L10n78{0;1} - HFL and FL

details/L10n78_0_1_479a3ed6.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, 1/2, -3/2)`	`(1/2, 1/2, 1)`	`x1^(-1/2)x2^(-1/2)x3^(3/2)`	`q^(0)`	`{"0": [-1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1], "1": [-1, -1, -1, -1], "2": [1, 1, 1, -1, 1, 1, 1, 1]}`	(q^(-8))x1^(-1/2)x2^(-9/2)x3^(11/2) + (q^(-4) + q^(-5) + q^(-6))x1^(-3/2)x2^(-7/2)x3^(11/2) + (-q^(-5))x1^(-1/2)x2^(-7/2)x3^(9/2) + (-q^(-5) - q^(-6) - q^(-7))x1^(-1/2)x2^(-7/2)x3^(11/2) + (q^(-1) + q^(-2))x1^(-5/2)x2^(-5/2)x3^(11/2) + (-q^(-3))x1^(-3/2)x2^(-5/2)x3^(9/2) + (-q^(-2) - 3q^(-3) - q^(-4))x1^(-3/2)x2^(-5/2)x3^(11/2) + (q^(-4))x1^(-1/2)x2^(-5/2)x3^(9/2) + (q^(-4) + q^(-5))x1^(-1/2)x2^(-5/2)x3^(11/2) + (-q^(5))x1^(-7/2)x2^(-3/2)x3^(11/2) + (q^(2))x1^(-5/2)x2^(-3/2)x3^(9/2) + (q^(4) + q^(3) + q^(2) - q - 1)x1^(-5/2)x2^(-3/2)x3^(11/2) + (-1)x1^(-3/2)x2^(-3/2)x3^(7/2) + (-q - 1)x1^(-3/2)x2^(-3/2)x3^(9/2) + (-q^(2) - q - 1 + q^(-1) + q^(-2))x1^(-3/2)x2^(-3/2)x3^(11/2) + (q^(-1))x1^(-1/2)x2^(-3/2)x3^(5/2) + (q^(-1))x1^(-1/2)x2^(-3/2)x3^(7/2) + (q^(-1))x1^(-1/2)x2^(-3/2)x3^(9/2) + (q^(-1))x1^(-1/2)x2^(-3/2)x3^(11/2) + (-q^(10))x1^(-9/2)x2^(-1/2)x3^(11/2) + (q^(6))x1^(-7/2)x2^(-1/2)x3^(9/2) + (q^(9) + 2q^(8) + 2q^(7) + 2q^(6))x1^(-7/2)x2^(-1/2)x3^(11/2) + (-q^(3))x1^(-5/2)x2^(-1/2)x3^(7/2) + (-q^(5) - 2q^(4) - 2q^(3))x1^(-5/2)x2^(-1/2)x3^(9/2) + (-q^(7) - 2q^(6) - 4q^(5) - 3q^(4) - 2q^(3))x1^(-5/2)x2^(-1/2)x3^(11/2) + (q)x1^(-3/2)x2^(-1/2)x3^(5/2) + (q^(2) + 2q)x1^(-3/2)x2^(-1/2)x3^(7/2) + (q^(3) + 2q^(2) + 2q)x1^(-3/2)x2^(-1/2)x3^(9/2) + (q^(4) + 2q^(3) + 2q^(2) + 2q)x1^(-3/2)x2^(-1/2)x3^(11/2) + (-1)x1^(-1/2)x2^(-1/2)x3^(3/2) + (-1)x1^(-1/2)x2^(-1/2)x3^(5/2) + (-1)x1^(-1/2)x2^(-1/2)x3^(7/2) + (-1)x1^(-1/2)x2^(-1/2)x3^(9/2) + (-1)x1^(-1/2)x2^(-1/2)x3^(11/2) + (q^(14) + q^(13) + q^(12) + q^(11))x1^(-9/2)x2^(1/2)x3^(11/2) + (-q^(9) - q^(8) - q^(7))x1^(-7/2)x2^(1/2)x3^(9/2) + (-q^(12) - 2q^(11) - 4q^(10) - 4q^(9) - 3q^(8) - q^(7))x1^(-7/2)x2^(1/2)x3^(11/2) + (q^(5) + q^(4))x1^(-5/2)x2^(1/2)x3^(7/2) + (q^(7) + 2q^(6) + 3q^(5) + q^(4))x1^(-5/2)x2^(1/2)x3^(9/2) + (q^(9) + 2q^(8) + 4q^(7) + 