details/L10a120_0_29ff7351.json

FL expansions

Newt(ΔL) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle FL
(-2, 0) (1, 1/2) x1^(2)x2^(0) 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]}
 
(-q^(-5/2))*x1^(2) + (q^(-3/2))*x1^(3)*x2^(-1) + (-q^(-5/2))*x1^(3) + (q^(-7/2))*x1^(3)*x2 + (q^(-3/2))*x1^(4)*x2^(-1) + (-2*q^(-5/2))*x1^(4) + (q^(-7/2))*x1^(4)*x2 + (-q^(5/2))*x1^(5)*x2^(-3) + (q^(3/2))*x1^(5)*x2^(-2) + (q^(-3/2))*x1^(5)*x2^(-1) + (-2*q^(-5/2))*x1^(5) + (q^(-7/2))*x1^(5)*x2 + (q^(-13/2))*x1^(5)*x2^(2) + (-q^(-15/2))*x1^(5)*x2^(3) + (q^(11/2))*x1^(6)*x2^(-4) + (-q^(9/2) - q^(7/2) - q^(5/2))*x1^(6)*x2^(-3) + (q^(5/2) + 2*q^(3/2))*x1^(6)*x2^(-2) + (-q^(1/2) + q^(-3/2))*x1^(6)*x2^(-1) + (-2*q^(-5/2))*x1^(6) + (q^(-7/2) - q^(-11/2))*x1^(6)*x2 + (2*q^(-13/2) + q^(-15/2))*x1^(6)*x2^(2) + (-q^(-15/2) - q^(-17/2) - q^(-19/2))*x1^(6)*x2^(3) + (q^(-21/2))*x1^(6)*x2^(4) + (q^(13/2) + q^(11/2))*x1^(7)*x2^(-4) + (-q^(11/2) - 3*q^(9/2) - q^(7/2) - q^(5/2))*x1^(7)*x2^(-3) + (2*q^(7/2) + 2*q^(5/2) + 2*q^(3/2))*x1^(7)*x2^(-2) + (-q^(3/2) - q^(1/2) + q^(-3/2))*x1^(7)*x2^(-1) + (-3*q^(-5/2))*x1^(7) + (q^(-7/2) - q^(-11/2) - q^(-13/2))*x1^(7)*x2 + (2*q^(-13/2) + 2*q^(-15/2) + 2*q^(-17/2))*x1^(7)*x2^(2) + (-q^(-15/2) - q^(-17/2) - 3*q^(-19/2) - q^(-21/2))*x1^(7)*x2^(3) + (q^(-21/2) + q^(-23/2))*x1^(7)*x2^(4) + (-q^(27/2))*x1^(8)*x2^(-6) + (q^(25/2) + q^(23/2))*x1^(8)*x2^(-5) + (-q^(21/2) + q^(15/2) + q^(13/2) + q^(11/2))*x1^(8)*x2^(-4) + (-q^(13/2) - 3*q^(11/2) - 3*q^(9/2) - q^(7/2) - q^(5/2))*x1^(8)*x2^(-3) + (2*q^(9/2) + 3*q^(7/2) + 2*q^(5/2) + 2*q^(3/2))*x1^(8)*x2^(-2) + (-q^(5/2) - q^(3/2) + q^(-1/2) + 2*q^(-3/2))*x1^(8)*x2^(-1) + (-q^(-3/2) - 5*q^(-5/2) - q^(-7/2))*x1^(8) + (2*q^(-7/2) + q^(-9/2) - q^(-13/2) - q^(-15/2))*x1^(8)*x2 + (2*q^(-13/2) + 2*q^(-15/2) + 3*q^(-17/2) + 2*q^(-19/2))*x1^(8)*x2^(2) + (-q^(-15/2) - q^(-17/2) - 3*q^(-19/2) - 3*q^(-21/2) - q^(-23/2))*x1^(8)*x2^(3) + (q^(-21/2) + q^(-23/2) + q^(-25/2) - q^(-31/2))*x1^(8)*x2^(4) + (q^(-33/2) + q^(-35/2))*x1^(8)*x2^(5) + (-q^(-37/2))*x1^(8)*x2^(6) + (q^(37/2))*x1^(9)*x2^(-7) + (-q^(35/2) - q^(33/2) - q^(31/2) - q^(29/2) - q^(27/2))*x1^(9)*x2^(-6) + (q^(31/2) + q^(29/2) + 2*q^(27/2) + 3*q^(25/2) + q^(23/2))*x1^(9)*x2^(-5) + (-q^(25/2) - 2*q^(23/2) - 2*q^(21/2) + q^(17/2) + q^(15/2) + q^(13/2) + q^(11/2))*x1^(9)*x2^(-4) + (q^(19/2) - q^(15/2) - 3*q^(13/2) - 3*q^(11/2) - 3*q^(9/2) - q^(7/2) - q^(5/2))*x1^(9)*x2^(-3) + (2*q^(11/2) + 3*q^(9/2) + 3*q^(7/2) + q^(5/2) + q^(3/2))*x1^(9)*x2^(-2) + (-q^(7/2) - q^(5/2) + 3*q^(1/2) + 3*q^(-1/2) + 3*q^(-3/2) + q^(-5/2))*x1^(9)*x2^(-1) + (-2*q^(-1/2) - 4*q^(-3/2) - 8*q^(-5/2) - 4*q^(-7/2) - 2*q^(-9/2))*x1^(9) + (q^(-5/2) + 3*q^(-7/2) + 3*q^(-9/2) + 3*q^(-11/2) - q^(-15/2) - q^(-17/2))*x1^(9)*x2 + (q^(-13/2) + q^(-15/2) + 3*q^(-17/2) + 3*q^(-19/2) + 2*q^(-21/2))*x1^(9)*x2^(2) + (-q^(-15/2) - q^(-17/2) - 3*q^(-19/2) - 3*q^(-21/2) - 3*q^(-23/2) - q^(-25/2) + q^(-29/2))*x1^(9)*x2^(3) + (q^(-21/2) + q^(-23/2) + q^(-25/2) + q^(-27/2) - 2*q^(-31/2) - 2*q^(-33/2) - q^(-35/2))*x1^(9)*x2^(4) + (q^(-33/2) + 3*q^(-35/2) + 2*q^(-37/2) + q^(-39/2) + q^(-41/2))*x1^(9)*x2^(5) + (-q^(-37/2) - q^(-39/2) - q^(-41/2) - q^(-43/2) - q^(-45/2))*x1^(9)*x2^(6) + (q^(-47/2))*x1^(9)*x2^(7)
(0, -2) (1/2, 1) x1^(0)x2^(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]}
 
