{ "Index":207, "Name":"10_123", "RolfsenName":"10_123", "DTname":"10a_121", "TunnelNumber":2, "BridgeNumber":"Not implemented", "Hyperbolic":true, "Diagram":{ "Scode":"{-15, 17, -19, 1, -3, 5, -7, 9, -11, 13}", "Acode":"{-8, 9, -10, 1, -2, 3, -4, 5, -6, 7}", "PDcode":[ "{8, 2, 9, 1}", "{10, 3, 11, 4}", "{12, 6, 13, 5}", "{4, 18, 5, 17}", "{18, 11, 19, 12}", "{2, 15, 3, 16}", "{16, 10, 17, 9}", "{20, 14, 1, 13}", "{14, 7, 15, 8}", "{6, 19, 7, 20}" ], "CBtype":"{3, 0}", "ParabolicReps":{ "SolvingSeq":[ "{4, 1, 7}", [], [ "{4, 1, 5, 1}", "{7, -4, 8, 1}", "{1, -8, 2, 1}", "{8, 5, 9, 1}", "{1, 7, 10, 2}", "{4, -10, 3, 2}", "{7, 3, 6, 2}" ], "{2, 5}", "{9}", 9 ], "SolvingSeqIdx":4, "Comps":{ "u":{ "CheckEq":[ "-1 + 2*a*b*u + b^2*u + a^2*b^2*u + a*b^3*u - a^2*u^2 - a^3*b*u^2 - 2*a^2*u^3 - 2*a*b*u^3 - 2*a^3*b*u^3 - 3*a^2*b^2*u^3 + b^4*u^3 - a^2*u^5 + a^4*u^5 - 2*a*b*u^5 + a^3*b*u^5 - b^2*u^5 - 3*a^2*b^2*u^5 - 5*a*b^3*u^5 - 2*b^4*u^5 + a^4*u^7 + 4*a^3*b*u^7 + 6*a^2*b^2*u^7 + 4*a*b^3*u^7 + b^4*u^7", "u + b^2*u + a*b^3*u + b^4*u - 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b^5*v^2 + b^7*v^4" ], "TimingForPrimaryIdeals":9.923400000000003e-2 }, "PrimaryIdeals":[ { "IdealName":"J10_123_0", "Generators":[ "1 + b + 2*u + 2*u^2 + u^3", "-1 + a", "1 + 2*u + 4*u^2 + 3*u^3 + u^4" ], "VariableOrder":[ "b", "a", "u" ], "Characteristic":0, "KnownGroebner":[], "Status":[ "vCompNormalize" ], "MonomialOrder":"lex", "IsHomogeneous":false, "IsZeroDim":true, "IdealDimension":0, "Timings":{ "TimingGroebner":0.13327, "TimingZeroDimVars":7.280700000000001e-2, "TimingmagmaVCompNormalize":7.427500000000001e-2, "TimingNumberOfSols":5.3974e-2, "TimingIsRadical":2.164e-3, "TimingArcColoring":7.1215e-2, "TimingObstruction":4.691e-3, "TimingComplexVolumeN":2.462511, "TimingaCuspShapeN":1.9975e-2, "TiminguValues":0.635476, "TiminguPolysN":1.4e-3, "TiminguPolys":0.824781, "TimingaCuspShape":9.4602e-2, "TimingRepresentationsN":4.5375e-2, "TiminguValues_ij":0.168491, "TiminguPoly_ij":0.58732, "TiminguPolys_ij_N":1.08e-3 }, "ZeroDimensionalVars":[ "b", "a", "u" ], "NumberOfSols":4, "IsRadical":true, "ArcColoring":[ [ 0, "u" ], [ "1 + u + u^2", "-u^2 - u^3" ], [ "-u - 2*u^2 - u^3", "u + u^2 + u^3" ], "{1, 0}", [ 1, "u^2" ], [ "-2*u - 3*u^2 - u^3", "u^2 + u^3" ], [ 1, "-1 - 2*u - 2*u^2 - u^3" ], [ "-2*u - 2*u^2 - u^3", "-1 - 2*u - 2*u^2 - u^3" ], [ "-u - 2*u^2 - u^3", "-1 - 2*u - 2*u^2" ], [ "u", "1 + 2*u + 2*u^2 + u^3" ] ], "Obstruction":-1, "ComplexVolumeN":[ "0. + 1.38939*I", "0. - 1.38939*I", "0. + 17.0857*I", "0. - 17.0857*I" ], "uPolysN":[ "1 - 2*u + 4*u^2 - 3*u^3 + u^4", "1 + 2*u + 4*u^2 + 3*u^3 + u^4", "1 - 2*u + 4*u^2 - 3*u^3 + u^4", "1 + 2*u + 4*u^2 + 3*u^3 + u^4", "1 - 2*u + 4*u^2 - 3*u^3 + u^4", "1 + 2*u + 4*u^2 + 3*u^3 + u^4", "1 - 2*u + 4*u^2 - 3*u^3 + u^4", "1 + 2*u + 4*u^2 + 3*u^3 + u^4", "1 - 2*u + 4*u^2 - 3*u^3 + u^4", "1 + 2*u + 4*u^2 + 3*u^3 + u^4" ], "uPolys":[ "1 - 2*u + 4*u^2 - 3*u^3 + u^4", "1 + 2*u + 4*u^2 + 3*u^3 + u^4", "1 - 2*u + 4*u^2 - 3*u^3 + u^4", "1 + 2*u + 4*u^2 + 3*u^3 + u^4", "1 - 2*u + 4*u^2 - 3*u^3 + u^4", "1 + 2*u + 4*u^2 + 3*u^3 + u^4", "1 - 2*u + 4*u^2 - 3*u^3 + u^4", "1 + 2*u + 4*u^2 + 3*u^3 + u^4", "1 - 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22*u + 42*u^2 + 33*u^3 - 97*u^4 + 13*u^5 + 96*u^6 - 41*u^7 - 27*u^8 + 24*u^9)\/2", "(-1 - 6*u + 7*u^2 + 9*u^3 - 20*u^4 - 4*u^5 + 17*u^6 - 4*u^7 - 6*u^8 + 3*u^9)\/2" ], [ "1 - 5*u - 3*u^2 + 8*u^3 - 2*u^4 - 10*u^5 + 4*u^6 + 3*u^7 - 3*u^8", "(5 + 4*u - 17*u^2 - 8*u^3 + 31*u^4 - 7*u^5 - 33*u^6 + 15*u^7 + 9*u^8 - 9*u^9)\/2" ], "{1, 0}", [ 1, "u^2" ], [ "(1 + 21*u - 5*u^2 - 101*u^3 + 84*u^4 + 86*u^5 - 160*u^6 + 11*u^7 + 75*u^8 - 42*u^9)\/2", "(2 + 9*u - 3*u^2 - 30*u^3 + 31*u^4 + 22*u^5 - 49*u^6 + 7*u^7 + 21*u^8 - 12*u^9)\/2" ], [ "(-2 + 9*u + 13*u^2 - 36*u^3 + 5*u^4 + 48*u^5 - 31*u^6 - 13*u^7 + 21*u^8 - 6*u^9)\/2", "(-6 - 2*u + 22*u^2 - 5*u^3 - 31*u^4 + 19*u^5 + 22*u^6 - 17*u^7 - 3*u^8 + 6*u^9)\/2" ], [ "(-8 + 7*u + 35*u^2 - 41*u^3 - 26*u^4 + 67*u^5 - 9*u^6 - 30*u^7 + 18*u^8)\/2", "(-6 - 2*u + 22*u^2 - 5*u^3 - 31*u^4 + 19*u^5 + 22*u^6 - 17*u^7 - 3*u^8 + 6*u^9)\/2" ], [ "(-8 + 9*u + 35*u^2 - 41*u^3 - 26*u^4 + 67*u^5 - 9*u^6 - 30*u^7 + 18*u^8)\/2", "(-6 - 2*u + 22*u^2 - 3*u^3 - 31*u^4 + 19*u^5 + 22*u^6 - 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(5*u^2)\/3 + (2*u^3)\/3 + (11*u^4)\/3 - (10*u^5)\/3 - (8*u^6)\/3 + (14*u^7)\/3 - u^8\/3 - 2*u^9 + u^10", "1\/3 - (5*u^2)\/3 - (2*u^3)\/3 + (11*u^4)\/3 + (10*u^5)\/3 - (8*u^6)\/3 - (14*u^7)\/3 - u^8\/3 + 2*u^9 + u^10", "3 - 12*u + 23*u^2 - 30*u^3 + 31*u^4 - 26*u^5 + 20*u^6 - 14*u^7 + 9*u^8 - 4*u^9 + u^10" ], "uPolys":[ "32 - 96*u + 200*u^2 - 288*u^3 + 308*u^4 - 251*u^5 + 159*u^6 - 77*u^7 + 28*u^8 - 7*u^9 + u^10", "3 - 12*u + 23*u^2 - 30*u^3 + 31*u^4 - 26*u^5 + 20*u^6 - 14*u^7 + 9*u^8 - 4*u^9 + u^10", "3*(1 - 5*u^2 - 2*u^3 + 11*u^4 + 10*u^5 - 8*u^6 - 14*u^7 - u^8 + 6*u^9 + 3*u^10)", "3*(1 - 5*u^2 + 2*u^3 + 11*u^4 - 10*u^5 - 8*u^6 + 14*u^7 - u^8 - 6*u^9 + 3*u^10)", "3 + 12*u + 23*u^2 + 30*u^3 + 31*u^4 + 26*u^5 + 20*u^6 + 14*u^7 + 9*u^8 + 4*u^9 + u^10", "32 + 96*u + 200*u^2 + 288*u^3 + 308*u^4 + 251*u^5 + 159*u^6 + 77*u^7 + 28*u^8 + 7*u^9 + u^10", "3 + 12*u + 23*u^2 + 30*u^3 + 31*u^4 + 26*u^5 + 20*u^6 + 14*u^7 + 9*u^8 + 4*u^9 + u^10", "3*(1 - 5*u^2 + 2*u^3 + 11*u^4 - 10*u^5 - 8*u^6 + 14*u^7 - 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1016*u - 1808*u^2 - 2338*u^3 - 2247*u^4 - 1591*u^5 - 863*u^6 - 338*u^7 - 87*u^8 - 11*u^9)\/288", "(112 + 1136*u + 2792*u^2 + 4288*u^3 + 4695*u^4 + 3739*u^5 + 2189*u^6 + 944*u^7 + 267*u^8 + 41*u^9)\/144" ], [ "(-16 - 92*u - 182*u^2 - 218*u^3 - 193*u^4 - 131*u^5 - 67*u^6 - 26*u^7 - 7*u^8 - u^9)\/16", "(-16 + 16*u + 46*u^2 + 83*u^3 + 90*u^4 + 74*u^5 + 43*u^6 + 19*u^7 + 6*u^8 + u^9)\/24" ] ], "Obstruction":-1, "ComplexVolumeN":[ "3.61397 + 2.21654*I", "3.61397 - 2.21654*I", "-3.61397 + 2.21654*I", "-3.61397 - 2.21654*I", "2.49243 - 8.64801*I", "2.49243 + 8.64801*I", "0. + 0.806279*I", "0. - 0.806279*I", "-2.49243 + 8.64801*I", "-2.49243 - 8.64801*I" ], "uPolysN":[ "1\/3 - (5*u^2)\/3 - (2*u^3)\/3 + (11*u^4)\/3 + (10*u^5)\/3 - (8*u^6)\/3 - (14*u^7)\/3 - u^8\/3 + 2*u^9 + u^10", "1\/3 - (5*u^2)\/3 + (2*u^3)\/3 + (11*u^4)\/3 - (10*u^5)\/3 - (8*u^6)\/3 + (14*u^7)\/3 - u^8\/3 - 2*u^9 + u^10", "3 + 12*u + 23*u^2 + 30*u^3 + 31*u^4 + 26*u^5 + 20*u^6 + 14*u^7 + 9*u^8 + 4*u^9 + u^10", "32 + 96*u + 200*u^2 + 288*u^3 + 308*u^4 + 251*u^5 + 159*u^6 + 77*u^7 + 28*u^8 + 7*u^9 + u^10", "3 + 12*u + 23*u^2 + 30*u^3 + 31*u^4 + 26*u^5 + 20*u^6 + 14*u^7 + 9*u^8 + 4*u^9 + u^10", "1\/3 - 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0.608563 I", "b->0.744942 + 0.201707 I" ], [ "u->-0.2445 + 1.63857 I", "a->0.613351 - 0.157946 I", "b->-0.550514 - 0.187402 I" ], [ "u->-0.2445 - 1.63857 I", "a->0.613351 + 0.157946 I", "b->-0.550514 + 0.187402 I" ], [ "u->-1.31322 + 1.0805 I", "a->-0.888779 - 0.031915 I", "b->1.0815 + 0.798609 I" ], [ "u->-1.31322 - 1.0805 I", "a->-0.888779 + 0.031915 I", "b->1.0815 - 0.798609 I" ] ], "Epsilon":0.715713, "uPolys_ij":[ "32 + 96*u + 200*u^2 + 288*u^3 + 308*u^4 + 251*u^5 + 159*u^6 + 77*u^7 + 28*u^8 + 7*u^9 + u^10", "1024 - 3584*u + 4416*u^2 - 2240*u^3 + 896*u^4 - 511*u^5 + 243*u^6 - 77*u^7 + 24*u^8 - 7*u^9 + u^10", "9 + 6*u - 5*u^2 - 22*u^3 + 39*u^4 - 48*u^5 + 36*u^6 - 18*u^7 + 9*u^8 - 2*u^9 + u^10", "9*(1 - 10*u + 47*u^2 - 130*u^3 + 239*u^4 - 316*u^5 + 316*u^6 - 234*u^7 + 121*u^8 - 42*u^9 + 9*u^10)", "9*(1024 + 4864*u + 10880*u^2 + 15216*u^3 + 14852*u^4 + 10611*u^5 + 5621*u^6 + 2183*u^7 + 598*u^8 + 105*u^9 + 9*u^10)", "1024 + 3584*u + 4416*u^2 + 2240*u^3 + 896*u^4 + 511*u^5 + 243*u^6 + 77*u^7 + 24*u^8 + 7*u^9 + u^10", "3*(17405 + 385*u^2 + 2267*u^4 + 720*u^6 + 77*u^8 + 3*u^10)", "32 - 96*u + 200*u^2 - 288*u^3 + 308*u^4 - 251*u^5 + 159*u^6 - 77*u^7 + 28*u^8 - 7*u^9 + u^10", "1 - 2*u - 3*u^2 - 2*u^3 + 15*u^4 + 10*u^5 - 6*u^6 - 10*u^7 - u^8 + 2*u^9 + u^10", "9*(1 + 10*u + 47*u^2 + 130*u^3 + 239*u^4 + 316*u^5 + 316*u^6 + 234*u^7 + 121*u^8 + 42*u^9 + 9*u^10)", "3*(37 - 56*u + 65*u^2 - 122*u^3 + 55*u^4 + 92*u^5 - 78*u^6 - 18*u^7 + 41*u^8 - 18*u^9 + 3*u^10)", "3 - 12*u + 23*u^2 - 30*u^3 + 31*u^4 - 26*u^5 + 20*u^6 - 14*u^7 + 9*u^8 - 4*u^9 + u^10", "1 + 2*u - 3*u^2 + 2*u^3 + 15*u^4 - 10*u^5 - 6*u^6 + 10*u^7 - u^8 - 2*u^9 + u^10", "3*(1 - 5*u^2 - 2*u^3 + 11*u^4 + 10*u^5 - 8*u^6 - 14*u^7 - u^8 + 6*u^9 + 3*u^10)", "3*(5 + 25*u^2 + 47*u^4 + 40*u^6 + 17*u^8 + 3*u^10)", "9*(1024 - 4864*u + 10880*u^2 - 15216*u^3 + 14852*u^4 - 10611*u^5 + 5621*u^6 - 2183*u^7 + 598*u^8 - 105*u^9 + 9*u^10)", "15 - 65*u^2 + 381*u^4 + 136*u^6 + 19*u^8 + u^10", "9 - 6*u - 5*u^2 + 22*u^3 + 39*u^4 + 48*u^5 + 36*u^6 + 18*u^7 + 9*u^8 + 2*u^9 + u^10", "3*(1 - 5*u^2 + 2*u^3 + 11*u^4 - 10*u^5 - 8*u^6 + 14*u^7 - u^8 - 6*u^9 + 3*u^10)", "27*(5 + 45*u^2 + 167*u^4 + 232*u^6 + 125*u^8 + 27*u^10)", "3*(37 + 56*u + 65*u^2 + 122*u^3 + 55*u^4 - 92*u^5 - 78*u^6 + 18*u^7 + 41*u^8 + 18*u^9 + 3*u^10)", "3*(5 + 25*u^2 + 27*u^4 + 16*u^6 + 5*u^8 + 3*u^10)", "3 + 12*u + 23*u^2 + 30*u^3 + 31*u^4 + 26*u^5 + 20*u^6 + 14*u^7 + 9*u^8 + 4*u^9 + u^10" ], "GeometricComponent":0, "uPolys_ij_N":[ "32 + 96*u + 200*u^2 + 288*u^3 + 308*u^4 + 251*u^5 + 159*u^6 + 77*u^7 + 28*u^8 + 7*u^9 + u^10", "1024 - 3584*u + 4416*u^2 - 2240*u^3 + 896*u^4 - 511*u^5 + 243*u^6 - 77*u^7 + 24*u^8 - 7*u^9 + u^10", "9 + 6*u - 5*u^2 - 22*u^3 + 39*u^4 - 48*u^5 + 36*u^6 - 18*u^7 + 9*u^8 - 2*u^9 + u^10", "1\/9 - (10*u)\/9 + (47*u^2)\/9 - (130*u^3)\/9 + (239*u^4)\/9 - (316*u^5)\/9 + (316*u^6)\/9 - 26*u^7 + (121*u^8)\/9 - (14*u^9)\/3 + u^10", "1024\/9 + (4864*u)\/9 + (10880*u^2)\/9 + (5072*u^3)\/3 + (14852*u^4)\/9 + 1179*u^5 + (5621*u^6)\/9 + (2183*u^7)\/9 + (598*u^8)\/9 + (35*u^9)\/3 + u^10", "1024 + 3584*u + 4416*u^2 + 2240*u^3 + 896*u^4 + 511*u^5 + 243*u^6 + 77*u^7 + 24*u^8 + 7*u^9 + u^10", "17405\/3 + (385*u^2)\/3 + (2267*u^4)\/3 + 240*u^6 + (77*u^8)\/3 + u^10", "32 - 96*u + 200*u^2 - 288*u^3 + 308*u^4 - 251*u^5 + 159*u^6 - 77*u^7 + 28*u^8 - 7*u^9 + u^10", "1 - 2*u - 3*u^2 - 2*u^3 + 15*u^4 + 10*u^5 - 6*u^6 - 10*u^7 - u^8 + 2*u^9 + u^10", "1\/9 + (10*u)\/9 + (47*u^2)\/9 + (130*u^3)\/9 + (239*u^4)\/9 + (316*u^5)\/9 + (316*u^6)\/9 + 26*u^7 + (121*u^8)\/9 + (14*u^9)\/3 + u^10", "37\/3 - (56*u)\/3 + (65*u^2)\/3 - (122*u^3)\/3 + (55*u^4)\/3 + (92*u^5)\/3 - 26*u^6 - 6*u^7 + (41*u^8)\/3 - 6*u^9 + u^10", "3 - 12*u + 23*u^2 - 30*u^3 + 31*u^4 - 26*u^5 + 20*u^6 - 14*u^7 + 9*u^8 - 4*u^9 + u^10", "1 + 2*u - 3*u^2 + 2*u^3 + 15*u^4 - 10*u^5 - 6*u^6 + 10*u^7 - u^8 - 2*u^9 + u^10", "1\/3 - (5*u^2)\/3 - (2*u^3)\/3 + (11*u^4)\/3 + (10*u^5)\/3 - (8*u^6)\/3 - (14*u^7)\/3 - u^8\/3 + 2*u^9 + u^10", "5\/3 + (25*u^2)\/3 + (47*u^4)\/3 + (40*u^6)\/3 + (17*u^8)\/3 + u^10", "1024\/9 - (4864*u)\/9 + (10880*u^2)\/9 - (5072*u^3)\/3 + (14852*u^4)\/9 - 1179*u^5 + (5621*u^6)\/9 - (2183*u^7)\/9 + (598*u^8)\/9 - (35*u^9)\/3 + u^10", "15 - 65*u^2 + 381*u^4 + 136*u^6 + 19*u^8 + u^10", "9 - 6*u - 5*u^2 + 22*u^3 + 39*u^4 + 48*u^5 + 36*u^6 + 18*u^7 + 9*u^8 + 2*u^9 + u^10", "1\/3 - (5*u^2)\/3 + (2*u^3)\/3 + (11*u^4)\/3 - (10*u^5)\/3 - (8*u^6)\/3 + (14*u^7)\/3 - u^8\/3 - 2*u^9 + u^10", "5\/27 + (5*u^2)\/3 + (167*u^4)\/27 + (232*u^6)\/27 + (125*u^8)\/27 + u^10", "37\/3 + (56*u)\/3 + (65*u^2)\/3 + (122*u^3)\/3 + (55*u^4)\/3 - (92*u^5)\/3 - 26*u^6 + 6*u^7 + (41*u^8)\/3 + 6*u^9 + u^10", "5\/3 + (25*u^2)\/3 + 9*u^4 + (16*u^6)\/3 + (5*u^8)\/3 + u^10", "3 + 12*u + 23*u^2 + 30*u^3 + 31*u^4 + 26*u^5 + 20*u^6 + 14*u^7 + 9*u^8 + 4*u^9 + u^10" ], "Multiplicity":1, "MinRepresentationVolume":[ "{7, 8}", 0.806279 ], "ij_list":[ [ "{1, 4}", "{1, 5}" ], [ "{4, 5}" ], [ "{1, 10}", "{8, 9}" ], [ "{1, 2}", "{7, 8}" ], [ "{2, 4}" ], [ "{9, 10}" ], [ "{4, 9}" ], [ "{6, 9}", "{6, 10}" ], [ "{1, 3}", "{3, 5}" ], [ "{2, 3}", "{6, 7}" ], [ "{2, 10}", "{4, 6}" ], [ "{1, 7}", "{5, 8}", "{5, 9}", "{7, 10}" ], [ "{6, 8}", "{8, 10}" ], [ "{1, 8}", "{2, 8}", "{4, 7}", "{4, 8}" ], [ "{1, 6}" ], [ "{7, 9}" ], [ "{5, 10}" ], [ "{3, 4}", "{5, 6}" ], [ "{2, 9}", "{3, 6}", "{3, 7}", "{3, 9}" ], [ "{2, 7}" ], [ "{1, 9}", "{5, 7}" ], [ "{3, 8}" ], [ "{2, 5}", "{2, 6}", "{3, 10}", "{4, 10}" ] ], "SortedReprnIndices":"{6, 9, 5, 10, 1, 3, 2, 4, 7, 8}", "aCuspShapeN":[ "5.3869898461014987179`5.0268018489186455 - 