L9n16{0} - HFL and FL

details/L9n16_0_7f0b0741.json

F_L expansions

Newt(Δ_L) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle F_L

Newt(Δ_L) vertex	Exposing functional	Leading x-power	Leading q-power	Inversion datum	F_L
`(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]}`	(-q^(17/2))x1^(-2)x2^(8) + (-q^(21/2) - q^(19/2) - q^(17/2))x1^(-2)x2^(9) + (q^(5/2))x1^(-1)x2^(5) + (q^(7/2) + q^(5/2))x1^(-1)x2^(6) + (-q^(11/2) + q^(7/2) + q^(5/2))x1^(-1)x2^(7) + (-q^(13/2) - q^(11/2) + q^(7/2) + q^(5/2))x1^(-1)x2^(8) + (q^(19/2) + q^(17/2) + q^(15/2) - q^(13/2) - q^(11/2) + q^(7/2) + q^(5/2))x1^(-1)x2^(9) + (-q^(-1/2))x2^(2) + (-q^(-1/2))x2^(3) + (q^(1/2) - q^(-1/2))x2^(4) + (q^(1/2) - q^(-1/2))x2^(5) + (-q^(5/2) - q^(3/2) + q^(1/2) - q^(-1/2))x2^(6) + (-2q^(5/2) - 2q^(3/2) - q^(-1/2))x2^(7) + (q^(11/2) + q^(9/2) + q^(7/2) - 2q^(5/2) - 3q^(3/2) - q^(1/2) - 2q^(-1/2))x2^(8) + (2q^(11/2) + 3q^(9/2) + 3q^(7/2) - q^(5/2) - 3q^(3/2) - 2q^(1/2) - 3q^(-1/2) - q^(-3/2))x2^(9) + (q^(-3/2))x1x2^(3) + (q^(-3/2) + q^(-5/2))x1x2^(4) + (-q^(-1/2) + q^(-5/2) + q^(-7/2))x1x2^(5) + (-q^(-1/2) - q^(-3/2) + q^(-7/2) + q^(-9/2))x1x2^(6) + (q^(3/2) + q^(1/2) + q^(-1/2) - q^(-3/2) - q^(-5/2) + q^(-9/2) + q^(-11/2))x1x2^(7) + (q^(3/2) + 3q^(1/2) + 3q^(-1/2) + 2q^(-3/2) - q^(-7/2) + q^(-11/2) + q^(-13/2))x1x2^(8) + (-q^(9/2) - q^(7/2) - 2q^(5/2) - q^(3/2) + 2q^(1/2) + 5q^(-1/2) + 5q^(-3/2) + 4q^(-5/2) + q^(-7/2) + q^(-13/2) + q^(-15/2))x1x2^(9) + (-q^(-7/2))x1^(2)x2^(4) + (-q^(-7/2) - q^(-9/2) - q^(-11/2))x1^(2)x2^(5) + (q^(-5/2) - 2q^(-11/2) - q^(-13/2) - q^(-15/2))x1^(2)x2^(6) + (q^(-5/2) + q^(-7/2) + 2q^(-9/2) - q^(-13/2) - 2q^(-15/2) - q^(-17/2) - q^(-19/2))x1^(2)x2^(7) + (-q^(-1/2) - q^(-3/2) - q^(-5/2) - q^(-7/2) + 2q^(-9/2) + 2q^(-11/2) + 2q^(-13/2) - q^(-15/2) - q^(-17/2) - 2q^(-19/2) - q^(-21/2) - q^(-23/2))x1^(2)x2^(8) + (-q^(-1/2) - 2q^(-3/2) - 4q^(-5/2) - 5q^(-7/2) - 3q^(-9/2) - q^(-11/2) + 2q^(-13/2) + 2q^(-15/2) + q^(-17/2) - q^(-19/2) - q^(-21/2) - 2q^(-23/2) - q^(-25/2) - q^(-27/2))x1^(2)x2^(9) + (q^(-13/2))x1^(3)x2^(5) + (q^(-13/2) + q^(-15/2) + q^(-17/2) + q^(-19/2))x1^(3)x2^(6) + (-q^(-11/2) + q^(-17/2) + 2q^(-19/2) + 2q^(-21/2) + q^(-23/2) + q^(-25/2))x1^(3)x2^(7) + (-q^(-11/2) - q^(-13/2) - 2q^(-15/2) - 2q^(-17/2) + q^(-21/2) + 2q^(-23/2) + 3q^(-25/2) + 2q^(-27/2) + q^(-29/2) + q^(-31/2))x1^(3)x2^(8) + (q^(-7/2) + q^(-9/2) + q^(-11/2) + q^(-13/2) - 3q^(-17/2) - 