(q^(37/2))*x1^(-7)*x2^(9) + (-q^(27/2))*x1^(-6)*x2^(8) + (-q^(35/2) - q^(33/2) - q^(31/2) - q^(29/2) - q^(27/2))*x1^(-6)*x2^(9) + (q^(25/2) + q^(23/2))*x1^(-5)*x2^(8) + (q^(31/2) + q^(29/2) + 2*q^(27/2) + 3*q^(25/2) + q^(23/2))*x1^(-5)*x2^(9) + (q^(11/2))*x1^(-4)*x2^(6) + (q^(13/2) + q^(11/2))*x1^(-4)*x2^(7) + (-q^(21/2) + q^(15/2) + q^(13/2) + q^(11/2))*x1^(-4)*x2^(8) + (-q^(25/2) - 2*q^(23/2) - 2*q^(21/2) + q^(17/2) + q^(15/2) + q^(13/2) + q^(11/2))*x1^(-4)*x2^(9) + (-q^(5/2))*x1^(-3)*x2^(5) + (-q^(9/2) - q^(7/2) - q^(5/2))*x1^(-3)*x2^(6) + (-q^(11/2) - 3*q^(9/2) - q^(7/2) - q^(5/2))*x1^(-3)*x2^(7) + (-q^(13/2) - 3*q^(11/2) - 3*q^(9/2) - q^(7/2) - q^(5/2))*x1^(-3)*x2^(8) + (q^(19/2) - q^(15/2) - 3*q^(13/2) - 3*q^(11/2) - 3*q^(9/2) - q^(7/2) - q^(5/2))*x1^(-3)*x2^(9) + (q^(3/2))*x1^(-2)*x2^(5) + (q^(5/2) + 2*q^(3/2))*x1^(-2)*x2^(6) + (2*q^(7/2) + 2*q^(5/2) + 2*q^(3/2))*x1^(-2)*x2^(7) + (2*q^(9/2) + 3*q^(7/2) + 2*q^(5/2) + 2*q^(3/2))*x1^(-2)*x2^(8) + (2*q^(11/2) + 3*q^(9/2) + 3*q^(7/2) + q^(5/2) + q^(3/2))*x1^(-2)*x2^(9) + (q^(-3/2))*x1^(-1)*x2^(3) + (q^(-3/2))*x1^(-1)*x2^(4) + (q^(-3/2))*x1^(-1)*x2^(5) + (-q^(1/2) + q^(-3/2))*x1^(-1)*x2^(6) + (-q^(3/2) - q^(1/2) + q^(-3/2))*x1^(-1)*x2^(7) + (-q^(5/2) - q^(3/2) + q^(-1/2) + 2*q^(-3/2))*x1^(-1)*x2^(8) + (-q^(7/2) - q^(5/2) + 3*q^(1/2) + 3*q^(-1/2) + 3*q^(-3/2) + q^(-5/2))*x1^(-1)*x2^(9) + (-q^(-5/2))*x2^(2) + (-q^(-5/2))*x2^(3) + (-2*q^(-5/2))*x2^(4) + (-2*q^(-5/2))*x2^(5) + (-2*q^(-5/2))*x2^(6) + (-3*q^(-5/2))*x2^(7) + (-q^(-3/2) - 5*q^(-5/2) - q^(-7/2))*x2^(8) + (-2*q^(-1/2) - 4*q^(-3/2) - 8*q^(-5/2) - 4*q^(-7/2) - 2*q^(-9/2))*x2^(9) + (q^(-7/2))*x1*x2^(3) + (q^(-7/2))*x1*x2^(4) + (q^(-7/2))*x1*x2^(5) + (q^(-7/2) - q^(-11/2))*x1*x2^(6) + (q^(-7/2) - q^(-11/2) - q^(-13/2))*x1*x2^(7) + (2*q^(-7/2) + q^(-9/2) - q^(-13/2) - q^(-15/2))*x1*x2^(8) + (q^(-5/2) + 3*q^(-7/2) + 3*q^(-9/2) + 3*q^(-11/2) - q^(-15/2) - q^(-17/2))*x1*x2^(9) + (q^(-13/2))*x1^(2)*x2^(5) + (2*q^(-13/2) + q^(-15/2))*x1^(2)*x2^(6) + (2*q^(-13/2) + 2*q^(-15/2) + 2*q^(-17/2))*x1^(2)*x2^(7) + (2*q^(-13/2) + 2*q^(-15/2) + 3*q^(-17/2) + 2*q^(-19/2))*x1^(2)*x2^(8) + (q^(-13/2) + q^(-15/2) + 3*q^(-17/2) + 3*q^(-19/2) + 2*q^(-21/2))*x1^(2)*x2^(9) + (-q^(-15/2))*x1^(3)*x2^(5) + (-q^(-15/2) - q^(-17/2) - q^(-19/2))*x1^(3)*x2^(6) + (-q^(-15/2) - q^(-17/2) - 3*q^(-19/2) - q^(-21/2))*x1^(3)*x2^(7) + (-q^(-15/2) - q^(-17/2) - 3*q^(-19/2) - 3*q^(-21/2) - q^(-23/2))*x1^(3)*x2^(8) + (-q^(-15/2) - q^(-17/2) - 3*q^(-19/2) - 3*q^(-21/2) - 3*q^(-23/2) - q^(-25/2) + q^(-29/2))*x1^(3)*x2^(9) + (q^(-21/2))*x1^(4)*x2^(6) + (q^(-21/2) + q^(-23/2))*x1^(4)*x2^(7) + (q^(-21/2) + q^(-23/2) + q^(-25/2) - q^(-31/2))*x1^(4)*x2^(8) + (q^(-21/2) + q^(-23/2) + q^(-25/2) + q^(-27/2) - 2*q^(-31/2) - 2*q^(-33/2) - q^(-35/2))*x1^(4)*x2^(9) + (q^(-33/2) + q^(-35/2))*x1^(5)*x2^(8) + (q^(-33/2) + 3*q^(-35/2) + 2*q^(-37/2) + q^(-39/2) + q^(-41/2))*x1^(5)*x2^(9) + (-q^(-37/2))*x1^(6)*x2^(8) + (-q^(-37/2) - q^(-39/2) - q^(-41/2) - q^(-43/2) - q^(-45/2))*x1^(6)*x2^(9) + (q^(-47/2))*x1^(7)*x2^(9)
(-2, 0) (1, 1/2) x1^(2)x2^(0) 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]}
 
