details/L10n47_0_afccb2ae.json
FL expansions
| Newt(ΔL) vertex |
Exposing functional |
Leading x-power |
Leading q-power |
Inversion datum |
Inversion cycle |
FL |
(0, -2) |
(1, 1) |
x1^(0)x2^(2) |
q^(-1/2) |
{"0": [-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^(-1/2))*x2^(2) + (-2*q^(-1/2))*x2^(3) + (2*q^(-3/2))*x1*x2^(3) + (-q^(3/2))*x1^(-1)*x2^(4) + (2*q^(1/2) - 3*q^(-1/2))*x2^(4) + (4*q^(-3/2) + 3*q^(-5/2))*x1*x2^(4) + (-q^(-5/2) - 3*q^(-7/2))*x1^(2)*x2^(4) + (-2*q^(3/2))*x1^(-1)*x2^(5) + (2*q^(3/2) + 6*q^(1/2) - 2*q^(-1/2))*x2^(5) + (-q^(1/2) - 4*q^(-1/2) + 3*q^(-3/2) + 6*q^(-5/2) + 4*q^(-7/2))*x1*x2^(5) + (-2*q^(-5/2) - 8*q^(-7/2) - 6*q^(-9/2) - 4*q^(-11/2))*x1^(2)*x2^(5) + (2*q^(-9/2) + 2*q^(-11/2) + 4*q^(-13/2))*x1^(3)*x2^(5) + (-q^(11/2))*x1^(-2)*x2^(6) + (2*q^(9/2) + 3*q^(7/2) - 3*q^(3/2))*x1^(-1)*x2^(6) + (-q^(7/2) - 2*q^(5/2) + 4*q^(3/2) + 13*q^(1/2) + 2*q^(-1/2) + 2*q^(-3/2))*x2^(6) + (-q^(3/2) - 6*q^(1/2) - 14*q^(-1/2) - 9*q^(-3/2) + q^(-5/2) + 6*q^(-7/2) + 5*q^(-9/2))*x1*x2^(6) + (2*q^(-1/2) + 4*q^(-3/2) + 5*q^(-5/2) - 7*q^(-7/2) - 11*q^(-9/2) - 17*q^(-11/2) - 8*q^(-13/2) - 5*q^(-15/2))*x1^(2)*x2^(6) + (4*q^(-9/2) + 8*q^(-11/2) + 15*q^(-13/2) + 12*q^(-15/2) + 8*q^(-17/2) + 5*q^(-19/2))*x1^(3)*x2^(6) + (-q^(-13/2) - 3*q^(-15/2) - 4*q^(-17/2) - 3*q^(-19/2) - 5*q^(-21/2))*x1^(4)*x2^(6) + (-2*q^(11/2))*x1^(-2)*x2^(7) + (q^(13/2) + 2*q^(11/2) + 9*q^(9/2) + 8*q^(7/2) + 2*q^(5/2) - 4*q^(3/2))*x1^(-1)*x2^(7) + (-q^(11/2) - 5*q^(9/2) - 10*q^(7/2) - 15*q^(5/2) - q^(3/2) + 18*q^(1/2) + 10*q^(-1/2) + 8*q^(-3/2) + 2*q^(-5/2))*x2^(7) + (2*q^(7/2) + 3*q^(5/2) + 4*q^(3/2) - 8*q^(1/2) - 28*q^(-1/2) - 36*q^(-3/2) - 26*q^(-5/2) - 9*q^(-7/2) + 4*q^(-9/2) + 4*q^(-11/2))*x1*x2^(7) + (2*q^(1/2) + 8*q^(-1/2) + 20*q^(-3/2) + 31*q^(-5/2) + 23*q^(-7/2) + 14*q^(-9/2) - 13*q^(-11/2) - 19*q^(-13/2) - 20*q^(-15/2) - 10*q^(-17/2) - 6*q^(-19/2))*x1^(2)*x2^(7) + (-q^(-3/2) - 4*q^(-5/2) - 8*q^(-7/2) - 5*q^(-9/2) - q^(-11/2) + 20*q^(-13/2) + 28*q^(-15/2) + 35*q^(-17/2) + 32*q^(-19/2) + 22*q^(-21/2) + 10*q^(-23/2) + 6*q^(-25/2))*x1^(3)*x2^(7) + (-2*q^(-13/2) - 8*q^(-15/2) - 16*q^(-17/2) - 20*q^(-19/2) - 28*q^(-21/2) - 22*q^(-23/2) - 16*q^(-25/2) - 10*q^(-27/2) - 6*q^(-29/2))*x1^(4)*x2^(7) + (2*q^(-19/2) + 2*q^(-21/2) + 6*q^(-23/2) + 6*q^(-25/2) + 6*q^(-27/2) + 4*q^(-29/2) + 6*q^(-31/2))*x1^(5)*x2^(7) + (-q^(23/2))*x1^(-3)*x2^(8) + (2*q^(21/2) + 2*q^(19/2) + 3*q^(17/2) + q^(15/2) - 3*q^(11/2))*x1^(-2)*x2^(8) + (-q^(19/2) - 3*q^(17/2) - 5*q^(15/2) - 3*q^(13/2) + 8*q^(11/2) + 19*q^(9/2) + 18*q^(7/2) + 6*q^(5/2) - 3*q^(3/2))*x1^(-1)*x2^(8) + (q^(15/2) - q^(13/2) - 3*q^(11/2) - 21*q^(9/2) - 39*q^(7/2) - 54*q^(5/2) - 30*q^(3/2) + 8*q^(1/2) + 14*q^(-1/2) + 