3q^(-19/2) - 3q^(-21/2) - 2q^(-23/2) + q^(-25/2) + 2q^(-27/2) + 3q^(-29/2) + 3q^(-31/2) + 2q^(-33/2) + q^(-35/2) + q^(-37/2))x1^(3)x2^(9) + (-q^(-21/2))x1^(4)x2^(6) + (-q^(-21/2) - q^(-23/2) - q^(-25/2) - q^(-27/2) - q^(-29/2))x1^(4)x2^(7) + (q^(-19/2) - q^(-25/2) - q^(-27/2) - 3q^(-29/2) - 2q^(-31/2) - 2q^(-33/2) - q^(-35/2) - q^(-37/2))x1^(4)x2^(8) + (q^(-19/2) + q^(-21/2) + 2q^(-23/2) + 2q^(-25/2) + 2q^(-27/2) - q^(-31/2) - 3q^(-33/2) - 3q^(-35/2) - 4q^(-37/2) - 3q^(-39/2) - 2q^(-41/2) - q^(-43/2) - q^(-45/2))x1^(4)x2^(9) + (q^(-31/2))x1^(5)x2^(7) + (q^(-31/2) + q^(-33/2) + q^(-35/2) + q^(-37/2) + q^(-39/2) + q^(-41/2))x1^(5)x2^(8) + (-q^(-29/2) + q^(-35/2) + q^(-37/2) + 2q^(-39/2) + 3q^(-41/2) + 3q^(-43/2) + 2q^(-45/2) + 2q^(-47/2) + q^(-49/2) + q^(-51/2))x1^(5)x2^(9) + (-q^(-43/2))x1^(6)x2^(8) + (-q^(-43/2) - q^(-45/2) - q^(-47/2) - q^(-49/2) - q^(-51/2) - q^(-53/2) - q^(-55/2))x1^(6)x2^(9) + (q^(-57/2))x1^(7)x2^(9)
`(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]}`	(-q^(17/2))x1^(-2)x2^(8) + (-q^(21/2) - q^(19/2) - q^(17/2))x1^(-2)x2^(9) + (q^(5/2))x1^(-1)x2^(5) + (q^(7/2) + q^(5/2))x1^(-1)x2^(6) + (-q^(11/2) + q^(7/2) + q^(5/2))x1^(-1)x2^(7) + (-q^(13/2) - q^(11/2) + q^(7/2) + q^(5/2))x1^(-1)x2^(8) + (q^(19/2) + q^(17/2) + q^(15/2) - q^(13/2) - q^(11/2) + q^(7/2) + q^(5/2))x1^(-1)x2^(9) + (-q^(-1/2))x2^(2) + (-q^(-1/2))x2^(3) + (q^(1/2) - q^(-1/2))x2^(4) + (q^(1/2) - q^(-1/2))x2^(5) + (-q^(5/2) - q^(3/2) + q^(1/2) - q^(-1/2))x2^(6) + (-2q^(5/2) - 2q^(3/2) - q^(-1/2))x2^(7) + (q^(11/2) + q^(9/2) + q^(7/2) - 2q^(5/2) - 3q^(3/2) - q^(1/2) - 2q^(-1/2))x2^(8) + (2q^(11/2) + 3q^(9/2) + 3q^(7/2) - q^(5/2) - 3q^(3/2) - 2q^(1/2) - 3q^(-1/2) - q^(-3/2))x2^(9) + (q^(-3/2))x1x2^(3) + (q^(-3/2) + q^(-5/2))x1x2^(4) + (-q^(-1/2) + q^(-5/2) + q^(-7/2))x1x2^(5) + (-q^(-1/2) - q^(-3/2) + q^(-7/2) + q^(-9/2))x1x2^(6) + (q^(3/2) + q^(1/2) + q^(-1/2) - q^(-3/2) - q^(-5/2) + q^(-9/2) + q^(-11/2))x1x2^(7) + (q^(3/2) + 3q^(1/2) + 3q^(-1/2) + 2q^(-3/2) - q^(-7/2) + q^(-11/2) + q^(-13/2))x1x2^(8) + (-q^(9/2) - q^(7/2) - 2q^(5/2) - q^(3/2) + 2q^(1/2) + 5q^(-1/2) + 5q^(-3/2) + 4q^(-5/2) + q^(-7/2) + q^(-13/2) + q^(-15/2))x1x2^(9) + (-q^(-7/2))x1^(2)x2^(4) + (-q^(-7/2) - q^(-9/2) - q^(-11/2))x1^(2)x2^(5) + (q^(-5/2) - 2q^(-11/2) - q^(-13/2) - q^(-15/2))x1^(2)x2^(6) + (q^(-5/2) + q^(-7/2) + 2q^(-9/2) - q^(-13/2) - 2q^(-15/2) - q^(-17/2) - q^(-19/2))x1^(2)x2^(7) + (-q^(-1/2) - q^(-3/2) - q^(-5/2) - q^(-7/2) + 