details/L10a33_1_2c75cf0d.json
FL expansions
| Newt(ΔL) vertex |
Exposing functional |
Leading x-power |
Leading q-power |
Inversion datum |
Inversion cycle |
FL |
(-1/2, -5/2) |
(1, 1) |
x1^(1/2)x2^(5/2) |
q^(5/2) |
{"0": [-1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1], "1": [1, 1, -1, 1, -1, 1]}
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(-q^(5/2))*x1^(1/2)*x2^(5/2) + (-4*q^(5/2))*x1^(1/2)*x2^(7/2) + (2*q^(7/2))*x1^(3/2)*x2^(7/2) + (q^(7/2) - 10*q^(5/2) - 3*q^(3/2))*x1^(1/2)*x2^(9/2) + (2*q^(9/2) + 8*q^(7/2) + 2*q^(5/2))*x1^(3/2)*x2^(9/2) + (-3*q^(11/2) - q^(9/2))*x1^(5/2)*x2^(9/2) + (4*q^(7/2) - 20*q^(5/2) - 12*q^(3/2) - 8*q^(1/2))*x1^(1/2)*x2^(11/2) + (2*q^(11/2) + 6*q^(9/2) + 24*q^(7/2) + 14*q^(5/2) + 6*q^(3/2))*x1^(3/2)*x2^(11/2) + (-2*q^(15/2) - 4*q^(13/2) - 14*q^(11/2) - 8*q^(9/2) - 4*q^(7/2))*x1^(5/2)*x2^(11/2) + (4*q^(17/2) + 2*q^(15/2) + 2*q^(13/2))*x1^(7/2)*x2^(11/2) + (-2*q^(11/2) + 10*q^(7/2) - 32*q^(5/2) - 30*q^(3/2) - 33*q^(1/2) - 18*q^(-1/2) - 5*q^(-3/2))*x1^(1/2)*x2^(13/2) + (2*q^(13/2) + 6*q^(11/2) + 16*q^(9/2) + 60*q^(7/2) + 56*q^(5/2) + 42*q^(3/2) + 18*q^(1/2) + 4*q^(-1/2))*x1^(3/2)*x2^(13/2) + (-2*q^(19/2) - 2*q^(17/2) - 13*q^(15/2) - 20*q^(13/2) - 49*q^(11/2) - 43*q^(9/2) - 31*q^(7/2) - 13*q^(5/2) - 3*q^(3/2))*x1^(5/2)*x2^(13/2) + (2*q^(23/2) + 4*q^(21/2) + 8*q^(19/2) + 22*q^(17/2) + 18*q^(15/2) + 16*q^(13/2) + 8*q^(11/2) + 2*q^(9/2))*x1^(7/2)*x2^(13/2) + (-5*q^(25/2) - 3*q^(23/2) - 4*q^(21/2) - 3*q^(19/2) - q^(17/2))*x1^(9/2)*x2^(13/2) + (-2*q^(13/2) - 8*q^(11/2) - 2*q^(9/2) + 20*q^(7/2) - 44*q^(5/2) - 52*q^(3/2) - 84*q^(1/2) - 76*q^(-1/2) - 56*q^(-3/2) - 20*q^(-5/2) - 12*q^(-7/2))*x1^(1/2)*x2^(15/2) + (2*q^(15/2) + 10*q^(13/2) + 17*q^(11/2) + 38*q^(9/2) + 132*q^(7/2) + 162*q^(5/2) + 170*q^(3/2) + 124*q^(1/2) + 70*q^(-1/2) + 26*q^(-3/2) + 10*q^(-5/2))*x1^(3/2)*x2^(15/2) + (-2*q^(23/2) - 2*q^(21/2) - 10*q^(19/2) - 16*q^(17/2) - 48*q^(15/2) - 76*q^(13/2) - 156*q^(11/2) - 168*q^(9/2) - 160*q^(7/2) - 106*q^(5/2) - 60*q^(3/2) - 20*q^(1/2) - 8*q^(-1/2))*x1^(5/2)*x2^(15/2) + (2*q^(29/2) + 2*q^(27/2) + 6*q^(25/2) + 16*q^(23/2) + 34*q^(21/2) + 50*q^(19/2) + 96*q^(17/2) + 98*q^(15/2) + 96*q^(13/2) + 68*q^(11/2) + 40*q^(9/2) + 14*q^(7/2) + 6*q^(5/2))*x1^(7/2)*x2^(15/2) + (-2*q^(33/2) - 4*q^(31/2) - 8*q^(29/2) - 14*q^(27/2) - 34*q^(25/2) - 32*q^(23/2) - 36*q^(21/2) - 30*q^(19/2) - 20*q^(17/2) - 8*q^(15/2) - 4*q^(13/2))*x1^(9/2)*x2^(15/2) + (6*q^(35/2) + 4*q^(33/2) + 6*q^(31/2) + 6*q^(29/2) + 6*q^(27/2) + 2*q^(25/2) + 2*q^(23/2))*x1^(11/2)*x2^(15/2) + (2*q^(17/2) - 2*q^(15/2) - 8*q^(13/2) - 24*q^(11/2) - 14*q^(9/2) + 29*q^(7/2) - 54*q^(5/2) - 72*q^(3/2) - 152*q^(1/2) - 191*q^(-1/2) - 204*q^(-3/2) - 148*q^(-5/2) - 102*q^(-7/2) - 51*q^(-9/2) - 26*q^(-11/2) - 