4q^(6) + 3q^(5) + q^(4))x1^(-5/2)x2^(1/2)x3^(11/2) + (-q^(2))x1^(-3/2)x2^(1/2)x3^(5/2) + (-q^(3) - q^(2))x1^(-3/2)x2^(1/2)x3^(7/2) + (-q^(4) - q^(3) - q^(2))x1^(-3/2)x2^(1/2)x3^(9/2) + (-q^(5) - q^(4) - q^(3) - q^(2))x1^(-3/2)x2^(1/2)x3^(11/2) + (-q^(17) - q^(16) - 2q^(15) - q^(14) - q^(13))x1^(-9/2)x2^(3/2)x3^(11/2) + (q^(11) + q^(10) + q^(9))x1^(-7/2)x2^(3/2)x3^(9/2) + (q^(14) + 2q^(13) + 3q^(12) + 4q^(11) + 2q^(10) + q^(9))x1^(-7/2)x2^(3/2)x3^(11/2) + (-q^(6))x1^(-5/2)x2^(3/2)x3^(7/2) + (-q^(8) - q^(7) - q^(6))x1^(-5/2)x2^(3/2)x3^(9/2) + (-q^(10) - q^(9) - 2q^(8) - q^(7) - q^(6))x1^(-5/2)x2^(3/2)x3^(11/2) + (q^(19) + q^(18) + q^(17) + q^(16))x1^(-9/2)x2^(5/2)x3^(11/2) + (-q^(12))x1^(-7/2)x2^(5/2)x3^(9/2) + (-q^(15) - q^(14) - q^(13) - q^(12))x1^(-7/2)x2^(5/2)x3^(11/2) + (-q^(20))x1^(-9/2)x2^(7/2)x3^(11/2)
`(1/2, 1/2, -3/2)`	`(1/2, 1/2, 1)`	`x1^(-1/2)x2^(-1/2)x3^(3/2)`	`q^(0)`	`{"0": [1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1], "1": [-1, -1, -1, 1], "2": [1, 1, 1, -1, 1, 1, 1, 1]}`	(q^(-8))x1^(-1/2)x2^(-9/2)x3^(11/2) + (q^(-4) + q^(-5) + q^(-6))x1^(-3/2)x2^(-7/2)x3^(11/2) + (-q^(-5))x1^(-1/2)x2^(-7/2)x3^(9/2) + (-q^(-5) - q^(-6) - q^(-7))x1^(-1/2)x2^(-7/2)x3^(11/2) + (q^(-1) + q^(-2))x1^(-5/2)x2^(-5/2)x3^(11/2) + (-q^(-3))x1^(-3/2)x2^(-5/2)x3^(9/2) + (-q^(-2) - 3q^(-3) - q^(-4))x1^(-3/2)x2^(-5/2)x3^(11/2) + (q^(-4))x1^(-1/2)x2^(-5/2)x3^(9/2) + (q^(-4) + q^(-5))x1^(-1/2)x2^(-5/2)x3^(11/2) + (-q^(5))x1^(-7/2)x2^(-3/2)x3^(11/2) + (q^(2))x1^(-5/2)x2^(-3/2)x3^(9/2) + (q^(4) + q^(3) + q^(2) - q - 1)x1^(-5/2)x2^(-3/2)x3^(11/2) + (-1)x1^(-3/2)x2^(-3/2)x3^(7/2) + (-q - 1)x1^(-3/2)x2^(-3/2)x3^(9/2) + (-q^(2) - q - 1 + q^(-1) + q^(-2))x1^(-3/2)x2^(-3/2)x3^(11/2) + (q^(-1))x1^(-1/2)x2^(-3/2)x3^(5/2) + (q^(-1))x1^(-1/2)x2^(-3/2)x3^(7/2) + (q^(-1))x1^(-1/2)x2^(-3/2)x3^(9/2) + (q^(-1))x1^(-1/2)x2^(-3/2)x3^(11/2) + (-q^(10))x1^(-9/2)x2^(-1/2)x3^(11/2) + (q^(6))x1^(-7/2)x2^(-1/2)x3^(9/2) + (q^(9) + 2q^(8) + 2q^(7) + 2q^(6))x1^(-7/2)x2^(-1/2)x3^(11/2) + (-q^(3))x1^(-5/2)x2^(-1/2)x3^(7/2) + (-q^(5) - 2q^(4) - 2q^(3))x1^(-5/2)x2^(-1/2)x3^(9/2) + (-q^(7) - 2q^(6) - 4q^(5) - 