2q^(-9/2) + 2q^(-11/2) + 2q^(-13/2) - q^(-15/2) - q^(-17/2) - 2q^(-19/2) - q^(-21/2) - q^(-23/2))x1^(2)x2^(8) + (-q^(-1/2) - 2q^(-3/2) - 4q^(-5/2) - 5q^(-7/2) - 3q^(-9/2) - q^(-11/2) + 2q^(-13/2) + 2q^(-15/2) + q^(-17/2) - q^(-19/2) - q^(-21/2) - 2q^(-23/2) - q^(-25/2) - q^(-27/2))x1^(2)x2^(9) + (q^(-13/2))x1^(3)x2^(5) + (q^(-13/2) + q^(-15/2) + q^(-17/2) + q^(-19/2))x1^(3)x2^(6) + (-q^(-11/2) + q^(-17/2) + 2q^(-19/2) + 2q^(-21/2) + q^(-23/2) + q^(-25/2))x1^(3)x2^(7) + (-q^(-11/2) - q^(-13/2) - 2q^(-15/2) - 2q^(-17/2) + q^(-21/2) + 2q^(-23/2) + 3q^(-25/2) + 2q^(-27/2) + q^(-29/2) + q^(-31/2))x1^(3)x2^(8) + (q^(-7/2) + q^(-9/2) + q^(-11/2) + q^(-13/2) - 3q^(-17/2) - 3q^(-19/2) - 3q^(-21/2) - 2q^(-23/2) + q^(-25/2) + 2q^(-27/2) + 3q^(-29/2) + 3q^(-31/2) + 2q^(-33/2) + q^(-35/2) + q^(-37/2))x1^(3)x2^(9) + (-q^(-21/2))x1^(4)x2^(6) + (-q^(-21/2) - q^(-23/2) - q^(-25/2) - q^(-27/2) - q^(-29/2))x1^(4)x2^(7) + (q^(-19/2) - q^(-25/2) - q^(-27/2) - 3q^(-29/2) - 2q^(-31/2) - 2q^(-33/2) - q^(-35/2) - q^(-37/2))x1^(4)x2^(8) + (q^(-19/2) + q^(-21/2) + 2q^(-23/2) + 2q^(-25/2) + 2q^(-27/2) - q^(-31/2) - 3q^(-33/2) - 3q^(-35/2) - 4q^(-37/2) - 3q^(-39/2) - 2q^(-41/2) - q^(-43/2) - q^(-45/2))x1^(4)x2^(9) + (q^(-31/2))x1^(5)x2^(7) + (q^(-31/2) + q^(-33/2) + q^(-35/2) + q^(-37/2) + q^(-39/2) + q^(-41/2))x1^(5)x2^(8) + (-q^(-29/2) + q^(-35/2) + q^(-37/2) + 2q^(-39/2) + 3q^(-41/2) + 3q^(-43/2) + 2q^(-45/2) + 2q^(-47/2) + q^(-49/2) + q^(-51/2))x1^(5)x2^(9) + (-q^(-43/2))x1^(6)x2^(8) + (-q^(-43/2) - q^(-45/2) - q^(-47/2) - q^(-49/2) - q^(-51/2) - q^(-53/2) - q^(-55/2))x1^(6)x2^(9) + (q^(-57/2))x1^(7)x2^(9)
`(0, 2)`		`x1^(0)x2^(-2)`	`q^(-1/2)`		(-q^(17/2))x1^(2)x2^(-8) + (-q^(21/2) - q^(19/2) - q^(17/2))x1^(2)x2^(-9) + (q^(5/2))x1x2^(-5) + (q^(7/2) + q^(5/2))x1x2^(-6) + (-q^(11/2) + q^(7/2) + q^(5/2))x1x2^(-7) + (-q^(13/2) - q^(11/2) + q^(7/2) + q^(5/2))x1x2^(-8) + (q^(19/2) + q^(17/2) + q^(15/2) - q^(13/2) - q^(11/2) + q^(7/2) + q^(5/2))x1x2^(-9) + (-q^(-1/2))x2^(-2) + (-q^(-1/2))x2^(-3) + (q^(1/2) - q^(-1/2))x2^(-4) + (q^(1/2) - q^(-1/2))x2^(-5) + (-q^(5/2) - q^(3/2) + q^(1/2) - q^(-1/2))x2^(-6) + (-2q^(5/2) - 2q^(3/2) - q^(-1/2))x2^(-7) + (q^(11/2) + q^(9/2) + q^(7/2) - 2q^(5/2) - 3q^(3/2) - q^(1/2) - 2q^(-1/2))x2^(-8) + (2q^(11/2) + 3q^(9/2) + 3q^(7/2) - q^(5/2) - 3q^(3/2) - 2q^(1/2) - 