 87*u^4 + 47*u^5 - 5*u^7 - 8*u^8 + 11*u^9 - 5*u^10 + u^11", "4 + 16*u + 29*u^2 + 45*u^3 + 20*u^4 + 85*u^6 + 165*u^7 + 129*u^8 + 52*u^9 + 11*u^10 + u^11", "64 + 52*u - 187*u^2 + 1269*u^3 - 1326*u^4 + 500*u^5 + 7*u^6 - 43*u^7 + 19*u^8 + 8*u^9 - 3*u^10 + u^11", "8 - 6*u - u^2 + 35*u^3 - 38*u^4 + 42*u^5 - 39*u^6 + 25*u^7 - 13*u^8 + 6*u^9 - 3*u^10 + u^11", "7\/2 + 28*u + (167*u^2)\/2 + 108*u^3 + (75*u^4)\/2 - 44*u^5 - 36*u^6 + (47*u^7)\/2 + (29*u^8)\/2 - 7*u^9 - (3*u^10)\/2 + u^11", "7 + (125*u)\/4 - (161*u^2)\/4 - 90*u^3 + (19*u^4)\/2 + (391*u^5)\/4 + (201*u^6)\/4 - (29*u^7)\/4 + (11*u^8)\/2 + (71*u^9)\/4 + (31*u^10)\/4 + u^11", "1\/4 + (5*u)\/2 + (39*u^2)\/4 + (51*u^3)\/2 + (191*u^4)\/4 + 67*u^5 + 65*u^6 + (143*u^7)\/4 + (69*u^8)\/4 + (25*u^9)\/2 + u^10\/4 + u^11", "49\/2 + (945*u)\/4 + (3973*u^2)\/4 + (4809*u^3)\/2 + 3736*u^4 + (15739*u^5)\/4 + (11529*u^6)\/4 + (5899*u^7)\/4 + 518*u^8 + (477*u^9)\/4 + (65*u^10)\/4 + u^11", "1\/2 + 4*u + (25*u^2)\/2 + 17*u^3 - (19*u^4)\/2 - 35*u^5 - 6*u^6 + (49*u^7)\/2 + (11*u^8)\/2 - 7*u^9 - u^10\/2 + u^11", "17\/2 + 54*u + (291*u^2)\/2 + 248*u^3 + (635*u^4)\/2 + 311*u^5 + 216*u^6 + (199*u^7)\/2 + (59*u^8)\/2 + 8*u^9 + (7*u^10)\/2 + u^11", "4 + 9*u - 16*u^2 - 5*u^3 + 10*u^4 - u^5 - 2*u^6 + 4*u^7 + u^8 - 3*u^9 + u^11", "1\/2 - (5*u^2)\/2 + 3*u^3 + (7*u^4)\/2 - 7*u^5 + u^6 + (11*u^7)\/2 - (3*u^8)\/2 + u^10\/2 + u^11", "1\/2 + 11*u + (167*u^2)\/2 + 255*u^3 + (617*u^4)\/2 + 213*u^5 + 61*u^6 - (85*u^7)\/2 - (73*u^8)\/2 - 2*u^9 + (9*u^10)\/2 + u^11", "16 + 209*u + 426*u^2 + 343*u^3 + 90*u^4 - 21*u^5 - 16*u^6 + 16*u^7 + 27*u^8 + 17*u^9 + 6*u^10 + u^11" ], "Multiplicity":1, "ij_list":[ [ "{1, 7}", "{1, 8}", "{2, 7}", "{5, 9}", "{6, 8}", "{6, 9}" ], [ "{1, 2}", "{5, 6}", "{7, 8}", "{8, 9}" ], [ "{2, 8}", "{5, 8}" ], [ "{3, 4}" ], [ "{3, 8}", "{4, 8}" ], [ "{3, 9}", "{4, 7}" ], [ "{7, 9}" ], [ "{1, 9}", "{6, 7}" ], [ "{1, 6}" ], [ "{2, 9}", "{5, 7}" ], [ "{1, 5}", "{2, 6}" ], [ "{2, 4}", "{2, 5}", "{3, 5}" ], [ "{1, 4}", "{3, 6}", "{3, 7}", "{4, 9}" ], [ "{1, 3}", "{4, 6}" ], [ "{2, 3}", "{4, 5}" ] ], "SortedReprnIndices":"{10, 9, 8, 7, 1, 2, 6, 5, 4, 3, 11}", "aCuspShapeN":[ "-8.2199373902981158474`5.00582403771972 - 7.9994460607432846924`4.994015442461122*I", "-8.2199373902981158474`5.00582403771972 + 7.9994460607432846924`4.994015442461122*I", "-9.6106816852782148993`5.038033045101869 + 7.9173849021642557151`4.95386061044682*I", "-9.6106816852782148993`5.038033045101869 - 7.9173849021642557151`4.95386061044682*I", "-10.729828727336370595`5.116738616171831 + 4.4017892735812675065`4.7297750742646345*I", "-10.729828727336370595`5.116738616171831 - 4.4017892735812675065`4.7297750742646345*I", "-3.6148533671129051812`4.883743524054552 + 5.6189722119884413951`5.075309723129508*I", "-3.6148533671129051812`4.883743524054552 - 5.6189722119884413951`5.075309723129508*I", "-6.7308462691381160487`4.965307329838961 + 7.8103105016987496686`5.029905958100947*I", "-6.7308462691381160487`4.965307329838961 - 7.8103105016987496686`5.029905958100947*I", -1.4437999999999999e1 ], "Abelian":false }, { "IdealName":"J9_38_1", "Generators":[ "-19142 + 11959*b + 17972*u - 55123*u^2 + 173098*u^3 - 389944*u^4 + 924180*u^5 - 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70078*u + 113257*u^2 - 330602*u^3 + 746850*u^4 - 1923198*u^5 + 3271766*u^6 - 4693246*u^7 + 5629178*u^8 - 5623796*u^9 + 5073374*u^10 - 3861390*u^11 + 2643126*u^12 - 1580644*u^13 + 787762*u^14 - 370093*u^15 + 108460*u^16 - 36158*u^17)\/11959", "(3818 + 14327*u + 10746*u^2 - 48510*u^3 + 127351*u^4 - 384202*u^5 + 597336*u^6 - 967830*u^7 + 1233752*u^8 - 1284687*u^9 + 1273092*u^10 - 1002910*u^11 + 753196*u^12 - 474843*u^13 + 249688*u^14 - 134475*u^15 + 39246*u^16 - 18150*u^17)\/11959" ], [ "(19787 + 1372*u + 31235*u^2 - 101840*u^3 + 166731*u^4 - 375606*u^5 + 425118*u^6 - 463990*u^7 + 461586*u^8 - 325146*u^9 + 267582*u^10 - 144130*u^11 + 84494*u^12 - 52202*u^13 + 9078*u^14 - 15634*u^15 - 1462*u^16 - 3284*u^17)\/11959", "(19142 - 17972*u + 55123*u^2 - 173098*u^3 + 389944*u^4 - 924180*u^5 + 1428387*u^6 - 2013394*u^7 + 2375134*u^8 - 2338544*u^9 + 2132236*u^10 - 1615766*u^11 + 1128106*u^12 - 685104*u^13 + 341804*u^14 - 172248*u^15 + 48508*u^16 - 20020*u^17)\/11959" ], [ "(645 + 19344*u - 23888*u^2 + 71258*u^3 - 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76*u^13 + 44*u^14 - 22*u^15 + 10*u^16 - 3*u^17 + u^18", "1 - 2*u + 2*u^2 - 7*u^3 + 19*u^4 - 45*u^5 + 87*u^6 - 129*u^7 + 169*u^8 - 186*u^9 + 178*u^10 - 153*u^11 + 113*u^12 - 76*u^13 + 44*u^14 - 22*u^15 + 10*u^16 - 3*u^17 + u^18", "11 + 4*u + 58*u^2 + 21*u^3 + 119*u^4 + 47*u^5 + 99*u^6 + 105*u^7 + 77*u^8 + 134*u^9 + 54*u^10 + 63*u^11 + 39*u^12 + 28*u^13 + 28*u^14 + 6*u^15 + 8*u^16 - 3*u^17 + u^18" ], "uPolys":[ "1 - 2*u + 2*u^2 - 7*u^3 + 19*u^4 - 45*u^5 + 87*u^6 - 129*u^7 + 169*u^8 - 186*u^9 + 178*u^10 - 153*u^11 + 113*u^12 - 76*u^13 + 44*u^14 - 22*u^15 + 10*u^16 - 3*u^17 + u^18", "(1 - u + 2*u^3 - 3*u^4 + u^5 + 3*u^6 - 2*u^7 - u^8 + u^9)^2", "(-1 + u + 2*u^3 + u^4 + 3*u^5 + u^6 + 2*u^7 + u^8 + u^9)^2", "(1 - u + 2*u^3 - 3*u^4 + u^5 + 3*u^6 - 2*u^7 - u^8 + u^9)^2", "1 - 2*u + 2*u^2 - 7*u^3 + 19*u^4 - 45*u^5 + 87*u^6 - 129*u^7 + 169*u^8 - 186*u^9 + 178*u^10 - 153*u^11 + 113*u^12 - 76*u^13 + 44*u^14 - 22*u^15 + 10*u^16 - 3*u^17 + u^18", "11 + 4*u + 58*u^2 + 21*u^3 + 119*u^4 + 47*u^5 + 99*u^6 + 105*u^7 + 77*u^8 + 134*u^9 + 54*u^10 + 63*u^11 + 39*u^12 + 28*u^13 + 28*u^14 + 6*u^15 + 8*u^16 - 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218*u^13 + 290*u^14 - 166*u^15 + 56*u^16 - 11*u^17 + u^18", "1 - 16*u + 122*u^2 - 559*u^3 + 1647*u^4 - 3089*u^5 + 3275*u^6 - 795*u^7 - 2355*u^8 + 2408*u^9 + 72*u^10 - 1257*u^11 + 539*u^12 + 132*u^13 - 132*u^14 - 6*u^15 + 28*u^16 - 9*u^17 + u^18", "11 + 4*u + 58*u^2 + 21*u^3 + 119*u^4 + 47*u^5 + 99*u^6 + 105*u^7 + 77*u^8 + 134*u^9 + 54*u^10 + 63*u^11 + 39*u^12 + 28*u^13 + 28*u^14 + 6*u^15 + 8*u^16 - 3*u^17 + u^18", "49 - 546*u + 2753*u^2 - 7956*u^3 + 13982*u^4 - 14516*u^5 + 8036*u^6 - 3518*u^7 + 6883*u^8 - 10226*u^9 + 6497*u^10 - 1286*u^11 + 539*u^12 - 1648*u^13 + 1316*u^14 - 362*u^15 - 11*u^16 + 14*u^17 + u^18", "1 + 2*u - 3*u^2 - 12*u^3 - 6*u^4 + 32*u^5 + 68*u^6 + 26*u^7 - 97*u^8 - 174*u^9 - 63*u^10 + 202*u^11 + 423*u^12 + 448*u^13 + 312*u^14 + 150*u^15 + 49*u^16 + 10*u^17 + u^18", "373 + 406*u + 360*u^2 + 399*u^3 + 2505*u^4 + 4281*u^5 + 3401*u^6 + 663*u^7 + 269*u^8 + 1324*u^9 + 960*u^10 - 67*u^11 + 93*u^12 + 136*u^13 + 26*u^14 - 26*u^15 + 22*u^16 - 5*u^17 + u^18", "1 + 8*u + 62*u^2 + 101*u^3 + 415*u^4 + 1159*u^5 + 785*u^6 - 1111*u^7 - 1571*u^8 + 