3q^(4) - 2q^(3))x1^(-5/2)x2^(-1/2)x3^(11/2) + (q)x1^(-3/2)x2^(-1/2)x3^(5/2) + (q^(2) + 2q)x1^(-3/2)x2^(-1/2)x3^(7/2) + (q^(3) + 2q^(2) + 2q)x1^(-3/2)x2^(-1/2)x3^(9/2) + (q^(4) + 2q^(3) + 2q^(2) + 2q)x1^(-3/2)x2^(-1/2)x3^(11/2) + (-1)x1^(-1/2)x2^(-1/2)x3^(3/2) + (-1)x1^(-1/2)x2^(-1/2)x3^(5/2) + (-1)x1^(-1/2)x2^(-1/2)x3^(7/2) + (-1)x1^(-1/2)x2^(-1/2)x3^(9/2) + (-1)x1^(-1/2)x2^(-1/2)x3^(11/2) + (q^(14) + q^(13) + q^(12) + q^(11))x1^(-9/2)x2^(1/2)x3^(11/2) + (-q^(9) - q^(8) - q^(7))x1^(-7/2)x2^(1/2)x3^(9/2) + (-q^(12) - 2q^(11) - 4q^(10) - 4q^(9) - 3q^(8) - q^(7))x1^(-7/2)x2^(1/2)x3^(11/2) + (q^(5) + q^(4))x1^(-5/2)x2^(1/2)x3^(7/2) + (q^(7) + 2q^(6) + 3q^(5) + q^(4))x1^(-5/2)x2^(1/2)x3^(9/2) + (q^(9) + 2q^(8) + 4q^(7) + 4q^(6) + 3q^(5) + q^(4))x1^(-5/2)x2^(1/2)x3^(11/2) + (-q^(2))x1^(-3/2)x2^(1/2)x3^(5/2) + (-q^(3) - q^(2))x1^(-3/2)x2^(1/2)x3^(7/2) + (-q^(4) - q^(3) - q^(2))x1^(-3/2)x2^(1/2)x3^(9/2) + (-q^(5) - q^(4) - q^(3) - q^(2))x1^(-3/2)x2^(1/2)x3^(11/2) + (-q^(17) - q^(16) - 2q^(15) - q^(14) - q^(13))x1^(-9/2)x2^(3/2)x3^(11/2) + (q^(11) + q^(10) + q^(9))x1^(-7/2)x2^(3/2)x3^(9/2) + (q^(14) + 2q^(13) + 3q^(12) + 4q^(11) + 2q^(10) + q^(9))x1^(-7/2)x2^(3/2)x3^(11/2) + (-q^(6))x1^(-5/2)x2^(3/2)x3^(7/2) + (-q^(8) - q^(7) - q^(6))x1^(-5/2)x2^(3/2)x3^(9/2) + (-q^(10) - q^(9) - 2q^(8) - q^(7) - q^(6))x1^(-5/2)x2^(3/2)x3^(11/2) + (q^(19) + q^(18) + q^(17) + q^(16))x1^(-9/2)x2^(5/2)x3^(11/2) + (-q^(12))x1^(-7/2)x2^(5/2)x3^(9/2) + (-q^(15) - q^(14) - q^(13) - q^(12))x1^(-7/2)x2^(5/2)x3^(11/2) + (-q^(20))x1^(-9/2)x2^(7/2)x3^(11/2)
`(-1/2, -1/2, 3/2)`		`x1^(1/2)x2^(1/2)x3^(-3/2)`	`q^(0)`		(q^(-8))x1^(1/2)x2^(9/2)x3^(-11/2) + (q^(-4) + q^(-5) + q^(-6))x1^(3/2)x2^(7/2)x3^(-11/2) + (-q^(-5))x1^(1/2)x2^(7/2)x3^(-9/2) + (-q^(-5) - q^(-6) - q^(-7))x1^(1/2)x2^(7/2)x3^(-11/2) + (q^(-1) + q^(-2))x1^(5/2)x2^(5/2)x3^(-11/2) + (-q^(-3))x1^(3/2)x2^(5/2)x3^(-9/2) + (-q^(-2) - 3q^(-3) - q^(-4))x1^(3/2)x2^(5/2)x3^(-11/2) + (q^(-4))x1^(1/2)x2^(5/2)x3^(-9/2) + (q^(-4) + q^(-5))x1^(1/2)x2^(5/2)x3^(-11/2) + (-q^(5))x1^(7/2)x2^(3/2)x3^(-11/2) + (q^(2))x1^(5/2)x2^(3/2)x3^(-9/2) + (q^(4) + q^(3) + q^(2) - q - 