3q^(-1/2) - q^(-3/2))x2^(-9) + (q^(-3/2))x1^(-1)x2^(-3) + (q^(-3/2) + q^(-5/2))x1^(-1)x2^(-4) + (-q^(-1/2) + q^(-5/2) + q^(-7/2))x1^(-1)x2^(-5) + (-q^(-1/2) - q^(-3/2) + q^(-7/2) + q^(-9/2))x1^(-1)x2^(-6) + (q^(3/2) + q^(1/2) + q^(-1/2) - q^(-3/2) - q^(-5/2) + q^(-9/2) + q^(-11/2))x1^(-1)x2^(-7) + (q^(3/2) + 3q^(1/2) + 3q^(-1/2) + 2q^(-3/2) - q^(-7/2) + q^(-11/2) + q^(-13/2))x1^(-1)x2^(-8) + (-q^(9/2) - q^(7/2) - 2q^(5/2) - q^(3/2) + 2q^(1/2) + 5q^(-1/2) + 5q^(-3/2) + 4q^(-5/2) + q^(-7/2) + q^(-13/2) + q^(-15/2))x1^(-1)x2^(-9) + (-q^(-7/2))x1^(-2)x2^(-4) + (-q^(-7/2) - q^(-9/2) - q^(-11/2))x1^(-2)x2^(-5) + (q^(-5/2) - 2q^(-11/2) - q^(-13/2) - q^(-15/2))x1^(-2)x2^(-6) + (q^(-5/2) + q^(-7/2) + 2q^(-9/2) - q^(-13/2) - 2q^(-15/2) - q^(-17/2) - q^(-19/2))x1^(-2)x2^(-7) + (-q^(-1/2) - q^(-3/2) - q^(-5/2) - q^(-7/2) + 2q^(-9/2) + 2q^(-11/2) + 2q^(-13/2) - q^(-15/2) - q^(-17/2) - 2q^(-19/2) - q^(-21/2) - q^(-23/2))x1^(-2)x2^(-8) + (-q^(-1/2) - 2q^(-3/2) - 4q^(-5/2) - 5q^(-7/2) - 3q^(-9/2) - q^(-11/2) + 2q^(-13/2) + 2q^(-15/2) + q^(-17/2) - q^(-19/2) - q^(-21/2) - 2q^(-23/2) - q^(-25/2) - q^(-27/2))x1^(-2)x2^(-9) + (q^(-13/2))x1^(-3)x2^(-5) + (q^(-13/2) + q^(-15/2) + q^(-17/2) + q^(-19/2))x1^(-3)x2^(-6) + (-q^(-11/2) + q^(-17/2) + 2q^(-19/2) + 2q^(-21/2) + q^(-23/2) + q^(-25/2))x1^(-3)x2^(-7) + (-q^(-11/2) - q^(-13/2) - 2q^(-15/2) - 2q^(-17/2) + q^(-21/2) + 2q^(-23/2) + 3q^(-25/2) + 2q^(-27/2) + q^(-29/2) + q^(-31/2))x1^(-3)x2^(-8) + (q^(-7/2) + q^(-9/2) + q^(-11/2) + q^(-13/2) - 3q^(-17/2) - 3q^(-19/2) - 3q^(-21/2) - 2q^(-23/2) + q^(-25/2) + 2q^(-27/2) + 3q^(-29/2) + 3q^(-31/2) + 2q^(-33/2) + q^(-35/2) + q^(-37/2))x1^(-3)x2^(-9) + (-q^(-21/2))x1^(-4)x2^(-6) + (-q^(-21/2) - q^(-23/2) - q^(-25/2) - q^(-27/2) - q^(-29/2))x1^(-4)x2^(-7) + (q^(-19/2) - q^(-25/2) - q^(-27/2) - 3q^(-29/2) - 2q^(-31/2) - 2q^(-33/2) - q^(-35/2) - q^(-37/2))x1^(-4)x2^(-8) + (q^(-19/2) + q^(-21/2) + 2q^(-23/2) + 2q^(-25/2) + 2q^(-27/2) - q^(-31/2) - 3q^(-33/2) - 3q^(-35/2) - 4q^(-37/2) - 3q^(-39/2) - 2q^(-41/2) - q^(-43/2) - q^(-45/2))x1^(-4)x2^(-9) + (q^(-31/2))x1^(-5)x2^(-7) + (q^(-31/2) + q^(-33/2) + q^(-35/2) + q^(-37/2) + q^(-39/2) + q^(-41/2))x1^(-5)x2^(-8) + (-q^(-29/2) + q^(-35/2) + q^(-37/2) + 2q^(-39/2) + 3q^(-41/2) + 3q^(-43/2) + 2q^(-45/2) + 2q^(-47/2) + q^(-49/2) + q^(-51/2))x1^(-5)x2^(-9) + (-q^(-43/2))x1^(-6)x2^(-8) + (-q^(-43/2) - q^(-45/2) - q^(-47/2) - q^(-49/2) - q^(-51/2) - q^(-53/2) - q^(-55/2))x1^(-6)x2^(-9) + (q^(-57/2))x1^(-7)x2^(-9)

