details/L9a28_0_cdcdf8d7.json
FL expansions
| Newt(ΔL) vertex |
Exposing functional |
Leading x-power |
Leading q-power |
Inversion datum |
Inversion cycle |
FL |
(-1, -2) |
(1, 1) |
x1^(1)x2^(2) |
q^(-3/2) |
{"0": [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], "1": [-1, 1, -1, 1, -1, 1]}
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(-q^(-3/2))*x1*x2^(2) + (-2*q^(-3/2))*x1*x2^(3) + (2*q^(-5/2))*x1^(2)*x2^(3) + (q^(-1/2) - 3*q^(-3/2))*x1*x2^(4) + (4*q^(-5/2) + q^(-7/2))*x1^(2)*x2^(4) + (-q^(-7/2) - q^(-9/2))*x1^(3)*x2^(4) + (2*q^(1/2) + 2*q^(-1/2) - 4*q^(-3/2))*x1*x2^(5) + (-q^(-1/2) - 2*q^(-3/2) + 6*q^(-5/2) + 2*q^(-7/2) + q^(-9/2))*x1^(2)*x2^(5) + (-2*q^(-7/2) - 3*q^(-9/2) - q^(-13/2))*x1^(3)*x2^(5) + (q^(-11/2) - 2*q^(-13/2) + q^(-15/2))*x1^(4)*x2^(5) + (2*q^(3/2) + 4*q^(1/2) + 3*q^(-1/2) - 5*q^(-3/2))*x1*x2^(6) + (-2*q^(1/2) - 6*q^(-1/2) - 5*q^(-3/2) + 7*q^(-5/2) + 3*q^(-7/2) + 2*q^(-9/2) + q^(-11/2))*x1^(2)*x2^(6) + (2*q^(-3/2) + 2*q^(-5/2) - 2*q^(-7/2) - 5*q^(-9/2) - q^(-11/2) - 2*q^(-13/2) - q^(-15/2) - q^(-17/2))*x1^(3)*x2^(6) + (2*q^(-11/2) - 4*q^(-13/2) + q^(-19/2) + q^(-21/2))*x1^(4)*x2^(6) + (q^(-15/2) + q^(-17/2) + 3*q^(-19/2) - q^(-23/2))*x1^(5)*x2^(6) + (-2*q^(7/2) + 2*q^(5/2) + 4*q^(3/2) + 6*q^(1/2) + 4*q^(-1/2) - 6*q^(-3/2))*x1*x2^(7) + (q^(5/2) - 2*q^(3/2) - 8*q^(1/2) - 13*q^(-1/2) - 10*q^(-3/2) + 7*q^(-5/2) + 3*q^(-7/2) + 3*q^(-9/2) + 2*q^(-11/2) + q^(-13/2))*x1^(2)*x2^(7) + (4*q^(-1/2) + 8*q^(-3/2) + 8*q^(-5/2) - 6*q^(-9/2) - q^(-11/2) - 4*q^(-13/2) - 2*q^(-15/2) - 3*q^(-17/2) - q^(-19/2) - q^(-21/2))*x1^(3)*x2^(7) + (-q^(-5/2) - 2*q^(-7/2) - q^(-9/2) + 4*q^(-11/2) - 7*q^(-13/2) - 2*q^(-15/2) - 3*q^(-17/2) + 3*q^(-19/2) + 3*q^(-21/2) + 2*q^(-23/2) + q^(-25/2) + q^(-27/2))*x1^(4)*x2^(7) + (2*q^(-15/2) + 5*q^(-17/2) + 10*q^(-19/2) + 5*q^(-21/2) - 2*q^(-23/2) - q^(-25/2) - q^(-27/2) - q^(-29/2) - q^(-31/2))*x1^(5)*x2^(7) + (-q^(-19/2) - 2*q^(-21/2) - 4*q^(-23/2) - q^(-25/2) - q^(-27/2) + q^(-33/2))*x1^(6)*x2^(7) + (-3*q^(11/2) - 3*q^(9/2) - 2*q^(7/2) + 4*q^(5/2) + 6*q^(3/2) + 8*q^(1/2) + 5*q^(-1/2) - 7*q^(-3/2))*x1*x2^(8) + (2*q^(9/2) + 4*q^(7/2) + 4*q^(5/2) - 7*q^(3/2) - 