1)x1^(5/2)x2^(3/2)x3^(-11/2) + (-1)x1^(3/2)x2^(3/2)x3^(-7/2) + (-q - 1)x1^(3/2)x2^(3/2)x3^(-9/2) + (-q^(2) - q - 1 + q^(-1) + q^(-2))x1^(3/2)x2^(3/2)x3^(-11/2) + (q^(-1))x1^(1/2)x2^(3/2)x3^(-5/2) + (q^(-1))x1^(1/2)x2^(3/2)x3^(-7/2) + (q^(-1))x1^(1/2)x2^(3/2)x3^(-9/2) + (q^(-1))x1^(1/2)x2^(3/2)x3^(-11/2) + (-q^(10))x1^(9/2)x2^(1/2)x3^(-11/2) + (q^(6))x1^(7/2)x2^(1/2)x3^(-9/2) + (q^(9) + 2q^(8) + 2q^(7) + 2q^(6))x1^(7/2)x2^(1/2)x3^(-11/2) + (-q^(3))x1^(5/2)x2^(1/2)x3^(-7/2) + (-q^(5) - 2q^(4) - 2q^(3))x1^(5/2)x2^(1/2)x3^(-9/2) + (-q^(7) - 2q^(6) - 4q^(5) - 3q^(4) - 2q^(3))x1^(5/2)x2^(1/2)x3^(-11/2) + (q)x1^(3/2)x2^(1/2)x3^(-5/2) + (q^(2) + 2q)x1^(3/2)x2^(1/2)x3^(-7/2) + (q^(3) + 2q^(2) + 2q)x1^(3/2)x2^(1/2)x3^(-9/2) + (q^(4) + 2q^(3) + 2q^(2) + 2q)x1^(3/2)x2^(1/2)x3^(-11/2) + (-1)x1^(1/2)x2^(1/2)x3^(-3/2) + (-1)x1^(1/2)x2^(1/2)x3^(-5/2) + (-1)x1^(1/2)x2^(1/2)x3^(-7/2) + (-1)x1^(1/2)x2^(1/2)x3^(-9/2) + (-1)x1^(1/2)x2^(1/2)x3^(-11/2) + (q^(14) + q^(13) + q^(12) + q^(11))x1^(9/2)x2^(-1/2)x3^(-11/2) + (-q^(9) - q^(8) - q^(7))x1^(7/2)x2^(-1/2)x3^(-9/2) + (-q^(12) - 2q^(11) - 4q^(10) - 4q^(9) - 3q^(8) - q^(7))x1^(7/2)x2^(-1/2)x3^(-11/2) + (q^(5) + q^(4))x1^(5/2)x2^(-1/2)x3^(-7/2) + (q^(7) + 2q^(6) + 3q^(5) + q^(4))x1^(5/2)x2^(-1/2)x3^(-9/2) + (q^(9) + 2q^(8) + 4q^(7) + 4q^(6) + 3q^(5) + q^(4))x1^(5/2)x2^(-1/2)x3^(-11/2) + (-q^(2))x1^(3/2)x2^(-1/2)x3^(-5/2) + (-q^(3) - q^(2))x1^(3/2)x2^(-1/2)x3^(-7/2) + (-q^(4) - q^(3) - q^(2))x1^(3/2)x2^(-1/2)x3^(-9/2) + (-q^(5) - q^(4) - q^(3) - q^(2))x1^(3/2)x2^(-1/2)x3^(-11/2) + (-q^(17) - q^(16) - 2q^(15) - q^(14) - q^(13))x1^(9/2)x2^(-3/2)x3^(-11/2) + (q^(11) + q^(10) + q^(9))x1^(7/2)x2^(-3/2)x3^(-9/2) + (q^(14) + 2q^(13) + 3q^(12) + 4q^(11) + 2q^(10) + q^(9))x1^(7/2)x2^(-3/2)x3^(-11/2) + (-q^(6))x1^(5/2)x2^(-3/2)x3^(-7/2) + (-q^(8) - q^(7) - q^(6))x1^(5/2)x2^(-3/2)x3^(-9/2) + (-q^(10) - q^(9) - 2q^(8) - q^(7) - q^(6))x1^(5/2)x2^(-3/2)x3^(-11/2) + (q^(19) + q^(18) + q^(17) + q^(16))x1^(9/2)x2^(-5/2)x3^(-11/2) + (-q^(12))x1^(7/2)x2^(-5/2)x3^(-9/2) + (-q^(15) - q^(14) - q^(13) - q^(12))x1^(7/2)x2^(-5/2)x3^(-11/2) + (-q^(20))x1^(9/2)x2^(-7/2)x3^(-11/2)