190*u^9 + 1058*u^10 + 189*u^11 - 365*u^12 - 106*u^13 + 74*u^14 + 20*u^15 - 10*u^16 - u^17 + u^18", "121 - 1260*u + 5814*u^2 - 15165*u^3 + 24525*u^4 - 25991*u^5 + 19247*u^6 - 6747*u^7 - 5959*u^8 + 10394*u^9 - 6716*u^10 + 2105*u^11 + 1469*u^12 - 2466*u^13 + 1558*u^14 - 658*u^15 + 156*u^16 - 7*u^17 + u^18", "7 - 28*u + 26*u^2 + 31*u^3 + 103*u^4 - 405*u^5 + 11*u^6 + 581*u^7 + 321*u^8 - 870*u^9 - 296*u^10 + 571*u^11 + 187*u^12 - 226*u^13 - 46*u^14 + 44*u^15 + 4*u^16 - 5*u^17 + u^18", "7 - 28*u + 26*u^2 + 31*u^3 + 103*u^4 - 405*u^5 + 11*u^6 + 581*u^7 + 321*u^8 - 870*u^9 - 296*u^10 + 571*u^11 + 187*u^12 - 226*u^13 - 46*u^14 + 44*u^15 + 4*u^16 - 5*u^17 + u^18", "1 - 22*u + 257*u^2 - 1888*u^3 + 9590*u^4 - 34536*u^5 + 90896*u^6 - 180102*u^7 + 274907*u^8 - 328078*u^9 + 308177*u^10 - 227526*u^11 + 130663*u^12 - 57116*u^13 + 18300*u^14 - 4034*u^15 + 549*u^16 - 38*u^17 + u^18", "1 - 16*u + 122*u^2 - 559*u^3 + 1647*u^4 - 3089*u^5 + 3275*u^6 - 795*u^7 - 2355*u^8 + 2408*u^9 + 72*u^10 - 1257*u^11 + 539*u^12 + 132*u^13 - 132*u^14 - 6*u^15 + 28*u^16 - 9*u^17 + u^18", "11 + 4*u + 58*u^2 + 21*u^3 + 119*u^4 + 47*u^5 + 99*u^6 + 105*u^7 + 77*u^8 + 134*u^9 + 54*u^10 + 63*u^11 + 39*u^12 + 28*u^13 + 28*u^14 + 6*u^15 + 8*u^16 - 3*u^17 + u^18", "1 - 2*u + u^2 - 4*u^3 + 2*u^4 - 4*u^5 + 8*u^6 + 2*u^7 + 15*u^8 + 10*u^9 + 21*u^10 + 14*u^11 + 19*u^12 + 12*u^13 + 12*u^14 + 6*u^15 + 5*u^16 + 2*u^17 + u^18" ], "GeometricComponent":0, "Multiplicity":1, "ij_list":[ [ "{5, 9}", "{6, 8}", "{6, 9}" ], [ "{5, 6}", "{8, 9}" ], [ "{2, 8}", "{5, 8}" ], [ "{6, 7}" ], [ "{2, 4}", "{2, 5}", "{3, 5}" ], [ "{1, 5}" ], [ "{1, 7}", "{1, 8}", "{2, 7}" ], [ "{3, 4}" ], [ "{1, 3}" ], [ "{1, 2}", "{7, 8}" ], [ "{2, 9}" ], [ "{3, 6}", "{3, 7}" ], [ "{1, 6}" ], [ "{2, 3}", "{4, 5}" ], [ "{2, 6}" ], [ "{4, 6}" ], [ "{1, 9}" ], [ "{3, 9}" ], [ "{4, 7}" ], [ "{7, 9}" ], [ "{5, 7}" ], [ "{1, 4}", "{4, 9}" ], [ "{3, 8}", "{4, 8}" ] ], "SortedReprnIndices":"{3, 13, 4, 14, 7, 12, 8, 11, 10, 15, 9, 16, 6, 18, 5, 17, 1, 2}", "aCuspShapeN":[ "-12.6523487732486772332`5.150514997831949 + 0``4.048343842709541*I", "-12.6523487732486772332`5.150514997831949 + 0``4.048343842709541*I", "-9.576801436179176129`5.080376622099554 - 5.913348694671883787`4.870989628137708*I", "-9.576801436179176129`5.080376622099554 + 5.913348694671883787`4.870989628137708*I", "-11.2840934311056142022`5.149676798529587 + 0.7017499616665639674`3.943392522701711*I", "-11.2840934311056142022`5.149676798529587 - 0.7017499616665639674`3.943392522701711*I", "-6.3279222537923598534`5.108779804763183 - 2.9129760189197737686`4.771855579388068*I", "-6.3279222537923598534`5.108779804763183 + 2.9129760189197737686`4.771855579388068*I", "-3.4850084922985111373`4.957995995425533 + 4.1628312734295381598`5.035180963253591*I", "-3.4850084922985111373`4.957995995425533 - 4.1628312734295381598`5.035180963253591*I", "-6.3279222537923597514`5.108779804763183 + 2.9129760189197737438`4.771855579388068*I", "-6.3279222537923597514`5.108779804763183 - 2.9129760189197737438`4.771855579388068*I", "-9.5768014361791758141`5.080376622099554 - 5.9133486946718834076`4.870989628137708*I", "-9.5768014361791758141`5.080376622099554 + 5.9133486946718834076`4.870989628137708*I", "-3.4850084922985112776`4.957995995425533 - 4.1628312734295377602`5.035180963253591*I", "-3.4850084922985112776`4.957995995425533 + 4.1628312734295377602`5.035180963253591*I", "-11.2840934311056142186`5.149676798529587 + 0.7017499616665639505`3.943392522701711*I", "-11.2840934311056142186`5.149676798529587 - 0.7017499616665639505`3.943392522701711*I" ], "Abelian":false }, { "IdealName":"J9_38_2", "Generators":[ "1 + b", "1 + 2*a", "-1 + u" ], "VariableOrder":[ "b", "a", "u" ], "Characteristic":0, "KnownGroebner":[], "Status":[ "vCompNormalize" ], "MonomialOrder":"lex", "IsHomogeneous":false, "IsZeroDim":true, "IdealDimension":0, "Timings":{ "TimingGroebner":5.4895e-2, "TimingZeroDimVars":4.4162e-2, "TimingmagmaVCompNormalize":4.5507e-2, "TimingNumberOfSols":1.8434e-2, "TimingIsRadical":1.296e-3, "TimingArcColoring":4.2203e-2, "TimingObstruction":4.1100000000000007e-4, "TimingComplexVolumeN":0.880861, "TimingaCuspShapeN":4.118e-3, "TimingaCuspShape":9.0107e-2, "TiminguValues":0.724648, "TiminguPolys":0.725189, "TimingRepresentationsN":2.1766e-2, "TiminguValues_ij":0.107189, "TiminguPoly_ij":0.935753, "TiminguPolys_ij_N":1.75e-4 }, "ZeroDimensionalVars":[ "b", "a", "u" ], "NumberOfSols":1, "IsRadical":true, "ArcColoring":[ [ -0.25, 0.5 ], [ -1.5, -1 ], [ -0.5, -1 ], [ -0.5, -1 ], "{1, 0}", "{1, 1}", [ 1.25, 1.5 ], "{1, 2}", "{0, 1}" ], "Obstruction":1, "ComplexVolumeN":[ -3.28987 ], "aCuspShape":-9.75, "uPolys":[ "1 + u", "-1 + u", "u", "1 + u", "-1 + u", "2*(1 + 2*u)", "-1 + u", "1 + u", "2*(-1 + 2*u)" ], "RepresentationsN":[ [ "u->1.", "a->-0.5", "b->-1." ] ], "Epsilon":"Infinity", "uPolys_ij":[ "2 + u", "2*(3 + 2*u)", "1 + u", "4*(3 + 4*u)", "2*(1 + 2*u)", "4*(1 + 4*u)", "u", "4*(-1 + 4*u)", "2*(-1 + 2*u)", "-1 + u", "4*(-5 + 4*u)", "2*(-3 + 2*u)", "-2 + u" ], "GeometricComponent":0, "uPolys_ij_N":[ "2 + u", "3\/2 + u", "1 + u", "3\/4 + u", "1\/2 + u", "1\/4 + u", "u", "-1\/4 + u", "-1\/2 + u", "-1 + u", "-5\/4 + u", "-3\/2 + u", "-2 + u" ], "Multiplicity":1, "ij_list":[ [ "{2, 8}" ], [ "{2, 9}" ], [ "{1, 7}", "{1, 8}", "{2, 7}" ], [ "{1, 6}" ], [ "{1, 5}", "{2, 6}", "{3, 9}", "{4, 9}" ], [ "{1, 9}" ], [ "{3, 4}", "{3, 8}", "{4, 8}" ], [ "{6, 7}" ], [ "{1, 3}", "{1, 4}", "{3, 6}", "{3, 7}", "{4, 6}", "{4, 7}" ], [ "{1, 2}", "{2, 3}", "{2, 4}", "{2, 5}", "{3, 5}", "{4, 5}", "{5, 6}", "{5, 9}", "{6, 8}", "{6, 9}", "{7, 8}", "{8, 9}" ], [ "{7, 9}" ], [ "{5, 7}" ], [ "{5, 8}" ] ], "SortedReprnIndices":"{1}", "aCuspShapeN":[ -9.75 ], "Abelian":false }, { "IdealName":"abJ9_38_3", "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":5.3492e-2, "TimingZeroDimVars":4.5141e-2, "TimingmagmaVCompNormalize":4.6391e-2, "TimingNumberOfSols":2.1576e-2, "TimingIsRadical":1.4950000000000002e-3, "TimingArcColoring":4.6713e-2, "TimingObstruction":4.2400000000000006e-4, "TimingComplexVolumeN":0.232883, "TimingaCuspShapeN":3.952e-3, "TiminguValues":0.586672, "TiminguPolysN":7.000000000000002e-5, "TiminguPolys":0.723344, "TimingaCuspShape":8.965400000000001e-2, "TimingRepresentationsN":2.2331e-2, "TiminguValues_ij":0.10648, "TiminguPoly_ij":0.12445, "TiminguPolys_ij_N":3.1e-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":[ "(1 + u)*(1 + 3*u + 3*u^2 + 9*u^3 + 9*u^4 + 11*u^5 + 10*u^6 + 7*u^7 + 6*u^8 + 3*u^9 + u^10 + u^11)*(1 - 2*u + 2*u^2 - 7*u^3 + 19*u^4 - 45*u^5 + 87*u^6 - 129*u^7 + 169*u^8 - 186*u^9 + 178*u^10 - 153*u^11 + 113*u^12 - 76*u^13 + 44*u^14 - 22*u^15 + 10*u^16 - 3*u^17 + u^18)", "(-1 + u)*(1 - u + 2*u^3 - 3*u^4 + u^5 + 3*u^6 - 2*u^7 - u^8 + u^9)^2*(4 + 9*u - 16*u^2 - 5*u^3 + 10*u^4 - u^5 - 2*u^6 + 4*u^7 + u^8 - 3*u^9 + u^11)", "u*(-1 + u + 2*u^3 + u^4 + 3*u^5 + u^6 + 2*u^7 + u^8 + u^9)^2*(8 - 6*u - u^2 + 35*u^3 - 38*u^4 + 42*u^5 - 39*u^6 + 25*u^7 - 13*u^8 + 6*u^9 - 3*u^10 + u^11)", "(1 + u)*(1 - u + 2*u^3 - 3*u^4 + u^5 + 3*u^6 - 2*u^7 - u^8 + u^9)^2*(4 + 9*u - 16*u^2 - 5*u^3 + 10*u^4 - u^5 - 2*u^6 + 4*u^7 + u^8 - 3*u^9 + u^11)", "(-1 + u)*(1 + 3*u + 3*u^2 + 9*u^3 + 9*u^4 + 11*u^5 + 10*u^6 + 7*u^7 + 6*u^8 + 3*u^9 + u^10 + u^11)*(1 - 2*u + 2*u^2 - 7*u^3 + 19*u^4 - 45*u^5 + 87*u^6 - 129*u^7 + 169*u^8 - 186*u^9 + 178*u^10 - 153*u^11 + 113*u^12 - 76*u^13 + 44*u^14 - 22*u^15 + 10*u^16 - 3*u^17 + u^18)", "4*(1 + 2*u)*(1 - 5*u^2 + 6*u^3 + 7*u^4 - 14*u^5 + 2*u^6 + 11*u^7 - 3*u^8 + u^10 + 2*u^11)*(11 + 4*u + 58*u^2 + 21*u^3 + 119*u^4 + 47*u^5 + 99*u^6 + 105*u^7 + 77*u^8 + 134*u^9 + 54*u^10 + 63*u^11 + 39*u^12 + 28*u^13 + 28*u^14 + 6*u^15 + 8*u^16 - 3*u^17 + u^18)", "(-1 + u)*(1 + 3*u + 3*u^2 + 9*u^3 + 9*u^4 + 11*u^5 + 10*u^6 + 7*u^7 + 6*u^8 + 3*u^9 + u^10 + u^11)*(1 - 2*u + 2*u^2 - 7*u^3 + 19*u^4 - 45*u^5 + 87*u^6 - 129*u^7 + 169*u^8 - 186*u^9 + 178*u^10 - 153*u^11 + 113*u^12 - 76*u^13 + 44*u^14 - 22*u^15 + 10*u^16 - 3*u^17 + u^18)", "(1 + u)*(1 + 3*u + 3*u^2 + 9*u^3 + 9*u^4 + 11*u^5 + 10*u^6 + 7*u^7 + 6*u^8 + 3*u^9 + u^10 + u^11)*(1 - 2*u + 2*u^2 - 7*u^3 + 19*u^4 - 45*u^5 + 87*u^6 - 129*u^7 + 169*u^8 - 186*u^9 + 178*u^10 - 153*u^11 + 113*u^12 - 76*u^13 + 44*u^14 - 22*u^15 + 10*u^16 - 3*u^17 + u^18)", "4*(-1 + 2*u)*(1 - 5*u^2 + 6*u^3 + 7*u^4 - 14*u^5 + 2*u^6 + 11*u^7 - 3*u^8 + u^10 + 2*u^11)*(11 + 4*u + 58*u^2 + 21*u^3 + 119*u^4 + 47*u^5 + 99*u^6 + 105*u^7 + 77*u^8 + 134*u^9 + 54*u^10 + 63*u^11 + 39*u^12 + 28*u^13 + 28*u^14 + 6*u^15 + 8*u^16 - 3*u^17 + u^18)" ], "RileyPolyC":[ "(-1 + y)*(-1 + 3*y + 27*y^2 + 73*y^3 + 87*y^4 + 47*y^5 - 5*y^7 + 8*y^8 + 11*y^9 + 5*y^10 + y^11)*(1 + 14*y^2 + 21*y^3 - 99*y^4 - 237*y^5 + 103*y^6 + 883*y^7 + 1113*y^8 + 310*y^9 - 628*y^10 - 749*y^11 - 227*y^12 + 218*y^13 + 290*y^14 + 166*y^15 + 56*y^16 + 11*y^17 + y^18)", "(-1 + y)*(-1 + y + 2*y^2 - 4*y^3 + y^4 + 9*y^5 - 15*y^6 + 12*y^7 - 5*y^8 + y^9)^2*(-16 + 209*y - 426*y^2 + 343*y^3 - 90*y^4 - 21*y^5 + 16*y^6 + 16*y^7 - 27*y^8 + 17*y^9 - 6*y^10 + y^11)", "y*(-1 + y + 6*y^2 + 12*y^3 + 17*y^4 + 17*y^5 + 13*y^6 + 8*y^7 + 3*y^8 + y^9)^2*(-64 + 52*y + 187*y^2 + 1269*y^3 + 1326*y^4 + 500*y^5 - 7*y^6 - 43*y^7 - 19*y^8 + 8*y^9 + 3*y^10 + y^11)", "(-1 + y)*(-1 + y + 2*y^2 - 4*y^3 + y^4 + 9*y^5 - 15*y^6 + 12*y^7 - 5*y^8 + y^9)^2*(-16 + 209*y - 426*y^2 + 343*y^3 - 90*y^4 - 21*y^5 + 16*y^6 + 16*y^7 - 27*y^8 + 17*y^9 - 6*y^10 + y^11)", "(-1 + y)*(-1 + 3*y + 27*y^2 + 73*y^3 + 87*y^4 + 47*y^5 - 5*y^7 + 8*y^8 + 11*y^9 + 5*y^10 + y^11)*(1 + 14*y^2 + 21*y^3 - 99*y^4 - 237*y^5 + 103*y^6 + 883*y^7 + 1113*y^8 + 310*y^9 - 628*y^10 - 749*y^11 - 227*y^12 + 218*y^13 + 290*y^14 + 166*y^15 + 56*y^16 + 11*y^17 + y^18)", "16*(-1 + 4*y)*(-1 + 10*y - 39*y^2 + 102*y^3 - 191*y^4 + 268*y^5 - 260*y^6 + 143*y^7 - 69*y^8 + 50*y^9 - y^10 + 4*y^11)*(121 + 1260*y + 5814*y^2 + 15165*y^3 + 24525*y^4 + 25991*y^5 + 19247*y^6 + 6747*y^7 - 5959*y^8 - 10394*y^9 - 6716*y^10 - 2105*y^11 + 1469*y^12 + 2466*y^13 + 1558*y^14 + 658*y^15 + 156*y^16 + 7*y^17 + y^18)", "(-1 + y)*(-1 + 3*y + 27*y^2 + 73*y^3 + 87*y^4 + 47*y^5 - 5*y^7 + 8*y^8 + 11*y^9 + 5*y^10 + y^11)*(1 + 14*y^2 + 21*y^3 - 99*y^4 - 237*y^5 + 103*y^6 + 883*y^7 + 1113*y^8 + 310*y^9 - 628*y^10 - 749*y^11 - 227*y^12 + 218*y^13 + 290*y^14 + 166*y^15 + 56*y^16 + 11*y^17 + y^18)", "(-1 + y)*(-1 + 3*y + 27*y^2 + 73*y^3 + 87*y^4 + 47*y^5 - 5*y^7 + 8*y^8 + 11*y^9 + 5*y^10 + y^11)*(1 + 14*y^2 + 21*y^3 - 99*y^4 - 237*y^5 + 103*y^6 + 883*y^7 + 1113*y^8 + 310*y^9 - 628*y^10 - 749*y^11 - 227*y^12 + 218*y^13 + 290*y^14 + 166*y^15 + 56*y^16 + 11*y^17 + y^18)", "16*(-1 + 4*y)*(-1 + 10*y - 39*y^2 + 102*y^3 - 191*y^4 + 268*y^5 - 260*y^6 + 143*y^7 - 69*y^8 + 50*y^9 - y^10 + 4*y^11)*(121 + 1260*y + 5814*y^2 + 15165*y^3 + 24525*y^4 + 25991*y^5 + 19247*y^6 + 6747*y^7 - 5959*y^8 - 10394*y^9 - 6716*y^10 - 2105*y^11 + 1469*y^12 + 2466*y^13 + 1558*y^14 + 658*y^15 + 156*y^16 + 7*y^17 + y^18)" ] }, "GeometricRepresentation":[ 1.29329e1, [ "J9_38_0", 1, "{9, 10}" ] ] } }