(-q^(-5/2))*x1^(2) + (q^(-3/2))*x1^(3)*x2^(-1) + (-q^(-5/2))*x1^(3) + (q^(-7/2))*x1^(3)*x2 + (q^(-3/2))*x1^(4)*x2^(-1) + (-2*q^(-5/2))*x1^(4) + (q^(-7/2))*x1^(4)*x2 + (-q^(5/2))*x1^(5)*x2^(-3) + (q^(3/2))*x1^(5)*x2^(-2) + (q^(-3/2))*x1^(5)*x2^(-1) + (-2*q^(-5/2))*x1^(5) + (q^(-7/2))*x1^(5)*x2 + (q^(-13/2))*x1^(5)*x2^(2) + (-q^(-15/2))*x1^(5)*x2^(3) + (q^(11/2))*x1^(6)*x2^(-4) + (-q^(9/2) - q^(7/2) - q^(5/2))*x1^(6)*x2^(-3) + (q^(5/2) + 2*q^(3/2))*x1^(6)*x2^(-2) + (-q^(1/2) + q^(-3/2))*x1^(6)*x2^(-1) + (-2*q^(-5/2))*x1^(6) + (q^(-7/2) - q^(-11/2))*x1^(6)*x2 + (2*q^(-13/2) + q^(-15/2))*x1^(6)*x2^(2) + (-q^(-15/2) - q^(-17/2) - q^(-19/2))*x1^(6)*x2^(3) + (q^(-21/2))*x1^(6)*x2^(4) + (q^(13/2) + q^(11/2))*x1^(7)*x2^(-4) + (-q^(11/2) - 3*q^(9/2) - q^(7/2) - q^(5/2))*x1^(7)*x2^(-3) + (2*q^(7/2) + 2*q^(5/2) + 2*q^(3/2))*x1^(7)*x2^(-2) + (-q^(3/2) - q^(1/2) + q^(-3/2))*x1^(7)*x2^(-1) + (-3*q^(-5/2))*x1^(7) + (q^(-7/2) - q^(-11/2) - q^(-13/2))*x1^(7)*x2 + (2*q^(-13/2) + 2*q^(-15/2) + 2*q^(-17/2))*x1^(7)*x2^(2) + (-q^(-15/2) - q^(-17/2) - 3*q^(-19/2) - q^(-21/2))*x1^(7)*x2^(3) + (q^(-21/2) + q^(-23/2))*x1^(7)*x2^(4) + (-q^(27/2))*x1^(8)*x2^(-6) + (q^(25/2) + q^(23/2))*x1^(8)*x2^(-5) + (-q^(21/2) + q^(15/2) + q^(13/2) + q^(11/2))*x1^(8)*x2^(-4) + (-q^(13/2) - 3*q^(11/2) - 3*q^(9/2) - q^(7/2) - q^(5/2))*x1^(8)*x2^(-3) + (2*q^(9/2) + 3*q^(7/2) + 2*q^(5/2) + 2*q^(3/2))*x1^(8)*x2^(-2) + (-q^(5/2) - q^(3/2) + q^(-1/2) + 2*q^(-3/2))*x1^(8)*x2^(-1) + (-q^(-3/2) - 5*q^(-5/2) - q^(-7/2))*x1^(8) + (2*q^(-7/2) + q^(-9/2) - q^(-13/2) - q^(-15/2))*x1^(8)*x2 + (2*q^(-13/2) + 2*q^(-15/2) + 3*q^(-17/2) + 2*q^(-19/2))*x1^(8)*x2^(2) + (-q^(-15/2) - q^(-17/2) - 3*q^(-19/2) - 3*q^(-21/2) - q^(-23/2))*x1^(8)*x2^(3) + (q^(-21/2) + q^(-23/2) + q^(-25/2) - q^(-31/2))*x1^(8)*x2^(4) + (q^(-33/2) + q^(-35/2))*x1^(8)*x2^(5) + (-q^(-37/2))*x1^(8)*x2^(6) + (q^(37/2))*x1^(9)*x2^(-7) + (-q^(35/2) - q^(33/2) - q^(31/2) - q^(29/2) - q^(27/2))*x1^(9)*x2^(-6) + (q^(31/2) + q^(29/2) + 2*q^(27/2) + 3*q^(25/2) + q^(23/2))*x1^(9)*x2^(-5) + (-q^(25/2) - 2*q^(23/2) - 2*q^(21/2) + q^(17/2) + q^(15/2) + q^(13/2) + q^(11/2))*x1^(9)*x2^(-4) + (q^(19/2) - q^(15/2) - 3*q^(13/2) - 3*q^(11/2) - 3*q^(9/2) - q^(7/2) - q^(5/2))*x1^(9)*x2^(-3) + (2*q^(11/2) + 3*q^(9/2) + 3*q^(7/2) + q^(5/2) + q^(3/2))*x1^(9)*x2^(-2) + (-q^(7/2) - q^(5/2) + 3*q^(1/2) + 3*q^(-1/2) + 3*q^(-3/2) + q^(-5/2))*x1^(9)*x2^(-1) + (-2*q^(-1/2) - 4*q^(-3/2) - 8*q^(-5/2) - 4*q^(-7/2) - 2*q^(-9/2))*x1^(9) + (q^(-5/2) + 3*q^(-7/2) + 3*q^(-9/2) + 3*q^(-11/2) - q^(-15/2) - q^(-17/2))*x1^(9)*x2 + (q^(-13/2) + q^(-15/2) + 3*q^(-17/2) + 3*q^(-19/2) + 2*q^(-21/2))*x1^(9)*x2^(2) + (-q^(-15/2) - q^(-17/2) - 3*q^(-19/2) - 3*q^(-21/2) - 3*q^(-23/2) - q^(-25/2) + q^(-29/2))*x1^(9)*x2^(3) + (q^(-21/2) + q^(-23/2) + q^(-25/2) + q^(-27/2) - 2*q^(-31/2) - 2*q^(-33/2) - q^(-35/2))*x1^(9)*x2^(4) + (q^(-33/2) + 3*q^(-35/2) + 2*q^(-37/2) + q^(-39/2) + q^(-41/2))*x1^(9)*x2^(5) + (-q^(-37/2) - q^(-39/2) - q^(-41/2) - q^(-43/2) - q^(-45/2))*x1^(9)*x2^(6) + (q^(-47/2))*x1^(9)*x2^(7)
(0, -2) (1/2, 1) x1^(0)x2^(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]}
 