(1/2, 1/2, -3/2)

(1/2, 1/2, 1)

x1^(-1/2)x2^(-1/2)x3^(3/2)

q^(0)

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

(q^(-8))*x1^(-1/2)*x2^(-9/2)*x3^(11/2) + (q^(-4) + q^(-5) + q^(-6))*x1^(-3/2)*x2^(-7/2)*x3^(11/2) + (-q^(-5))*x1^(-1/2)*x2^(-7/2)*x3^(9/2) + (-q^(-5) - q^(-6) - q^(-7))*x1^(-1/2)*x2^(-7/2)*x3^(11/2) + (q^(-1) + q^(-2))*x1^(-5/2)*x2^(-5/2)*x3^(11/2) + (-q^(-3))*x1^(-3/2)*x2^(-5/2)*x3^(9/2) + (-q^(-2) - 3*q^(-3) - q^(-4))*x1^(-3/2)*x2^(-5/2)*x3^(11/2) + (q^(-4))*x1^(-1/2)*x2^(-5/2)*x3^(9/2) + (q^(-4) + q^(-5))*x1^(-1/2)*x2^(-5/2)*x3^(11/2) + (-q^(5))*x1^(-7/2)*x2^(-3/2)*x3^(11/2) + (q^(2))*x1^(-5/2)*x2^(-3/2)*x3^(9/2) + (q^(4) + q^(3) + q^(2) - q - 1)*x1^(-5/2)*x2^(-3/2)*x3^(11/2) + (-1)*x1^(-3/2)*x2^(-3/2)*x3^(7/2) + (-q - 1)*x1^(-3/2)*x2^(-3/2)*x3^(9/2) + (-q^(2) - q - 1 + q^(-1) + q^(-2))*x1^(-3/2)*x2^(-3/2)*x3^(11/2) + (q^(-1))*x1^(-1/2)*x2^(-3/2)*x3^(5/2) + (q^(-1))*x1^(-1/2)*x2^(-3/2)*x3^(7/2) + (q^(-1))*x1^(-1/2)*x2^(-3/2)*x3^(9/2) + (q^(-1))*x1^(-1/2)*x2^(-3/2)*x3^(11/2) + (-q^(10))*x1^(-9/2)*x2^(-1/2)*x3^(11/2) + (q^(6))*x1^(-7/2)*x2^(-1/2)*x3^(9/2) + (q^(9) + 2*q^(8) + 2*q^(7) + 2*q^(6))*x1^(-7/2)*x2^(-1/2)*x3^(11/2) + (-q^(3))*x1^(-5/2)*x2^(-1/2)*x3^(7/2) + (-q^(5) - 2*q^(4) - 2*q^(3))*x1^(-5/2)*x2^(-1/2)*x3^(9/2) + (-q^(7) - 2*q^(6) - 4*q^(5) - 3*q^(4) - 2*q^(3))*x1^(-5/2)*x2^(-1/2)*x3^(11/2) + (q)*x1^(-3/2)*x2^(-1/2)*x3^(5/2) + (q^(2) + 2*q)*x1^(-3/2)*x2^(-1/2)*x3^(7/2) + (q^(3) + 2*q^(2) + 2*q)*x1^(-3/2)*x2^(-1/2)*x3^(9/2) + (q^(4) + 2*q^(3) + 2*q^(2) + 2*q)*x1^(-3/2)*x2^(-1/2)*x3^(11/2) + (-1)*x1^(-1/2)*x2^(-1/2)*x3^(3/2) + (-1)*x1^(-1/2)*x2^(-1/2)*x3^(5/2) + (-1)*x1^(-1/2)*x2^(-1/2)*x3^(7/2) + (-1)*x1^(-1/2)*x2^(-1/2)*x3^(9/2) + (-1)*x1^(-1/2)*x2^(-1/2)*x3^(11/2) + (q^(14) + q^(13) + q^(12) + q^(11))*x1^(-9/2)*x2^(1/2)*x3^(11/2) + (-q^(9) - q^(8) - q^(7))*x1^(-7/2)*x2^(1/2)*x3^(9/2) + (-q^(12) - 2*q^(11) - 4*q^(10) - 4*q^(9) - 3*q^(8) - q^(7))*x1^(-7/2)*x2^(1/2)*x3^(11/2) + (q^(5) + q^(4))*x1^(-5/2)*x2^(1/2)*x3^(7/2) + (q^(7) + 2*q^(6) + 3*q^(5) + q^(4))*x1^(-5/2)*x2^(1/2)*x3^(9/2) + (q^(9) + 2*q^(8) + 4*q^(7) + 4*q^(6) + 3*q^(5) + q^(4))*x1^(-5/2)*x2^(1/2)*x3^(11/2) + (-q^(2))*x1^(-3/2)*x2^(1/2)*x3^(5/2) + (-q^(3) - q^(2))*x1^(-3/2)*x2^(1/2)*x3^(7/2) + (-q^(4) - q^(3) - q^(2))*x1^(-3/2)*x2^(1/2)*x3^(9/2) + (-q^(5) - q^(4) - q^(3) - q^(2))*x1^(-3/2)*x2^(1/2)*x3^(11/2) + (-q^(17) - q^(16) - 2*q^(15) - q^(14) - q^(13))*x1^(-9/2)*x2^(3/2)*x3^(11/2) + (q^(11) + q^(10) + q^(9))*x1^(-7/2)*x2^(3/2)*x3^(9/2) + (q^(14) + 2*q^(13) + 3*q^(12) + 4*q^(11) + 2*q^(10) + q^(9))*x1^(-7/2)*x2^(3/2)*x3^(11/2) + (-q^(6))*x1^(-5/2)*x2^(3/2)*x3^(7/2) + (-q^(8) - q^(7) - q^(6))*x1^(-5/2)*x2^(3/2)*x3^(9/2) + (-q^(10) - q^(9) - 2*q^(8) - q^(7) - q^(6))*x1^(-5/2)*x2^(3/2)*x3^(11/2) + (q^(19) + q^(18) + q^(17) + q^(16))*x1^(-9/2)*x2^(5/2)*x3^(11/2) + (-q^(12))*x1^(-7/2)*x2^(5/2)*x3^(9/2) + (-q^(15) - q^(14) - q^(13) - q^(12))*x1^(-7/2)*x2^(5/2)*x3^(11/2) + (-q^(20))*x1^(-9/2)*x2^(7/2)*x3^(11/2)

(1/2, 1/2, -3/2)

(1/2, 1/2, 1)

x1^(-1/2)x2^(-1/2)x3^(3/2)

q^(0)