17*q^(-3/2) + 9*q^(-5/2) + 2*q^(-7/2))*x2^(8) + (2*q^(11/2) + 6*q^(9/2) + 17*q^(7/2) + 30*q^(5/2) + 42*q^(3/2) + 30*q^(1/2) - 14*q^(-1/2) - 54*q^(-3/2) - 71*q^(-5/2) - 60*q^(-7/2) - 28*q^(-9/2) - 7*q^(-11/2) + q^(-13/2) - 2*q^(-15/2))*x1*x2^(8) + (-q^(7/2) - 4*q^(5/2) - 7*q^(3/2) - 7*q^(1/2) + 2*q^(-1/2) + 31*q^(-3/2) + 70*q^(-5/2) + 94*q^(-7/2) + 108*q^(-9/2) + 72*q^(-11/2) + 36*q^(-13/2) - 7*q^(-15/2) - 16*q^(-17/2) - 21*q^(-19/2) - 10*q^(-21/2) - 7*q^(-23/2))*x1^(2)*x2^(8) + (-q^(-1/2) - 6*q^(-3/2) - 18*q^(-5/2) - 37*q^(-7/2) - 54*q^(-9/2) - 67*q^(-11/2) - 49*q^(-13/2) - 24*q^(-15/2) + 12*q^(-17/2) + 49*q^(-19/2) + 61*q^(-21/2) + 57*q^(-23/2) + 46*q^(-25/2) + 27*q^(-27/2) + 12*q^(-29/2) + 7*q^(-31/2))*x1^(3)*x2^(8) + (2*q^(-7/2) + 4*q^(-9/2) + 10*q^(-11/2) + 13*q^(-13/2) + 9*q^(-15/2) - 7*q^(-17/2) - 22*q^(-19/2) - 56*q^(-21/2) - 70*q^(-23/2) - 81*q^(-25/2) - 72*q^(-27/2) - 67*q^(-29/2) - 41*q^(-31/2) - 27*q^(-33/2) - 12*q^(-35/2) - 7*q^(-37/2))*x1^(4)*x2^(8) + (4*q^(-19/2) + 8*q^(-21/2) + 20*q^(-23/2) + 31*q^(-25/2) + 40*q^(-27/2) + 44*q^(-29/2) + 49*q^(-31/2) + 40*q^(-33/2) + 29*q^(-35/2) + 20*q^(-37/2) + 12*q^(-39/2) + 7*q^(-41/2))*x1^(5)*x2^(8) + (-q^(-25/2) - 3*q^(-27/2) - 4*q^(-29/2) - 7*q^(-31/2) - 9*q^(-33/2) - 11*q^(-35/2) - 9*q^(-37/2) - 8*q^(-39/2) - 5*q^(-41/2) - 7*q^(-43/2))*x1^(6)*x2^(8) + (-2*q^(23/2))*x1^(-3)*x2^(9) + (q^(27/2) + q^(25/2) + 2*q^(23/2) + 7*q^(21/2) + 9*q^(19/2) + 10*q^(17/2) + 4*q^(15/2) - 4*q^(11/2))*x1^(-2)*x2^(9) + (-q^(25/2) - 3*q^(23/2) - 6*q^(21/2) - 14*q^(19/2) - 27*q^(17/2) - 33*q^(15/2) - 21*q^(13/2) + 6*q^(11/2) + 31*q^(9/2) + 32*q^(7/2) + 16*q^(5/2) + 2*q^(1/2))*x1^(-1)*x2^(9) + (2*q^(21/2) + 5*q^(19/2) + 11*q^(17/2) + 21*q^(15/2) + 24*q^(13/2) + 17*q^(11/2) - 31*q^(9/2) - 86*q^(7/2) - 133*q^(5/2) - 108*q^(3/2) - 47*q^(1/2) - 9*q^(-1/2) + 16*q^(-3/2) + 18*q^(-5/2) + 8*q^(-7/2) + 2*q^(-9/2))*x2^(9) + (-q^(17/2) - 2*q^(15/2) - 3*q^(13/2) + 4*q^(11/2) + 15*q^(9/2) + 56*q^(7/2) + 108*q^(5/2) + 170*q^(3/2) + 184*q^(1/2) + 132*q^(-1/2) + 31*q^(-3/2) - 58*q^(-5/2) - 111*q^(-7/2) - 100*q^(-9/2) - 65*q^(-11/2) - 26*q^(-13/2) - 12*q^(-15/2) - 6*q^(-17/2) - 2*q^(-19/2))*x1*x2^(9) + (-q^(11/2) - 5*q^(9/2) - 15*q^(7/2) - 32*q^(5/2) - 61*q^(3/2) - 88*q^(1/2) - 103*q^(-1/2) - 72*q^(-3/2) + q^(-5/2) + 105*q^(-7/2) + 211*q^(-9/2) + 251*q^(-11/2) + 240*q^(-13/2) + 162*q^(-15/2) + 89*q^(-17/2) + 25*q^(-19/2) + q^(-21/2) - 16*q^(-23/2) - 8*q^(-25/2) - 6*q^(-27/2))*x1^(2)*x2^(9) + (2*q^(5/2) + 4*q^(3/2) + 11*q^(1/2) + 14*q^(-1/2) + 13*q^(-3/2) - 9*q^(-5/2) - 50*q^(-7/2) - 119*q^(-9/2) - 198*q^(-11/2) - 250*q^(-13/2) - 275*q^(-15/2) - 245*q^(-17/2) - 162*q^(-19/2) - 70*q^(-21/2) + 6*q^(-23/2) + 66*q^(-25/2) + 79*q^(-27/2) + 