7*q^(-13/2))*x1^(1/2)*x2^(17/2) + (2*q^(17/2) + 14*q^(15/2) + 36*q^(13/2) + 50*q^(11/2) + 88*q^(9/2) + 264*q^(7/2) + 386*q^(5/2) + 494*q^(3/2) + 490*q^(1/2) + 402*q^(-1/2) + 262*q^(-3/2) + 152*q^(-5/2) + 70*q^(-7/2) + 28*q^(-9/2) + 6*q^(-11/2))*x1^(3/2)*x2^(17/2) + (-2*q^(27/2) - 2*q^(25/2) - 10*q^(23/2) - 12*q^(21/2) - 41*q^(19/2) - 72*q^(17/2) - 157*q^(15/2) - 247*q^(13/2) - 452*q^(11/2) - 558*q^(9/2) - 617*q^(7/2) - 542*q^(5/2) - 415*q^(3/2) - 255*q^(1/2) - 141*q^(-1/2) - 61*q^(-3/2) - 23*q^(-5/2) - 5*q^(-7/2))*x1^(5/2)*x2^(17/2) + (2*q^(35/2) + 2*q^(33/2) + 4*q^(31/2) + 14*q^(29/2) + 22*q^(27/2) + 44*q^(25/2) + 88*q^(23/2) + 160*q^(21/2) + 236*q^(19/2) + 372*q^(17/2) + 430*q^(15/2) + 456*q^(13/2) + 398*q^(11/2) + 304*q^(9/2) + 190*q^(7/2) + 106*q^(5/2) + 46*q^(3/2) + 18*q^(1/2) + 4*q^(-1/2))*x1^(7/2)*x2^(17/2) + (-2*q^(41/2) - 2*q^(39/2) - 6*q^(37/2) - 8*q^(35/2) - 25*q^(33/2) - 43*q^(31/2) - 77*q^(29/2) - 109*q^(27/2) - 182*q^(25/2) - 202*q^(23/2) - 221*q^(21/2) - 204*q^(19/2) - 168*q^(17/2) - 110*q^(15/2) - 66*q^(13/2) - 31*q^(11/2) - 13*q^(9/2) - 3*q^(7/2))*x1^(9/2)*x2^(17/2) + (2*q^(45/2) + 4*q^(43/2) + 8*q^(41/2) + 14*q^(39/2) + 24*q^(37/2) + 50*q^(35/2) + 54*q^(33/2) + 64*q^(31/2) + 66*q^(29/2) + 62*q^(27/2) + 44*q^(25/2) + 30*q^(23/2) + 16*q^(21/2) + 8*q^(19/2) + 2*q^(17/2))*x1^(11/2)*x2^(17/2) + (-7*q^(47/2) - 5*q^(45/2) - 8*q^(43/2) - 9*q^(41/2) - 11*q^(39/2) - 9*q^(37/2) - 7*q^(35/2) - 4*q^(33/2) - 3*q^(31/2) - q^(29/2))*x1^(13/2)*x2^(17/2) + (2*q^(19/2) + 6*q^(17/2) - 6*q^(15/2) - 24*q^(13/2) - 62*q^(11/2) - 56*q^(9/2) + 14*q^(7/2) - 78*q^(5/2) - 88*q^(3/2) - 224*q^(1/2) - 344*q^(-1/2) - 480*q^(-3/2) - 480*q^(-5/2) - 456*q^(-7/2) - 328*q^(-9/2) - 248*q^(-11/2) - 144*q^(-13/2) - 80*q^(-15/2) - 28*q^(-17/2) - 16*q^(-19/2))*x1^(1/2)*x2^(19/2) + (-2*q^(19/2) + 17*q^(17/2) + 56*q^(15/2) + 118*q^(13/2) + 154*q^(11/2) + 218*q^(9/2) + 514*q^(7/2) + 807*q^(5/2) + 1172*q^(3/2) + 1402*q^(1/2) + 1454*q^(-1/2) + 1266*q^(-3/2) + 996*q^(-5/2) + 674*q^(-7/2) + 426*q^(-9/2) + 226*q^(-11/2) + 106*q^(-13/2) + 38*q^(-15/2) + 14*q^(-17/2))*x1^(3/2)*x2^(19/2) + (-2*q^(31/2) - 2*q^(29/2) - 10*q^(27/2) - 12*q^(25/2) - 36*q^(23/2) - 60*q^(21/2) - 150*q^(19/2) - 260*q^(17/2) - 480*q^(15/2) - 732*q^(13/2) - 1230*q^(11/2) - 1630*q^(9/2) - 1998*q^(7/2) - 2064*q^(5/2) - 1936*q^(3/2) - 1548*q^(1/2) - 1148*q^(-1/2) - 728*q^(-3/2) - 438*q^(-5/2) - 216*q^(-7/2) - 100*q^(-9/2) - 32*q^(-11/2) - 12*q^(-13/2))*x1^(5/2)*x2^(19/2) + (2*q^(41/2) + 2*q^(39/2) + 4*q^(37/2) + 12*q^(35/2) + 20*q^(33/2) + 32*q^(31/2) + 74*q^(29/2) + 120*q^(27/2) + 220*q^(25/2) + 384*q^(23/2) + 633*q^(21/2) + 920*q^(19/2) + 1342*q^(17/2) + 1633*q^(15/2) + 1854*q^(13/2) + 1836*q^(11/2) + 1654*q^(9/2) + 1306*q^(7/2) + 954*q^(5/2) + 600*q^(3/2) + 356*q^(1/2) + 178*q^(-1/2) + 