L10n78{1;1} - HFL and FL

details/L10n78_1_1_31b7275a.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, -3/2, -1/2)`	`(1, 1, 1)`	`x1^(1/2)x2^(3/2)x3^(1/2)`	`q^(-2)`	`{"0": [-1, -1, 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^(3/2)x3^(1/2) + (-q^(-2))x1^(1/2)x2^(5/2)x3^(1/2) + (-q^(-2))x1^(1/2)x2^(7/2)x3^(1/2) + (-q^(-2))x1^(1/2)x2^(9/2)x3^(1/2) + (-q^(-2))x1^(1/2)x2^(11/2)x3^(1/2) + (q^(-3))x1^(1/2)x2^(5/2)x3^(3/2) + (q^(-3))x1^(1/2)x2^(7/2)x3^(3/2) + (q^(-3))x1^(1/2)x2^(9/2)x3^(3/2) + (q^(-3))x1^(1/2)x2^(11/2)x3^(3/2) + (q^(-6))x1^(1/2)x2^(9/2)x3^(5/2) + (q^(-6) + q^(-7))x1^(1/2)x2^(11/2)x3^(5/2) + (-q^(-7))x1^(1/2)x2^(9/2)x3^(7/2) + (-q^(-7) - q^(-8) - q^(-9))x1^(1/2)x2^(11/2)x3^(7/2) + (q^(-10))x1^(1/2)x2^(11/2)x3^(9/2) + (-1)x1^(3/2)x2^(5/2)x3^(-1/2) + (-q - 1)x1^(3/2)x2^(7/2)x3^(-1/2) + (-q^(2) - q - 1)x1^(3/2)x2^(9/2)x3^(-1/2) + (-q^(3) - q^(2) - q - 1)x1^(3/2)x2^(11/2)x3^(-1/2) + (q^(-1))x1^(3/2)x2^(5/2)x3^(1/2) + (1 + 2q^(-1))x1^(3/2)x2^(7/2)x3^(1/2) + (q + 21 + 2q^(-1))x1^(3/2)x2^(9/2)x3^(1/2) + (q^(2) + 2q + 21 + 2q^(-1))x1^(3/2)x2^(11/2)x3^(1/2) + (-q^(-2))x1^(3/2)x2^(7/2)x3^(3/2) + (-q^(-1) - q^(-2))x1^(3/2)x2^(9/2)x3^(3/2) + (-1 - q^(-1) - q^(-2) + q^(-3) + q^(-4))x1^(3/2)x2^(11/2)x3^(3/2) + (-q^(-5))x1^(3/2)x2^(9/2)x3^(5/2) + (-q^(-4) - 3q^(-5) - q^(-6))x1^(3/2)x2^(11/2)x3^(5/2) + (q^(-6) + q^(-7) + q^(-8))x1^(3/2)x2^(11/2)x3^(7/2) + (-q^(4))x1^(5/2)x2^(7/2)x3^(-3/2) + (-q^(6) - q^(5) - q^(4))x1^(5/2)x2^(9/2)x3^(-3/2) + (-q^(8) - q^(7) - 2q^(6) - q^(5) - q^(4))x1^(5/2)x2^(11/2)x3^(-3/2) + (q^(3) + q^(2))x1^(5/2)x2^(7/2)x3^(-1/2) + (q^(5) + 2q^(4) + 3q^(3) + q^(2))x1^(5/2)x2^(9/2)x3^(-1/2) + (q^(7) + 2q^(6) + 4q^(5) + 4q^(4) + 3q^(3) + q^(2))x1^(5/2)x2^(11/2)x3^(-1/2) + (-q)x1^(5/2)x2^(7/2)x3^(1/2) + (-q^(3) - 2q^(2) - 2q)x1^(5/2)x2^(9/2)x3^(1/2) + (-q^(5) - 2q^(4) - 4q^(3) - 3q^(2) - 2q)x1^(5/2)x2^(11/2)x3^(1/2) + (1)x1^(5/2)x2^(9/2)x3^(3/2) + (q^(2) + q + 1 - q^(-1) - q^(-2))x1^(5/2)x2^(11/2)x3^(3/2) + (q^(-3) + q^(-4))x1^(5/2)x2^(11/2)x3^(5/2) + (-q^(10))x1^(7/2)x2^(9/2)x3^(-5/2) + (-q^(13) - q^(12) - q^(11) - q^(10))x1^(7/2)x2^(11/2)x3^(-5/2) + (q^(9) + q^(8) + q^(7))x1^(7/2)x2^(9/2)x3^(-3/2) + (q^(12) + 2q^(11) + 3q^(10) + 4q^(9) + 2q^(8) + q^(7))x1^(7/2)x2^(11/2)x3^(-3/2) + (-q^(7) - q^(6) - q^(5))x1^(7/2)x2^(9/2)x3^(-1/2) + (-q^(10) - 2q^(9) - 4q^(8) - 4q^(7) - 3q^(6) - q^(5))x1^(7/2)x2^(11/2)x3^(-1/2) + (q^(4))x1^(7/2)x2^(9/2)x3^(1/2) + (q^(7) + 2q^(6) + 2q^(5) + 2q^(4))x1^(7/2)x2^(11/2)x3^(1/2) + (-q^(3))x1^(7/2)x2^(11/2)x3^(3/2) + (-q^(18))x1^(9/2)x2^(11/2)x3^(-7/2) + (q^(17) + q^(16) + q^(15) + q^(14))x1^(9/2)x2^(11/2)x3^(-5/2) + (-q^(15) - q^(14) - 2q^(13) - q^(12) - q^(11))x1^(9/2)x2^(11/2)x3^(-3/2) + (q^(12) + q^(11) + q^(10) + q^(9))x1^(9/2)x2^(11/2)x3^(-1/2) + (-q^(8))x1^(9/2)x2^(11/2)x3^(1/2)
`(-1/2, -3/2, -1/2)`	`(1, 1, 1)`	`x1^(1/2)x2^(3/2)x3^(1/2)`	`q^(-2)`	`{"0": [1, -1, 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^(3/2)x3^(1/2) + (-q^(-2))x1^(1/2)x2^(5/2)x3^(1/2) + (-q^(-2))x1^(1/2)x2^(7/2)x3^(1/2) + (-q^(-2))x1^(1/2)x2^(9/2)x3^(1/2) + (-q^(-2))x1^(1/2)x2^(11/2)x3^(1/2) + (q^(-3))x1^(1/2)x2^(5/2)x3^(3/2) + (q^(-3))x1^(1/2)x2^(7/2)x3^(3/2) + (q^(-3))x1^(1/2)x2^(9/2)x3^(3/2) + (q^(-3))x1^(1/2)x2^(11/2)x3^(3/2) + (q^(-6))x1^(1/2)x2^(9/2)x3^(5/2) + (q^(-6) + q^(-7))x1^(1/2)x2^(11/2)x3^(5/2) + (-q^(-7))x1^(1/2)x2^(9/2)x3^(7/2) + (-q^(-7) - q^(-8) - q^(-9))x1^(1/2)x2^(11/2)x3^(7/2) + (q^(-10))x1^(1/2)x2^(11/2)x3^(9/2) + (-1)x1^(3/2)x2^(5/2)x3^(-1/2) + (-q - 1)x1^(3/2)x2^(7/2)x3^(-1/2) + (-q^(2) - q - 1)x1^(3/2)x2^(9/2)x3^(-1/2) + (-q^(3) - q^(2) - q - 1)x1^(3/2)x2^(11/2)x3^(-1/2) + (q^(-1))x1^(3/2)x2^(5/2)x3^(1/2) + (1 + 2q^(-1))x1^(3/2)x2^(7/2)x3^(1/2) + (q + 21 + 2q^(-1))x1^(3/2)x2^(9/2)x3^(1/2) + (q^(2) + 2q + 21 + 2q^(-1))x1^(3/2)x2^(11/2)x3^(1/2) + (-q^(-2))x1^(3/2)x2^(7/2)x3^(3/2) + (-q^(-1) - q^(-2))x1^(3/2)x2^(9/2)x3^(3/2) + (-1 - q^(-1) - q^(-2) + q^(-3) + q^(-4))x1^(3/2)x2^(11/2)x3^(3/2) + (-q^(-5))x1^(3/2)x2^(9/2)x3^(5/2) + (-q^(-4) - 3q^(-5) - q^(-6))x1^(3/2)x2^(11/2)x3^(5/2) + (q^(-6) + q^(-7) + q^(-8))x1^(3/2)x2^(11/2)x3^(7/2) + (-q^(4))x1^(5/2)x2^(7/2)x3^(-3/2) + (-q^(6) - q^(5) - q^(4))x1^(5/2)x2^(9/2)x3^(-3/2) + (-q^(8) - q^(7) - 2q^(6) - q^(5) - q^(4))x1^(5/2)x2^(11/2)x3^(-3/2) + (q^(3) + q^(2))x1^(5/2)x2^(7/2)x3^(-1/2) + (q^(5) + 2q^(4) + 3q^(3) + q^(2))x1^(5/2)x2^(9/2)x3^(-1/2) + (q^(7) + 2q^(6) + 4q^(5) + 4q^(4) + 3q^(3) + q^(2))x1^(5/2)x2^(11/2)x3^(-1/2) + (-q)x1^(5/2)x2^(7/2)x3^(1/2) + (-q^(3) - 2q^(2) - 2q)x1^(5/2)x2^(9/2)x3^(1/2) + (-q^(5) - 2q^(4) - 4q^(3) - 3q^(2) - 2q)x1^(5/2)x2^(11/2)x3^(1/2) + (1)x1^(5/2)x2^(9/2)x3^(3/2) + (q^(2) + q + 1 - q^(-1) - q^(-2))x1^(5/2)x2^(11/2)x3^(3/2) + (q^(-3) + q^(-4))x1^(5/2)x2^(11/2)x3^(5/2) + (-q^(10))x1^(7/2)x2^(9/2)x3^(-5/2) + (-q^(13) - q^(12) - q^(11) - q^(10))x1^(7/2)x2^(11/2)x3^(-5/2) + (q^(9) + q^(8) + q^(7))x1^(7/2)x2^(9/2)x3^(-3/2) + (q^(12) + 2q^(11) + 3q^(10) + 4q^(9) + 2q^(8) + q^(7))x1^(7/2)x2^(11/2)x3^(-3/2) + (-q^(7) - q^(6) - q^(5))x1^(7/2)x2^(9/2)x3^(-1/2) + (-q^(10) - 2q^(9) - 4q^(8) - 4q^(7) - 3q^(6) - q^(5))x1^(7/2)x2^(11/2)x3^(-1/2) + (q^(4))x1^(7/2)x2^(9/2)x3^(1/2) + (q^(7) + 2q^(6) + 2q^(5) + 2q^(4))x1^(7/2)x2^(11/2)x3^(1/2) + (-q^(3))x1^(7/2)x2^(11/2)x3^(3/2) + (-q^(18))x1^(9/2)x2^(11/2)x3^(-7/2) + (q^(17) + q^(16) + q^(15) + q^(14))x1^(9/2)x2^(11/2)x3^(-5/2) + (-q^(15) - q^(14) - 2q^(13) - q^(12) - q^(11))x1^(9/2)x2^(11/2)x3^(-3/2) + (q^(12) + q^(11) + q^(10) + q^(9))x1^(9/2)x2^(11/2)x3^(-1/2) + (-q^(8))x1^(9/2)x2^(11/2)x3^(1/2)