71*q^(-29/2) + 52*q^(-31/2) + 30*q^(-33/2) + 14*q^(-35/2) + 8*q^(-37/2))*x1^(3)*x2^(9) + (2*q^(-5/2) + 8*q^(-7/2) + 22*q^(-9/2) + 48*q^(-11/2) + 81*q^(-13/2) + 111*q^(-15/2) + 127*q^(-17/2) + 128*q^(-19/2) + 79*q^(-21/2) + 24*q^(-23/2) - 52*q^(-25/2) - 109*q^(-27/2) - 164*q^(-29/2) - 169*q^(-31/2) - 163*q^(-33/2) - 125*q^(-35/2) - 96*q^(-37/2) - 58*q^(-39/2) - 32*q^(-41/2) - 14*q^(-43/2) - 8*q^(-45/2))*x1^(4)*x2^(9) + (-q^(-11/2) - 4*q^(-13/2) - 8*q^(-15/2) - 15*q^(-17/2) - 18*q^(-19/2) - 21*q^(-21/2) - 3*q^(-23/2) + 22*q^(-25/2) + 63*q^(-27/2) + 97*q^(-29/2) + 148*q^(-31/2) + 169*q^(-33/2) + 182*q^(-35/2) + 166*q^(-37/2) + 149*q^(-39/2) + 118*q^(-41/2) + 84*q^(-43/2) + 50*q^(-45/2) + 32*q^(-47/2) + 14*q^(-49/2) + 8*q^(-51/2))*x1^(5)*x2^(9) + (-2*q^(-25/2) - 8*q^(-27/2) - 16*q^(-29/2) - 30*q^(-31/2) - 46*q^(-33/2) - 66*q^(-35/2) - 78*q^(-37/2) - 86*q^(-39/2) - 84*q^(-41/2) - 86*q^(-43/2) - 68*q^(-45/2) - 52*q^(-47/2) - 36*q^(-49/2) - 24*q^(-51/2) - 14*q^(-53/2) - 8*q^(-55/2))*x1^(6)*x2^(9) + (2*q^(-33/2) + 2*q^(-35/2) + 6*q^(-37/2) + 8*q^(-39/2) + 12*q^(-41/2) + 12*q^(-43/2) + 18*q^(-45/2) + 16*q^(-47/2) + 16*q^(-49/2) + 12*q^(-51/2) + 10*q^(-53/2) + 6*q^(-55/2) + 8*q^(-57/2))*x1^(7)*x2^(9)
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(0, -2) |
(1, 1) |
x1^(0)x2^(2) |
q^(-1/2) |
{"0": [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^(-1/2))*x2^(2) + (-2*q^(-1/2))*x2^(3) + (2*q^(-3/2))*x1*x2^(3) + (-q^(3/2))*x1^(-1)*x2^(4) + (2*q^(1/2) - 3*q^(-1/2))*x2^(4) + (4*q^(-3/2) + 3*q^(-5/2))*x1*x2^(4) + (-q^(-5/2) - 3*q^(-7/2))*x1^(2)*x2^(4) + (-2*q^(3/2))*x1^(-1)*x2^(5) + (2*q^(3/2) + 6*q^(1/2) - 2*q^(-1/2))*x2^(5) + (-q^(1/2) - 4*q^(-1/2) + 3*q^(-3/2) + 6*q^(-5/2) + 4*q^(-7/2))*x1*x2^(5) + (-2*q^(-5/2) - 8*q^(-7/2) - 6*q^(-9/2) - 4*q^(-11/2))*x1^(2)*x2^(5) + (2*q^(-9/2) + 2*q^(-11/2) + 4*q^(-13/2))*x1^(3)*x2^(5) + (-q^(11/2))*x1^(-2)*x2^(6) + (2*q^(9/2) + 3*q^(7/2) - 3*q^(3/2))*x1^(-1)*x2^(6) + (-q^(7/2) - 2*q^(5/2) + 4*q^(3/2) + 13*q^(1/2) + 2*q^(-1/2) + 2*q^(-3/2))*x2^(6) + (-q^(3/2) - 6*q^(1/2) - 14*q^(-1/2) - 9*q^(-3/2) + q^(-5/2) + 6*q^(-7/2) + 5*q^(-9/2))*x1*x2^(6) + (2*q^(-1/2) + 4*q^(-3/2) + 5*q^(-5/2) - 7*q^(-7/2) - 11*q^(-9/2) - 17*q^(-11/2) - 8*q^(-13/2) - 5*q^(-15/2))*x1^(2)*x2^(6) + (4*q^(-9/2) + 8*q^(-11/2) + 15*q^(-13/2) + 12*q^(-15/2) + 8*q^(-17/2) + 5*q^(-19/2))*x1^(3)*x2^(6) + (-q^(-13/2) - 3*q^(-15/2) - 4*q^(-17/2) - 3*q^(-19/2) - 5*q^(-21/2))*x1^(4)*x2^(6) + (-2*q^(11/2))*x1^(-2)*x2^(7) + (q^(13/2) + 2*q^(11/2) + 9*q^(9/2) + 8*q^(7/2) + 2*q^(5/2) - 4*q^(3/2))*x1^(-1)*x2^(7) + (-q^(11/2) - 5*q^(9/2) - 10*q^(7/2) - 15*q^(5/2) - q^(3/2) + 18*q^(1/2) + 10*q^(-1/2) + 8*q^(-3/2) + 2*q^(-5/2))*x2^(7) + (2*q^(7/2) + 3*q^(5/2) + 