(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]}

(-q^(17/2))*x1^(-2)*x2^(8) + (-q^(21/2) - q^(19/2) - q^(17/2))*x1^(-2)*x2^(9) + (q^(5/2))*x1^(-1)*x2^(5) + (q^(7/2) + q^(5/2))*x1^(-1)*x2^(6) + (-q^(11/2) + q^(7/2) + q^(5/2))*x1^(-1)*x2^(7) + (-q^(13/2) - q^(11/2) + q^(7/2) + q^(5/2))*x1^(-1)*x2^(8) + (q^(19/2) + q^(17/2) + q^(15/2) - q^(13/2) - q^(11/2) + q^(7/2) + q^(5/2))*x1^(-1)*x2^(9) + (-q^(-1/2))*x2^(2) + (-q^(-1/2))*x2^(3) + (q^(1/2) - q^(-1/2))*x2^(4) + (q^(1/2) - q^(-1/2))*x2^(5) + (-q^(5/2) - q^(3/2) + q^(1/2) - q^(-1/2))*x2^(6) + (-2*q^(5/2) - 2*q^(3/2) - q^(-1/2))*x2^(7) + (q^(11/2) + q^(9/2) + q^(7/2) - 2*q^(5/2) - 3*q^(3/2) - q^(1/2) - 2*q^(-1/2))*x2^(8) + (2*q^(11/2) + 3*q^(9/2) + 3*q^(7/2) - q^(5/2) - 3*q^(3/2) - 2*q^(1/2) - 3*q^(-1/2) - q^(-3/2))*x2^(9) + (q^(-3/2))*x1*x2^(3) + (q^(-3/2) + q^(-5/2))*x1*x2^(4) + (-q^(-1/2) + q^(-5/2) + q^(-7/2))*x1*x2^(5) + (-q^(-1/2) - q^(-3/2) + q^(-7/2) + q^(-9/2))*x1*x2^(6) + (q^(3/2) + q^(1/2) + q^(-1/2) - q^(-3/2) - q^(-5/2) + q^(-9/2) + q^(-11/2))*x1*x2^(7) + (q^(3/2) + 3*q^(1/2) + 3*q^(-1/2) + 2*q^(-3/2) - q^(-7/2) + q^(-11/2) + q^(-13/2))*x1*x2^(8) + (-q^(9/2) - q^(7/2) - 2*q^(5/2) - q^(3/2) + 2*q^(1/2) + 5*q^(-1/2) + 5*q^(-3/2) + 4*q^(-5/2) + q^(-7/2) + q^(-13/2) + q^(-15/2))*x1*x2^(9) + (-q^(-7/2))*x1^(2)*x2^(4) + (-q^(-7/2) - q^(-9/2) - q^(-11/2))*x1^(2)*x2^(5) + (q^(-5/2) - 2*q^(-11/2) - q^(-13/2) - q^(-15/2))*x1^(2)*x2^(6) + (q^(-5/2) + q^(-7/2) + 2*q^(-9/2) - q^(-13/2) - 2*q^(-15/2) - q^(-17/2) - q^(-19/2))*x1^(2)*x2^(7) + (-q^(-1/2) - q^(-3/2) - q^(-5/2) - q^(-7/2) + 2*q^(-9/2) + 2*q^(-11/2) + 2*q^(-13/2) - q^(-15/2) - q^(-17/2) - 2*q^(-19/2) - q^(-21/2) - q^(-23/2))*x1^(2)*x2^(8) + (-q^(-1/2) - 2*q^(-3/2) - 4*q^(-5/2) - 5*q^(-7/2) - 3*q^(-9/2) - q^(-11/2) + 2*q^(-13/2) + 2*q^(-15/2) + q^(-17/2) - q^(-19/2) - q^(-21/2) - 2*q^(-23/2) - q^(-25/2) - q^(-27/2))*x1^(2)*x2^(9) + (q^(-13/2))*x1^(3)*x2^(5) + (q^(-13/2) + q^(-15/2) + q^(-17/2) + q^(-19/2))*x1^(3)*x2^(6) + (-q^(-11/2) + q^(-17/2) + 2*q^(-19/2) + 2*q^(-21/2) + q^(-23/2) + q^(-25/2))*x1^(3)*x2^(7) + (-q^(-11/2) - q^(-13/2) - 2*q^(-15/2) - 2*q^(-17/2) + q^(-21/2) + 2*q^(-23/2) + 3*q^(-25/2) + 2*q^(-27/2) + q^(-29/2) + q^(-31/2))*x1^(3)*x2^(8) + (q^(-7/2) + q^(-9/2) + q^(-11/2) + q^(-13/2) - 3*q^(-17/2) - 3*q^(-19/2) - 3*q^(-21/2) - 2*q^(-23/2) + q^(-25/2) + 2*q^(-27/2) + 3*q^(-29/2) + 3*q^(-31/2) + 2*q^(-33/2) + q^(-35/2) + q^(-37/2))*x1^(3)*x2^(9) + (-q^(-21/2))*x1^(4)*x2^(6) + (-q^(-21/2) - q^(-23/2) - q^(-25/2) - q^(-27/2) - q^(-29/2))*x1^(4)*x2^(7) + (q^(-19/2) - q^(-25/2) - q^(-27/2) - 3*q^(-29/2) - 2*q^(-31/2) - 2*q^(-33/2) - q^(-35/2) - q^(-37/2))*x1^(4)*x2^(8) + (q^(-19/2) + q^(-21/2) + 2*q^(-23/2) + 2*q^(-25/2) + 2*q^(-27/2) - q^(-31/2) - 3*q^(-33/2) - 3*q^(-35/2) - 4*q^(-37/2) - 3*q^(-39/2) - 2*q^(-41/2) - q^(-43/2) - q^(-45/2))*x1^(4)*x2^(9) + (q^(-31/2))*x1^(5)*x2^(7) + (q^(-31/2) + q^(-33/2) + q^(-35/2) + q^(-37/2) + q^(-39/2) + q^(-41/2))*x1^(5)*x2^(8) + (-q^(-29/2) + q^(-35/2) + q^(-37/2) + 2*q^(-39/2) + 3*q^(-41/2) + 3*q^(-43/2) + 2*q^(-45/2) + 2*q^(-47/2) + q^(-49/2) + q^(-51/2))*x1^(5)*x2^(9) + (-q^(-43/2))*x1^(6)*x2^(8) + (-q^(-43/2) - q^(-45/2) - q^(-47/2) - q^(-49/2) - q^(-51/2) - q^(-53/2) - q^(-55/2))*x1^(6)*x2^(9) + (q^(-57/2))*x1^(7)*x2^(9)