4.720221144309750302`4.969418037957015*I", "5.3869898461014987179`5.0268018489186455 + 4.720221144309750302`4.969418037957015*I", "-5.3869898461014987129`5.0268018489186455 - 4.7202211443097503039`4.969418037957015*I", "-5.3869898461014987129`5.0268018489186455 + 4.7202211443097503039`4.969418037957015*I", "4.0412602521567725781`4.826557540201074 + 7.5013472432719192282`5.095179990592408*I", "4.0412602521567725781`4.826557540201074 - 7.5013472432719192282`5.095179990592408*I", "0``4.235299049831837 - 8.2265160243407823946`5.150514997831984*I", "0``4.235299049831837 + 8.2265160243407823946`5.150514997831984*I", "-4.0412602521567725798`4.826557540201074 - 7.5013472432719192401`5.095179990592408*I", "-4.0412602521567725798`4.826557540201074 + 7.5013472432719192401`5.095179990592408*I" ], "Abelian":false }, { "IdealName":"J10_123_7", "Generators":[ "1 - a + a^2 + a*b - a*u + a^2*u + a*u^2 - 2*a^2*u^2 + a^3*u^2", "a + b + a*u + b*u - a*u^2 + a^2*u^2", "-1 - u + a*u - a*u^3 + a^2*u^3" ], "VariableOrder":[ "b", "a", "u" ], "Characteristic":0, "KnownGroebner":[], "Status":[ "vCompNormalize" ], "MonomialOrder":"lex", "IsHomogeneous":false, "IsZeroDim":false, "IdealDimension":1, "Timings":{ "TimingGroebner":0.12361, "TimingZeroDimVars":7.0982e-2, "TimingmagmaVCompNormalize":7.2146e-2, "TimingNumberOfSols":2.905104, "TimingIsRadical":1.7659e-2, "TimingArcColoring":7.5351e-2, "TimingObstruction":6.163e-3, "TimingComplexVolumeN":1.203662, "TimingaCuspShapeN":2.8862000000000002e-2, "TiminguValues":0.677272, "TimingaCuspShape":0.166225, "TimingRepresentationsN":2.850872 }, "ZeroDimensionalVars":[], "NumberOfSols":-1, "IsRadical":true, "ArcColoring":[ [ 0, "u" ], [ "1 - a + a^2 - b^2 - 2*a*u + 2*a^2*u + a*u^2 - 2*a^2*u^2 + a^3*u^2", "a^2 - b^2 + u - a*u + a^2*u - a^2*u^2 + a^3*u^2" ], [ "1 - a^2 + a^2*u^2 - a^3*u^2", "-1 + a^2 - a*u + a^2*u + u^2 - a*u^2 - a^2*u^2 + a^3*u^2" ], "{1, 0}", [ 1, "u^2" ], [ "2*a + b - a*u^2 + 2*a^2*u^2 - a^3*u^2", "-1 + a + b + u^2 - 2*a*u^2 + a^2*u^2" ], [ "a", "b" ], [ "a + b", "b" ], [ "-1 + 2*a + b - u + a*u - a*u^2 + a^2*u^2", "b + u - u^3 + a*u^3" ], [ "a^2*u", "1 - a + u - a*u + a*u^2 - a^2*u^2" ] ], "Obstruction":1, "ComplexVolumeN":"{0, 0, 0, 0, 0, 0}", "aCuspShape":0, "RepresentationsN":[ [ "u->-0.394212 - 0.82432 I", "a->-0.17897 + 0.664196 I", "b->0.02434 - 1.408 I" ], [ "u->-0.394212 - 0.82432 I", "a->1.93083 + 0.26816 I", "b->-0.552177 + 0.420682 I" ], [ "u->0.728533 - 0.51253 I", "a->1.28756 + 0.511314 I", "b->-1.60168 - 0.68235 I" ], [ "u->0.728533 - 0.51253 I", "a->-0.71338 - 1.69753 I", "b->-0.316505 + 0.036392 I" ], [ "u->-0.378262 + 0.633197 I", "a->-0.420427 - 0.806651 I", "b->0.1352 + 1.67176 I" ], [ "u->-0.378262 + 0.633197 I", "a->2.29168 - 0.81192 I", "b->-0.439896 - 0.507841 I" ] ], "Epsilon":2.03687, "GeometricComponent":0, "Multiplicity":{ "IdealName":"J10_123_7", "Generators":[ "1 - a + a^2 + a*b - a*u + a^2*u + a*u^2 - 2*a^2*u^2 + a^3*u^2", "a + b + a*u + b*u - a*u^2 + a^2*u^2", "-1 - u + a*u - a*u^3 + a^2*u^3" ], "VariableOrder":[ "b", "a", "u" ], "Characteristic":0, "KnownGroebner":[], "Status":[ "vCompNormalize" ], "MonomialOrder":"lex", "IsHomogeneous":false, "IsZeroDim":false, "IdealDimension":1, "Timings":{ "TimingGroebner":0.12361, "TimingZeroDimVars":7.0982e-2, "TimingmagmaVCompNormalize":7.2146e-2, "TimingNumberOfSols":2.905104, "TimingIsRadical":1.7659e-2, "TimingArcColoring":7.5351e-2, "TimingObstruction":6.163e-3, "TimingComplexVolumeN":1.203662, "TimingaCuspShapeN":2.8862000000000002e-2, "TiminguValues":0.677272, "TimingaCuspShape":0.166225, "TimingRepresentationsN":2.850872 }, "ZeroDimensionalVars":[], "NumberOfSols":-1, "IsRadical":true, "ArcColoring":[ [ 0, "u" ], [ "1 - a + a^2 - b^2 - 2*a*u + 2*a^2*u + a*u^2 - 2*a^2*u^2 + a^3*u^2", "a^2 - b^2 + u - a*u + a^2*u - a^2*u^2 + a^3*u^2" ], [ "1 - a^2 + a^2*u^2 - a^3*u^2", "-1 + a^2 - a*u + a^2*u + u^2 - a*u^2 - a^2*u^2 + a^3*u^2" ], "{1, 0}", [ 1, "u^2" ], [ "2*a + b - a*u^2 + 2*a^2*u^2 - a^3*u^2", "-1 + a + b + u^2 - 2*a*u^2 + a^2*u^2" ], [ "a", "b" ], [ "a + b", "b" ], [ "-1 + 2*a + b - u + a*u - a*u^2 + a^2*u^2", "b + u - u^3 + a*u^3" ], [ "a^2*u", "1 - a + u - a*u + a*u^2 - a^2*u^2" ] ], "Obstruction":1, "ComplexVolumeN":"{0, 0, 0, 0, 0, 0}", "aCuspShape":0, "RepresentationsN":[ [ "u->-0.394212 - 0.82432 I", "a->-0.17897 + 0.664196 I", "b->0.02434 - 1.408 I" ], [ "u->-0.394212 - 0.82432 I", "a->1.93083 + 0.26816 I", "b->-0.552177 + 0.420682 I" ], [ "u->0.728533 - 0.51253 I", "a->1.28756 + 0.511314 I", "b->-1.60168 - 0.68235 I" ], [ "u->0.728533 - 0.51253 I", "a->-0.71338 - 1.69753 I", "b->-0.316505 + 0.036392 I" ], [ "u->-0.378262 + 0.633197 I", "a->-0.420427 - 0.806651 I", "b->0.1352 + 1.67176 I" ], [ "u->-0.378262 + 0.633197 I", "a->2.29168 - 0.81192 I", "b->-0.439896 - 0.507841 I" ] ], "Epsilon":2.03687, "GeometricComponent":0 }, "SortedReprnIndices":"{1, 2, 3, 4, 5, 6}", "Abelian":false }, { "IdealName":"abJ10_123_8", "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":0.124373, "TimingZeroDimVars":7.962100000000001e-2, "TimingmagmaVCompNormalize":8.0875e-2, "TimingNumberOfSols":2.4867e-2, "TimingIsRadical":1.75e-3, "TimingArcColoring":6.1909e-2, "TimingObstruction":4.2500000000000003e-4, "TimingComplexVolumeN":0.312996, "TimingaCuspShapeN":4.511e-3, "TiminguValues":0.624252, "TiminguPolysN":7.000000000000002e-5, "TiminguPolys":0.809973, "TimingaCuspShape":8.6854e-2, "TimingRepresentationsN":2.8867e-2, "TiminguValues_ij":0.155186, "TiminguPoly_ij":0.141832, "TiminguPolys_ij_N":3.000000000000001e-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}", "{1, 0}" ], "Obstruction":1, "ComplexVolumeN":"{0}", "uPolysN":[ "u", "u", "u", "u", "u", "u", "u", "u", "u", "u" ], "uPolys":[ "u", "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}", "{1, 10}", "{2, 3}", "{2, 4}", "{2, 5}", "{2, 6}", "{2, 7}", "{2, 8}", "{2, 9}", "{2, 10}", "{3, 4}", "{3, 5}", "{3, 6}", "{3, 7}", "{3, 8}", "{3, 9}", "{3, 10}", "{4, 5}", "{4, 6}", "{4, 7}", "{4, 8}", "{4, 9}", "{4, 10}", "{5, 6}", "{5, 7}", "{5, 8}", "{5, 9}", "{5, 10}", "{6, 7}", "{6, 