4*q^(3/2) - 8*q^(1/2) - 28*q^(-1/2) - 36*q^(-3/2) - 26*q^(-5/2) - 9*q^(-7/2) + 4*q^(-9/2) + 4*q^(-11/2))*x1*x2^(7) + (2*q^(1/2) + 8*q^(-1/2) + 20*q^(-3/2) + 31*q^(-5/2) + 23*q^(-7/2) + 14*q^(-9/2) - 13*q^(-11/2) - 19*q^(-13/2) - 20*q^(-15/2) - 10*q^(-17/2) - 6*q^(-19/2))*x1^(2)*x2^(7) + (-q^(-3/2) - 4*q^(-5/2) - 8*q^(-7/2) - 5*q^(-9/2) - q^(-11/2) + 20*q^(-13/2) + 28*q^(-15/2) + 35*q^(-17/2) + 32*q^(-19/2) + 22*q^(-21/2) + 10*q^(-23/2) + 6*q^(-25/2))*x1^(3)*x2^(7) + (-2*q^(-13/2) - 8*q^(-15/2) - 16*q^(-17/2) - 20*q^(-19/2) - 28*q^(-21/2) - 22*q^(-23/2) - 16*q^(-25/2) - 10*q^(-27/2) - 6*q^(-29/2))*x1^(4)*x2^(7) + (2*q^(-19/2) + 2*q^(-21/2) + 6*q^(-23/2) + 6*q^(-25/2) + 6*q^(-27/2) + 4*q^(-29/2) + 6*q^(-31/2))*x1^(5)*x2^(7) + (-q^(23/2))*x1^(-3)*x2^(8) + (2*q^(21/2) + 2*q^(19/2) + 3*q^(17/2) + q^(15/2) - 3*q^(11/2))*x1^(-2)*x2^(8) + (-q^(19/2) - 3*q^(17/2) - 5*q^(15/2) - 3*q^(13/2) + 8*q^(11/2) + 19*q^(9/2) + 18*q^(7/2) + 6*q^(5/2) - 3*q^(3/2))*x1^(-1)*x2^(8) + (q^(15/2) - q^(13/2) - 3*q^(11/2) - 21*q^(9/2) - 39*q^(7/2) - 54*q^(5/2) - 30*q^(3/2) + 8*q^(1/2) + 14*q^(-1/2) + 17*q^(-3/2) + 9*q^(-5/2) + 2*q^(-7/2))*x2^(8) + (2*q^(11/2) + 6*q^(9/2) + 17*q^(7/2) + 30*q^(5/2) + 42*q^(3/2) + 30*q^(1/2) - 14*q^(-1/2) - 54*q^(-3/2) - 71*q^(-5/2) - 60*q^(-7/2) - 28*q^(-9/2) - 7*q^(-11/2) + q^(-13/2) - 2*q^(-15/2))*x1*x2^(8) + (-q^(7/2) - 4*q^(5/2) - 7*q^(3/2) - 7*q^(1/2) + 2*q^(-1/2) + 31*q^(-3/2) + 70*q^(-5/2) + 94*q^(-7/2) + 108*q^(-9/2) + 72*q^(-11/2) + 36*q^(-13/2) - 7*q^(-15/2) - 16*q^(-17/2) - 21*q^(-19/2) - 10*q^(-21/2) - 7*q^(-23/2))*x1^(2)*x2^(8) + (-q^(-1/2) - 6*q^(-3/2) - 18*q^(-5/2) - 37*q^(-7/2) - 54*q^(-9/2) - 67*q^(-11/2) - 49*q^(-13/2) - 24*q^(-15/2) + 12*q^(-17/2) + 49*q^(-19/2) + 61*q^(-21/2) + 57*q^(-23/2) + 46*q^(-25/2) + 27*q^(-27/2) + 12*q^(-29/2) + 7*q^(-31/2))*x1^(3)*x2^(8) + (2*q^(-7/2) + 4*q^(-9/2) + 10*q^(-11/2) + 13*q^(-13/2) + 9*q^(-15/2) - 7*q^(-17/2) - 22*q^(-19/2) - 56*q^(-21/2) - 70*q^(-23/2) - 81*q^(-25/2) - 72*q^(-27/2) - 67*q^(-29/2) - 41*q^(-31/2) - 27*q^(-33/2) - 12*q^(-35/2) - 7*q^(-37/2))*x1^(4)*x2^(8) + (4*q^(-19/2) + 8*q^(-21/2) + 20*q^(-23/2) + 31*q^(-25/2) + 40*q^(-27/2) + 44*q^(-29/2) + 49*q^(-31/2) + 40*q^(-33/2) + 29*q^(-35/2) + 20*q^(-37/2) + 12*q^(-39/2) + 7*q^(-41/2))*x1^(5)*x2^(8) + (-q^(-25/2) - 3*q^(-27/2) - 4*q^(-29/2) - 7*q^(-31/2) - 9*q^(-33/2) - 11*q^(-35/2) - 9*q^(-37/2) - 8*q^(-39/2) - 5*q^(-41/2) - 7*q^(-43/2))*x1^(6)*x2^(8) + (-2*q^(23/2))*x1^(-3)*x2^(9) + (q^(27/2) + q^(25/2) + 2*q^(23/2) + 7*q^(21/2) + 9*q^(19/2) + 10*q^(17/2) + 4*q^(15/2) - 4*q^(11/2))*x1^(-2)*x2^(9) + (-q^(25/2) - 3*q^(23/2) - 6*q^(21/2) - 14*q^(19/2) - 27*q^(17/2) - 33*q^(15/2) - 21*q^(13/2) + 6*q^(11/2) + 31*q^(9/2) + 