(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]}

(-q^(17/2))*x1^(-2)*x2^(8) + (-q^(21/2) - q^(19/2) - q^(17/2))*x1^(-2)*x2^(9) + (q^(5/2))*x1^(-1)*x2^(5) + (q^(7/2) + q^(5/2))*x1^(-1)*x2^(6) + (-q^(11/2) + q^(7/2) + q^(5/2))*x1^(-1)*x2^(7) + (-q^(13/2) - q^(11/2) + q^(7/2) + q^(5/2))*x1^(-1)*x2^(8) + (q^(19/2) + q^(17/2) + q^(15/2) - q^(13/2) - q^(11/2) + q^(7/2) + q^(5/2))*x1^(-1)*x2^(9) + (-q^(-1/2))*x2^(2) + (-q^(-1/2))*x2^(3) + (q^(1/2) - q^(-1/2))*x2^(4) + (q^(1/2) - q^(-1/2))*x2^(5) + (-q^(5/2) - q^(3/2) + q^(1/2) - q^(-1/2))*x2^(6) + (-2*q^(5/2) - 2*q^(3/2) - q^(-1/2))*x2^(7) + (q^(11/2) + q^(9/2) + q^(7/2) - 2*q^(5/2) - 3*q^(3/2) - q^(1/2) - 2*q^(-1/2))*x2^(8) + (2*q^(11/2) + 3*q^(9/2) + 3*q^(7/2) - q^(5/2) - 3*q^(3/2) - 2*q^(1/2) - 3*q^(-1/2) - q^(-3/2))*x2^(9) + (q^(-3/2))*x1*x2^(3) + (q^(-3/2) + q^(-5/2))*x1*x2^(4) + (-q^(-1/2) + q^(-5/2) + q^(-7/2))*x1*x2^(5) + (-q^(-1/2) - q^(-3/2) + q^(-7/2) + q^(-9/2))*x1*x2^(6) + (q^(3/2) + q^(1/2) + q^(-1/2) - q^(-3/2) - q^(-5/2) + q^(-9/2) + q^(-11/2))*x1*x2^(7) + (q^(3/2) + 3*q^(1/2) + 3*q^(-1/2) + 2*q^(-3/2) - q^(-7/2) + q^(-11/2) + q^(-13/2))*x1*x2^(8) + (-q^(9/2) - q^(7/2) - 2*q^(5/2) - q^(3/2) + 2*q^(1/2) + 5*q^(-1/2) + 5*q^(-3/2) + 4*q^(-5/2) + q^(-7/2) + q^(-13/2) + q^(-15/2))*x1*x2^(9) + (-q^(-7/2))*x1^(2)*x2^(4) + (-q^(-7/2) - q^(-9/2) - q^(-11/2))*x1^(2)*x2^(5) + (q^(-5/2) - 2*q^(-11/2) - q^(-13/2) - q^(-15/2))*x1^(2)*x2^(6) + (q^(-5/2) + q^(-7/2) + 2*q^(-9/2) - q^(-13/2) - 2*q^(-15/2) - q^(-17/2) - q^(-19/2))*x1^(2)*x2^(7) + (-q^(-1/2) - q^(-3/2) - q^(-5/2) - q^(-7/2) + 2*q^(-9/2) + 2*q^(-11/2) + 2*q^(-13/2) - q^(-15/2) - q^(-17/2) - 2*q^(-19/2) - q^(-21/2) - q^(-23/2))*x1^(2)*x2^(8) + (-q^(-1/2) - 2*q^(-3/2) - 4*q^(-5/2) - 5*q^(-7/2) - 3*q^(-9/2) - q^(-11/2) + 2*q^(-13/2) + 2*q^(-15/2) + q^(-17/2) - q^(-19/2) - q^(-21/2) - 2*q^(-23/2) - q^(-25/2) - q^(-27/2))*x1^(2)*x2^(9) + (q^(-13/2))*x1^(3)*x2^(5) + (q^(-13/2) + q^(-15/2) + q^(-17/2) + q^(-19/2))*x1^(3)*x2^(6) + (-q^(-11/2) + q^(-17/2) + 2*q^(-19/2) + 2*q^(-21/2) + q^(-23/2) + q^(-25/2))*x1^(3)*x2^(7) + (-q^(-11/2) - q^(-13/2) - 2*q^(-15/2) - 2*q^(-17/2) + q^(-21/2) + 2*q^(-23/2) + 3*q^(-25/2) + 2*q^(-27/2) + q^(-29/2) + q^(-31/2))*x1^(3)*x2^(8) + (q^(-7/2) + q^(-9/2) + q^(-11/2) + q^(-13/2) - 3*q^(-17/2) - 3*q^(-19/2) - 3*q^(-21/2) - 2*q^(-23/2) + q^(-25/2) + 2*q^(-27/2) + 3*q^(-29/2) + 3*q^(-31/2) + 2*q^(-33/2) + q^(-35/2) + q^(-37/2))*x1^(3)*x2^(9) + (-q^(-21/2))*x1^(4)*x2^(6) + (-q^(-21/2) - q^(-23/2) - q^(-25/2) - q^(-27/2) - q^(-29/2))*x1^(4)*x2^(7) + (q^(-19/2) - q^(-25/2) - q^(-27/2) - 3*q^(-29/2) - 2*q^(-31/2) - 2*q^(-33/2) - q^(-35/2) - q^(-37/2))*x1^(4)*x2^(8) + (q^(-19/2) + q^(-21/2) + 2*q^(-23/2) + 2*q^(-25/2) + 2*q^(-27/2) - q^(-31/2) - 3*q^(-33/2) - 3*q^(-35/2) - 4*q^(-37/2) - 3*q^(-39/2) - 2*q^(-41/2) - q^(-43/2) - q^(-45/2))*x1^(4)*x2^(9) + (q^(-31/2))*x1^(5)*x2^(7) + (q^(-31/2) + q^(-33/2) + q^(-35/2) + q^(-37/2) + q^(-39/2) + q^(-41/2))*x1^(5)*x2^(8) + (-q^(-29/2) + q^(-35/2) + q^(-37/2) + 2*q^(-39/2) + 3*q^(-41/2) + 3*q^(-43/2) + 2*q^(-45/2) + 2*q^(-47/2) + q^(-49/2) + q^(-51/2))*x1^(5)*x2^(9) + (-q^(-43/2))*x1^(6)*x2^(8) + (-q^(-43/2) - q^(-45/2) - q^(-47/2) - q^(-49/2) - q^(-51/2) - q^(-53/2) - q^(-55/2))*x1^(6)*x2^(9) + (q^(-57/2))*x1^(7)*x2^(9)