16*q^(1/2) - 22*q^(-1/2) - 17*q^(-3/2) + 5*q^(-5/2) + 2*q^(-7/2) + 3*q^(-9/2) + 3*q^(-11/2) + 2*q^(-13/2) + q^(-15/2))*x1^(2)*x2^(8) + (-q^(5/2) - 2*q^(3/2) + 3*q^(1/2) + 12*q^(-1/2) + 20*q^(-3/2) + 18*q^(-5/2) + 6*q^(-7/2) - 3*q^(-9/2) + q^(-11/2) - 4*q^(-13/2) - 3*q^(-15/2) - 5*q^(-17/2) - 3*q^(-19/2) - 3*q^(-21/2) - q^(-23/2) - q^(-25/2))*x1^(3)*x2^(8) + (-2*q^(-3/2) - 6*q^(-5/2) - 7*q^(-7/2) - q^(-9/2) + 5*q^(-11/2) - 10*q^(-13/2) - 6*q^(-15/2) - 10*q^(-17/2) + 6*q^(-21/2) + 6*q^(-23/2) + 4*q^(-25/2) + 4*q^(-27/2) + 2*q^(-29/2) + q^(-31/2) + q^(-33/2))*x1^(4)*x2^(8) + (q^(-9/2) - q^(-11/2) - 2*q^(-13/2) + q^(-15/2) + 7*q^(-17/2) + 23*q^(-19/2) + 19*q^(-21/2) + 5*q^(-23/2) - q^(-25/2) - 3*q^(-27/2) - 5*q^(-29/2) - 4*q^(-31/2) - 2*q^(-33/2) - 2*q^(-35/2) - q^(-37/2) - q^(-39/2))*x1^(5)*x2^(8) + (-2*q^(-19/2) - 6*q^(-21/2) - 15*q^(-23/2) - 11*q^(-25/2) - 8*q^(-27/2) - 3*q^(-29/2) + q^(-31/2) + 3*q^(-33/2) + q^(-35/2) + q^(-37/2) + q^(-39/2) + q^(-41/2) + q^(-43/2))*x1^(6)*x2^(8) + (2*q^(-25/2) + 2*q^(-27/2) + 3*q^(-29/2) + 3*q^(-31/2) + q^(-33/2) - 3*q^(-35/2) + q^(-37/2) - q^(-45/2))*x1^(7)*x2^(8) + (-2*q^(15/2) - 4*q^(13/2) - 10*q^(11/2) - 4*q^(9/2) - 2*q^(7/2) + 6*q^(5/2) + 8*q^(3/2) + 10*q^(1/2) + 6*q^(-1/2) - 8*q^(-3/2))*x1*x2^(9) + (2*q^(13/2) + 6*q^(11/2) + 16*q^(9/2) + 14*q^(7/2) + 7*q^(5/2) - 12*q^(3/2) - 25*q^(1/2) - 33*q^(-1/2) - 26*q^(-3/2) + q^(-5/2) - q^(-7/2) + 2*q^(-9/2) + 3*q^(-11/2) + 3*q^(-13/2) + 2*q^(-15/2) + q^(-17/2))*x1^(2)*x2^(9) + (-2*q^(9/2) - 6*q^(7/2) - 12*q^(5/2) - 7*q^(3/2) + 5*q^(1/2) + 25*q^(-1/2) + 35*q^(-3/2) + 34*q^(-5/2) + 18*q^(-7/2) + 6*q^(-9/2) + 9*q^(-11/2) - q^(-15/2) - 6*q^(-17/2) - 4*q^(-19/2) - 6*q^(-21/2) - 3*q^(-23/2) - 3*q^(-25/2) - q^(-27/2) - q^(-29/2))*x1^(3)*x2^(9) + (2*q^(3/2) + 2*q^(1/2) + q^(-1/2) - 8*q^(-3/2) - 14*q^(-5/2) - 12*q^(-7/2) - 2*q^(-9/2) + 7*q^(-11/2) - 14*q^(-13/2) - 15*q^(-15/2) - 24*q^(-17/2) - 11*q^(-19/2) + 9*q^(-23/2) + 8*q^(-25/2) + 10*q^(-27/2) + 6*q^(-29/2) + 5*q^(-31/2) + 4*q^(-33/2) + 2*q^(-35/2) + q^(-37/2) + q^(-39/2))*x1^(4)*x2^(9) + (2*q^(-7/2) - 6*q^(-11/2) - 13*q^(-13/2) - 14*q^(-15/2) + 2*q^(-17/2) + 36*q^(-19/2) + 