32*q^(7/2) + 16*q^(5/2) + 2*q^(1/2))*x1^(-1)*x2^(9) + (2*q^(21/2) + 5*q^(19/2) + 11*q^(17/2) + 21*q^(15/2) + 24*q^(13/2) + 17*q^(11/2) - 31*q^(9/2) - 86*q^(7/2) - 133*q^(5/2) - 108*q^(3/2) - 47*q^(1/2) - 9*q^(-1/2) + 16*q^(-3/2) + 18*q^(-5/2) + 8*q^(-7/2) + 2*q^(-9/2))*x2^(9) + (-q^(17/2) - 2*q^(15/2) - 3*q^(13/2) + 4*q^(11/2) + 15*q^(9/2) + 56*q^(7/2) + 108*q^(5/2) + 170*q^(3/2) + 184*q^(1/2) + 132*q^(-1/2) + 31*q^(-3/2) - 58*q^(-5/2) - 111*q^(-7/2) - 100*q^(-9/2) - 65*q^(-11/2) - 26*q^(-13/2) - 12*q^(-15/2) - 6*q^(-17/2) - 2*q^(-19/2))*x1*x2^(9) + (-q^(11/2) - 5*q^(9/2) - 15*q^(7/2) - 32*q^(5/2) - 61*q^(3/2) - 88*q^(1/2) - 103*q^(-1/2) - 72*q^(-3/2) + q^(-5/2) + 105*q^(-7/2) + 211*q^(-9/2) + 251*q^(-11/2) + 240*q^(-13/2) + 162*q^(-15/2) + 89*q^(-17/2) + 25*q^(-19/2) + q^(-21/2) - 16*q^(-23/2) - 8*q^(-25/2) - 6*q^(-27/2))*x1^(2)*x2^(9) + (2*q^(5/2) + 4*q^(3/2) + 11*q^(1/2) + 14*q^(-1/2) + 13*q^(-3/2) - 9*q^(-5/2) - 50*q^(-7/2) - 119*q^(-9/2) - 198*q^(-11/2) - 250*q^(-13/2) - 275*q^(-15/2) - 245*q^(-17/2) - 162*q^(-19/2) - 70*q^(-21/2) + 6*q^(-23/2) + 66*q^(-25/2) + 79*q^(-27/2) + 71*q^(-29/2) + 52*q^(-31/2) + 30*q^(-33/2) + 14*q^(-35/2) + 8*q^(-37/2))*x1^(3)*x2^(9) + (2*q^(-5/2) + 8*q^(-7/2) + 22*q^(-9/2) + 48*q^(-11/2) + 81*q^(-13/2) + 111*q^(-15/2) + 127*q^(-17/2) + 128*q^(-19/2) + 79*q^(-21/2) + 24*q^(-23/2) - 52*q^(-25/2) - 109*q^(-27/2) - 164*q^(-29/2) - 169*q^(-31/2) - 163*q^(-33/2) - 125*q^(-35/2) - 96*q^(-37/2) - 58*q^(-39/2) - 32*q^(-41/2) - 14*q^(-43/2) - 8*q^(-45/2))*x1^(4)*x2^(9) + (-q^(-11/2) - 4*q^(-13/2) - 8*q^(-15/2) - 15*q^(-17/2) - 18*q^(-19/2) - 21*q^(-21/2) - 3*q^(-23/2) + 22*q^(-25/2) + 63*q^(-27/2) + 97*q^(-29/2) + 148*q^(-31/2) + 169*q^(-33/2) + 182*q^(-35/2) + 166*q^(-37/2) + 149*q^(-39/2) + 118*q^(-41/2) + 84*q^(-43/2) + 50*q^(-45/2) + 32*q^(-47/2) + 14*q^(-49/2) + 8*q^(-51/2))*x1^(5)*x2^(9) + (-2*q^(-25/2) - 8*q^(-27/2) - 16*q^(-29/2) - 30*q^(-31/2) - 46*q^(-33/2) - 66*q^(-35/2) - 78*q^(-37/2) - 86*q^(-39/2) - 84*q^(-41/2) - 86*q^(-43/2) - 68*q^(-45/2) - 52*q^(-47/2) - 36*q^(-49/2) - 24*q^(-51/2) - 14*q^(-53/2) - 8*q^(-55/2))*x1^(6)*x2^(9) + (2*q^(-33/2) + 2*q^(-35/2) + 6*q^(-37/2) + 8*q^(-39/2) + 12*q^(-41/2) + 12*q^(-43/2) + 18*q^(-45/2) + 16*q^(-47/2) + 16*q^(-49/2) + 12*q^(-51/2) + 10*q^(-53/2) + 6*q^(-55/2) + 8*q^(-57/2))*x1^(7)*x2^(9)
|
(0, 2) |
|
x1^(0)x2^(-2) |
q^(-1/2) |
|
|