80*q^(-3/2) + 26*q^(-5/2) + 10*q^(-7/2))*x1^(7/2)*x2^(19/2) + (-2*q^(49/2) - 2*q^(47/2) - 4*q^(45/2) - 8*q^(43/2) - 18*q^(41/2) - 28*q^(39/2) - 58*q^(37/2) - 88*q^(35/2) - 170*q^(33/2) - 276*q^(31/2) - 436*q^(29/2) - 598*q^(27/2) - 856*q^(25/2) - 1004*q^(23/2) - 1128*q^(21/2) - 1118*q^(19/2) - 1032*q^(17/2) - 830*q^(15/2) - 626*q^(13/2) - 404*q^(11/2) - 250*q^(9/2) - 128*q^(7/2) - 60*q^(5/2) - 20*q^(3/2) - 8*q^(1/2))*x1^(9/2)*x2^(19/2) + (2*q^(55/2) + 2*q^(53/2) + 6*q^(51/2) + 8*q^(49/2) + 16*q^(47/2) + 32*q^(45/2) + 62*q^(43/2) + 98*q^(41/2) + 158*q^(39/2) + 220*q^(37/2) + 334*q^(35/2) + 392*q^(33/2) + 452*q^(31/2) + 466*q^(29/2) + 460*q^(27/2) + 388*q^(25/2) + 312*q^(23/2) + 214*q^(21/2) + 144*q^(19/2) + 78*q^(17/2) + 40*q^(15/2) + 14*q^(13/2) + 6*q^(11/2))*x1^(11/2)*x2^(19/2) + (-2*q^(59/2) - 4*q^(57/2) - 8*q^(55/2) - 14*q^(53/2) - 24*q^(51/2) - 38*q^(49/2) - 74*q^(47/2) - 84*q^(45/2) - 106*q^(43/2) - 118*q^(41/2) - 128*q^(39/2) - 118*q^(37/2) - 104*q^(35/2) - 76*q^(33/2) - 58*q^(31/2) - 36*q^(29/2) - 20*q^(27/2) - 8*q^(25/2) - 4*q^(23/2))*x1^(13/2)*x2^(19/2) + (8*q^(61/2) + 6*q^(59/2) + 10*q^(57/2) + 12*q^(55/2) + 16*q^(53/2) + 16*q^(51/2) + 18*q^(49/2) + 12*q^(47/2) + 12*q^(45/2) + 8*q^(43/2) + 6*q^(41/2) + 2*q^(39/2) + 2*q^(37/2))*x1^(15/2)*x2^(19/2)
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(-1/2, -5/2) |
(1, 1) |
x1^(1/2)x2^(5/2) |
q^(5/2) |
{"0": [1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], "1": [1, 1, -1, 1, -1, 1]}
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(-q^(5/2))*x1^(1/2)*x2^(5/2) + (-4*q^(5/2))*x1^(1/2)*x2^(7/2) + (2*q^(7/2))*x1^(3/2)*x2^(7/2) + (q^(7/2) - 10*q^(5/2) - 3*q^(3/2))*x1^(1/2)*x2^(9/2) + (2*q^(9/2) + 8*q^(7/2) + 2*q^(5/2))*x1^(3/2)*x2^(9/2) + (-3*q^(11/2) - q^(9/2))*x1^(5/2)*x2^(9/2) + (4*q^(7/2) - 20*q^(5/2) - 12*q^(3/2) - 8*q^(1/2))*x1^(1/2)*x2^(11/2) + (2*q^(11/2) + 6*q^(9/2) + 24*q^(7/2) + 14*q^(5/2) + 6*q^(3/2))*x1^(3/2)*x2^(11/2) + (-2*q^(15/2) - 4*q^(13/2) - 14*q^(11/2) - 8*q^(9/2) - 4*q^(7/2))*x1^(5/2)*x2^(11/2) + (4*q^(17/2) + 2*q^(15/2) + 2*q^(13/2))*x1^(7/2)*x2^(11/2) + (-2*q^(11/2) + 10*q^(7/2) - 32*q^(5/2) - 30*q^(3/2) - 33*q^(1/2) - 18*q^(-1/2) - 5*q^(-3/2))*x1^(1/2)*x2^(13/2) + (2*q^(13/2) + 6*q^(11/2) + 16*q^(9/2) + 60*q^(7/2) + 56*q^(5/2) + 42*q^(3/2) + 18*q^(1/2) + 4*q^(-1/2))*x1^(3/2)*x2^(13/2) + (-2*q^(19/2) - 2*q^(17/2) - 13*q^(15/2) - 20*q^(13/2) - 49*q^(11/2) - 43*q^(9/2) - 31*q^(7/2) - 13*q^(5/2) - 3*q^(3/2))*x1^(5/2)*x2^(13/2) + (2*q^(23/2) + 4*q^(21/2) + 8*q^(19/2) + 22*q^(17/2) + 18*q^(15/2) + 16*q^(13/2) + 8*q^(11/2) + 2*q^(9/2))*x1^(7/2)*x2^(13/2) + (-5*q^(25/2) - 3*q^(23/2) - 4*q^(21/2) - 3*q^(19/2) - q^(17/2))*x1^(9/2)*x2^(13/2) + (-2*q^(13/2) - 8*q^(11/2) - 2*q^(9/2) + 20*q^(7/2) - 44*q^(5/2) - 52*q^(3/2) - 84*q^(1/2) - 