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

(q^(-8))*x1^(-1/2)*x2^(-9/2)*x3^(11/2) + (q^(-4) + q^(-5) + q^(-6))*x1^(-3/2)*x2^(-7/2)*x3^(11/2) + (-q^(-5))*x1^(-1/2)*x2^(-7/2)*x3^(9/2) + (-q^(-5) - q^(-6) - q^(-7))*x1^(-1/2)*x2^(-7/2)*x3^(11/2) + (q^(-1) + q^(-2))*x1^(-5/2)*x2^(-5/2)*x3^(11/2) + (-q^(-3))*x1^(-3/2)*x2^(-5/2)*x3^(9/2) + (-q^(-2) - 3*q^(-3) - q^(-4))*x1^(-3/2)*x2^(-5/2)*x3^(11/2) + (q^(-4))*x1^(-1/2)*x2^(-5/2)*x3^(9/2) + (q^(-4) + q^(-5))*x1^(-1/2)*x2^(-5/2)*x3^(11/2) + (-q^(5))*x1^(-7/2)*x2^(-3/2)*x3^(11/2) + (q^(2))*x1^(-5/2)*x2^(-3/2)*x3^(9/2) + (q^(4) + q^(3) + q^(2) - q - 1)*x1^(-5/2)*x2^(-3/2)*x3^(11/2) + (-1)*x1^(-3/2)*x2^(-3/2)*x3^(7/2) + (-q - 1)*x1^(-3/2)*x2^(-3/2)*x3^(9/2) + (-q^(2) - q - 1 + q^(-1) + q^(-2))*x1^(-3/2)*x2^(-3/2)*x3^(11/2) + (q^(-1))*x1^(-1/2)*x2^(-3/2)*x3^(5/2) + (q^(-1))*x1^(-1/2)*x2^(-3/2)*x3^(7/2) + (q^(-1))*x1^(-1/2)*x2^(-3/2)*x3^(9/2) + (q^(-1))*x1^(-1/2)*x2^(-3/2)*x3^(11/2) + (-q^(10))*x1^(-9/2)*x2^(-1/2)*x3^(11/2) + (q^(6))*x1^(-7/2)*x2^(-1/2)*x3^(9/2) + (q^(9) + 2*q^(8) + 2*q^(7) + 2*q^(6))*x1^(-7/2)*x2^(-1/2)*x3^(11/2) + (-q^(3))*x1^(-5/2)*x2^(-1/2)*x3^(7/2) + (-q^(5) - 2*q^(4) - 2*q^(3))*x1^(-5/2)*x2^(-1/2)*x3^(9/2) + (-q^(7) - 2*q^(6) - 4*q^(5) - 3*q^(4) - 2*q^(3))*x1^(-5/2)*x2^(-1/2)*x3^(11/2) + (q)*x1^(-3/2)*x2^(-1/2)*x3^(5/2) + (q^(2) + 2*q)*x1^(-3/2)*x2^(-1/2)*x3^(7/2) + (q^(3) + 2*q^(2) + 2*q)*x1^(-3/2)*x2^(-1/2)*x3^(9/2) + (q^(4) + 2*q^(3) + 2*q^(2) + 2*q)*x1^(-3/2)*x2^(-1/2)*x3^(11/2) + (-1)*x1^(-1/2)*x2^(-1/2)*x3^(3/2) + (-1)*x1^(-1/2)*x2^(-1/2)*x3^(5/2) + (-1)*x1^(-1/2)*x2^(-1/2)*x3^(7/2) + (-1)*x1^(-1/2)*x2^(-1/2)*x3^(9/2) + (-1)*x1^(-1/2)*x2^(-1/2)*x3^(11/2) + (q^(14) + q^(13) + q^(12) + q^(11))*x1^(-9/2)*x2^(1/2)*x3^(11/2) + (-q^(9) - q^(8) - q^(7))*x1^(-7/2)*x2^(1/2)*x3^(9/2) + (-q^(12) - 2*q^(11) - 4*q^(10) - 4*q^(9) - 3*q^(8) - q^(7))*x1^(-7/2)*x2^(1/2)*x3^(11/2) + (q^(5) + q^(4))*x1^(-5/2)*x2^(1/2)*x3^(7/2) + (q^(7) + 2*q^(6) + 3*q^(5) + q^(4))*x1^(-5/2)*x2^(1/2)*x3^(9/2) + (q^(9) + 2*q^(8) + 4*q^(7) + 4*q^(6) + 3*q^(5) + q^(4))*x1^(-5/2)*x2^(1/2)*x3^(11/2) + (-q^(2))*x1^(-3/2)*x2^(1/2)*x3^(5/2) + (-q^(3) - q^(2))*x1^(-3/2)*x2^(1/2)*x3^(7/2) + (-q^(4) - q^(3) - q^(2))*x1^(-3/2)*x2^(1/2)*x3^(9/2) + (-q^(5) - q^(4) - q^(3) - q^(2))*x1^(-3/2)*x2^(1/2)*x3^(11/2) + (-q^(17) - q^(16) - 2*q^(15) - q^(14) - q^(13))*x1^(-9/2)*x2^(3/2)*x3^(11/2) + (q^(11) + q^(10) + q^(9))*x1^(-7/2)*x2^(3/2)*x3^(9/2) + (q^(14) + 2*q^(13) + 3*q^(12) + 4*q^(11) + 2*q^(10) + q^(9))*x1^(-7/2)*x2^(3/2)*x3^(11/2) + (-q^(6))*x1^(-5/2)*x2^(3/2)*x3^(7/2) + (-q^(8) - q^(7) - q^(6))*x1^(-5/2)*x2^(3/2)*x3^(9/2) + (-q^(10) - q^(9) - 2*q^(8) - q^(7) - q^(6))*x1^(-5/2)*x2^(3/2)*x3^(11/2) + (q^(19) + q^(18) + q^(17) + q^(16))*x1^(-9/2)*x2^(5/2)*x3^(11/2) + (-q^(12))*x1^(-7/2)*x2^(5/2)*x3^(9/2) + (-q^(15) - q^(14) - q^(13) - q^(12))*x1^(-7/2)*x2^(5/2)*x3^(11/2) + (-q^(20))*x1^(-9/2)*x2^(7/2)*x3^(11/2)

(-1/2, -1/2, 3/2)

x1^(1/2)x2^(1/2)x3^(-3/2)

q^(0)