44*q^(-21/2) + 28*q^(-23/2) + 14*q^(-25/2) - 8*q^(-29/2) - 10*q^(-31/2) - 8*q^(-33/2) - 8*q^(-35/2) - 5*q^(-37/2) - 5*q^(-39/2) - 3*q^(-41/2) - 2*q^(-43/2) - q^(-45/2) - q^(-47/2))*x1^(5)*x2^(9) + (q^(-13/2) + 2*q^(-15/2) + 6*q^(-17/2) + 5*q^(-19/2) - 5*q^(-21/2) - 28*q^(-23/2) - 33*q^(-25/2) - 33*q^(-27/2) - 20*q^(-29/2) - 7*q^(-31/2) + 4*q^(-33/2) + 2*q^(-35/2) + 4*q^(-37/2) + 4*q^(-39/2) + 5*q^(-41/2) + 4*q^(-43/2) + 3*q^(-45/2) + 2*q^(-47/2) + 2*q^(-49/2) + q^(-51/2) + q^(-53/2))*x1^(6)*x2^(9) + (4*q^(-25/2) + 8*q^(-27/2) + 13*q^(-29/2) + 16*q^(-31/2) + 10*q^(-33/2) - 3*q^(-35/2) - 2*q^(-45/2) - q^(-47/2) - q^(-49/2) - q^(-51/2) - q^(-53/2) - q^(-55/2) - q^(-57/2))*x1^(7)*x2^(9) + (-q^(-31/2) - 2*q^(-33/2) - 2*q^(-35/2) - q^(-37/2) + q^(-39/2) + q^(-41/2) + q^(-43/2) + 3*q^(-45/2) - q^(-49/2) + q^(-59/2))*x1^(8)*x2^(9)
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(-1, -2) |
(1, 1) |
x1^(1)x2^(2) |
q^(-3/2) |
{"0": [1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1], "1": [-1, 1, -1, 1, -1, 1]}
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(-q^(-3/2))*x1*x2^(2) + (-2*q^(-3/2))*x1*x2^(3) + (2*q^(-5/2))*x1^(2)*x2^(3) + (q^(-1/2) - 3*q^(-3/2))*x1*x2^(4) + (4*q^(-5/2) + q^(-7/2))*x1^(2)*x2^(4) + (-q^(-7/2) - q^(-9/2))*x1^(3)*x2^(4) + (2*q^(1/2) + 2*q^(-1/2) - 4*q^(-3/2))*x1*x2^(5) + (-q^(-1/2) - 2*q^(-3/2) + 6*q^(-5/2) + 2*q^(-7/2) + q^(-9/2))*x1^(2)*x2^(5) + (-2*q^(-7/2) - 3*q^(-9/2) - q^(-13/2))*x1^(3)*x2^(5) + (q^(-11/2) - 2*q^(-13/2) + q^(-15/2))*x1^(4)*x2^(5) + (2*q^(3/2) + 4*q^(1/2) + 3*q^(-1/2) - 5*q^(-3/2))*x1*x2^(6) + (-2*q^(1/2) - 6*q^(-1/2) - 5*q^(-3/2) + 7*q^(-5/2) + 3*q^(-7/2) + 2*q^(-9/2) + q^(-11/2))*x1^(2)*x2^(6) + (2*q^(-3/2) + 2*q^(-5/2) - 2*q^(-7/2) - 5*q^(-9/2) - q^(-11/2) - 2*q^(-13/2) - q^(-15/2) - q^(-17/2))*x1^(3)*x2^(6) + (2*q^(-11/2) - 4*q^(-13/2) + q^(-19/2) + q^(-21/2))*x1^(4)*x2^(6) + (q^(-15/2) + q^(-17/2) + 3*q^(-19/2) - q^(-23/2))*x1^(5)*x2^(6) + (-2*q^(7/2) + 2*q^(5/2) + 4*q^(3/2) + 6*q^(1/2) + 4*q^(-1/2) - 6*q^(-3/2))*x1*x2^(7) + (q^(5/2) - 2*q^(3/2) - 8*q^(1/2) - 13*q^(-1/2) - 10*q^(-3/2) + 7*q^(-5/2) + 3*q^(-7/2) + 3*q^(-9/2) + 