(0, 2)

x1^(0)x2^(-2)

q^(-1/2)

(-q^(17/2))*x1^(2)*x2^(-8) + (-q^(21/2) - q^(19/2) - q^(17/2))*x1^(2)*x2^(-9) + (q^(5/2))*x1*x2^(-5) + (q^(7/2) + q^(5/2))*x1*x2^(-6) + (-q^(11/2) + q^(7/2) + q^(5/2))*x1*x2^(-7) + (-q^(13/2) - q^(11/2) + q^(7/2) + q^(5/2))*x1*x2^(-8) + (q^(19/2) + q^(17/2) + q^(15/2) - q^(13/2) - q^(11/2) + q^(7/2) + q^(5/2))*x1*x2^(-9) + (-q^(-1/2))*x2^(-2) + (-q^(-1/2))*x2^(-3) + (q^(1/2) - q^(-1/2))*x2^(-4) + (q^(1/2) - q^(-1/2))*x2^(-5) + (-q^(5/2) - q^(3/2) + q^(1/2) - q^(-1/2))*x2^(-6) + (-2*q^(5/2) - 2*q^(3/2) - q^(-1/2))*x2^(-7) + (q^(11/2) + q^(9/2) + q^(7/2) - 2*q^(5/2) - 3*q^(3/2) - q^(1/2) - 2*q^(-1/2))*x2^(-8) + (2*q^(11/2) + 3*q^(9/2) + 3*q^(7/2) - q^(5/2) - 3*q^(3/2) - 2*q^(1/2) - 3*q^(-1/2) - q^(-3/2))*x2^(-9) + (q^(-3/2))*x1^(-1)*x2^(-3) + (q^(-3/2) + q^(-5/2))*x1^(-1)*x2^(-4) + (-q^(-1/2) + q^(-5/2) + q^(-7/2))*x1^(-1)*x2^(-5) + (-q^(-1/2) - q^(-3/2) + q^(-7/2) + q^(-9/2))*x1^(-1)*x2^(-6) + (q^(3/2) + q^(1/2) + q^(-1/2) - q^(-3/2) - q^(-5/2) + q^(-9/2) + q^(-11/2))*x1^(-1)*x2^(-7) + (q^(3/2) + 3*q^(1/2) + 3*q^(-1/2) + 2*q^(-3/2) - q^(-7/2) + q^(-11/2) + q^(-13/2))*x1^(-1)*x2^(-8) + (-q^(9/2) - q^(7/2) - 2*q^(5/2) - q^(3/2) + 2*q^(1/2) + 5*q^(-1/2) + 5*q^(-3/2) + 4*q^(-5/2) + q^(-7/2) + q^(-13/2) + q^(-15/2))*x1^(-1)*x2^(-9) + (-q^(-7/2))*x1^(-2)*x2^(-4) + (-q^(-7/2) - q^(-9/2) - q^(-11/2))*x1^(-2)*x2^(-5) + (q^(-5/2) - 2*q^(-11/2) - q^(-13/2) - q^(-15/2))*x1^(-2)*x2^(-6) + (q^(-5/2) + q^(-7/2) + 2*q^(-9/2) - q^(-13/2) - 2*q^(-15/2) - q^(-17/2) - q^(-19/2))*x1^(-2)*x2^(-7) + (-q^(-1/2) - q^(-3/2) - q^(-5/2) - q^(-7/2) + 2*q^(-9/2) + 2*q^(-11/2) + 2*q^(-13/2) - q^(-15/2) - q^(-17/2) - 2*q^(-19/2) - q^(-21/2) - q^(-23/2))*x1^(-2)*x2^(-8) + (-q^(-1/2) - 2*q^(-3/2) - 4*q^(-5/2) - 5*q^(-7/2) - 3*q^(-9/2) - q^(-11/2) + 2*q^(-13/2) + 2*q^(-15/2) + q^(-17/2) - q^(-19/2) - q^(-21/2) - 2*q^(-23/2) - q^(-25/2) - q^(-27/2))*x1^(-2)*x2^(-9) + (q^(-13/2))*x1^(-3)*x2^(-5) + (q^(-13/2) + q^(-15/2) + q^(-17/2) + q^(-19/2))*x1^(-3)*x2^(-6) + (-q^(-11/2) + q^(-17/2) + 2*q^(-19/2) + 2*q^(-21/2) + q^(-23/2) + q^(-25/2))*x1^(-3)*x2^(-7) + (-q^(-11/2) - q^(-13/2) - 2*q^(-15/2) - 2*q^(-17/2) + q^(-21/2) + 2*q^(-23/2) + 3*q^(-25/2) + 2*q^(-27/2) + q^(-29/2) + q^(-31/2))*x1^(-3)*x2^(-8) + (q^(-7/2) + q^(-9/2) + q^(-11/2) + q^(-13/2) - 3*q^(-17/2) - 3*q^(-19/2) - 3*q^(-21/2) - 2*q^(-23/2) + q^(-25/2) + 2*q^(-27/2) + 3*q^(-29/2) + 3*q^(-31/2) + 2*q^(-33/2) + q^(-35/2) + q^(-37/2))*x1^(-3)*x2^(-9) + (-q^(-21/2))*x1^(-4)*x2^(-6) + (-q^(-21/2) - q^(-23/2) - q^(-25/2) - q^(-27/2) - q^(-29/2))*x1^(-4)*x2^(-7) + (q^(-19/2) - q^(-25/2) - q^(-27/2) - 3*q^(-29/2) - 2*q^(-31/2) - 2*q^(-33/2) - q^(-35/2) - q^(-37/2))*x1^(-4)*x2^(-8) + (q^(-19/2) + q^(-21/2) + 2*q^(-23/2) + 2*q^(-25/2) + 2*q^(-27/2) - q^(-31/2) - 3*q^(-33/2) - 3*q^(-35/2) - 4*q^(-37/2) - 3*q^(-39/2) - 2*q^(-41/2) - q^(-43/2) - q^(-45/2))*x1^(-4)*x2^(-9) + (q^(-31/2))*x1^(-5)*x2^(-7) + (q^(-31/2) + q^(-33/2) + q^(-35/2) + q^(-37/2) + q^(-39/2) + q^(-41/2))*x1^(-5)*x2^(-8) + (-q^(-29/2) + q^(-35/2) + q^(-37/2) + 2*q^(-39/2) + 3*q^(-41/2) + 3*q^(-43/2) + 2*q^(-45/2) + 2*q^(-47/2) + q^(-49/2) + q^(-51/2))*x1^(-5)*x2^(-9) + (-q^(-43/2))*x1^(-6)*x2^(-8) + (-q^(-43/2) - q^(-45/2) - q^(-47/2) - q^(-49/2) - q^(-51/2) - q^(-53/2) - q^(-55/2))*x1^(-6)*x2^(-9) + (q^(-57/2))*x1^(-7)*x2^(-9)