(q^(-8))*x1^(1/2)*x2^(9/2)*x3^(-11/2) + (q^(-4) + q^(-5) + q^(-6))*x1^(3/2)*x2^(7/2)*x3^(-11/2) + (-q^(-5))*x1^(1/2)*x2^(7/2)*x3^(-9/2) + (-q^(-5) - q^(-6) - q^(-7))*x1^(1/2)*x2^(7/2)*x3^(-11/2) + (q^(-1) + q^(-2))*x1^(5/2)*x2^(5/2)*x3^(-11/2) + (-q^(-3))*x1^(3/2)*x2^(5/2)*x3^(-9/2) + (-q^(-2) - 3*q^(-3) - q^(-4))*x1^(3/2)*x2^(5/2)*x3^(-11/2) + (q^(-4))*x1^(1/2)*x2^(5/2)*x3^(-9/2) + (q^(-4) + q^(-5))*x1^(1/2)*x2^(5/2)*x3^(-11/2) + (-q^(5))*x1^(7/2)*x2^(3/2)*x3^(-11/2) + (q^(2))*x1^(5/2)*x2^(3/2)*x3^(-9/2) + (q^(4) + q^(3) + q^(2) - q - 1)*x1^(5/2)*x2^(3/2)*x3^(-11/2) + (-1)*x1^(3/2)*x2^(3/2)*x3^(-7/2) + (-q - 1)*x1^(3/2)*x2^(3/2)*x3^(-9/2) + (-q^(2) - q - 1 + q^(-1) + q^(-2))*x1^(3/2)*x2^(3/2)*x3^(-11/2) + (q^(-1))*x1^(1/2)*x2^(3/2)*x3^(-5/2) + (q^(-1))*x1^(1/2)*x2^(3/2)*x3^(-7/2) + (q^(-1))*x1^(1/2)*x2^(3/2)*x3^(-9/2) + (q^(-1))*x1^(1/2)*x2^(3/2)*x3^(-11/2) + (-q^(10))*x1^(9/2)*x2^(1/2)*x3^(-11/2) + (q^(6))*x1^(7/2)*x2^(1/2)*x3^(-9/2) + (q^(9) + 2*q^(8) + 2*q^(7) + 2*q^(6))*x1^(7/2)*x2^(1/2)*x3^(-11/2) + (-q^(3))*x1^(5/2)*x2^(1/2)*x3^(-7/2) + (-q^(5) - 2*q^(4) - 2*q^(3))*x1^(5/2)*x2^(1/2)*x3^(-9/2) + (-q^(7) - 2*q^(6) - 4*q^(5) - 3*q^(4) - 2*q^(3))*x1^(5/2)*x2^(1/2)*x3^(-11/2) + (q)*x1^(3/2)*x2^(1/2)*x3^(-5/2) + (q^(2) + 2*q)*x1^(3/2)*x2^(1/2)*x3^(-7/2) + (q^(3) + 2*q^(2) + 2*q)*x1^(3/2)*x2^(1/2)*x3^(-9/2) + (q^(4) + 2*q^(3) + 2*q^(2) + 2*q)*x1^(3/2)*x2^(1/2)*x3^(-11/2) + (-1)*x1^(1/2)*x2^(1/2)*x3^(-3/2) + (-1)*x1^(1/2)*x2^(1/2)*x3^(-5/2) + (-1)*x1^(1/2)*x2^(1/2)*x3^(-7/2) + (-1)*x1^(1/2)*x2^(1/2)*x3^(-9/2) + (-1)*x1^(1/2)*x2^(1/2)*x3^(-11/2) + (q^(14) + q^(13) + q^(12) + q^(11))*x1^(9/2)*x2^(-1/2)*x3^(-11/2) + (-q^(9) - q^(8) - q^(7))*x1^(7/2)*x2^(-1/2)*x3^(-9/2) + (-q^(12) - 2*q^(11) - 4*q^(10) - 4*q^(9) - 3*q^(8) - q^(7))*x1^(7/2)*x2^(-1/2)*x3^(-11/2) + (q^(5) + q^(4))*x1^(5/2)*x2^(-1/2)*x3^(-7/2) + (q^(7) + 2*q^(6) + 3*q^(5) + q^(4))*x1^(5/2)*x2^(-1/2)*x3^(-9/2) + (q^(9) + 2*q^(8) + 4*q^(7) + 4*q^(6) + 3*q^(5) + q^(4))*x1^(5/2)*x2^(-1/2)*x3^(-11/2) + (-q^(2))*x1^(3/2)*x2^(-1/2)*x3^(-5/2) + (-q^(3) - q^(2))*x1^(3/2)*x2^(-1/2)*x3^(-7/2) + (-q^(4) - q^(3) - q^(2))*x1^(3/2)*x2^(-1/2)*x3^(-9/2) + (-q^(5) - q^(4) - q^(3) - q^(2))*x1^(3/2)*x2^(-1/2)*x3^(-11/2) + (-q^(17) - q^(16) - 2*q^(15) - q^(14) - q^(13))*x1^(9/2)*x2^(-3/2)*x3^(-11/2) + (q^(11) + q^(10) + q^(9))*x1^(7/2)*x2^(-3/2)*x3^(-9/2) + (q^(14) + 2*q^(13) + 3*q^(12) + 4*q^(11) + 2*q^(10) + q^(9))*x1^(7/2)*x2^(-3/2)*x3^(-11/2) + (-q^(6))*x1^(5/2)*x2^(-3/2)*x3^(-7/2) + (-q^(8) - q^(7) - q^(6))*x1^(5/2)*x2^(-3/2)*x3^(-9/2) + (-q^(10) - q^(9) - 2*q^(8) - q^(7) - q^(6))*x1^(5/2)*x2^(-3/2)*x3^(-11/2) + (q^(19) + q^(18) + q^(17) + q^(16))*x1^(9/2)*x2^(-5/2)*x3^(-11/2) + (-q^(12))*x1^(7/2)*x2^(-5/2)*x3^(-9/2) + (-q^(15) - q^(14) - q^(13) - q^(12))*x1^(7/2)*x2^(-5/2)*x3^(-11/2) + (-q^(20))*x1^(9/2)*x2^(-7/2)*x3^(-11/2)

