L9n23{0;0} - HFL and FL

details/L9n23_0_0_1bca4468.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
`(-1/2, -1, -1)`	`(1, 1, 1)`	`x1^(1/2)x2^(1)x3^(1)`	`q^(-2)`	`{"0": [-1, -1, -1, -1], "1": [-1, -1, -1, -1, 1, -1], "2": [-1, -1, -1, -1, -1, 1, -1, -1]}`	(-q^(-2))x1^(1/2)x2x3 + (-q^(-2))x1^(1/2)x2x3^(2) + (-q^(-2))x1^(1/2)x2x3^(3) + (-q^(-2))x1^(1/2)x2x3^(4) + (-q^(-2))x1^(1/2)x2x3^(5) + (-q^(-2))x1^(1/2)x2^(2)x3 + (-q^(-1) - q^(-2))x1^(1/2)x2^(2)x3^(2) + (-1 - q^(-1) - q^(-2))x1^(1/2)x2^(2)x3^(3) + (-q - 1 - q^(-1) - q^(-2))x1^(1/2)x2^(2)x3^(4) + (-q^(2) - q - 1 - q^(-1) - q^(-2))x1^(1/2)x2^(2)x3^(5) + (-q^(-2))x1^(1/2)x2^(3)x3 + (-1 - q^(-1) - q^(-2))x1^(1/2)x2^(3)x3^(2) + (-q^(2) - q - 21 - q^(-1) - q^(-2))x1^(1/2)x2^(3)x3^(3) + (-q^(4) - q^(3) - 2q^(2) - 2q - 21 - q^(-1) - q^(-2))x1^(1/2)x2^(3)x3^(4) + (-q^(6) - q^(5) - 2q^(4) - 2q^(3) - 3q^(2) - 2q - 21 - q^(-1) - q^(-2))x1^(1/2)x2^(3)x3^(5) + (-q^(-2))x1^(1/2)x2^(4)x3 + (-q - 1 - q^(-1) - q^(-2))x1^(1/2)x2^(4)x3^(2) + (-q^(4) - q^(3) - 2q^(2) - 2q - 21 - q^(-1) - q^(-2))x1^(1/2)x2^(4)x3^(3) + (-q^(7) - q^(6) - 2q^(5) - 3q^(4) - 3q^(3) - 3q^(2) - 3q - 21 - q^(-1) - q^(-2))x1^(1/2)x2^(4)x3^(4) + (-q^(10) - q^(9) - 2q^(8) - 3q^(7) - 4q^(6) - 4q^(5) - 5q^(4) - 4q^(3) - 4q^(2) - 3q - 21 - q^(-1) - q^(-2))x1^(1/2)x2^(4)x3^(5) + (-q^(-2))x1^(1/2)x2^(5)x3 + (-q^(2) - q - 1 - q^(-1) - q^(-2))x1^(1/2)x2^(5)x3^(2) + (-q^(6) - q^(5) - 2q^(4) - 2q^(3) - 3q^(2) - 2q - 21 - q^(-1) - q^(-2))x1^(1/2)x2^(5)x3^(3) + (-q^(10) - q^(9) - 2q^(8) - 3q^(7) - 4q^(6) - 4q^(5) - 5q^(4) - 4q^(3) - 4q^(2) - 3q - 21 - q^(-1) - q^(-2))x1^(1/2)x2^(5)x3^(4) + (-q^(14) - q^(13) - 2q^(12) - 3q^(11) - 5q^(10) - 5q^(9) - 7q^(8) - 7q^(7) - 8q^(6) - 7q^(5) - 7q^(4) - 5q^(3) - 5q^(2) - 3q - 21 - q^(-1) - q^(-2))x1^(1/2)x2^(5)x3^(5) + (q^(-5))x1^(3/2)x2^(2)x3^(3) + (q^(-5) + q^(-6))x1^(3/2)x2^(2)x3^(4) + (q^(-5) + q^(-6) + q^(-7))x1^(3/2)x2^(2)x3^(5) + (q^(-5))x1^(3/2)x2^(3)x3^(2) + (q^(-4) + 2q^(-5))x1^(3/2)x2^(3)x3^(3) + (q^(-3) + 2q^(-4) + 3q^(-5) + q^(-6))x1^(3/2)x2^(3)x3^(4) + (q^(-2) + 2q^(-3) + 3q^(-4) + 4q^(-5) + 2q^(-6) + q^(-7))x1^(3/2)x2^(3)x3^(5) + (q^(-5) + q^(-6))x1^(3/2)x2^(4)x3^(2) + (q^(-3) + 2q^(-4) + 3q^(-5) + q^(-6))x1^(3/2)x2^(4)x3^(3) + (q^(-1) + 2q^(-2) + 4q^(-3) + 5q^(-4) + 4q^(-5) + 