Braid

Braid word	Components	Crossings	Strands
`[-1, -2, 1, -2, -2, 1, -2, -1, 2]`	2	9	3

Multivariable Alexander polynomial

Δ_L
`-A1A2^(-1) - A2^(2) + A2 - 1 + A2^(-1) - A2^(-2) - A1^(-1)A2`

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

Dual Thurston polytope

Vertex	Dual to fibered face
`(0, -4)`	yes
`(2, -2)`	yes
`(0, 4)`	yes
`(-2, 2)`	yes

HFL polytope

Poincaré polynomial
`m^(-3)A1^(-1/2)A2^(-5/2) + 2m^(-2)A1^(-1/2)A2^(-3/2) + m^(-2)A1^(1/2)A2^(-5/2) + m^(-1)A1^(-3/2)A2^(1/2) + 2m^(-1)A1^(-1/2)A2^(-1/2) + 3m^(-1)A1^(1/2)A2^(-3/2) + A1^(-3/2)A2^(3/2) + 3A1^(-1/2)A2^(1/2) + 3A1^(1/2)A2^(-1/2) + A1^(3/2)A2^(-3/2) + 3mA1^(-1/2)A2^(3/2) + 2mA1^(1/2)A2^(1/2) + mA1^(3/2)A2^(-1/2) + m^2A1^(-1/2)A2^(5/2) + 2m^2A1^(1/2)A2^(3/2) + m^3A1^(1/2)A2^(5/2)`

Vertex	Maslov	Rank
`(-3/2, 1/2)`	-1	1
`(-1/2, -5/2)`	-3	1
`(1/2, -5/2)`	-2	1
`(3/2, -3/2)`	0	1
`(3/2, -1/2)`	1	1
`(1/2, 5/2)`	3	1
`(-1/2, 5/2)`	2	1
`(-3/2, 3/2)`	0	1

Record

FL/HFL Links

`orderOption(int)`	`173`
`namestring`	`L9n16{0}`
`statusstring`	`success`
`slugstring`	`L9n16_0_7f0b0741`
`result_filestring`	`details/L9n16_0_7f0b0741.json`
`complexity_scoreOption(int)`	`162`
`strandsOption(int)`	`null`
`crossingsOption(int)`	`9`
`component_countOption(int)`	`2`
`girthOption(int)`	`6`
`total_rankOption(int)`	`28`
`wall_secondsOption(float)`	`0.001653`
`backend_secondsOption(float)`	`0.0`
`errorstring`
`dimensionOption(int)`	`2`
`support_sizeOption(int)`	`16`
`vertex_countOption(int)`	`8`
`fibered_vertex_countOption(int)`	`4`
`polytope_statusstring`	`computed`
`alexander_support_sizeOption(int)`	`7`
`alexander_vertex_countOption(int)`	`4`
`alexander_relationstring`	`not_computed`
`fk_countint`	`3`
`detailsRowRef(FLHFLLinks)`	{ "dataset": "FLHFLLinks", "key": "L9n16_0_7f0b0741" }
`detail_assetstring`	`/api/v1/datasets/FLHFLLinks/assets/L9n16_0_7f0b0741`

FL expansions

Braid

Multivariable Alexander polynomial

Dual Thurston polytope

HFL polytope

Record

F_L expansions