(q^(37/2))*x1^(-7)*x2^(9) + (-q^(27/2))*x1^(-6)*x2^(8) + (-q^(35/2) - q^(33/2) - q^(31/2) - q^(29/2) - q^(27/2))*x1^(-6)*x2^(9) + (q^(25/2) + q^(23/2))*x1^(-5)*x2^(8) + (q^(31/2) + q^(29/2) + 2*q^(27/2) + 3*q^(25/2) + q^(23/2))*x1^(-5)*x2^(9) + (q^(11/2))*x1^(-4)*x2^(6) + (q^(13/2) + q^(11/2))*x1^(-4)*x2^(7) + (-q^(21/2) + q^(15/2) + q^(13/2) + q^(11/2))*x1^(-4)*x2^(8) + (-q^(25/2) - 2*q^(23/2) - 2*q^(21/2) + q^(17/2) + q^(15/2) + q^(13/2) + q^(11/2))*x1^(-4)*x2^(9) + (-q^(5/2))*x1^(-3)*x2^(5) + (-q^(9/2) - q^(7/2) - q^(5/2))*x1^(-3)*x2^(6) + (-q^(11/2) - 3*q^(9/2) - q^(7/2) - q^(5/2))*x1^(-3)*x2^(7) + (-q^(13/2) - 3*q^(11/2) - 3*q^(9/2) - q^(7/2) - q^(5/2))*x1^(-3)*x2^(8) + (q^(19/2) - q^(15/2) - 3*q^(13/2) - 3*q^(11/2) - 3*q^(9/2) - q^(7/2) - q^(5/2))*x1^(-3)*x2^(9) + (q^(3/2))*x1^(-2)*x2^(5) + (q^(5/2) + 2*q^(3/2))*x1^(-2)*x2^(6) + (2*q^(7/2) + 2*q^(5/2) + 2*q^(3/2))*x1^(-2)*x2^(7) + (2*q^(9/2) + 3*q^(7/2) + 2*q^(5/2) + 2*q^(3/2))*x1^(-2)*x2^(8) + (2*q^(11/2) + 3*q^(9/2) + 3*q^(7/2) + q^(5/2) + q^(3/2))*x1^(-2)*x2^(9) + (q^(-3/2))*x1^(-1)*x2^(3) + (q^(-3/2))*x1^(-1)*x2^(4) + (q^(-3/2))*x1^(-1)*x2^(5) + (-q^(1/2) + q^(-3/2))*x1^(-1)*x2^(6) + (-q^(3/2) - q^(1/2) + q^(-3/2))*x1^(-1)*x2^(7) + (-q^(5/2) - q^(3/2) + q^(-1/2) + 2*q^(-3/2))*x1^(-1)*x2^(8) + (-q^(7/2) - q^(5/2) + 3*q^(1/2) + 3*q^(-1/2) + 3*q^(-3/2) + q^(-5/2))*x1^(-1)*x2^(9) + (-q^(-5/2))*x2^(2) + (-q^(-5/2))*x2^(3) + (-2*q^(-5/2))*x2^(4) + (-2*q^(-5/2))*x2^(5) + (-2*q^(-5/2))*x2^(6) + (-3*q^(-5/2))*x2^(7) + (-q^(-3/2) - 5*q^(-5/2) - q^(-7/2))*x2^(8) + (-2*q^(-1/2) - 4*q^(-3/2) - 8*q^(-5/2) - 4*q^(-7/2) - 2*q^(-9/2))*x2^(9) + (q^(-7/2))*x1*x2^(3) + (q^(-7/2))*x1*x2^(4) + (q^(-7/2))*x1*x2^(5) + (q^(-7/2) - q^(-11/2))*x1*x2^(6) + (q^(-7/2) - q^(-11/2) - q^(-13/2))*x1*x2^(7) + (2*q^(-7/2) + q^(-9/2) - q^(-13/2) - q^(-15/2))*x1*x2^(8) + (q^(-5/2) + 3*q^(-7/2) + 3*q^(-9/2) + 3*q^(-11/2) - q^(-15/2) - q^(-17/2))*x1*x2^(9) + (q^(-13/2))*x1^(2)*x2^(5) + (2*q^(-13/2) + q^(-15/2))*x1^(2)*x2^(6) + (2*q^(-13/2) + 2*q^(-15/2) + 2*q^(-17/2))*x1^(2)*x2^(7) + (2*q^(-13/2) + 2*q^(-15/2) + 3*q^(-17/2) + 2*q^(-19/2))*x1^(2)*x2^(8) + (q^(-13/2) + q^(-15/2) + 3*q^(-17/2) + 3*q^(-19/2) + 2*q^(-21/2))*x1^(2)*x2^(9) + (-q^(-15/2))*x1^(3)*x2^(5) + (-q^(-15/2) - q^(-17/2) - q^(-19/2))*x1^(3)*x2^(6) + (-q^(-15/2) - q^(-17/2) - 