2*q^(-11/2) + q^(-13/2))*x1^(2)*x2^(7) + (4*q^(-1/2) + 8*q^(-3/2) + 8*q^(-5/2) - 6*q^(-9/2) - q^(-11/2) - 4*q^(-13/2) - 2*q^(-15/2) - 3*q^(-17/2) - q^(-19/2) - q^(-21/2))*x1^(3)*x2^(7) + (-q^(-5/2) - 2*q^(-7/2) - q^(-9/2) + 4*q^(-11/2) - 7*q^(-13/2) - 2*q^(-15/2) - 3*q^(-17/2) + 3*q^(-19/2) + 3*q^(-21/2) + 2*q^(-23/2) + q^(-25/2) + q^(-27/2))*x1^(4)*x2^(7) + (2*q^(-15/2) + 5*q^(-17/2) + 10*q^(-19/2) + 5*q^(-21/2) - 2*q^(-23/2) - q^(-25/2) - q^(-27/2) - q^(-29/2) - q^(-31/2))*x1^(5)*x2^(7) + (-q^(-19/2) - 2*q^(-21/2) - 4*q^(-23/2) - q^(-25/2) - q^(-27/2) + q^(-33/2))*x1^(6)*x2^(7) + (-3*q^(11/2) - 3*q^(9/2) - 2*q^(7/2) + 4*q^(5/2) + 6*q^(3/2) + 8*q^(1/2) + 5*q^(-1/2) - 7*q^(-3/2))*x1*x2^(8) + (2*q^(9/2) + 4*q^(7/2) + 4*q^(5/2) - 7*q^(3/2) - 16*q^(1/2) - 22*q^(-1/2) - 17*q^(-3/2) + 5*q^(-5/2) + 2*q^(-7/2) + 3*q^(-9/2) + 3*q^(-11/2) + 2*q^(-13/2) + q^(-15/2))*x1^(2)*x2^(8) + (-q^(5/2) - 2*q^(3/2) + 3*q^(1/2) + 12*q^(-1/2) + 20*q^(-3/2) + 18*q^(-5/2) + 6*q^(-7/2) - 3*q^(-9/2) + q^(-11/2) - 4*q^(-13/2) - 3*q^(-15/2) - 5*q^(-17/2) - 3*q^(-19/2) - 3*q^(-21/2) - q^(-23/2) - q^(-25/2))*x1^(3)*x2^(8) + (-2*q^(-3/2) - 6*q^(-5/2) - 7*q^(-7/2) - q^(-9/2) + 5*q^(-11/2) - 10*q^(-13/2) - 6*q^(-15/2) - 10*q^(-17/2) + 6*q^(-21/2) + 6*q^(-23/2) + 4*q^(-25/2) + 4*q^(-27/2) + 2*q^(-29/2) + q^(-31/2) + q^(-33/2))*x1^(4)*x2^(8) + (q^(-9/2) - q^(-11/2) - 2*q^(-13/2) + q^(-15/2) + 7*q^(-17/2) + 23*q^(-19/2) + 19*q^(-21/2) + 5*q^(-23/2) - q^(-25/2) - 3*q^(-27/2) - 5*q^(-29/2) - 4*q^(-31/2) - 2*q^(-33/2) - 2*q^(-35/2) - q^(-37/2) - q^(-39/2))*x1^(5)*x2^(8) + (-2*q^(-19/2) - 6*q^(-21/2) - 15*q^(-23/2) - 11*q^(-25/2) - 8*q^(-27/2) - 3*q^(-29/2) + q^(-31/2) + 3*q^(-33/2) + q^(-35/2) + q^(-37/2) + q^(-39/2) + q^(-41/2) + q^(-43/2))*x1^(6)*x2^(8) + (2*q^(-25/2) + 2*q^(-27/2) + 3*q^(-29/2) + 3*q^(-31/2) + q^(-33/2) - 3*q^(-35/2) + q^(-37/2) - q^(-45/2))*x1^(7)*x2^(8) + (-2*q^(15/2) - 4*q^(13/2) - 10*q^(11/2) - 4*q^(9/2) - 2*q^(7/2) + 6*q^(5/2) + 8*q^(3/2) + 10*q^(1/2) + 6*q^(-1/2) - 8*q^(-3/2))*x1*x2^(9) + (2*q^(13/2) + 6*q^(11/2) + 16*q^(9/2) + 14*q^(7/2) + 7*q^(5/2) - 12*q^(3/2) - 25*q^(1/2) - 33*q^(-1/2) - 26*q^(-3/2) + q^(-5/2) - q^(-7/2) + 2*q^(-9/2) + 