76*q^(-1/2) - 56*q^(-3/2) - 20*q^(-5/2) - 12*q^(-7/2))*x1^(1/2)*x2^(15/2) + (2*q^(15/2) + 10*q^(13/2) + 17*q^(11/2) + 38*q^(9/2) + 132*q^(7/2) + 162*q^(5/2) + 170*q^(3/2) + 124*q^(1/2) + 70*q^(-1/2) + 26*q^(-3/2) + 10*q^(-5/2))*x1^(3/2)*x2^(15/2) + (-2*q^(23/2) - 2*q^(21/2) - 10*q^(19/2) - 16*q^(17/2) - 48*q^(15/2) - 76*q^(13/2) - 156*q^(11/2) - 168*q^(9/2) - 160*q^(7/2) - 106*q^(5/2) - 60*q^(3/2) - 20*q^(1/2) - 8*q^(-1/2))*x1^(5/2)*x2^(15/2) + (2*q^(29/2) + 2*q^(27/2) + 6*q^(25/2) + 16*q^(23/2) + 34*q^(21/2) + 50*q^(19/2) + 96*q^(17/2) + 98*q^(15/2) + 96*q^(13/2) + 68*q^(11/2) + 40*q^(9/2) + 14*q^(7/2) + 6*q^(5/2))*x1^(7/2)*x2^(15/2) + (-2*q^(33/2) - 4*q^(31/2) - 8*q^(29/2) - 14*q^(27/2) - 34*q^(25/2) - 32*q^(23/2) - 36*q^(21/2) - 30*q^(19/2) - 20*q^(17/2) - 8*q^(15/2) - 4*q^(13/2))*x1^(9/2)*x2^(15/2) + (6*q^(35/2) + 4*q^(33/2) + 6*q^(31/2) + 6*q^(29/2) + 6*q^(27/2) + 2*q^(25/2) + 2*q^(23/2))*x1^(11/2)*x2^(15/2) + (2*q^(17/2) - 2*q^(15/2) - 8*q^(13/2) - 24*q^(11/2) - 14*q^(9/2) + 29*q^(7/2) - 54*q^(5/2) - 72*q^(3/2) - 152*q^(1/2) - 191*q^(-1/2) - 204*q^(-3/2) - 148*q^(-5/2) - 102*q^(-7/2) - 51*q^(-9/2) - 26*q^(-11/2) - 7*q^(-13/2))*x1^(1/2)*x2^(17/2) + (2*q^(17/2) + 14*q^(15/2) + 36*q^(13/2) + 50*q^(11/2) + 88*q^(9/2) + 264*q^(7/2) + 386*q^(5/2) + 494*q^(3/2) + 490*q^(1/2) + 402*q^(-1/2) + 262*q^(-3/2) + 152*q^(-5/2) + 70*q^(-7/2) + 28*q^(-9/2) + 6*q^(-11/2))*x1^(3/2)*x2^(17/2) + (-2*q^(27/2) - 2*q^(25/2) - 10*q^(23/2) - 12*q^(21/2) - 41*q^(19/2) - 72*q^(17/2) - 157*q^(15/2) - 247*q^(13/2) - 452*q^(11/2) - 558*q^(9/2) - 617*q^(7/2) - 542*q^(5/2) - 415*q^(3/2) - 255*q^(1/2) - 141*q^(-1/2) - 61*q^(-3/2) - 23*q^(-5/2) - 5*q^(-7/2))*x1^(5/2)*x2^(17/2) + (2*q^(35/2) + 2*q^(33/2) + 4*q^(31/2) + 14*q^(29/2) + 22*q^(27/2) + 44*q^(25/2) + 88*q^(23/2) + 160*q^(21/2) + 236*q^(19/2) + 372*q^(17/2) + 430*q^(15/2) + 456*q^(13/2) + 398*q^(11/2) + 304*q^(9/2) + 190*q^(7/2) + 106*q^(5/2) + 46*q^(3/2) + 18*q^(1/2) + 4*q^(-1/2))*x1^(7/2)*x2^(17/2) + (-2*q^(41/2) - 2*q^(39/2) - 6*q^(37/2) - 8*q^(35/2) - 25*q^(33/2) - 43*q^(31/2) - 77*q^(29/2) - 109*q^(27/2) - 182*q^(25/2) - 202*q^(23/2) - 221*q^(21/2) - 204*q^(19/2) - 168*q^(17/2) - 110*q^(15/2) - 66*q^(13/2) - 31*q^(11/2) - 13*q^(9/2) - 3*q^(7/2))*x1^(9/2)*x2^(17/2) + (2*q^(45/2) + 4*q^(43/2) + 8*q^(41/2) + 14*q^(39/2) + 24*q^(37/2) + 50*q^(35/2) + 54*q^(33/2) + 64*q^(31/2) + 66*q^(29/2) + 62*q^(27/2) + 44*q^(25/2) + 30*q^(23/2) + 16*q^(21/2) + 8*q^(19/2) + 2*q^(17/2))*x1^(11/2)*x2^(17/2) + (-7*q^(47/2) - 5*q^(45/2) - 8*q^(43/2) - 9*q^(41/2) - 11*q^(39/2) - 9*q^(37/2) - 7*q^(35/2) - 4*q^(33/2) - 3*q^(31/2) - q^(29/2))*x1^(13/2)*x2^(17/2) + (2*q^(19/2) + 6*q^(17/2) - 6*q^(15/2) - 24*q^(13/2) - 62*q^(11/2) - 56*q^(9/2) + 14*q^(7/2) - 78*q^(5/2) - 88*q^(3/2) - 224*q^(1/2) - 