2q^(-6))x1^(3/2)x2^(4)x3^(4) + (q + 21 + 4q^(-1) + 6q^(-2) + 8q^(-3) + 7q^(-4) + 6q^(-5) + 3q^(-6) + q^(-7))x1^(3/2)x2^(4)x3^(5) + (q^(-5) + q^(-6) + q^(-7))x1^(3/2)x2^(5)x3^(2) + (q^(-2) + 2q^(-3) + 3q^(-4) + 4q^(-5) + 2q^(-6) + q^(-7))x1^(3/2)x2^(5)x3^(3) + (q + 21 + 4q^(-1) + 6q^(-2) + 8q^(-3) + 7q^(-4) + 6q^(-5) + 3q^(-6) + q^(-7))x1^(3/2)x2^(5)x3^(4) + (q^(4) + 2q^(3) + 4q^(2) + 7q + 101 + 13q^(-1) + 14q^(-2) + 14q^(-3) + 11q^(-4) + 8q^(-5) + 4q^(-6) + 2q^(-7))x1^(3/2)x2^(5)x3^(5) + (-q^(-11))x1^(5/2)x2^(3)x3^(5) + (-q^(-10) - q^(-11))x1^(5/2)x2^(4)x3^(4) + (-q^(-9) - 2q^(-10) - 3q^(-11) - q^(-12))x1^(5/2)x2^(4)x3^(5) + (-q^(-11))x1^(5/2)x2^(5)x3^(3) + (-q^(-9) - 2q^(-10) - 3q^(-11) - q^(-12))x1^(5/2)x2^(5)x3^(4) + (-q^(-7) - 2q^(-8) - 5q^(-9) - 6q^(-10) - 7q^(-11) - 3q^(-12) - q^(-13))x1^(5/2)x2^(5)x3^(5)
`(-1/2, -1, -1)`	`(1, 1, 1)`	`x1^(1/2)x2^(1)x3^(1)`	`q^(-2)`	`{"0": [1, -1, -1, -1], "1": [-1, 1, -1, -1, 1, -1], "2": [-1, -1, 1, -1, -1, 1, -1, -1]}`	(-q^(-2))x1^(1/2)x2x3 + (-q^(-2))x1^(1/2)x2x3^(2) + (-q^(-2))x1^(1/2)x2x3^(3) + (-q^(-2))x1^(1/2)x2x3^(4) + (-q^(-2))x1^(1/2)x2x3^(5) + (-q^(-2))x1^(1/2)x2^(2)x3 + (-q^(-1) - q^(-2))x1^(1/2)x2^(2)x3^(2) + (-1 - q^(-1) - q^(-2))x1^(1/2)x2^(2)x3^(3) + (-q - 1 - q^(-1) - q^(-2))x1^(1/2)x2^(2)x3^(4) + (-q^(2) - q - 1 - q^(-1) - q^(-2))x1^(1/2)x2^(2)x3^(5) + (-q^(-2))x1^(1/2)x2^(3)x3 + (-1 - q^(-1) - q^(-2))x1^(1/2)x2^(3)x3^(2) + (-q^(2) - q - 21 - q^(-1) - q^(-2))x1^(1/2)x2^(3)x3^(3) + (-q^(4) - q^(3) - 2q^(2) - 2q - 21 - q^(-1) - q^(-2))x1^(1/2)x2^(3)x3^(4) + (-q^(6) - q^(5) - 2q^(4) - 2q^(3) - 3q^(2) - 2q - 21 - q^(-1) - q^(-2))x1^(1/2)x2^(3)x3^(5) + (-q^(-2))x1^(1/2)x2^(4)x3 + (-q - 1 - q^(-1) - q^(-2))x1^(1/2)x2^(4)x3^(2) + (-q^(4) - q^(3) - 2q^(2) - 2q - 21 - q^(-1) - q^(-2))x1^(1/2)x2^(4)x3^(3) + (-q^(7) - q^(6) - 2q^(5) - 3q^(4) - 3q^(3) - 3q^(2) - 3q - 21 - q^(-1) - q^(-2))x1^(1/2)x2^(4)x3^(4) + (-q^(10) - q^(9) - 2q^(8) - 3q^(7) - 4q^(6) - 4q^(5) - 5q^(4) - 4q^(3) - 4q^(2) - 3q - 21 - q^(-1) - q^(-2))x1^(1/2)x2^(4)x3^(5) + (-q^(-2))x1^(1/2)x2^(5)x3 + (-q^(2) - q - 1 - q^(-1) - q^(-2))x1^(1/2)x2^(5)x3^(2) + (-q^(6) - q^(5) - 2q^(4) - 2q^(3) - 3q^(2) - 2q - 21 - q^(-1) - q^(-2))x1^(1/2)x2^(5)x3^(3) + (-q^(10) - q^(9) - 2q^(8) - 3q^(7) - 4q^(6) - 4q^(5) - 5q^(4) - 4q^(3) - 4q^(2) - 3q - 21 - q^(-1) - q^(-2))x1^(1/2)x2^(5)x3^(4) + (-q^(14) - q^(13) - 2q^(12) - 3q^(11) - 5q^(10) - 5q^(9) - 7q^(8) - 7q^(7) - 8q^(6) - 7q^(5) - 7q^(4) - 5q^(3) - 5q^(2) - 3q - 21 - q^(-1) - q^(-2))x1^(1/2)x2^(5)x3^(5) + (q^(-5))x1^(3/2)x2^(2)x3^(3) + (q^(-5) + q^(-6))x1^(3/2)x2^(2)x3^(4) + (q^(-5) + q^(-6) + q^(-7))x1^(3/2)x2^(2)x3^(5) + (q^(-5))x1^(3/2)x2^(3)x3^(2) + (q^(-4) + 2q^(-5))x1^(3/2)x2^(3)x3^(3) + (q^(-3) + 2q^(-4) + 3q^(-5) + q^(-6))x1^(3/2)x2^(3)x3^(4) + (q^(-2) + 2q^(-3) + 3q^(-4) + 4q^(-5) + 2q^(-6) + q^(-7))x1^(3/2)x2^(3)x3^(5) + (q^(-5) + q^(-6))x1^(3/2)x2^(4)x3^(2) + (q^(-3) + 2q^(-4) + 3q^(-5) + q^(-6))x1^(3/2)x2^(4)x3^(3) + (q^(-1) + 2q^(-2) + 4q^(-3) + 5q^(-4) + 4q^(-5) + 2q^(-6))x1^(3/2)x2^(4)x3^(4) + (q + 21 + 4q^(-1) + 6q^(-2) + 8q^(-3) + 7q^(-4) + 6q^(-5) + 3q^(-6) + q^(-7))x1^(3/2)x2^(4)x3^(5) + (q^(-5) + q^(-6) + q^(-7))x1^(3/2)x2^(5)x3^(2) + (q^(-2) + 2q^(-3) + 3q^(-4) + 4q^(-5) + 2q^(-6) + q^(-7))x1^(3/2)x2^(5)x3^(3) + (q + 21 + 4q^(-1) + 6q^(-2) + 8q^(-3) + 7q^(-4) + 6q^(-5) + 3q^(-6) + q^(-7))x1^(3/2)x2^(5)x3^(4) + (q^(4) + 2q^(3) + 4q^(2) + 7q + 101 + 13q^(-1) + 14q^(-2) + 14q^(-3) + 11q^(-4) + 8q^(-5) + 4q^(-6) + 2q^(-7))x1^(3/2)x2^(5)x3^(5) + (-q^(-11))x1^(5/2)x2^(3)x3^(5) + (-q^(-10) - q^(-11))x1^(5/2)x2^(4)x3^(4) + (-q^(-9) - 2q^(-10) - 3q^(-11) - q^(-12))x1^(5/2)x2^(4)x3^(5) + (-q^(-11))x1^(5/2)x2^(5)x3^(3) + (-q^(-9) - 2q^(-10) - 3q^(-11) - q^(-12))x1^(5/2)x2^(5)x3^(4) + (-q^(-7) - 2q^(-8) - 5q^(-9) - 6q^(-10) - 7q^(-11) - 3q^(-12) - q^(-13))x1^(5/2)x2^(5)x3^(5)
`(1/2, 1, 1)`		`x1^(-1/2)x2^(-1)x3^(-1)`	`q^(-2)`		(-q^(-2))x1^(-1/2)x2^(-1)x3^(-1) + (-q^(-2))x1^(-1/2)x2^(-1)x3^(-2) + (-q^(-2))x1^(-1/2)x2^(-1)x3^(-3) + (-q^(-2))x1^(-1/2)x2^(-1)x3^(-4) + (-q^(-2))x1^(-1/2)x2^(-1)x3^(-5) + (-q^(-2))x1^(-1/2)x2^(-2)x3^(-1) + (-q^(-1) - q^(-2))x1^(-1/2)x2^(-2)x3^(-2) + (-1 - q^(-1) - q^(-2))x1^(-1/2)x2^(-2)x3^(-3) + (-q - 1 - q^(-1) - q^(-2))x1^(-1/2)x2^(-2)x3^(-4) + (-q^(2) - q - 1 - q^(-1) - q^(-2))x1^(-1/2)x2^(-2)x3^(-5) + (-q^(-2))x1^(-1/2)x2^(-3)x3^(-1) + (-1 - q^(-1) - q^(-2))x1^(-1/2)x2^(-3)x3^(-2) + (-q^(2) - q - 21 - q^(-1) - q^(-2))x1^(-1/2)x2^(-3)x3^(-3) + (-q^(4) - q^(3) - 2q^(2) - 2q - 21 - q^(-1) - q^(-2))x1^(-1/2)x2^(-3)x3^(-4) + (-q^(6) - q^(5) - 2q^(4) - 2q^(3) - 3q^(2) - 2q - 21 - q^(-1) - q^(-2))x1^(-1/2)x2^(-3)x3^(-5) + (-q^(-2))x1^(-1/2)x2^(-4)x3^(-1) + (-q - 1 - q^(-1) - q^(-2))x1^(-1/2)x2^(-4)x3^(-2) + (-q^(4) - q^(3) - 2q^(2) - 2q - 21 - q^(-1) - q^(-2))x1^(-1/2)x2^(-4)x3^(-3) + (-q^(7) - q^(6) - 2q^(5) - 3q^(4) - 3q^(3) - 3q^(2) - 3q - 21 - q^(-1) - q^(-2))x1^(-1/2)x2^(-4)x3^(-4) + (-q^(10) - q^(9) - 2q^(8) - 3q^(7) - 4q^(6) - 4q^(5) - 5q^(4) - 4q^(3) - 4q^(2) - 3q - 21 - q^(-1) - q^(-2))x1^(-1/2)x2^(-4)x3^(-5) + (-q^(-2))x1^(-1/2)x2^(-5)x3^(-1) + (-q^(2) - q - 1 - q^(-1) - q^(-2))x1^(-1/2)x2^(-5)x3^(-2) + (-q^(6) - q^(5) - 2q^(4) - 2q^(3) - 3q^(2) - 2q - 21 - q^(-1) - q^(-2))x1^(-1/2)x2^(-5)x3^(-3) + (-q^(10) - q^(9) - 2q^(8) - 3q^(7) - 4q^(6) - 4q^(5) - 5q^(4) - 4q^(3) - 4q^(2) - 3q - 21 - q^(-1) - q^(-2))x1^(-1/2)x2^(-5)x3^(-4) + (-q^(14) - q^(13) - 2q^(12) - 3q^(11) - 5q^(10) - 5q^(9) - 7q^(8) - 7q^(7) - 8q^(6) - 7q^(5) - 7q^(4) - 5q^(3) - 5q^(2) - 3q - 21 - q^(-1) - q^(-2))x1^(-1/2)x2^(-5)x3^(-5) + (q^(-5))x1^(-3/2)x2^(-2)x3^(-3) + (q^(-5) + q^(-6))x1^(-3/2)x2^(-2)x3^(-4) + (q^(-5) + q^(-6) + q^(-7))x1^(-3/2)x2^(-2)x3^(-5) + (q^(-5))x1^(-3/2)x2^(-3)x3^(-2) + (q^(-4) + 2q^(-5))x1^(-3/2)x2^(-3)x3^(-3) + (q^(-3) + 2q^(-4) + 3q^(-5) + q^(-6))x1^(-3/2)x2^(-3)x3^(-4) + (q^(-2) + 2q^(-3) + 3q^(-4) + 4q^(-5) + 2q^(-6) + q^(-7))x1^(-3/2)x2^(-3)x3^(-5) + (q^(-5) + q^(-6))x1^(-3/2)x2^(-4)x3^(-2) + (q^(-3) + 2q^(-4) + 3q^(-5) + q^(-6))x1^(-3/2)x2^(-4)x3^(-3) + (q^(-1) + 2q^(-2) + 4q^(-3) + 5q^(-4) + 4q^(-5) + 2q^(-6))x1^(-3/2)x2^(-4)x3^(-4) + (q + 21 + 4q^(-1) + 6q^(-2) + 8q^(-3) + 7q^(-4) + 6q^(-5) + 3q^(-6) + q^(-7))x1^(-3/2)x2^(-4)x3^(-5) + (q^(-5) + q^(-6) + q^(-7))x1^(-3/2)x2^(-5)x3^(-2) + (q^(-2) + 2q^(-3) + 3q^(-4) + 4q^(-5) + 2q^(-6) + q^(-7))x1^(-3/2)x2^(-5)x3^(-3) + (q + 21 + 4q^(-1) + 6q^(-2) + 8q^(-3) + 7q^(-4) + 6q^(-5) + 3q^(-6) + q^(-7))x1^(-3/2)x2^(-5)x3^(-4) + (q^(4) + 2q^(3) + 4q^(2) + 7q + 101 + 13q^(-1) + 14q^(-2) + 14q^(-3) + 11q^(-4) + 8q^(-5) + 4q^(-6) + 2q^(-7))x1^(-3/2)x2^(-5)x3^(-5) + (-q^(-11))x1^(-5/2)x2^(-3)x3^(-5) + (-q^(-10) - q^(-11))x1^(-5/2)x2^(-4)x3^(-4) + (-q^(-9) - 2q^(-10) - 3q^(-11) - q^(-12))x1^(-5/2)x2^(-4)x3^(-5) + (-q^(-11))x1^(-5/2)x2^(-5)x3^(-3) + (-q^(-9) - 2q^(-10) - 3q^(-11) - q^(-12))x1^(-5/2)x2^(-5)x3^(-4) + (-q^(-7) - 2q^(-8) - 5q^(-9) - 6q^(-10) - 7q^(-11) - 3q^(-12) - q^(-13))x1^(-5/2)x2^(-5)x3^(-5)