3*q^(-19/2) - q^(-21/2))*x1^(3)*x2^(7) + (-q^(-15/2) - q^(-17/2) - 3*q^(-19/2) - 3*q^(-21/2) - q^(-23/2))*x1^(3)*x2^(8) + (-q^(-15/2) - q^(-17/2) - 3*q^(-19/2) - 3*q^(-21/2) - 3*q^(-23/2) - q^(-25/2) + q^(-29/2))*x1^(3)*x2^(9) + (q^(-21/2))*x1^(4)*x2^(6) + (q^(-21/2) + q^(-23/2))*x1^(4)*x2^(7) + (q^(-21/2) + q^(-23/2) + q^(-25/2) - q^(-31/2))*x1^(4)*x2^(8) + (q^(-21/2) + q^(-23/2) + q^(-25/2) + q^(-27/2) - 2*q^(-31/2) - 2*q^(-33/2) - q^(-35/2))*x1^(4)*x2^(9) + (q^(-33/2) + q^(-35/2))*x1^(5)*x2^(8) + (q^(-33/2) + 3*q^(-35/2) + 2*q^(-37/2) + q^(-39/2) + q^(-41/2))*x1^(5)*x2^(9) + (-q^(-37/2))*x1^(6)*x2^(8) + (-q^(-37/2) - q^(-39/2) - q^(-41/2) - q^(-43/2) - q^(-45/2))*x1^(6)*x2^(9) + (q^(-47/2))*x1^(7)*x2^(9)
(2, 0) x1^(-2)x2^(0) q^(-5/2) 
(-q^(-5/2))*x1^(-2) + (q^(-3/2))*x1^(-3)*x2 + (-q^(-5/2))*x1^(-3) + (q^(-7/2))*x1^(-3)*x2^(-1) + (q^(-3/2))*x1^(-4)*x2 + (-2*q^(-5/2))*x1^(-4) + (q^(-7/2))*x1^(-4)*x2^(-1) + (-q^(5/2))*x1^(-5)*x2^(3) + (q^(3/2))*x1^(-5)*x2^(2) + (q^(-3/2))*x1^(-5)*x2 + (-2*q^(-5/2))*x1^(-5) + (q^(-7/2))*x1^(-5)*x2^(-1) + (q^(-13/2))*x1^(-5)*x2^(-2) + (-q^(-15/2))*x1^(-5)*x2^(-3) + (q^(11/2))*x1^(-6)*x2^(4) + (-q^(9/2) - q^(7/2) - q^(5/2))*x1^(-6)*x2^(3) + (q^(5/2) + 2*q^(3/2))*x1^(-6)*x2^(2) + (-q^(1/2) + q^(-3/2))*x1^(-6)*x2 + (-2*q^(-5/2))*x1^(-6) + (q^(-7/2) - q^(-11/2))*x1^(-6)*x2^(-1) + (2*q^(-13/2) + q^(-15/2))*x1^(-6)*x2^(-2) + (-q^(-15/2) - q^(-17/2) - q^(-19/2))*x1^(-6)*x2^(-3) + (q^(-21/2))*x1^(-6)*x2^(-4) + (q^(13/2) + q^(11/2))*x1^(-7)*x2^(4) + (-q^(11/2) - 3*q^(9/2) - q^(7/2) - q^(5/2))*x1^(-7)*x2^(3) + (2*q^(7/2) + 2*q^(5/2) + 2*q^(3/2))*x1^(-7)*x2^(2) + (-q^(3/2) - q^(1/2) + q^(-3/2))*x1^(-7)*x2 + (-3*q^(-5/2))*x1^(-7) + (q^(-7/2) - q^(-11/2) - q^(-13/2))*x1^(-7)*x2^(-1) + (2*q^(-13/2) + 2*q^(-15/2) + 2*q^(-17/2))*x1^(-7)*x2^(-2) + (-q^(-15/2) - q^(-17/2) - 3*q^(-19/2) - q^(-21/2))*x1^(-7)*x2^(-3) + (q^(-21/2) + q^(-23/2))*x1^(-7)*x2^(-4) + (-q^(27/2))*x1^(-8)*x2^(6) + (q^(25/2) + q^(23/2))*x1^(-8)*x2^(5) + (-q^(21/2) + q^(15/2) + q^(13/2) + q^(11/2))*x1^(-8)*x2^(4) + (-q^(13/2) - 3*q^(11/2) - 3*q^(9/2) - q^(7/2) - q^(5/2))*x1^(-8)*x2^(3) + (2*q^(9/2) + 3*q^(7/2) + 2*q^(5/2) + 2*q^(3/2))*x1^(-8)*x2^(2) + (-q^(5/2) - q^(3/2) + q^(-1/2) + 2*q^(-3/2))*x1^(-8)*x2 + (-q^(-3/2) - 5*q^(-5/2) - q^(-7/2))*x1^(-8) + (2*q^(-7/2) + q^(-9/2) - q^(-13/2) - q^(-15/2))*x1^(-8)*x2^(-1) + (2*q^(-13/2) + 