3*q^(-11/2) + 3*q^(-13/2) + 2*q^(-15/2) + q^(-17/2))*x1^(2)*x2^(9) + (-2*q^(9/2) - 6*q^(7/2) - 12*q^(5/2) - 7*q^(3/2) + 5*q^(1/2) + 25*q^(-1/2) + 35*q^(-3/2) + 34*q^(-5/2) + 18*q^(-7/2) + 6*q^(-9/2) + 9*q^(-11/2) - q^(-15/2) - 6*q^(-17/2) - 4*q^(-19/2) - 6*q^(-21/2) - 3*q^(-23/2) - 3*q^(-25/2) - q^(-27/2) - q^(-29/2))*x1^(3)*x2^(9) + (2*q^(3/2) + 2*q^(1/2) + q^(-1/2) - 8*q^(-3/2) - 14*q^(-5/2) - 12*q^(-7/2) - 2*q^(-9/2) + 7*q^(-11/2) - 14*q^(-13/2) - 15*q^(-15/2) - 24*q^(-17/2) - 11*q^(-19/2) + 9*q^(-23/2) + 8*q^(-25/2) + 10*q^(-27/2) + 6*q^(-29/2) + 5*q^(-31/2) + 4*q^(-33/2) + 2*q^(-35/2) + q^(-37/2) + q^(-39/2))*x1^(4)*x2^(9) + (2*q^(-7/2) - 6*q^(-11/2) - 13*q^(-13/2) - 14*q^(-15/2) + 2*q^(-17/2) + 36*q^(-19/2) + 44*q^(-21/2) + 28*q^(-23/2) + 14*q^(-25/2) - 8*q^(-29/2) - 10*q^(-31/2) - 8*q^(-33/2) - 8*q^(-35/2) - 5*q^(-37/2) - 5*q^(-39/2) - 3*q^(-41/2) - 2*q^(-43/2) - q^(-45/2) - q^(-47/2))*x1^(5)*x2^(9) + (q^(-13/2) + 2*q^(-15/2) + 6*q^(-17/2) + 5*q^(-19/2) - 5*q^(-21/2) - 28*q^(-23/2) - 33*q^(-25/2) - 33*q^(-27/2) - 20*q^(-29/2) - 7*q^(-31/2) + 4*q^(-33/2) + 2*q^(-35/2) + 4*q^(-37/2) + 4*q^(-39/2) + 5*q^(-41/2) + 4*q^(-43/2) + 3*q^(-45/2) + 2*q^(-47/2) + 2*q^(-49/2) + q^(-51/2) + q^(-53/2))*x1^(6)*x2^(9) + (4*q^(-25/2) + 8*q^(-27/2) + 13*q^(-29/2) + 16*q^(-31/2) + 10*q^(-33/2) - 3*q^(-35/2) - 2*q^(-45/2) - q^(-47/2) - q^(-49/2) - q^(-51/2) - q^(-53/2) - q^(-55/2) - q^(-57/2))*x1^(7)*x2^(9) + (-q^(-31/2) - 2*q^(-33/2) - 2*q^(-35/2) - q^(-37/2) + q^(-39/2) + q^(-41/2) + q^(-43/2) + 3*q^(-45/2) - q^(-49/2) + q^(-59/2))*x1^(8)*x2^(9)
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(1, 2) |
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x1^(-1)x2^(-2) |
q^(-3/2) |
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(-q^(-3/2))*x1^(-1)*x2^(-2) + (-2*q^(-3/2))*x1^(-1)*x2^(-3) + (2*q^(-5/2))*x1^(-2)*x2^(-3) + (q^(-1/2) - 3*q^(-3/2))*x1^(-1)*x2^(-4) + (4*q^(-5/2) + q^(-7/2))*x1^(-2)*x2^(-4) + (-q^(-7/2) - q^(-9/2))*x1^(-3)*x2^(-4) + (2*q^(1/2) + 2*q^(-1/2) - 4*q^(-3/2))*x1^(-1)*x2^(-5) + (-q^(-1/2) - 2*q^(-3/2) + 6*q^(-5/2) + 2*q^(-7/2) + q^(-9/2))*x1^(-2)*x2^(-5) + (-2*q^(-7/2) - 