(-q^(-1/2))*x2^(-2) + (-2*q^(-1/2))*x2^(-3) + (2*q^(-3/2))*x1^(-1)*x2^(-3) + (-q^(3/2))*x1*x2^(-4) + (2*q^(1/2) - 3*q^(-1/2))*x2^(-4) + (4*q^(-3/2) + 3*q^(-5/2))*x1^(-1)*x2^(-4) + (-q^(-5/2) - 3*q^(-7/2))*x1^(-2)*x2^(-4) + (-2*q^(3/2))*x1*x2^(-5) + (2*q^(3/2) + 6*q^(1/2) - 2*q^(-1/2))*x2^(-5) + (-q^(1/2) - 4*q^(-1/2) + 3*q^(-3/2) + 6*q^(-5/2) + 4*q^(-7/2))*x1^(-1)*x2^(-5) + (-2*q^(-5/2) - 8*q^(-7/2) - 6*q^(-9/2) - 4*q^(-11/2))*x1^(-2)*x2^(-5) + (2*q^(-9/2) + 2*q^(-11/2) + 4*q^(-13/2))*x1^(-3)*x2^(-5) + (-q^(11/2))*x1^(2)*x2^(-6) + (2*q^(9/2) + 3*q^(7/2) - 3*q^(3/2))*x1*x2^(-6) + (-q^(7/2) - 2*q^(5/2) + 4*q^(3/2) + 13*q^(1/2) + 2*q^(-1/2) + 2*q^(-3/2))*x2^(-6) + (-q^(3/2) - 6*q^(1/2) - 14*q^(-1/2) - 9*q^(-3/2) + q^(-5/2) + 6*q^(-7/2) + 5*q^(-9/2))*x1^(-1)*x2^(-6) + (2*q^(-1/2) + 4*q^(-3/2) + 5*q^(-5/2) - 7*q^(-7/2) - 11*q^(-9/2) - 17*q^(-11/2) - 8*q^(-13/2) - 5*q^(-15/2))*x1^(-2)*x2^(-6) + (4*q^(-9/2) + 8*q^(-11/2) + 15*q^(-13/2) + 12*q^(-15/2) + 8*q^(-17/2) + 5*q^(-19/2))*x1^(-3)*x2^(-6) + (-q^(-13/2) - 3*q^(-15/2) - 4*q^(-17/2) - 3*q^(-19/2) - 5*q^(-21/2))*x1^(-4)*x2^(-6) + (-2*q^(11/2))*x1^(2)*x2^(-7) + (q^(13/2) + 2*q^(11/2) + 9*q^(9/2) + 8*q^(7/2) + 2*q^(5/2) - 4*q^(3/2))*x1*x2^(-7) + (-q^(11/2) - 5*q^(9/2) - 10*q^(7/2) - 15*q^(5/2) - q^(3/2) + 18*q^(1/2) + 10*q^(-1/2) + 8*q^(-3/2) + 2*q^(-5/2))*x2^(-7) + (2*q^(7/2) + 3*q^(5/2) + 4*q^(3/2) - 8*q^(1/2) - 28*q^(-1/2) - 36*q^(-3/2) - 26*q^(-5/2) - 9*q^(-7/2) + 4*q^(-9/2) + 4*q^(-11/2))*x1^(-1)*x2^(-7) + (2*q^(1/2) + 8*q^(-1/2) + 20*q^(-3/2) + 31*q^(-5/2) + 23*q^(-7/2) + 14*q^(-9/2) - 13*q^(-11/2) - 19*q^(-13/2) - 20*q^(-15/2) - 10*q^(-17/2) - 6*q^(-19/2))*x1^(-2)*x2^(-7) + (-q^(-3/2) - 4*q^(-5/2) - 8*q^(-7/2) - 5*q^(-9/2) - q^(-11/2) + 20*q^(-13/2) + 28*q^(-15/2) + 35*q^(-17/2) + 32*q^(-19/2) + 22*q^(-21/2) + 10*q^(-23/2) + 6*q^(-25/2))*x1^(-3)*x2^(-7) + (-2*q^(-13/2) - 8*q^(-15/2) - 16*q^(-17/2) - 20*q^(-19/2) - 28*q^(-21/2) - 22*q^(-23/2) - 16*q^(-25/2) - 10*q^(-27/2) - 6*q^(-29/2))*x1^(-4)*x2^(-7) + (2*q^(-19/2) + 2*q^(-21/2) + 6*q^(-23/2) + 6*q^(-25/2) + 6*q^(-27/2) + 4*q^(-29/2) + 6*q^(-31/2))*x1^(-5)*x2^(-7) + (-q^(23/2))*x1^(3)*x2^(-8) + (2*q^(21/2) + 2*q^(19/2) + 3*q^(17/2) + q^(15/2) - 3*q^(11/2))*x1^(2)*x2^(-8) + (-q^(19/2) - 3*q^(17/2) - 5*q^(15/2) - 3*q^(13/2) + 8*q^(11/2) + 19*q^(9/2) + 18*q^(7/2) + 6*q^(5/2) - 3*q^(3/2))*x1*x2^(-8) + (q^(15/2) - q^(13/2) - 3*q^(11/2) - 21*q^(9/2) - 39*q^(7/2) - 54*q^(5/2) - 30*q^(3/2) + 8*q^(1/2) + 14*q^(-1/2) + 17*q^(-3/2) + 9*q^(-5/2) + 2*q^(-7/2))*x2^(-8) + (2*q^(11/2) + 6*q^(9/2) + 17*q^(7/2) + 30*q^(5/2) + 42*q^(3/2) + 30*q^(1/2) - 14*q^(-1/2) - 54*q^(-3/2) - 71*q^(-5/2) - 60*q^(-7/2) - 28*q^(-9/2) - 7*q^(-11/2) + q^(-13/2) - 2*q^(-15/2))*x1^(-1)*x2^(-8) + (-q^(7/2) - 4*q^(5/2) - 7*q^(3/2) - 7*q^(1/2) + 2*q^(-1/2) + 31*q^(-3/2) + 70*q^(-5/2) + 94*q^(-7/2) + 108*q^(-9/2) + 72*q^(-11/2) + 36*q^(-13/2) - 7*q^(-15/2) - 16*q^(-17/2) - 21*q^(-19/2) - 10*q^(-21/2) - 7*q^(-23/2))*x1^(-2)*x2^(-8) + (-q^(-1/2) - 6*q^(-3/2) - 18*q^(-5/2) - 37*q^(-7/2) - 54*q^(-9/2) - 67*q^(-11/2) - 