(-1/2, -1, -1)

(1, 1, 1)

x1^(1/2)x2^(1)x3^(1)

q^(-2)

{"0": [-1, -1, -1, -1], "1": [-1, -1, -1, -1, 1, -1], "2": [-1, -1, -1, -1, -1, 1, -1, -1]}

(-q^(-2))*x1^(1/2)*x2*x3 + (-q^(-2))*x1^(1/2)*x2*x3^(2) + (-q^(-2))*x1^(1/2)*x2*x3^(3) + (-q^(-2))*x1^(1/2)*x2*x3^(4) + (-q^(-2))*x1^(1/2)*x2*x3^(5) + (-q^(-2))*x1^(1/2)*x2^(2)*x3 + (-q^(-1) - q^(-2))*x1^(1/2)*x2^(2)*x3^(2) + (-1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(2)*x3^(3) + (-q - 1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(2)*x3^(4) + (-q^(2) - q - 1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(2)*x3^(5) + (-q^(-2))*x1^(1/2)*x2^(3)*x3 + (-1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(3)*x3^(2) + (-q^(2) - q - 2*1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(3)*x3^(3) + (-q^(4) - q^(3) - 2*q^(2) - 2*q - 2*1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(3)*x3^(4) + (-q^(6) - q^(5) - 2*q^(4) - 2*q^(3) - 3*q^(2) - 2*q - 2*1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(3)*x3^(5) + (-q^(-2))*x1^(1/2)*x2^(4)*x3 + (-q - 1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(4)*x3^(2) + (-q^(4) - q^(3) - 2*q^(2) - 2*q - 2*1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(4)*x3^(3) + (-q^(7) - q^(6) - 2*q^(5) - 3*q^(4) - 3*q^(3) - 3*q^(2) - 3*q - 2*1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(4)*x3^(4) + (-q^(10) - q^(9) - 2*q^(8) - 3*q^(7) - 4*q^(6) - 4*q^(5) - 5*q^(4) - 4*q^(3) - 4*q^(2) - 3*q - 2*1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(4)*x3^(5) + (-q^(-2))*x1^(1/2)*x2^(5)*x3 + (-q^(2) - q - 1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(5)*x3^(2) + (-q^(6) - q^(5) - 2*q^(4) - 2*q^(3) - 3*q^(2) - 2*q - 2*1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(5)*x3^(3) + (-q^(10) - q^(9) - 2*q^(8) - 3*q^(7) - 4*q^(6) - 4*q^(5) - 5*q^(4) - 4*q^(3) - 4*q^(2) - 3*q - 2*1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(5)*x3^(4) + (-q^(14) - q^(13) - 2*q^(12) - 3*q^(11) - 5*q^(10) - 5*q^(9) - 7*q^(8) - 7*q^(7) - 8*q^(6) - 7*q^(5) - 7*q^(4) - 5*q^(3) - 5*q^(2) - 3*q - 2*1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(5)*x3^(5) + (q^(-5))*x1^(3/2)*x2^(2)*x3^(3) + (q^(-5) + q^(-6))*x1^(3/2)*x2^(2)*x3^(4) + (q^(-5) + q^(-6) + q^(-7))*x1^(3/2)*x2^(2)*x3^(5) + (q^(-5))*x1^(3/2)*x2^(3)*x3^(2) + (q^(-4) + 2*q^(-5))*x1^(3/2)*x2^(3)*x3^(3) + (q^(-3) + 2*q^(-4) + 3*q^(-5) + q^(-6))*x1^(3/2)*x2^(3)*x3^(4) + (q^(-2) + 2*q^(-3) + 3*q^(-4) + 4*q^(-5) + 2*q^(-6) + q^(-7))*x1^(3/2)*x2^(3)*x3^(5) + (q^(-5) + q^(-6))*x1^(3/2)*x2^(4)*x3^(2) + (q^(-3) + 2*q^(-4) + 3*q^(-5) + q^(-6))*x1^(3/2)*x2^(4)*x3^(3) + (q^(-1) + 2*q^(-2) + 4*q^(-3) + 5*q^(-4) + 4*q^(-5) + 2*q^(-6))*x1^(3/2)*x2^(4)*x3^(4) + (q + 2*1 + 4*q^(-1) + 6*q^(-2) + 8*q^(-3) + 7*q^(-4) + 6*q^(-5) + 3*q^(-6) + q^(-7))*x1^(3/2)*x2^(4)*x3^(5) + (q^(-5) + q^(-6) + q^(-7))*x1^(3/2)*x2^(5)*x3^(2) + (q^(-2) + 2*q^(-3) + 3*q^(-4) + 4*q^(-5) + 2*q^(-6) + q^(-7))*x1^(3/2)*x2^(5)*x3^(3) + (q + 2*1 + 4*q^(-1) + 6*q^(-2) + 8*q^(-3) + 7*q^(-4) + 6*q^(-5) + 3*q^(-6) + q^(-7))*x1^(3/2)*x2^(5)*x3^(4) + (q^(4) + 2*q^(3) + 4*q^(2) + 7*q + 10*1 + 13*q^(-1) + 14*q^(-2) + 14*q^(-3) + 11*q^(-4) + 8*q^(-5) + 4*q^(-6) + 2*q^(-7))*x1^(3/2)*x2^(5)*x3^(5) + (-q^(-11))*x1^(5/2)*x2^(3)*x3^(5) + (-q^(-10) - q^(-11))*x1^(5/2)*x2^(4)*x3^(4) + (-q^(-9) - 2*q^(-10) - 3*q^(-11) - q^(-12))*x1^(5/2)*x2^(4)*x3^(5) + (-q^(-11))*x1^(5/2)*x2^(5)*x3^(3) + (-q^(-9) - 2*q^(-10) - 3*q^(-11) - q^(-12))*x1^(5/2)*x2^(5)*x3^(4) + (-q^(-7) - 2*q^(-8) - 5*q^(-9) - 6*q^(-10) - 7*q^(-11) - 3*q^(-12) - q^(-13))*x1^(5/2)*x2^(5)*x3^(5)

(-1/2, -1, -1)

(1, 1, 1)

x1^(1/2)x2^(1)x3^(1)

q^(-2)

{"0": [1, -1, -1, -1], "1": [-1, 1, -1, -1, 1, -1], "2": [-1, -1, 1, -1, -1, 1, -1, -1]}