344*q^(-1/2) - 480*q^(-3/2) - 480*q^(-5/2) - 456*q^(-7/2) - 328*q^(-9/2) - 248*q^(-11/2) - 144*q^(-13/2) - 80*q^(-15/2) - 28*q^(-17/2) - 16*q^(-19/2))*x1^(1/2)*x2^(19/2) + (-2*q^(19/2) + 17*q^(17/2) + 56*q^(15/2) + 118*q^(13/2) + 154*q^(11/2) + 218*q^(9/2) + 514*q^(7/2) + 807*q^(5/2) + 1172*q^(3/2) + 1402*q^(1/2) + 1454*q^(-1/2) + 1266*q^(-3/2) + 996*q^(-5/2) + 674*q^(-7/2) + 426*q^(-9/2) + 226*q^(-11/2) + 106*q^(-13/2) + 38*q^(-15/2) + 14*q^(-17/2))*x1^(3/2)*x2^(19/2) + (-2*q^(31/2) - 2*q^(29/2) - 10*q^(27/2) - 12*q^(25/2) - 36*q^(23/2) - 60*q^(21/2) - 150*q^(19/2) - 260*q^(17/2) - 480*q^(15/2) - 732*q^(13/2) - 1230*q^(11/2) - 1630*q^(9/2) - 1998*q^(7/2) - 2064*q^(5/2) - 1936*q^(3/2) - 1548*q^(1/2) - 1148*q^(-1/2) - 728*q^(-3/2) - 438*q^(-5/2) - 216*q^(-7/2) - 100*q^(-9/2) - 32*q^(-11/2) - 12*q^(-13/2))*x1^(5/2)*x2^(19/2) + (2*q^(41/2) + 2*q^(39/2) + 4*q^(37/2) + 12*q^(35/2) + 20*q^(33/2) + 32*q^(31/2) + 74*q^(29/2) + 120*q^(27/2) + 220*q^(25/2) + 384*q^(23/2) + 633*q^(21/2) + 920*q^(19/2) + 1342*q^(17/2) + 1633*q^(15/2) + 1854*q^(13/2) + 1836*q^(11/2) + 1654*q^(9/2) + 1306*q^(7/2) + 954*q^(5/2) + 600*q^(3/2) + 356*q^(1/2) + 178*q^(-1/2) + 80*q^(-3/2) + 26*q^(-5/2) + 10*q^(-7/2))*x1^(7/2)*x2^(19/2) + (-2*q^(49/2) - 2*q^(47/2) - 4*q^(45/2) - 8*q^(43/2) - 18*q^(41/2) - 28*q^(39/2) - 58*q^(37/2) - 88*q^(35/2) - 170*q^(33/2) - 276*q^(31/2) - 436*q^(29/2) - 598*q^(27/2) - 856*q^(25/2) - 1004*q^(23/2) - 1128*q^(21/2) - 1118*q^(19/2) - 1032*q^(17/2) - 830*q^(15/2) - 626*q^(13/2) - 404*q^(11/2) - 250*q^(9/2) - 128*q^(7/2) - 60*q^(5/2) - 20*q^(3/2) - 8*q^(1/2))*x1^(9/2)*x2^(19/2) + (2*q^(55/2) + 2*q^(53/2) + 6*q^(51/2) + 8*q^(49/2) + 16*q^(47/2) + 32*q^(45/2) + 62*q^(43/2) + 98*q^(41/2) + 158*q^(39/2) + 220*q^(37/2) + 334*q^(35/2) + 392*q^(33/2) + 452*q^(31/2) + 466*q^(29/2) + 460*q^(27/2) + 388*q^(25/2) + 312*q^(23/2) + 214*q^(21/2) + 144*q^(19/2) + 78*q^(17/2) + 40*q^(15/2) + 14*q^(13/2) + 6*q^(11/2))*x1^(11/2)*x2^(19/2) + (-2*q^(59/2) - 4*q^(57/2) - 8*q^(55/2) - 14*q^(53/2) - 24*q^(51/2) - 38*q^(49/2) - 74*q^(47/2) - 84*q^(45/2) - 106*q^(43/2) - 118*q^(41/2) - 128*q^(39/2) - 118*q^(37/2) - 104*q^(35/2) - 76*q^(33/2) - 58*q^(31/2) - 36*q^(29/2) - 20*q^(27/2) - 8*q^(25/2) - 4*q^(23/2))*x1^(13/2)*x2^(19/2) + (8*q^(61/2) + 6*q^(59/2) + 10*q^(57/2) + 12*q^(55/2) + 16*q^(53/2) + 16*q^(51/2) + 18*q^(49/2) + 12*q^(47/2) + 12*q^(45/2) + 8*q^(43/2) + 6*q^(41/2) + 2*q^(39/2) + 2*q^(37/2))*x1^(15/2)*x2^(19/2)
|
(1/2, 5/2) |
|
x1^(-1/2)x2^(-5/2) |
q^(5/2) |
|
|