49*q^(-13/2) - 24*q^(-15/2) + 12*q^(-17/2) + 49*q^(-19/2) + 61*q^(-21/2) + 57*q^(-23/2) + 46*q^(-25/2) + 27*q^(-27/2) + 12*q^(-29/2) + 7*q^(-31/2))*x1^(-3)*x2^(-8) + (2*q^(-7/2) + 4*q^(-9/2) + 10*q^(-11/2) + 13*q^(-13/2) + 9*q^(-15/2) - 7*q^(-17/2) - 22*q^(-19/2) - 56*q^(-21/2) - 70*q^(-23/2) - 81*q^(-25/2) - 72*q^(-27/2) - 67*q^(-29/2) - 41*q^(-31/2) - 27*q^(-33/2) - 12*q^(-35/2) - 7*q^(-37/2))*x1^(-4)*x2^(-8) + (4*q^(-19/2) + 8*q^(-21/2) + 20*q^(-23/2) + 31*q^(-25/2) + 40*q^(-27/2) + 44*q^(-29/2) + 49*q^(-31/2) + 40*q^(-33/2) + 29*q^(-35/2) + 20*q^(-37/2) + 12*q^(-39/2) + 7*q^(-41/2))*x1^(-5)*x2^(-8) + (-q^(-25/2) - 3*q^(-27/2) - 4*q^(-29/2) - 7*q^(-31/2) - 9*q^(-33/2) - 11*q^(-35/2) - 9*q^(-37/2) - 8*q^(-39/2) - 5*q^(-41/2) - 7*q^(-43/2))*x1^(-6)*x2^(-8) + (-2*q^(23/2))*x1^(3)*x2^(-9) + (q^(27/2) + q^(25/2) + 2*q^(23/2) + 7*q^(21/2) + 9*q^(19/2) + 10*q^(17/2) + 4*q^(15/2) - 4*q^(11/2))*x1^(2)*x2^(-9) + (-q^(25/2) - 3*q^(23/2) - 6*q^(21/2) - 14*q^(19/2) - 27*q^(17/2) - 33*q^(15/2) - 21*q^(13/2) + 6*q^(11/2) + 31*q^(9/2) + 32*q^(7/2) + 16*q^(5/2) + 2*q^(1/2))*x1*x2^(-9) + (2*q^(21/2) + 5*q^(19/2) + 11*q^(17/2) + 21*q^(15/2) + 24*q^(13/2) + 17*q^(11/2) - 31*q^(9/2) - 86*q^(7/2) - 133*q^(5/2) - 108*q^(3/2) - 47*q^(1/2) - 9*q^(-1/2) + 16*q^(-3/2) + 18*q^(-5/2) + 8*q^(-7/2) + 2*q^(-9/2))*x2^(-9) + (-q^(17/2) - 2*q^(15/2) - 3*q^(13/2) + 4*q^(11/2) + 15*q^(9/2) + 56*q^(7/2) + 108*q^(5/2) + 170*q^(3/2) + 184*q^(1/2) + 132*q^(-1/2) + 31*q^(-3/2) - 58*q^(-5/2) - 111*q^(-7/2) - 100*q^(-9/2) - 65*q^(-11/2) - 26*q^(-13/2) - 12*q^(-15/2) - 6*q^(-17/2) - 2*q^(-19/2))*x1^(-1)*x2^(-9) + (-q^(11/2) - 5*q^(9/2) - 15*q^(7/2) - 32*q^(5/2) - 61*q^(3/2) - 88*q^(1/2) - 103*q^(-1/2) - 72*q^(-3/2) + q^(-5/2) + 105*q^(-7/2) + 211*q^(-9/2) + 251*q^(-11/2) + 240*q^(-13/2) + 162*q^(-15/2) + 89*q^(-17/2) + 25*q^(-19/2) + q^(-21/2) - 16*q^(-23/2) - 8*q^(-25/2) - 6*q^(-27/2))*x1^(-2)*x2^(-9) + (2*q^(5/2) + 4*q^(3/2) + 11*q^(1/2) + 14*q^(-1/2) + 13*q^(-3/2) - 9*q^(-5/2) - 50*q^(-7/2) - 119*q^(-9/2) - 198*q^(-11/2) - 250*q^(-13/2) - 275*q^(-15/2) - 245*q^(-17/2) - 162*q^(-19/2) - 70*q^(-21/2) + 6*q^(-23/2) + 66*q^(-25/2) + 79*q^(-27/2) + 71*q^(-29/2) + 52*q^(-31/2) + 30*q^(-33/2) + 14*q^(-35/2) + 8*q^(-37/2))*x1^(-3)*x2^(-9) + (2*q^(-5/2) + 8*q^(-7/2) + 22*q^(-9/2) + 48*q^(-11/2) + 81*q^(-13/2) + 111*q^(-15/2) + 127*q^(-17/2) + 128*q^(-19/2) + 79*q^(-21/2) + 24*q^(-23/2) - 52*q^(-25/2) - 109*q^(-27/2) - 164*q^(-29/2) - 169*q^(-31/2) - 163*q^(-33/2) - 125*q^(-35/2) - 96*q^(-37/2) - 58*q^(-39/2) - 32*q^(-41/2) - 14*q^(-43/2) - 8*q^(-45/2))*x1^(-4)*x2^(-9) + (-q^(-11/2) - 4*q^(-13/2) - 8*q^(-15/2) - 15*q^(-17/2) - 18*q^(-19/2) - 21*q^(-21/2) - 3*q^(-23/2) + 22*q^(-25/2) + 