8}", "{6, 9}", "{6, 10}", "{7, 8}", "{7, 9}", "{7, 10}", "{8, 9}", "{8, 10}", "{9, 10}" ] ], "SortedReprnIndices":"{1}", "aCuspShapeN":"{0}", "Abelian":true } ] }, "uPolyC":[ "9*(1 - 2*u + 4*u^2 - 3*u^3 + u^4)*(-1 - 2*u + u^3 + u^4)*(32 - 96*u + 200*u^2 - 288*u^3 + 308*u^4 - 251*u^5 + 159*u^6 - 77*u^7 + 28*u^8 - 7*u^9 + u^10)*(3 + 12*u + 23*u^2 + 30*u^3 + 31*u^4 + 26*u^5 + 20*u^6 + 14*u^7 + 9*u^8 + 4*u^9 + u^10)^2*(1 - 5*u^2 - 2*u^3 + 11*u^4 + 10*u^5 - 8*u^6 - 14*u^7 - u^8 + 6*u^9 + 3*u^10)^2", "9*(-1 + 2*u - u^3 + u^4)*(1 + 2*u + 4*u^2 + 3*u^3 + u^4)*(3 - 12*u + 23*u^2 - 30*u^3 + 31*u^4 - 26*u^5 + 20*u^6 - 14*u^7 + 9*u^8 - 4*u^9 + u^10)^2*(32 + 96*u + 200*u^2 + 288*u^3 + 308*u^4 + 251*u^5 + 159*u^6 + 77*u^7 + 28*u^8 + 7*u^9 + u^10)*(1 - 5*u^2 + 2*u^3 + 11*u^4 - 10*u^5 - 8*u^6 + 14*u^7 - u^8 - 6*u^9 + 3*u^10)^2", "9*(1 - 2*u + 4*u^2 - 3*u^3 + u^4)*(-1 - 2*u + u^3 + u^4)*(32 - 96*u + 200*u^2 - 288*u^3 + 308*u^4 - 251*u^5 + 159*u^6 - 77*u^7 + 28*u^8 - 7*u^9 + u^10)*(3 + 12*u + 23*u^2 + 30*u^3 + 31*u^4 + 26*u^5 + 20*u^6 + 14*u^7 + 9*u^8 + 4*u^9 + u^10)^2*(1 - 5*u^2 - 2*u^3 + 11*u^4 + 10*u^5 - 8*u^6 - 14*u^7 - u^8 + 6*u^9 + 3*u^10)^2", "9*(-1 + 2*u - u^3 + u^4)*(1 + 2*u + 4*u^2 + 3*u^3 + u^4)*(3 - 12*u + 23*u^2 - 30*u^3 + 31*u^4 - 26*u^5 + 20*u^6 - 14*u^7 + 9*u^8 - 4*u^9 + u^10)^2*(32 + 96*u + 200*u^2 + 288*u^3 + 308*u^4 + 251*u^5 + 159*u^6 + 77*u^7 + 28*u^8 + 7*u^9 + u^10)*(1 - 5*u^2 + 2*u^3 + 11*u^4 - 10*u^5 - 8*u^6 + 14*u^7 - u^8 - 6*u^9 + 3*u^10)^2", "9*(1 - 2*u + 4*u^2 - 3*u^3 + u^4)*(-1 - 2*u + u^3 + u^4)*(32 - 96*u + 200*u^2 - 288*u^3 + 308*u^4 - 251*u^5 + 159*u^6 - 77*u^7 + 28*u^8 - 7*u^9 + u^10)*(3 + 12*u + 23*u^2 + 30*u^3 + 31*u^4 + 26*u^5 + 20*u^6 + 14*u^7 + 9*u^8 + 4*u^9 + u^10)^2*(1 - 5*u^2 - 2*u^3 + 11*u^4 + 10*u^5 - 8*u^6 - 14*u^7 - u^8 + 6*u^9 + 3*u^10)^2", "9*(-1 + 2*u - u^3 + u^4)*(1 + 2*u + 4*u^2 + 3*u^3 + u^4)*(3 - 12*u + 23*u^2 - 30*u^3 + 31*u^4 - 26*u^5 + 20*u^6 - 14*u^7 + 9*u^8 - 4*u^9 + u^10)^2*(32 + 96*u + 200*u^2 + 288*u^3 + 308*u^4 + 251*u^5 + 159*u^6 + 77*u^7 + 28*u^8 + 7*u^9 + u^10)*(1 - 5*u^2 + 2*u^3 + 11*u^4 - 10*u^5 - 8*u^6 + 14*u^7 - u^8 - 6*u^9 + 3*u^10)^2", "9*(1 - 2*u + 4*u^2 - 3*u^3 + u^4)*(-1 - 2*u + u^3 + u^4)*(32 - 96*u + 200*u^2 - 288*u^3 + 308*u^4 - 251*u^5 + 159*u^6 - 77*u^7 + 28*u^8 - 7*u^9 + u^10)*(3 + 12*u + 23*u^2 + 30*u^3 + 31*u^4 + 26*u^5 + 20*u^6 + 14*u^7 + 9*u^8 + 4*u^9 + u^10)^2*(1 - 5*u^2 - 2*u^3 + 11*u^4 + 10*u^5 - 8*u^6 - 14*u^7 - u^8 + 6*u^9 + 3*u^10)^2", "9*(-1 + 2*u - u^3 + u^4)*(1 + 2*u + 4*u^2 + 3*u^3 + u^4)*(3 - 12*u + 23*u^2 - 30*u^3 + 31*u^4 - 26*u^5 + 20*u^6 - 14*u^7 + 9*u^8 - 4*u^9 + u^10)^2*(32 + 96*u + 200*u^2 + 288*u^3 + 308*u^4 + 251*u^5 + 159*u^6 + 77*u^7 + 28*u^8 + 7*u^9 + u^10)*(1 - 5*u^2 + 2*u^3 + 11*u^4 - 10*u^5 - 8*u^6 + 14*u^7 - u^8 - 6*u^9 + 3*u^10)^2", "9*(1 - 2*u + 4*u^2 - 3*u^3 + u^4)*(-1 - 2*u + u^3 + u^4)*(32 - 96*u + 200*u^2 - 288*u^3 + 308*u^4 - 251*u^5 + 159*u^6 - 77*u^7 + 28*u^8 - 7*u^9 + u^10)*(3 + 12*u + 23*u^2 + 30*u^3 + 31*u^4 + 26*u^5 + 20*u^6 + 14*u^7 + 9*u^8 + 4*u^9 + u^10)^2*(1 - 5*u^2 - 