(-q^(5/2))*x1^(-1/2)*x2^(-5/2) + (-4*q^(5/2))*x1^(-1/2)*x2^(-7/2) + (2*q^(7/2))*x1^(-3/2)*x2^(-7/2) + (q^(7/2) - 10*q^(5/2) - 3*q^(3/2))*x1^(-1/2)*x2^(-9/2) + (2*q^(9/2) + 8*q^(7/2) + 2*q^(5/2))*x1^(-3/2)*x2^(-9/2) + (-3*q^(11/2) - q^(9/2))*x1^(-5/2)*x2^(-9/2) + (4*q^(7/2) - 20*q^(5/2) - 12*q^(3/2) - 8*q^(1/2))*x1^(-1/2)*x2^(-11/2) + (2*q^(11/2) + 6*q^(9/2) + 24*q^(7/2) + 14*q^(5/2) + 6*q^(3/2))*x1^(-3/2)*x2^(-11/2) + (-2*q^(15/2) - 4*q^(13/2) - 14*q^(11/2) - 8*q^(9/2) - 4*q^(7/2))*x1^(-5/2)*x2^(-11/2) + (4*q^(17/2) + 2*q^(15/2) + 2*q^(13/2))*x1^(-7/2)*x2^(-11/2) + (-2*q^(11/2) + 10*q^(7/2) - 32*q^(5/2) - 30*q^(3/2) - 33*q^(1/2) - 18*q^(-1/2) - 5*q^(-3/2))*x1^(-1/2)*x2^(-13/2) + (2*q^(13/2) + 6*q^(11/2) + 16*q^(9/2) + 60*q^(7/2) + 56*q^(5/2) + 42*q^(3/2) + 18*q^(1/2) + 4*q^(-1/2))*x1^(-3/2)*x2^(-13/2) + (-2*q^(19/2) - 2*q^(17/2) - 13*q^(15/2) - 20*q^(13/2) - 49*q^(11/2) - 43*q^(9/2) - 31*q^(7/2) - 13*q^(5/2) - 3*q^(3/2))*x1^(-5/2)*x2^(-13/2) + (2*q^(23/2) + 4*q^(21/2) + 8*q^(19/2) + 22*q^(17/2) + 18*q^(15/2) + 16*q^(13/2) + 8*q^(11/2) + 2*q^(9/2))*x1^(-7/2)*x2^(-13/2) + (-5*q^(25/2) - 3*q^(23/2) - 4*q^(21/2) - 3*q^(19/2) - q^(17/2))*x1^(-9/2)*x2^(-13/2) + (-2*q^(13/2) - 8*q^(11/2) - 2*q^(9/2) + 20*q^(7/2) - 44*q^(5/2) - 52*q^(3/2) - 84*q^(1/2) - 76*q^(-1/2) - 56*q^(-3/2) - 20*q^(-5/2) - 12*q^(-7/2))*x1^(-1/2)*x2^(-15/2) + (2*q^(15/2) + 10*q^(13/2) + 17*q^(11/2) + 38*q^(9/2) + 132*q^(7/2) + 162*q^(5/2) + 170*q^(3/2) + 124*q^(1/2) + 70*q^(-1/2) + 26*q^(-3/2) + 10*q^(-5/2))*x1^(-3/2)*x2^(-15/2) + (-2*q^(23/2) - 2*q^(21/2) - 10*q^(19/2) - 16*q^(17/2) - 48*q^(15/2) - 76*q^(13/2) - 156*q^(11/2) - 168*q^(9/2) - 160*q^(7/2) - 106*q^(5/2) - 60*q^(3/2) - 20*q^(1/2) - 8*q^(-1/2))*x1^(-5/2)*x2^(-15/2) + (2*q^(29/2) + 2*q^(27/2) + 6*q^(25/2) + 16*q^(23/2) + 34*q^(21/2) + 50*q^(19/2) + 96*q^(17/2) + 98*q^(15/2) + 96*q^(13/2) + 68*q^(11/2) + 40*q^(9/2) + 14*q^(7/2) + 6*q^(5/2))*x1^(-7/2)*x2^(-15/2) + (-2*q^(33/2) - 4*q^(31/2) - 8*q^(29/2) - 14*q^(27/2) - 34*q^(25/2) - 32*q^(23/2) - 36*q^(21/2) - 30*q^(19/2) - 20*q^(17/2) - 8*q^(15/2) - 4*q^(13/2))*x1^(-9/2)*x2^(-15/2) + (6*q^(35/2) + 4*q^(33/2) + 6*q^(31/2) + 6*q^(29/2) + 6*q^(27/2) + 2*q^(25/2) + 2*q^(23/2))*x1^(-11/2)*x2^(-15/2) + (2*q^(17/2) - 2*q^(15/2) - 8*q^(13/2) - 24*q^(11/2) - 14*q^(9/2) + 29*q^(7/2) - 54*q^(5/2) - 72*q^(3/2) - 152*q^(1/2) - 191*q^(-1/2) - 204*q^(-3/2) - 148*q^(-5/2) - 102*q^(-7/2) - 51*q^(-9/2) - 26*q^(-11/2) - 7*q^(-13/2))*x1^(-1/2)*x2^(-17/2) + (2*q^(17/2) + 14*q^(15/2) + 36*q^(13/2) + 50*q^(11/2) + 88*q^(9/2) + 264*q^(7/2) + 386*q^(5/2) + 494*q^(3/2) + 490*q^(1/2) + 402*q^(-1/2) + 262*q^(-3/2) + 152*q^(-5/2) + 70*q^(-7/2) + 28*q^(-9/2) + 6*q^(-11/2))*x1^(-3/2)*x2^(-17/2) + (-2*q^(27/2) - 2*q^(25/2) - 10*q^(23/2) - 12*q^(21/2) - 41*q^(19/2) - 72*q^(17/2) - 157*q^(15/2) - 247*q^(13/2) - 452*q^(11/2) - 558*q^(9/2) - 617*q^(7/2) - 542*q^(5/2) - 415*q^(3/2) - 255*q^(1/2) - 141*q^(-1/2) - 61*q^(-3/2) - 23*q^(-5/2) - 5*q^(-7/2))*x1^(-5/2)*x2^(-17/2) + (2*q^(35/2) + 2*q^(33/2) + 4*q^(31/2) + 14*q^(29/2) + 22*q^(27/2) + 