63*q^(-27/2) + 97*q^(-29/2) + 148*q^(-31/2) + 169*q^(-33/2) + 182*q^(-35/2) + 166*q^(-37/2) + 149*q^(-39/2) + 118*q^(-41/2) + 84*q^(-43/2) + 50*q^(-45/2) + 32*q^(-47/2) + 14*q^(-49/2) + 8*q^(-51/2))*x1^(-5)*x2^(-9) + (-2*q^(-25/2) - 8*q^(-27/2) - 16*q^(-29/2) - 30*q^(-31/2) - 46*q^(-33/2) - 66*q^(-35/2) - 78*q^(-37/2) - 86*q^(-39/2) - 84*q^(-41/2) - 86*q^(-43/2) - 68*q^(-45/2) - 52*q^(-47/2) - 36*q^(-49/2) - 24*q^(-51/2) - 14*q^(-53/2) - 8*q^(-55/2))*x1^(-6)*x2^(-9) + (2*q^(-33/2) + 2*q^(-35/2) + 6*q^(-37/2) + 8*q^(-39/2) + 12*q^(-41/2) + 12*q^(-43/2) + 18*q^(-45/2) + 16*q^(-47/2) + 16*q^(-49/2) + 12*q^(-51/2) + 10*q^(-53/2) + 6*q^(-55/2) + 8*q^(-57/2))*x1^(-7)*x2^(-9)
|
Braid
| Braid word |
Components |
Crossings |
Strands |
[1, -2, 3, -2, 1, -2, -2, -3, 2, -3] |
2 |
10 |
4 |
Multivariable Alexander polynomial
| ΔL |
A1 - 2*A1*A2^(-1) - A2^(2) + 2*A2 - 3 + 2*A2^(-1) - A2^(-2) - 2*A1^(-1)*A2 + A1^(-1) |
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 |
(0, -4) |
yes |
(2, -2) |
no |
(2, 0) |
yes |
(0, 4) |
yes |
(-2, 2) |
no |
(-2, 0) |
yes |
HFL polytope
| Poincaré polynomial |
m^(-3)*A1^(-1/2)*A2^(-5/2) + m^(-2)*A1^(-3/2)*A2^(-1/2) + 3*m^(-2)*A1^(-1/2)*A2^(-3/2) + m^(-2)*A1^(1/2)*A2^(-5/2) + 3*m^(-1)*A1^(-3/2)*A2^(1/2) + 6*m^(-1)*A1^(-1/2)*A2^(-1/2) + 5*m^(-1)*A1^(1/2)*A2^(-3/2) + 2*A1^(-3/2)*A2^(3/2) + 8*A1^(-1/2)*A2^(1/2) + 8*A1^(1/2)*A2^(-1/2) + 2*A1^(3/2)*A2^(-3/2) + 5*m*A1^(-1/2)*A2^(3/2) + 6*m*A1^(1/2)*A2^(1/2) + 3*m*A1^(3/2)*A2^(-1/2) + m^2*A1^(-1/2)*A2^(5/2) + 3*m^2*A1^(1/2)*A2^(3/2) + m^2*A1^(3/2)*A2^(1/2) + m^3*A1^(1/2)*A2^(5/2) |
| Vertex | Maslov | Rank |
(-3/2, -1/2) | -2 | 1 |
(-1/2, -5/2) | -3 | 1 |
(1/2, -5/2) | -2 | 1 |
(3/2, -3/2) | 0 | 2 |
(3/2, 1/2) | 2 | 1 |
(1/2, 5/2) | 3 | 1 |
(-1/2, 5/2) | 2 | 1 |
(-3/2, 3/2) | 0 | 2 |
Record
FL/HFL Links
orderOption(int) |
561 |
namestring |
L10n47{0} |
statusstring |
success |
slugstring |
L10n47_0_afccb2ae |
result_filestring |
details/L10n47_0_afccb2ae.json |
complexity_scoreOption(int) |
200 |
strandsOption(int) |
null |
crossingsOption(int) |
10 |
component_countOption(int) |
2 |
girthOption(int) |
6 |
total_rankOption(int) |
60 |
wall_secondsOption(float) |
0.002231 |
backend_secondsOption(float) |
0.0 |
errorstring |
|
dimensionOption(int) |
2 |
support_sizeOption(int) |
18 |
vertex_countOption(int) |
8 |
fibered_vertex_countOption(int) |
4 |
polytope_statusstring |
computed |
alexander_support_sizeOption(int) |
9 |
alexander_vertex_countOption(int) |
6 |
alexander_relationstring |
not_computed |
fk_countint |
4 |
detailsRowRef(FLHFLLinks) |
{
"dataset": "FLHFLLinks",
"key": "L10n47_0_afccb2ae"
} |
detail_assetstring |
/api/v1/datasets/FLHFLLinks/assets/L10n47_0_afccb2ae |