2*q^(-15/2) + 3*q^(-17/2) + 2*q^(-19/2))*x1^(-8)*x2^(-2) + (-q^(-15/2) - q^(-17/2) - 3*q^(-19/2) - 3*q^(-21/2) - q^(-23/2))*x1^(-8)*x2^(-3) + (q^(-21/2) + q^(-23/2) + q^(-25/2) - q^(-31/2))*x1^(-8)*x2^(-4) + (q^(-33/2) + q^(-35/2))*x1^(-8)*x2^(-5) + (-q^(-37/2))*x1^(-8)*x2^(-6) + (q^(37/2))*x1^(-9)*x2^(7) + (-q^(35/2) - q^(33/2) - q^(31/2) - q^(29/2) - q^(27/2))*x1^(-9)*x2^(6) + (q^(31/2) + q^(29/2) + 2*q^(27/2) + 3*q^(25/2) + q^(23/2))*x1^(-9)*x2^(5) + (-q^(25/2) - 2*q^(23/2) - 2*q^(21/2) + q^(17/2) + q^(15/2) + q^(13/2) + q^(11/2))*x1^(-9)*x2^(4) + (q^(19/2) - q^(15/2) - 3*q^(13/2) - 3*q^(11/2) - 3*q^(9/2) - q^(7/2) - q^(5/2))*x1^(-9)*x2^(3) + (2*q^(11/2) + 3*q^(9/2) + 3*q^(7/2) + q^(5/2) + q^(3/2))*x1^(-9)*x2^(2) + (-q^(7/2) - q^(5/2) + 3*q^(1/2) + 3*q^(-1/2) + 3*q^(-3/2) + q^(-5/2))*x1^(-9)*x2 + (-2*q^(-1/2) - 4*q^(-3/2) - 8*q^(-5/2) - 4*q^(-7/2) - 2*q^(-9/2))*x1^(-9) + (q^(-5/2) + 3*q^(-7/2) + 3*q^(-9/2) + 3*q^(-11/2) - q^(-15/2) - q^(-17/2))*x1^(-9)*x2^(-1) + (q^(-13/2) + q^(-15/2) + 3*q^(-17/2) + 3*q^(-19/2) + 2*q^(-21/2))*x1^(-9)*x2^(-2) + (-q^(-15/2) - q^(-17/2) - 3*q^(-19/2) - 3*q^(-21/2) - 3*q^(-23/2) - q^(-25/2) + q^(-29/2))*x1^(-9)*x2^(-3) + (q^(-21/2) + q^(-23/2) + q^(-25/2) + q^(-27/2) - 2*q^(-31/2) - 2*q^(-33/2) - q^(-35/2))*x1^(-9)*x2^(-4) + (q^(-33/2) + 3*q^(-35/2) + 2*q^(-37/2) + q^(-39/2) + q^(-41/2))*x1^(-9)*x2^(-5) + (-q^(-37/2) - q^(-39/2) - q^(-41/2) - q^(-43/2) - q^(-45/2))*x1^(-9)*x2^(-6) + (q^(-47/2))*x1^(-9)*x2^(-7)
(0, 2) x1^(0)x2^(-2) q^(-5/2) 
(q^(37/2))*x1^(7)*x2^(-9) + (-q^(27/2))*x1^(6)*x2^(-8) + (-q^(35/2) - q^(33/2) - q^(31/2) - q^(29/2) - q^(27/2))*x1^(6)*x2^(-9) + (q^(25/2) + q^(23/2))*x1^(5)*x2^(-8) + (q^(31/2) + q^(29/2) + 2*q^(27/2) + 3*q^(25/2) + q^(23/2))*x1^(5)*x2^(-9) + (q^(11/2))*x1^(4)*x2^(-6) + (q^(13/2) + q^(11/2))*x1^(4)*x2^(-7) + (-q^(21/2) + q^(15/2) + q^(13/2) + q^(11/2))*x1^(4)*x2^(-8) + (-q^(25/2) - 2*q^(23/2) - 2*q^(21/2) + q^(17/2) + q^(15/2) + q^(13/2) + q^(11/2))*x1^(4)*x2^(-9) + (-q^(5/2))*x1^(3)*x2^(-5) + (-q^(9/2) - q^(7/2) - q^(5/2))*x1^(3)*x2^(-6) + (-q^(11/2) - 3*q^(9/2) - q^(7/2) - q^(5/2))*x1^(3)*x2^(-7) + (-q^(13/2) - 3*q^(11/2) - 3*q^(9/2) - q^(7/2) - q^(5/2))*x1^(3)*x2^(-8) + (q^(19/2) - q^(15/2) - 3*q^(13/2) - 3*q^(11/2) - 