2*u^3 + 11*u^4 + 10*u^5 - 8*u^6 - 14*u^7 - u^8 + 6*u^9 + 3*u^10)^2", "9*(-1 + 2*u - u^3 + u^4)*(1 + 2*u + 4*u^2 + 3*u^3 + u^4)*(3 - 12*u + 23*u^2 - 30*u^3 + 31*u^4 - 26*u^5 + 20*u^6 - 14*u^7 + 9*u^8 - 4*u^9 + u^10)^2*(32 + 96*u + 200*u^2 + 288*u^3 + 308*u^4 + 251*u^5 + 159*u^6 + 77*u^7 + 28*u^8 + 7*u^9 + u^10)*(1 - 5*u^2 + 2*u^3 + 11*u^4 - 10*u^5 - 8*u^6 + 14*u^7 - u^8 - 6*u^9 + 3*u^10)^2" ], "RileyPolyC":[ "81*(1 - 4*y + 2*y^2 - y^3 + y^4)*(1 + 4*y + 6*y^2 - y^3 + y^4)*(9 - 6*y - 5*y^2 + 22*y^3 + 39*y^4 + 48*y^5 + 36*y^6 + 18*y^7 + 9*y^8 + 2*y^9 + y^10)^2*(1024 + 3584*y + 4416*y^2 + 2240*y^3 + 896*y^4 + 511*y^5 + 243*y^6 + 77*y^7 + 24*y^8 + 7*y^9 + y^10)*(1 - 10*y + 47*y^2 - 130*y^3 + 239*y^4 - 316*y^5 + 316*y^6 - 234*y^7 + 121*y^8 - 42*y^9 + 9*y^10)^2", "81*(1 - 4*y + 2*y^2 - y^3 + y^4)*(1 + 4*y + 6*y^2 - y^3 + y^4)*(9 - 6*y - 5*y^2 + 22*y^3 + 39*y^4 + 48*y^5 + 36*y^6 + 18*y^7 + 9*y^8 + 2*y^9 + y^10)^2*(1024 + 3584*y + 4416*y^2 + 2240*y^3 + 896*y^4 + 511*y^5 + 243*y^6 + 77*y^7 + 24*y^8 + 7*y^9 + y^10)*(1 - 10*y + 47*y^2 - 130*y^3 + 239*y^4 - 316*y^5 + 316*y^6 - 234*y^7 + 121*y^8 - 42*y^9 + 9*y^10)^2", "81*(1 - 4*y + 2*y^2 - y^3 + y^4)*(1 + 4*y + 6*y^2 - y^3 + y^4)*(9 - 6*y - 5*y^2 + 22*y^3 + 39*y^4 + 48*y^5 + 36*y^6 + 18*y^7 + 9*y^8 + 2*y^9 + y^10)^2*(1024 + 3584*y + 4416*y^2 + 2240*y^3 + 896*y^4 + 511*y^5 + 243*y^6 + 77*y^7 + 24*y^8 + 7*y^9 + y^10)*(1 - 10*y + 47*y^2 - 130*y^3 + 239*y^4 - 316*y^5 + 316*y^6 - 234*y^7 + 121*y^8 - 42*y^9 + 9*y^10)^2", "81*(1 - 4*y + 2*y^2 - y^3 + y^4)*(1 + 4*y + 6*y^2 - y^3 + y^4)*(9 - 6*y - 5*y^2 + 22*y^3 + 39*y^4 + 48*y^5 + 36*y^6 + 18*y^7 + 9*y^8 + 2*y^9 + y^10)^2*(1024 + 3584*y + 4416*y^2 + 2240*y^3 + 896*y^4 + 511*y^5 + 243*y^6 + 77*y^7 + 24*y^8 + 7*y^9 + y^10)*(1 - 10*y + 47*y^2 - 130*y^3 + 239*y^4 - 316*y^5 + 316*y^6 - 234*y^7 + 121*y^8 - 42*y^9 + 9*y^10)^2", "81*(1 - 4*y + 2*y^2 - y^3 + y^4)*(1 + 4*y + 6*y^2 - y^3 + y^4)*(9 - 6*y - 5*y^2 + 22*y^3 + 39*y^4 + 48*y^5 + 36*y^6 + 18*y^7 + 9*y^8 + 2*y^9 + y^10)^2*(1024 + 3584*y + 4416*y^2 + 2240*y^3 + 896*y^4 + 511*y^5 + 243*y^6 + 77*y^7 + 24*y^8 + 7*y^9 + y^10)*(1 - 10*y + 47*y^2 - 130*y^3 + 239*y^4 - 316*y^5 + 316*y^6 - 234*y^7 + 121*y^8 - 42*y^9 + 9*y^10)^2", "81*(1 - 4*y + 2*y^2 - y^3 + y^4)*(1 + 4*y + 6*y^2 - y^3 + y^4)*(9 - 6*y - 5*y^2 + 22*y^3 + 39*y^4 + 48*y^5 + 36*y^6 + 18*y^7 + 9*y^8 + 2*y^9 + y^10)^2*(1024 + 3584*y + 4416*y^2 + 2240*y^3 + 896*y^4 + 511*y^5 + 243*y^6 + 77*y^7 + 24*y^8 + 7*y^9 + y^10)*(1 - 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10*y + 47*y^2 - 130*y^3 + 239*y^4 - 316*y^5 + 316*y^6 - 234*y^7 + 121*y^8 - 42*y^9 + 9*y^10)^2", "81*(1 - 4*y + 2*y^2 - y^3 + y^4)*(1 + 4*y + 6*y^2 - y^3 + y^4)*(9 - 6*y - 5*y^2 + 22*y^3 + 39*y^4 + 48*y^5 + 36*y^6 + 18*y^7 + 9*y^8 + 2*y^9 + y^10)^2*(1024 + 3584*y + 4416*y^2 + 2240*y^3 + 896*y^4 + 511*y^5 + 243*y^6 + 77*y^7 + 24*y^8 + 7*y^9 + y^10)*(1 - 10*y + 47*y^2 - 130*y^3 + 239*y^4 - 316*y^5 + 316*y^6 - 234*y^7 + 121*y^8 - 42*y^9 + 9*y^10)^2" ] }, "GeometricRepresentation":[ 1.70857e1, [ "J10_123_0", 1, "{3, 4}" ] ] } }