44*q^(25/2) + 88*q^(23/2) + 160*q^(21/2) + 236*q^(19/2) + 372*q^(17/2) + 430*q^(15/2) + 456*q^(13/2) + 398*q^(11/2) + 304*q^(9/2) + 190*q^(7/2) + 106*q^(5/2) + 46*q^(3/2) + 18*q^(1/2) + 4*q^(-1/2))*x1^(-7/2)*x2^(-17/2) + (-2*q^(41/2) - 2*q^(39/2) - 6*q^(37/2) - 8*q^(35/2) - 25*q^(33/2) - 43*q^(31/2) - 77*q^(29/2) - 109*q^(27/2) - 182*q^(25/2) - 202*q^(23/2) - 221*q^(21/2) - 204*q^(19/2) - 168*q^(17/2) - 110*q^(15/2) - 66*q^(13/2) - 31*q^(11/2) - 13*q^(9/2) - 3*q^(7/2))*x1^(-9/2)*x2^(-17/2) + (2*q^(45/2) + 4*q^(43/2) + 8*q^(41/2) + 14*q^(39/2) + 24*q^(37/2) + 50*q^(35/2) + 54*q^(33/2) + 64*q^(31/2) + 66*q^(29/2) + 62*q^(27/2) + 44*q^(25/2) + 30*q^(23/2) + 16*q^(21/2) + 8*q^(19/2) + 2*q^(17/2))*x1^(-11/2)*x2^(-17/2) + (-7*q^(47/2) - 5*q^(45/2) - 8*q^(43/2) - 9*q^(41/2) - 11*q^(39/2) - 9*q^(37/2) - 7*q^(35/2) - 4*q^(33/2) - 3*q^(31/2) - q^(29/2))*x1^(-13/2)*x2^(-17/2) + (2*q^(19/2) + 6*q^(17/2) - 6*q^(15/2) - 24*q^(13/2) - 62*q^(11/2) - 56*q^(9/2) + 14*q^(7/2) - 78*q^(5/2) - 88*q^(3/2) - 224*q^(1/2) - 344*q^(-1/2) - 480*q^(-3/2) - 480*q^(-5/2) - 456*q^(-7/2) - 328*q^(-9/2) - 248*q^(-11/2) - 144*q^(-13/2) - 80*q^(-15/2) - 28*q^(-17/2) - 16*q^(-19/2))*x1^(-1/2)*x2^(-19/2) + (-2*q^(19/2) + 17*q^(17/2) + 56*q^(15/2) + 118*q^(13/2) + 154*q^(11/2) + 218*q^(9/2) + 514*q^(7/2) + 807*q^(5/2) + 1172*q^(3/2) + 1402*q^(1/2) + 1454*q^(-1/2) + 1266*q^(-3/2) + 996*q^(-5/2) + 674*q^(-7/2) + 426*q^(-9/2) + 226*q^(-11/2) + 106*q^(-13/2) + 38*q^(-15/2) + 14*q^(-17/2))*x1^(-3/2)*x2^(-19/2) + (-2*q^(31/2) - 2*q^(29/2) - 10*q^(27/2) - 12*q^(25/2) - 36*q^(23/2) - 60*q^(21/2) - 150*q^(19/2) - 260*q^(17/2) - 480*q^(15/2) - 732*q^(13/2) - 1230*q^(11/2) - 1630*q^(9/2) - 1998*q^(7/2) - 2064*q^(5/2) - 1936*q^(3/2) - 1548*q^(1/2) - 1148*q^(-1/2) - 728*q^(-3/2) - 438*q^(-5/2) - 216*q^(-7/2) - 100*q^(-9/2) - 32*q^(-11/2) - 12*q^(-13/2))*x1^(-5/2)*x2^(-19/2) + (2*q^(41/2) + 2*q^(39/2) + 4*q^(37/2) + 12*q^(35/2) + 20*q^(33/2) + 32*q^(31/2) + 74*q^(29/2) + 120*q^(27/2) + 220*q^(25/2) + 384*q^(23/2) + 633*q^(21/2) + 920*q^(19/2) + 1342*q^(17/2) + 1633*q^(15/2) + 1854*q^(13/2) + 1836*q^(11/2) + 1654*q^(9/2) + 1306*q^(7/2) + 954*q^(5/2) + 600*q^(3/2) + 356*q^(1/2) + 178*q^(-1/2) + 80*q^(-3/2) + 26*q^(-5/2) + 10*q^(-7/2))*x1^(-7/2)*x2^(-19/2) + (-2*q^(49/2) - 2*q^(47/2) - 4*q^(45/2) - 8*q^(43/2) - 18*q^(41/2) - 28*q^(39/2) - 58*q^(37/2) - 88*q^(35/2) - 170*q^(33/2) - 276*q^(31/2) - 436*q^(29/2) - 598*q^(27/2) - 856*q^(25/2) - 1004*q^(23/2) - 1128*q^(21/2) - 1118*q^(19/2) - 1032*q^(17/2) - 830*q^(15/2) - 626*q^(13/2) - 404*q^(11/2) - 250*q^(9/2) - 128*q^(7/2) - 60*q^(5/2) - 20*q^(3/2) - 8*q^(1/2))*x1^(-9/2)*x2^(-19/2) + (2*q^(55/2) + 2*q^(53/2) + 6*q^(51/2) + 8*q^(49/2) + 16*q^(47/2) + 32*q^(45/2) + 62*q^(43/2) + 98*q^(41/2) + 158*q^(39/2) + 220*q^(37/2) + 