3*q^(-9/2) - q^(-13/2))*x1^(-3)*x2^(-5) + (q^(-11/2) - 2*q^(-13/2) + q^(-15/2))*x1^(-4)*x2^(-5) + (2*q^(3/2) + 4*q^(1/2) + 3*q^(-1/2) - 5*q^(-3/2))*x1^(-1)*x2^(-6) + (-2*q^(1/2) - 6*q^(-1/2) - 5*q^(-3/2) + 7*q^(-5/2) + 3*q^(-7/2) + 2*q^(-9/2) + q^(-11/2))*x1^(-2)*x2^(-6) + (2*q^(-3/2) + 2*q^(-5/2) - 2*q^(-7/2) - 5*q^(-9/2) - q^(-11/2) - 2*q^(-13/2) - q^(-15/2) - q^(-17/2))*x1^(-3)*x2^(-6) + (2*q^(-11/2) - 4*q^(-13/2) + q^(-19/2) + q^(-21/2))*x1^(-4)*x2^(-6) + (q^(-15/2) + q^(-17/2) + 3*q^(-19/2) - q^(-23/2))*x1^(-5)*x2^(-6) + (-2*q^(7/2) + 2*q^(5/2) + 4*q^(3/2) + 6*q^(1/2) + 4*q^(-1/2) - 6*q^(-3/2))*x1^(-1)*x2^(-7) + (q^(5/2) - 2*q^(3/2) - 8*q^(1/2) - 13*q^(-1/2) - 10*q^(-3/2) + 7*q^(-5/2) + 3*q^(-7/2) + 3*q^(-9/2) + 2*q^(-11/2) + q^(-13/2))*x1^(-2)*x2^(-7) + (4*q^(-1/2) + 8*q^(-3/2) + 8*q^(-5/2) - 6*q^(-9/2) - q^(-11/2) - 4*q^(-13/2) - 2*q^(-15/2) - 3*q^(-17/2) - q^(-19/2) - q^(-21/2))*x1^(-3)*x2^(-7) + (-q^(-5/2) - 2*q^(-7/2) - q^(-9/2) + 4*q^(-11/2) - 7*q^(-13/2) - 2*q^(-15/2) - 3*q^(-17/2) + 3*q^(-19/2) + 3*q^(-21/2) + 2*q^(-23/2) + q^(-25/2) + q^(-27/2))*x1^(-4)*x2^(-7) + (2*q^(-15/2) + 5*q^(-17/2) + 10*q^(-19/2) + 5*q^(-21/2) - 2*q^(-23/2) - q^(-25/2) - q^(-27/2) - q^(-29/2) - q^(-31/2))*x1^(-5)*x2^(-7) + (-q^(-19/2) - 2*q^(-21/2) - 4*q^(-23/2) - q^(-25/2) - q^(-27/2) + q^(-33/2))*x1^(-6)*x2^(-7) + (-3*q^(11/2) - 3*q^(9/2) - 2*q^(7/2) + 4*q^(5/2) + 6*q^(3/2) + 8*q^(1/2) + 5*q^(-1/2) - 7*q^(-3/2))*x1^(-1)*x2^(-8) + (2*q^(9/2) + 4*q^(7/2) + 4*q^(5/2) - 7*q^(3/2) - 16*q^(1/2) - 22*q^(-1/2) - 17*q^(-3/2) + 5*q^(-5/2) + 2*q^(-7/2) + 3*q^(-9/2) + 3*q^(-11/2) + 2*q^(-13/2) + q^(-15/2))*x1^(-2)*x2^(-8) + (-q^(5/2) - 2*q^(3/2) + 3*q^(1/2) + 12*q^(-1/2) + 20*q^(-3/2) + 18*q^(-5/2) + 6*q^(-7/2) - 3*q^(-9/2) + q^(-11/2) - 4*q^(-13/2) - 3*q^(-15/2) - 5*q^(-17/2) - 3*q^(-19/2) - 3*q^(-21/2) - q^(-23/2) - q^(-25/2))*x1^(-3)*x2^(-8) + (-2*q^(-3/2) - 6*q^(-5/2) - 7*q^(-7/2) - q^(-9/2) + 5*q^(-11/2) - 10*q^(-13/2) - 6*q^(-15/2) - 10*q^(-17/2) + 6*q^(-21/2) + 6*q^(-23/2) + 4*q^(-25/2) + 4*q^(-27/2) + 2*q^(-29/2) + q^(-31/2) + q^(-33/2))*x1^(-4)*x2^(-8) + (q^(-9/2) - q^(-11/2) - 2*q^(-13/2) + q^(-15/2) + 7*q^(-17/2) + 23*q^(-19/2) + 