`(1/2, 3/2, 1/2)`		`x1^(-1/2)x2^(-3/2)x3^(-1/2)`	`q^(-2)`		(-q^(-2))x1^(-1/2)x2^(-3/2)x3^(-1/2) + (-q^(-2))x1^(-1/2)x2^(-5/2)x3^(-1/2) + (-q^(-2))x1^(-1/2)x2^(-7/2)x3^(-1/2) + (-q^(-2))x1^(-1/2)x2^(-9/2)x3^(-1/2) + (-q^(-2))x1^(-1/2)x2^(-11/2)x3^(-1/2) + (q^(-3))x1^(-1/2)x2^(-5/2)x3^(-3/2) + (q^(-3))x1^(-1/2)x2^(-7/2)x3^(-3/2) + (q^(-3))x1^(-1/2)x2^(-9/2)x3^(-3/2) + (q^(-3))x1^(-1/2)x2^(-11/2)x3^(-3/2) + (q^(-6))x1^(-1/2)x2^(-9/2)x3^(-5/2) + (q^(-6) + q^(-7))x1^(-1/2)x2^(-11/2)x3^(-5/2) + (-q^(-7))x1^(-1/2)x2^(-9/2)x3^(-7/2) + (-q^(-7) - q^(-8) - q^(-9))x1^(-1/2)x2^(-11/2)x3^(-7/2) + (q^(-10))x1^(-1/2)x2^(-11/2)x3^(-9/2) + (-1)x1^(-3/2)x2^(-5/2)x3^(1/2) + (-q - 1)x1^(-3/2)x2^(-7/2)x3^(1/2) + (-q^(2) - q - 1)x1^(-3/2)x2^(-9/2)x3^(1/2) + (-q^(3) - q^(2) - q - 1)x1^(-3/2)x2^(-11/2)x3^(1/2) + (q^(-1))x1^(-3/2)x2^(-5/2)x3^(-1/2) + (1 + 2q^(-1))x1^(-3/2)x2^(-7/2)x3^(-1/2) + (q + 21 + 2q^(-1))x1^(-3/2)x2^(-9/2)x3^(-1/2) + (q^(2) + 2q + 21 + 2q^(-1))x1^(-3/2)x2^(-11/2)x3^(-1/2) + (-q^(-2))x1^(-3/2)x2^(-7/2)x3^(-3/2) + (-q^(-1) - q^(-2))x1^(-3/2)x2^(-9/2)x3^(-3/2) + (-1 - q^(-1) - q^(-2) + q^(-3) + q^(-4))x1^(-3/2)x2^(-11/2)x3^(-3/2) + (-q^(-5))x1^(-3/2)x2^(-9/2)x3^(-5/2) + (-q^(-4) - 3q^(-5) - q^(-6))x1^(-3/2)x2^(-11/2)x3^(-5/2) + (q^(-6) + q^(-7) + q^(-8))x1^(-3/2)x2^(-11/2)x3^(-7/2) + (-q^(4))x1^(-5/2)x2^(-7/2)x3^(3/2) + (-q^(6) - q^(5) - q^(4))x1^(-5/2)x2^(-9/2)x3^(3/2) + (-q^(8) - q^(7) - 2q^(6) - q^(5) - q^(4))x1^(-5/2)x2^(-11/2)x3^(3/2) + (q^(3) + q^(2))x1^(-5/2)x2^(-7/2)x3^(1/2) + (q^(5) + 2q^(4) + 3q^(3) + q^(2))x1^(-5/2)x2^(-9/2)x3^(1/2) + (q^(7) + 2q^(6) + 4q^(5) + 4q^(4) + 3q^(3) + q^(2))x1^(-5/2)x2^(-11/2)x3^(1/2) + (-q)x1^(-5/2)x2^(-7/2)x3^(-1/2) + (-q^(3) - 2q^(2) - 2q)x1^(-5/2)x2^(-9/2)x3^(-1/2) + (-q^(5) - 2q^(4) - 4q^(3) - 3q^(2) - 2q)x1^(-5/2)x2^(-11/2)x3^(-1/2) + (1)x1^(-5/2)x2^(-9/2)x3^(-3/2) + (q^(2) + q + 1 - q^(-1) - q^(-2))x1^(-5/2)x2^(-11/2)x3^(-3/2) + (q^(-3) + q^(-4))x1^(-5/2)x2^(-11/2)x3^(-5/2) + (-q^(10))x1^(-7/2)x2^(-9/2)x3^(5/2) + (-q^(13) - q^(12) - q^(11) - q^(10))x1^(-7/2)x2^(-11/2)x3^(5/2) + (q^(9) + q^(8) + q^(7))x1^(-7/2)x2^(-9/2)x3^(3/2) + (q^(12) + 2q^(11) + 3q^(10) + 4q^(9) + 