3*q^(9/2) - q^(7/2) - q^(5/2))*x1^(3)*x2^(-9) + (q^(3/2))*x1^(2)*x2^(-5) + (q^(5/2) + 2*q^(3/2))*x1^(2)*x2^(-6) + (2*q^(7/2) + 2*q^(5/2) + 2*q^(3/2))*x1^(2)*x2^(-7) + (2*q^(9/2) + 3*q^(7/2) + 2*q^(5/2) + 2*q^(3/2))*x1^(2)*x2^(-8) + (2*q^(11/2) + 3*q^(9/2) + 3*q^(7/2) + q^(5/2) + q^(3/2))*x1^(2)*x2^(-9) + (q^(-3/2))*x1*x2^(-3) + (q^(-3/2))*x1*x2^(-4) + (q^(-3/2))*x1*x2^(-5) + (-q^(1/2) + q^(-3/2))*x1*x2^(-6) + (-q^(3/2) - q^(1/2) + q^(-3/2))*x1*x2^(-7) + (-q^(5/2) - q^(3/2) + q^(-1/2) + 2*q^(-3/2))*x1*x2^(-8) + (-q^(7/2) - q^(5/2) + 3*q^(1/2) + 3*q^(-1/2) + 3*q^(-3/2) + q^(-5/2))*x1*x2^(-9) + (-q^(-5/2))*x2^(-2) + (-q^(-5/2))*x2^(-3) + (-2*q^(-5/2))*x2^(-4) + (-2*q^(-5/2))*x2^(-5) + (-2*q^(-5/2))*x2^(-6) + (-3*q^(-5/2))*x2^(-7) + (-q^(-3/2) - 5*q^(-5/2) - q^(-7/2))*x2^(-8) + (-2*q^(-1/2) - 4*q^(-3/2) - 8*q^(-5/2) - 4*q^(-7/2) - 2*q^(-9/2))*x2^(-9) + (q^(-7/2))*x1^(-1)*x2^(-3) + (q^(-7/2))*x1^(-1)*x2^(-4) + (q^(-7/2))*x1^(-1)*x2^(-5) + (q^(-7/2) - q^(-11/2))*x1^(-1)*x2^(-6) + (q^(-7/2) - q^(-11/2) - q^(-13/2))*x1^(-1)*x2^(-7) + (2*q^(-7/2) + q^(-9/2) - q^(-13/2) - q^(-15/2))*x1^(-1)*x2^(-8) + (q^(-5/2) + 3*q^(-7/2) + 3*q^(-9/2) + 3*q^(-11/2) - q^(-15/2) - q^(-17/2))*x1^(-1)*x2^(-9) + (q^(-13/2))*x1^(-2)*x2^(-5) + (2*q^(-13/2) + q^(-15/2))*x1^(-2)*x2^(-6) + (2*q^(-13/2) + 2*q^(-15/2) + 2*q^(-17/2))*x1^(-2)*x2^(-7) + (2*q^(-13/2) + 2*q^(-15/2) + 3*q^(-17/2) + 2*q^(-19/2))*x1^(-2)*x2^(-8) + (q^(-13/2) + q^(-15/2) + 3*q^(-17/2) + 3*q^(-19/2) + 2*q^(-21/2))*x1^(-2)*x2^(-9) + (-q^(-15/2))*x1^(-3)*x2^(-5) + (-q^(-15/2) - q^(-17/2) - q^(-19/2))*x1^(-3)*x2^(-6) + (-q^(-15/2) - q^(-17/2) - 3*q^(-19/2) - q^(-21/2))*x1^(-3)*x2^(-7) + (-q^(-15/2) - q^(-17/2) - 3*q^(-19/2) - 3*q^(-21/2) - q^(-23/2))*x1^(-3)*x2^(-8) + (-q^(-15/2) - q^(-17/2) - 3*q^(-19/2) - 3*q^(-21/2) - 3*q^(-23/2) - q^(-25/2) + q^(-29/2))*x1^(-3)*x2^(-9) + (q^(-21/2))*x1^(-4)*x2^(-6) + (q^(-21/2) + q^(-23/2))*x1^(-4)*x2^(-7) + (q^(-21/2) + q^(-23/2) + q^(-25/2) - q^(-31/2))*x1^(-4)*x2^(-8) + (q^(-21/2) + q^(-23/2) + q^(-25/2) + q^(-27/2) - 2*q^(-31/2) - 2*q^(-33/2) - q^(-35/2))*x1^(-4)*x2^(-9) + (q^(-33/2) + q^(-35/2))*x1^(-5)*x2^(-8) + (q^(-33/2) + 3*q^(-35/2) + 2*q^(-37/2) + q^(-39/2) + q^(-41/2))*x1^(-5)*x2^(-9) + (-q^(-37/2))*x1^(-6)*x2^(-8) + (-q^(-37/2) - q^(-39/2) - q^(-41/2) - q^(-43/2) - q^(-45/2))*x1^(-6)*x2^(-9) + (q^(-47/2))*x1^(-7)*x2^(-9)