Braid

Braid word	Components	Crossings	Strands
`[-2, -2, -1, 2, -3, -4, 2, 3, 4, 4, 3, -1]`	3	12	5

Multivariable Alexander polynomial

Δ_L
`-A1^(1/2)A2^(1/2)A3^(-1/2) + A1^(1/2)A2^(1/2)A3^(-3/2) - A1^(1/2)A2^(-1/2)A3^(1/2) + A1^(1/2)A2^(-1/2)A3^(-1/2) + A1^(1/2)A2^(-3/2)A3^(1/2) - A1^(-1/2)A2^(3/2)A3^(-1/2) - A1^(-1/2)A2^(1/2)A3^(1/2) + A1^(-1/2)A2^(1/2)A3^(-1/2) - A1^(-1/2)A2^(-1/2)A3^(3/2) + A1^(-1/2)A2^(-1/2)A3^(1/2)`

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, 1, -3)`	yes
`(1, -3, 1)`	yes
`(-1, 1, -1)`	yes
`(-1, 3, -1)`	yes
`(1, -1, 1)`	yes
`(-1, -1, 1)`	yes
`(-1, -1, 3)`	yes
`(1, 1, -1)`	yes

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HFL polytope

Poincaré polynomial
m^(-3)A1^(-1)A2^(-1) + m^(-3)A1^(-1)A3^(-1) + m^(-3)A2^(-2) + m^(-3)A2^(-1)A3^(-1) + m^(-3)A3^(-2) + 2m^(-2)A1^(-1)A2^(-1)A3 + 3m^(-2)A1^(-1) + 2m^(-2)A1^(-1)A2A3^(-1) + m^(-2)A2^(-2)A3 + 4m^(-2)A2^(-1) + 4m^(-2)A3^(-1) + m^(-2)A2A3^(-2) + m^(-2)A1A2^(-2) + m^(-2)A1A2^(-1)A3^(-1) + m^(-2)A1A3^(-2) + m^(-1)A1^(-1)A2^(-1)A3^2 + 3m^(-1)A1^(-1)A3 + 3m^(-1)A1^(-1)A2 + m^(-1)A1^(-1)A2^2A3^(-1) + 4m^(-1)A2^(-1)A3 + 6m^(-1) + 4m^(-1)A2A3^(-1) + m^(-1)A1A2^(-2)A3 + 3m^(-1)A1A2^(-1) + 3m^(-1)A1A3^(-1) + m^(-1)A1A2A3^(-2) + A1^(-1)A3^2 + A1^(-1)A2A3 + A1^(-1)A2^2 + A2^(-1)A3^2 + 4A3 + 4A2 + A2^2A3^(-1) + 2A1A2^(-1)A3 + 3A1 + 2A1A2A3^(-1) + mA3^2 + mA2A3 + mA2^2 + mA1A3 + mA1*A2

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

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Record

FL/HFL Links

`orderOption(int)`	`2218`
`namestring`	`L10n78{0;1}`
`statusstring`	`success`
`slugstring`	`L10n78_0_1_479a3ed6`
`result_filestring`	`details/L10n78_0_1_479a3ed6.json`
`complexity_scoreOption(int)`	`300`
`strandsOption(int)`	`null`
`crossingsOption(int)`	`10`
`component_countOption(int)`	`3`
`girthOption(int)`	`6`
`total_rankOption(int)`	`80`
`wall_secondsOption(float)`	`0.001878`
`backend_secondsOption(float)`	`0.0`
`errorstring`
`dimensionOption(int)`	`3`
`support_sizeOption(int)`	`41`
`vertex_countOption(int)`	`20`
`fibered_vertex_countOption(int)`	`8`
`polytope_statusstring`	`computed`
`alexander_support_sizeOption(int)`	`10`
`alexander_vertex_countOption(int)`	`8`
`alexander_relationstring`	`not_computed`
`fk_countint`	`8`
`detailsRowRef(FLHFLLinks)`	{ "dataset": "FLHFLLinks", "key": "L10n78_0_1_479a3ed6" }
`detail_assetstring`	`/api/v1/datasets/FLHFLLinks/assets/L10n78_0_1_479a3ed6`

FL expansions

Braid

Multivariable Alexander polynomial

Dual Thurston polytope

HFL polytope

Record

F_L expansions