(-q^(-2))*x1^(1/2)*x2*x3 + (-q^(-2))*x1^(1/2)*x2*x3^(2) + (-q^(-2))*x1^(1/2)*x2*x3^(3) + (-q^(-2))*x1^(1/2)*x2*x3^(4) + (-q^(-2))*x1^(1/2)*x2*x3^(5) + (-q^(-2))*x1^(1/2)*x2^(2)*x3 + (-q^(-1) - q^(-2))*x1^(1/2)*x2^(2)*x3^(2) + (-1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(2)*x3^(3) + (-q - 1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(2)*x3^(4) + (-q^(2) - q - 1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(2)*x3^(5) + (-q^(-2))*x1^(1/2)*x2^(3)*x3 + (-1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(3)*x3^(2) + (-q^(2) - q - 2*1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(3)*x3^(3) + (-q^(4) - q^(3) - 2*q^(2) - 2*q - 2*1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(3)*x3^(4) + (-q^(6) - q^(5) - 2*q^(4) - 2*q^(3) - 3*q^(2) - 2*q - 2*1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(3)*x3^(5) + (-q^(-2))*x1^(1/2)*x2^(4)*x3 + (-q - 1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(4)*x3^(2) + (-q^(4) - q^(3) - 2*q^(2) - 2*q - 2*1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(4)*x3^(3) + (-q^(7) - q^(6) - 2*q^(5) - 3*q^(4) - 3*q^(3) - 3*q^(2) - 3*q - 2*1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(4)*x3^(4) + (-q^(10) - q^(9) - 2*q^(8) - 3*q^(7) - 4*q^(6) - 4*q^(5) - 5*q^(4) - 4*q^(3) - 4*q^(2) - 3*q - 2*1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(4)*x3^(5) + (-q^(-2))*x1^(1/2)*x2^(5)*x3 + (-q^(2) - q - 1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(5)*x3^(2) + (-q^(6) - q^(5) - 2*q^(4) - 2*q^(3) - 3*q^(2) - 2*q - 2*1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(5)*x3^(3) + (-q^(10) - q^(9) - 2*q^(8) - 3*q^(7) - 4*q^(6) - 4*q^(5) - 5*q^(4) - 4*q^(3) - 4*q^(2) - 3*q - 2*1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(5)*x3^(4) + (-q^(14) - q^(13) - 2*q^(12) - 3*q^(11) - 5*q^(10) - 5*q^(9) - 7*q^(8) - 7*q^(7) - 8*q^(6) - 7*q^(5) - 7*q^(4) - 5*q^(3) - 5*q^(2) - 3*q - 2*1 - q^(-1) - q^(-2))*x1^(1/2)*x2^(5)*x3^(5) + (q^(-5))*x1^(3/2)*x2^(2)*x3^(3) + (q^(-5) + q^(-6))*x1^(3/2)*x2^(2)*x3^(4) + (q^(-5) + q^(-6) + q^(-7))*x1^(3/2)*x2^(2)*x3^(5) + (q^(-5))*x1^(3/2)*x2^(3)*x3^(2) + (q^(-4) + 2*q^(-5))*x1^(3/2)*x2^(3)*x3^(3) + (q^(-3) + 2*q^(-4) + 3*q^(-5) + q^(-6))*x1^(3/2)*x2^(3)*x3^(4) + (q^(-2) + 2*q^(-3) + 3*q^(-4) + 4*q^(-5) + 2*q^(-6) + q^(-7))*x1^(3/2)*x2^(3)*x3^(5) + (q^(-5) + q^(-6))*x1^(3/2)*x2^(4)*x3^(2) + (q^(-3) + 2*q^(-4) + 3*q^(-5) + q^(-6))*x1^(3/2)*x2^(4)*x3^(3) + (q^(-1) + 2*q^(-2) + 4*q^(-3) + 5*q^(-4) + 4*q^(-5) + 2*q^(-6))*x1^(3/2)*x2^(4)*x3^(4) + (q + 2*1 + 4*q^(-1) + 6*q^(-2) + 8*q^(-3) + 7*q^(-4) + 6*q^(-5) + 3*q^(-6) + q^(-7))*x1^(3/2)*x2^(4)*x3^(5) + (q^(-5) + q^(-6) + q^(-7))*x1^(3/2)*x2^(5)*x3^(2) + (q^(-2) + 2*q^(-3) + 3*q^(-4) + 4*q^(-5) + 2*q^(-6) + q^(-7))*x1^(3/2)*x2^(5)*x3^(3) + (q + 2*1 + 4*q^(-1) + 6*q^(-2) + 8*q^(-3) + 7*q^(-4) + 6*q^(-5) + 3*q^(-6) + q^(-7))*x1^(3/2)*x2^(5)*x3^(4) + (q^(4) + 2*q^(3) + 4*q^(2) + 7*q + 10*1 + 13*q^(-1) + 14*q^(-2) + 14*q^(-3) + 11*q^(-4) + 8*q^(-5) + 4*q^(-6) + 2*q^(-7))*x1^(3/2)*x2^(5)*x3^(5) + (-q^(-11))*x1^(5/2)*x2^(3)*x3^(5) + (-q^(-10) - q^(-11))*x1^(5/2)*x2^(4)*x3^(4) + (-q^(-9) - 2*q^(-10) - 3*q^(-11) - q^(-12))*x1^(5/2)*x2^(4)*x3^(5) + (-q^(-11))*x1^(5/2)*x2^(5)*x3^(3) + (-q^(-9) - 2*q^(-10) - 3*q^(-11) - q^(-12))*x1^(5/2)*x2^(5)*x3^(4) + (-q^(-7) - 2*q^(-8) - 5*q^(-9) - 6*q^(-10) - 7*q^(-11) - 3*q^(-12) - q^(-13))*x1^(5/2)*x2^(5)*x3^(5)

(1/2, 1, 1)

x1^(-1/2)x2^(-1)x3^(-1)

q^(-2)