19*q^(-21/2) + 5*q^(-23/2) - q^(-25/2) - 3*q^(-27/2) - 5*q^(-29/2) - 4*q^(-31/2) - 2*q^(-33/2) - 2*q^(-35/2) - q^(-37/2) - q^(-39/2))*x1^(-5)*x2^(-8) + (-2*q^(-19/2) - 6*q^(-21/2) - 15*q^(-23/2) - 11*q^(-25/2) - 8*q^(-27/2) - 3*q^(-29/2) + q^(-31/2) + 3*q^(-33/2) + q^(-35/2) + q^(-37/2) + q^(-39/2) + q^(-41/2) + q^(-43/2))*x1^(-6)*x2^(-8) + (2*q^(-25/2) + 2*q^(-27/2) + 3*q^(-29/2) + 3*q^(-31/2) + q^(-33/2) - 3*q^(-35/2) + q^(-37/2) - q^(-45/2))*x1^(-7)*x2^(-8) + (-2*q^(15/2) - 4*q^(13/2) - 10*q^(11/2) - 4*q^(9/2) - 2*q^(7/2) + 6*q^(5/2) + 8*q^(3/2) + 10*q^(1/2) + 6*q^(-1/2) - 8*q^(-3/2))*x1^(-1)*x2^(-9) + (2*q^(13/2) + 6*q^(11/2) + 16*q^(9/2) + 14*q^(7/2) + 7*q^(5/2) - 12*q^(3/2) - 25*q^(1/2) - 33*q^(-1/2) - 26*q^(-3/2) + q^(-5/2) - q^(-7/2) + 2*q^(-9/2) + 3*q^(-11/2) + 3*q^(-13/2) + 2*q^(-15/2) + q^(-17/2))*x1^(-2)*x2^(-9) + (-2*q^(9/2) - 6*q^(7/2) - 12*q^(5/2) - 7*q^(3/2) + 5*q^(1/2) + 25*q^(-1/2) + 35*q^(-3/2) + 34*q^(-5/2) + 18*q^(-7/2) + 6*q^(-9/2) + 9*q^(-11/2) - q^(-15/2) - 6*q^(-17/2) - 4*q^(-19/2) - 6*q^(-21/2) - 3*q^(-23/2) - 3*q^(-25/2) - q^(-27/2) - q^(-29/2))*x1^(-3)*x2^(-9) + (2*q^(3/2) + 2*q^(1/2) + q^(-1/2) - 8*q^(-3/2) - 14*q^(-5/2) - 12*q^(-7/2) - 2*q^(-9/2) + 7*q^(-11/2) - 14*q^(-13/2) - 15*q^(-15/2) - 24*q^(-17/2) - 11*q^(-19/2) + 9*q^(-23/2) + 8*q^(-25/2) + 10*q^(-27/2) + 6*q^(-29/2) + 5*q^(-31/2) + 4*q^(-33/2) + 2*q^(-35/2) + q^(-37/2) + q^(-39/2))*x1^(-4)*x2^(-9) + (2*q^(-7/2) - 6*q^(-11/2) - 13*q^(-13/2) - 14*q^(-15/2) + 2*q^(-17/2) + 36*q^(-19/2) + 44*q^(-21/2) + 28*q^(-23/2) + 14*q^(-25/2) - 8*q^(-29/2) - 10*q^(-31/2) - 8*q^(-33/2) - 8*q^(-35/2) - 5*q^(-37/2) - 5*q^(-39/2) - 3*q^(-41/2) - 2*q^(-43/2) - q^(-45/2) - q^(-47/2))*x1^(-5)*x2^(-9) + (q^(-13/2) + 2*q^(-15/2) + 6*q^(-17/2) + 5*q^(-19/2) - 5*q^(-21/2) - 28*q^(-23/2) - 33*q^(-25/2) - 33*q^(-27/2) - 20*q^(-29/2) - 7*q^(-31/2) + 4*q^(-33/2) + 2*q^(-35/2) + 4*q^(-37/2) + 4*q^(-39/2) + 5*q^(-41/2) + 4*q^(-43/2) + 3*q^(-45/2) + 2*q^(-47/2) + 2*q^(-49/2) + q^(-51/2) + q^(-53/2))*x1^(-6)*x2^(-9) + (4*q^(-25/2) + 8*q^(-27/2) + 13*q^(-29/2) + 16*q^(-31/2) + 10*q^(-33/2) - 3*q^(-35/2) - 2*q^(-45/2) - q^(-47/2) - q^(-49/2) - q^(-51/2) - q^(-53/2) - q^(-55/2) - q^(-57/2))*x1^(-7)*x2^(-9) + (-q^(-31/2) - 2*q^(-33/2) - 2*q^(-35/2) - q^(-37/2) + q^(-39/2) + q^(-41/2) + q^(-43/2) + 3*q^(-45/2) - q^(-49/2) + q^(-59/2))*x1^(-8)*x2^(-9)