Braid

Braid word Components Crossings Strands
[-1, -2, -3, -3, -3, -3, -3, -3, -2, -1, 2, 3] 2 12 4

Multivariable Alexander polynomial

ΔL
-A1^(2) - A1*A2 + A1 - A1*A2^(-1) - A2^(2) + A2 - 1 + A2^(-1) - A2^(-2) - A1^(-1)*A2 + A1^(-1) - A1^(-1)*A2^(-1) - A1^(-2)

Warning: the A1, A2, … basis used for the HFL and Alexander data might not match the x1, x2, … basis used for FL.

Newton Polygon of Alexander-202-202A1A2

Dual Thurston polytope

VertexDual to fibered face
(0, -4) yes
(4, 0) yes
(0, 4) yes
(-4, 0) yes
Dual Thurston polygon-505-505h1h2

HFL polytope

Poincaré polynomial
m^(-1)*A1^(-5/2)*A2^(-1/2) + m^(-1)*A1^(-3/2)*A2^(-3/2) + m^(-1)*A1^(-1/2)*A2^(-5/2) + A1^(-5/2)*A2^(1/2) + 3*A1^(-3/2)*A2^(-1/2) + 3*A1^(-1/2)*A2^(-3/2) + A1^(1/2)*A2^(-5/2) + 3*m*A1^(-3/2)*A2^(1/2) + 4*m*A1^(-1/2)*A2^(-1/2) + 3*m*A1^(1/2)*A2^(-3/2) + m^2*A1^(-3/2)*A2^(3/2) + 4*m^2*A1^(-1/2)*A2^(1/2) + 4*m^2*A1^(1/2)*A2^(-1/2) + m^2*A1^(3/2)*A2^(-3/2) + 3*m^3*A1^(-1/2)*A2^(3/2) + 4*m^3*A1^(1/2)*A2^(1/2) + 3*m^3*A1^(3/2)*A2^(-1/2) + m^4*A1^(-1/2)*A2^(5/2) + 3*m^4*A1^(1/2)*A2^(3/2) + 3*m^4*A1^(3/2)*A2^(1/2) + m^4*A1^(5/2)*A2^(-1/2) + m^5*A1^(1/2)*A2^(5/2) + m^5*A1^(3/2)*A2^(3/2) + m^5*A1^(5/2)*A2^(1/2)
VertexMaslovRank
(-5/2, -1/2)-11
(-1/2, -5/2)-11
(1/2, -5/2)01
(5/2, -1/2)41
(5/2, 1/2)51
(1/2, 5/2)51
(-1/2, 5/2)41
(-5/2, 1/2)01
HFL polytope-202-202A1A2

Record

FL/HFL Links

orderOption(int) 283
namestring L10a120{0}
statusstring success
slugstring L10a120_0_29ff7351
result_filestring details/L10a120_0_29ff7351.json
complexity_scoreOption(int) 200
strandsOption(int) null
crossingsOption(int) 10
component_countOption(int) 2
girthOption(int) 4
total_rankOption(int) 52
wall_secondsOption(float) 0.001543
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 2
support_sizeOption(int) 24
vertex_countOption(int) 8
fibered_vertex_countOption(int) 4
polytope_statusstring computed
alexander_support_sizeOption(int) 13
alexander_vertex_countOption(int) 4
alexander_relationstring not_computed
fk_countint 4
detailsRowRef(FLHFLLinks) 
{
  "dataset": "FLHFLLinks",
  "key": "L10a120_0_29ff7351"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L10a120_0_29ff7351