(-q^(-2))*x1^(-1/2)*x2^(-1)*x3^(-1) + (-q^(-2))*x1^(-1/2)*x2^(-1)*x3^(-2) + (-q^(-2))*x1^(-1/2)*x2^(-1)*x3^(-3) + (-q^(-2))*x1^(-1/2)*x2^(-1)*x3^(-4) + (-q^(-2))*x1^(-1/2)*x2^(-1)*x3^(-5) + (-q^(-2))*x1^(-1/2)*x2^(-2)*x3^(-1) + (-q^(-1) - q^(-2))*x1^(-1/2)*x2^(-2)*x3^(-2) + (-1 - q^(-1) - q^(-2))*x1^(-1/2)*x2^(-2)*x3^(-3) + (-q - 1 - q^(-1) - q^(-2))*x1^(-1/2)*x2^(-2)*x3^(-4) + (-q^(2) - q - 1 - q^(-1) - q^(-2))*x1^(-1/2)*x2^(-2)*x3^(-5) + (-q^(-2))*x1^(-1/2)*x2^(-3)*x3^(-1) + (-1 - q^(-1) - q^(-2))*x1^(-1/2)*x2^(-3)*x3^(-2) + (-q^(2) - q - 2*1 - q^(-1) - q^(-2))*x1^(-1/2)*x2^(-3)*x3^(-3) + (-q^(4) - q^(3) - 2*q^(2) - 2*q - 2*1 - q^(-1) - q^(-2))*x1^(-1/2)*x2^(-3)*x3^(-4) + (-q^(6) - q^(5) - 2*q^(4) - 2*q^(3) - 3*q^(2) - 2*q - 2*1 - q^(-1) - q^(-2))*x1^(-1/2)*x2^(-3)*x3^(-5) + (-q^(-2))*x1^(-1/2)*x2^(-4)*x3^(-1) + (-q - 1 - q^(-1) - q^(-2))*x1^(-1/2)*x2^(-4)*x3^(-2) + (-q^(4) - q^(3) - 2*q^(2) - 2*q - 2*1 - q^(-1) - q^(-2))*x1^(-1/2)*x2^(-4)*x3^(-3) + (-q^(7) - q^(6) - 2*q^(5) - 3*q^(4) - 3*q^(3) - 3*q^(2) - 3*q - 2*1 - q^(-1) - q^(-2))*x1^(-1/2)*x2^(-4)*x3^(-4) + (-q^(10) - q^(9) - 2*q^(8) - 3*q^(7) - 4*q^(6) - 4*q^(5) - 5*q^(4) - 4*q^(3) - 4*q^(2) - 3*q - 2*1 - q^(-1) - q^(-2))*x1^(-1/2)*x2^(-4)*x3^(-5) + (-q^(-2))*x1^(-1/2)*x2^(-5)*x3^(-1) + (-q^(2) - q - 1 - q^(-1) - q^(-2))*x1^(-1/2)*x2^(-5)*x3^(-2) + (-q^(6) - q^(5) - 2*q^(4) - 2*q^(3) - 3*q^(2) - 2*q - 2*1 - q^(-1) - q^(-2))*x1^(-1/2)*x2^(-5)*x3^(-3) + (-q^(10) - q^(9) - 2*q^(8) - 3*q^(7) - 4*q^(6) - 4*q^(5) - 5*q^(4) - 4*q^(3) - 4*q^(2) - 3*q - 2*1 - q^(-1) - q^(-2))*x1^(-1/2)*x2^(-5)*x3^(-4) + (-q^(14) - q^(13) - 2*q^(12) - 3*q^(11) - 5*q^(10) - 5*q^(9) - 7*q^(8) - 7*q^(7) - 8*q^(6) - 7*q^(5) - 7*q^(4) - 5*q^(3) - 5*q^(2) - 3*q - 2*1 - q^(-1) - q^(-2))*x1^(-1/2)*x2^(-5)*x3^(-5) + (q^(-5))*x1^(-3/2)*x2^(-2)*x3^(-3) + (q^(-5) + q^(-6))*x1^(-3/2)*x2^(-2)*x3^(-4) + (q^(-5) + q^(-6) + q^(-7))*x1^(-3/2)*x2^(-2)*x3^(-5) + (q^(-5))*x1^(-3/2)*x2^(-3)*x3^(-2) + (q^(-4) + 2*q^(-5))*x1^(-3/2)*x2^(-3)*x3^(-3) + (q^(-3) + 2*q^(-4) + 3*q^(-5) + q^(-6))*x1^(-3/2)*x2^(-3)*x3^(-4) + (q^(-2) + 2*q^(-3) + 3*q^(-4) + 4*q^(-5) + 2*q^(-6) + q^(-7))*x1^(-3/2)*x2^(-3)*x3^(-5) + (q^(-5) + q^(-6))*x1^(-3/2)*x2^(-4)*x3^(-2) + (q^(-3) + 2*q^(-4) + 3*q^(-5) + q^(-6))*x1^(-3/2)*x2^(-4)*x3^(-3) + (q^(-1) + 2*q^(-2) + 4*q^(-3) + 5*q^(-4) + 4*q^(-5) + 2*q^(-6))*x1^(-3/2)*x2^(-4)*x3^(-4) + (q + 2*1 + 4*q^(-1) + 6*q^(-2) + 8*q^(-3) + 7*q^(-4) + 6*q^(-5) + 3*q^(-6) + q^(-7))*x1^(-3/2)*x2^(-4)*x3^(-5) + (q^(-5) + q^(-6) + q^(-7))*x1^(-3/2)*x2^(-5)*x3^(-2) + (q^(-2) + 2*q^(-3) + 3*q^(-4) + 4*q^(-5) + 2*q^(-6) + q^(-7))*x1^(-3/2)*x2^(-5)*x3^(-3) + (q + 2*1 + 4*q^(-1) + 6*q^(-2) + 8*q^(-3) + 7*q^(-4) + 6*q^(-5) + 3*q^(-6) + q^(-7))*x1^(-3/2)*x2^(-5)*x3^(-4) + (q^(4) + 2*q^(3) + 4*q^(2) + 7*q + 10*1 + 13*q^(-1) + 14*q^(-2) + 14*q^(-3) + 11*q^(-4) + 8*q^(-5) + 4*q^(-6) + 2*q^(-7))*x1^(-3/2)*x2^(-5)*x3^(-5) + (-q^(-11))*x1^(-5/2)*x2^(-3)*x3^(-5) + (-q^(-10) - q^(-11))*x1^(-5/2)*x2^(-4)*x3^(-4) + (-q^(-9) - 2*q^(-10) - 3*q^(-11) - q^(-12))*x1^(-5/2)*x2^(-4)*x3^(-5) + (-q^(-11))*x1^(-5/2)*x2^(-5)*x3^(-3) + (-q^(-9) - 2*q^(-10) - 3*q^(-11) - q^(-12))*x1^(-5/2)*x2^(-5)*x3^(-4) + (-q^(-7) - 2*q^(-8) - 5*q^(-9) - 6*q^(-10) - 7*q^(-11) - 3*q^(-12) - q^(-13))*x1^(-5/2)*x2^(-5)*x3^(-5)