|
Braid
| Braid word |
Components |
Crossings |
Strands |
[1, -2, -2, 1, -2, -2, -2, -2, 1] |
2 |
9 |
3 |
Multivariable Alexander polynomial
| ΔL |
-A1*A2^(2) + 2*A1*A2 - 2*A1 - 2*A2 + 3 - 2*A2^(-1) - 2*A1^(-1) + 2*A1^(-1)*A2^(-1) - A1^(-1)*A2^(-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 |
(-2, -4) |
yes |
(2, 0) |
no |
(2, 4) |
yes |
(-2, 0) |
no |
HFL polytope
| Poincaré polynomial |
m^(-3)*A1^(-3/2)*A2^(-5/2) + 3*m^(-2)*A1^(-3/2)*A2^(-3/2) + m^(-2)*A1^(-1/2)*A2^(-5/2) + 4*m^(-1)*A1^(-3/2)*A2^(-1/2) + 5*m^(-1)*A1^(-1/2)*A2^(-3/2) + 2*A1^(-3/2)*A2^(1/2) + 9*A1^(-1/2)*A2^(-1/2) + 2*A1^(1/2)*A2^(-3/2) + 7*m*A1^(-1/2)*A2^(1/2) + 7*m*A1^(1/2)*A2^(-1/2) + 2*m^2*A1^(-1/2)*A2^(3/2) + 9*m^2*A1^(1/2)*A2^(1/2) + 2*m^2*A1^(3/2)*A2^(-1/2) + 5*m^3*A1^(1/2)*A2^(3/2) + 4*m^3*A1^(3/2)*A2^(1/2) + m^4*A1^(1/2)*A2^(5/2) + 3*m^4*A1^(3/2)*A2^(3/2) + m^5*A1^(3/2)*A2^(5/2) |
| Vertex | Maslov | Rank |
(-3/2, -5/2) | -3 | 1 |
(-1/2, -5/2) | -2 | 1 |
(3/2, -1/2) | 2 | 2 |
(3/2, 5/2) | 5 | 1 |
(1/2, 5/2) | 4 | 1 |
(-3/2, 1/2) | 0 | 2 |
Record
FL/HFL Links
orderOption(int) |
115 |
namestring |
L9a28{0} |
statusstring |
success |
slugstring |
L9a28_0_cdcdf8d7 |
result_filestring |
details/L9a28_0_cdcdf8d7.json |
complexity_scoreOption(int) |
162 |
strandsOption(int) |
null |
crossingsOption(int) |
9 |
component_countOption(int) |
2 |
girthOption(int) |
6 |
total_rankOption(int) |
68 |
wall_secondsOption(float) |
0.001722 |
backend_secondsOption(float) |
0.0 |
errorstring |
|
dimensionOption(int) |
2 |
support_sizeOption(int) |
18 |
vertex_countOption(int) |
6 |
fibered_vertex_countOption(int) |
2 |
polytope_statusstring |
computed |
alexander_support_sizeOption(int) |
9 |
alexander_vertex_countOption(int) |
4 |
alexander_relationstring |
not_computed |
fk_countint |
2 |
detailsRowRef(FLHFLLinks) |
{
"dataset": "FLHFLLinks",
"key": "L9a28_0_cdcdf8d7"
} |
detail_assetstring |
/api/v1/datasets/FLHFLLinks/assets/L9a28_0_cdcdf8d7 |