334*q^(35/2) + 392*q^(33/2) + 452*q^(31/2) + 466*q^(29/2) + 460*q^(27/2) + 388*q^(25/2) + 312*q^(23/2) + 214*q^(21/2) + 144*q^(19/2) + 78*q^(17/2) + 40*q^(15/2) + 14*q^(13/2) + 6*q^(11/2))*x1^(-11/2)*x2^(-19/2) + (-2*q^(59/2) - 4*q^(57/2) - 8*q^(55/2) - 14*q^(53/2) - 24*q^(51/2) - 38*q^(49/2) - 74*q^(47/2) - 84*q^(45/2) - 106*q^(43/2) - 118*q^(41/2) - 128*q^(39/2) - 118*q^(37/2) - 104*q^(35/2) - 76*q^(33/2) - 58*q^(31/2) - 36*q^(29/2) - 20*q^(27/2) - 8*q^(25/2) - 4*q^(23/2))*x1^(-13/2)*x2^(-19/2) + (8*q^(61/2) + 6*q^(59/2) + 10*q^(57/2) + 12*q^(55/2) + 16*q^(53/2) + 16*q^(51/2) + 18*q^(49/2) + 12*q^(47/2) + 12*q^(45/2) + 8*q^(43/2) + 6*q^(41/2) + 2*q^(39/2) + 2*q^(37/2))*x1^(-15/2)*x2^(-19/2)
|
Braid
| Braid word |
Components |
Crossings |
Strands |
[-1, 2, 2, 2, 3, 2, 2, -1, 2, 2, -3, 2] |
2 |
12 |
4 |
Multivariable Alexander polynomial
| ΔL |
-A1^(1/2)*A2^(5/2) + 4*A1^(1/2)*A2^(3/2) - 4*A1^(1/2)*A2^(1/2) + 4*A1^(1/2)*A2^(-1/2) - 2*A1^(1/2)*A2^(-3/2) - 2*A1^(-1/2)*A2^(3/2) + 4*A1^(-1/2)*A2^(1/2) - 4*A1^(-1/2)*A2^(-1/2) + 4*A1^(-1/2)*A2^(-3/2) - A1^(-1/2)*A2^(-5/2) |
Warning: the A1, A2, … basis used for the HFL and Alexander data might not match the x1, x2, … basis used for FL.
Dual Thurston polytope
| Vertex | Dual to fibered face |
(-1, -5) |
yes |
(1, -3) |
no |
(1, 5) |
yes |
(-1, 3) |
no |
HFL polytope
| Poincaré polynomial |
m^(-7)*A1^(-1)*A2^(-3) + 5*m^(-6)*A1^(-1)*A2^(-2) + m^(-6)*A2^(-3) + 8*m^(-5)*A1^(-1)*A2^(-1) + 7*m^(-5)*A2^(-2) + 8*m^(-4)*A1^(-1) + 14*m^(-4)*A2^(-1) + 2*m^(-4)*A1*A2^(-2) + 6*m^(-3)*A1^(-1)*A2 + 16*m^(-3) + 6*m^(-3)*A1*A2^(-1) + 2*m^(-2)*A1^(-1)*A2^2 + 14*m^(-2)*A2 + 8*m^(-2)*A1 + 7*m^(-1)*A2^2 + 8*m^(-1)*A1*A2 + A2^3 + 5*A1*A2^2 + m*A1*A2^3 |
| Vertex | Maslov | Rank |
(-1, -3) | -7 | 1 |
(0, -3) | -6 | 1 |
(1, -2) | -4 | 2 |
(1, 3) | 1 | 1 |
(0, 3) | 0 | 1 |
(-1, 2) | -2 | 2 |
Record
FL/HFL Links
orderOption(int) |
334 |
namestring |
L10a33{1} |
statusstring |
success |
slugstring |
L10a33_1_2c75cf0d |
result_filestring |
details/L10a33_1_2c75cf0d.json |
complexity_scoreOption(int) |
200 |
strandsOption(int) |
null |
crossingsOption(int) |
10 |
component_countOption(int) |
2 |
girthOption(int) |
6 |
total_rankOption(int) |
120 |
wall_secondsOption(float) |
0.003383 |
backend_secondsOption(float) |
0.0 |
errorstring |
|
dimensionOption(int) |
2 |
support_sizeOption(int) |
19 |
vertex_countOption(int) |
6 |
fibered_vertex_countOption(int) |
2 |
polytope_statusstring |
computed |
alexander_support_sizeOption(int) |
10 |
alexander_vertex_countOption(int) |
4 |
alexander_relationstring |
not_computed |
fk_countint |
2 |
detailsRowRef(FLHFLLinks) |
{
"dataset": "FLHFLLinks",
"key": "L10a33_1_2c75cf0d"
} |
detail_assetstring |
/api/v1/datasets/FLHFLLinks/assets/L10a33_1_2c75cf0d |