Braid

Braid word	Components	Crossings	Strands
`[-1, -2, -1, -2, -1, 3, -2, 3, -2]`	3	9	4

Multivariable Alexander polynomial

Δ_L
`-A1^(1/2)A2A3 + A1^(1/2)A2 + A1^(1/2)A3 - A1^(-1/2)A3^(-1) - A1^(-1/2)A2^(-1) + A1^(-1/2)A2^(-1)A3^(-1)`

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

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Dual Thurston polytope

Vertex	Dual to fibered face
`(1, 0, 2)`	yes
`(-1, 0, -2)`	yes
`(1, 2, 0)`	yes
`(-1, -2, -2)`	yes
`(1, 2, 2)`	yes
`(-1, -2, 0)`	yes

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HFL polytope

Poincaré polynomial
m^(-3)A1^(-1)A2^(-3/2)A3^(-3/2) + 2m^(-2)A1^(-1)A2^(-3/2)A3^(-1/2) + 2m^(-2)A1^(-1)A2^(-1/2)A3^(-3/2) + m^(-2)A2^(-3/2)A3^(-3/2) + m^(-1)A1^(-1)A2^(-3/2)A3^(1/2) + 3m^(-1)A1^(-1)A2^(-1/2)A3^(-1/2) + m^(-1)A1^(-1)A2^(1/2)A3^(-3/2) + 2m^(-1)A2^(-3/2)A3^(-1/2) + 2m^(-1)A2^(-1/2)A3^(-3/2) + m^(-1)A2^(-1/2)A3^(-1/2) + A1^(-1)A2^(-1/2)A3^(1/2) + A1^(-1)A2^(1/2)A3^(-1/2) + A2^(-3/2)A3^(1/2) + 4A2^(-1/2)A3^(-1/2) + A2^(-1/2)A3^(1/2) + A2^(1/2)A3^(-3/2) + A2^(1/2)A3^(-1/2) + 3mA2^(-1/2)A3^(1/2) + 3mA2^(1/2)A3^(-1/2) + mA2^(1/2)A3^(1/2) + m^2A2^(-1/2)A3^(3/2) + 4m^2A2^(1/2)A3^(1/2) + m^2A2^(3/2)A3^(-1/2) + m^2A1A2^(-1/2)A3^(1/2) + m^2A1A2^(1/2)A3^(-1/2) + 2m^3A2^(1/2)A3^(3/2) + 2m^3A2^(3/2)A3^(1/2) + m^3A1A2^(-1/2)A3^(3/2) + 3m^3A1A2^(1/2)A3^(1/2) + m^3A1A2^(3/2)A3^(-1/2) + m^4A2^(3/2)A3^(3/2) + 2m^4A1A2^(1/2)A3^(3/2) + 2m^4A1A2^(3/2)A3^(1/2) + m^5A1A2^(3/2)*A3^(3/2)

Vertex	Maslov	Rank
`(-1, -3/2, -3/2)`	-3	1
`(-1, -3/2, 1/2)`	-1	1
`(-1, -1/2, 1/2)`	0	1
`(-1, 1/2, -3/2)`	-1	1
`(-1, 1/2, -1/2)`	0	1
`(0, -3/2, -3/2)`	-2	1
`(0, -3/2, 1/2)`	0	1
`(0, -1/2, 3/2)`	2	1
`(0, 1/2, -3/2)`	0	1
`(0, 3/2, -1/2)`	2	1
`(0, 3/2, 3/2)`	4	1
`(1, -1/2, 1/2)`	2	1
`(1, -1/2, 3/2)`	3	1
`(1, 1/2, -1/2)`	2	1
`(1, 3/2, -1/2)`	3	1
`(1, 3/2, 3/2)`	5	1

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Record

FL/HFL Links

`orderOption(int)`	`1945`
`namestring`	`L9n23{0;0}`
`statusstring`	`success`
`slugstring`	`L9n23_0_0_1bca4468`
`result_filestring`	`details/L9n23_0_0_1bca4468.json`
`complexity_scoreOption(int)`	`243`
`strandsOption(int)`	`null`
`crossingsOption(int)`	`9`
`component_countOption(int)`	`3`
`girthOption(int)`	`6`
`total_rankOption(int)`	`56`
`wall_secondsOption(float)`	`0.001651`
`backend_secondsOption(float)`	`0.0`
`errorstring`
`dimensionOption(int)`	`3`
`support_sizeOption(int)`	`30`
`vertex_countOption(int)`	`16`
`fibered_vertex_countOption(int)`	`6`
`polytope_statusstring`	`computed`
`alexander_support_sizeOption(int)`	`6`
`alexander_vertex_countOption(int)`	`6`
`alexander_relationstring`	`not_computed`
`fk_countint`	`2`
`detailsRowRef(FLHFLLinks)`	{ "dataset": "FLHFLLinks", "key": "L9n23_0_0_1bca4468" }
`detail_assetstring`	`/api/v1/datasets/FLHFLLinks/assets/L9n23_0_0_1bca4468`

FL expansions

Braid

Multivariable Alexander polynomial

Dual Thurston polytope

HFL polytope

Record

F_L expansions