2q^(8) + q^(7))x1^(-7/2)x2^(-11/2)x3^(3/2) + (-q^(7) - q^(6) - q^(5))x1^(-7/2)x2^(-9/2)x3^(1/2) + (-q^(10) - 2q^(9) - 4q^(8) - 4q^(7) - 3q^(6) - q^(5))x1^(-7/2)x2^(-11/2)x3^(1/2) + (q^(4))x1^(-7/2)x2^(-9/2)x3^(-1/2) + (q^(7) + 2q^(6) + 2q^(5) + 2q^(4))x1^(-7/2)x2^(-11/2)x3^(-1/2) + (-q^(3))x1^(-7/2)x2^(-11/2)x3^(-3/2) + (-q^(18))x1^(-9/2)x2^(-11/2)x3^(7/2) + (q^(17) + q^(16) + q^(15) + q^(14))x1^(-9/2)x2^(-11/2)x3^(5/2) + (-q^(15) - q^(14) - 2q^(13) - q^(12) - q^(11))x1^(-9/2)x2^(-11/2)x3^(3/2) + (q^(12) + q^(11) + q^(10) + q^(9))x1^(-9/2)x2^(-11/2)x3^(1/2) + (-q^(8))x1^(-9/2)x2^(-11/2)x3^(-1/2)

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

(1, 1, 1)

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

q^(-2)

{"0": [-1, -1, 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^(3/2)*x3^(1/2) + (-q^(-2))*x1^(1/2)*x2^(5/2)*x3^(1/2) + (-q^(-2))*x1^(1/2)*x2^(7/2)*x3^(1/2) + (-q^(-2))*x1^(1/2)*x2^(9/2)*x3^(1/2) + (-q^(-2))*x1^(1/2)*x2^(11/2)*x3^(1/2) + (q^(-3))*x1^(1/2)*x2^(5/2)*x3^(3/2) + (q^(-3))*x1^(1/2)*x2^(7/2)*x3^(3/2) + (q^(-3))*x1^(1/2)*x2^(9/2)*x3^(3/2) + (q^(-3))*x1^(1/2)*x2^(11/2)*x3^(3/2) + (q^(-6))*x1^(1/2)*x2^(9/2)*x3^(5/2) + (q^(-6) + q^(-7))*x1^(1/2)*x2^(11/2)*x3^(5/2) + (-q^(-7))*x1^(1/2)*x2^(9/2)*x3^(7/2) + (-q^(-7) - q^(-8) - q^(-9))*x1^(1/2)*x2^(11/2)*x3^(7/2) + (q^(-10))*x1^(1/2)*x2^(11/2)*x3^(9/2) + (-1)*x1^(3/2)*x2^(5/2)*x3^(-1/2) + (-q - 1)*x1^(3/2)*x2^(7/2)*x3^(-1/2) + (-q^(2) - q - 1)*x1^(3/2)*x2^(9/2)*x3^(-1/2) + (-q^(3) - q^(2) - q - 1)*x1^(3/2)*x2^(11/2)*x3^(-1/2) + (q^(-1))*x1^(3/2)*x2^(5/2)*x3^(1/2) + (1 + 2*q^(-1))*x1^(3/2)*x2^(7/2)*x3^(1/2) + (q + 2*1 + 2*q^(-1))*x1^(3/2)*x2^(9/2)*x3^(1/2) + (q^(2) + 2*q + 2*1 + 2*q^(-1))*x1^(3/2)*x2^(11/2)*x3^(1/2) + (-q^(-2))*x1^(3/2)*x2^(7/2)*x3^(3/2) + (-q^(-1) - q^(-2))*x1^(3/2)*x2^(9/2)*x3^(3/2) + (-1 - q^(-1) - q^(-2) + q^(-3) + q^(-4))*x1^(3/2)*x2^(11/2)*x3^(3/2) + (-q^(-5))*x1^(3/2)*x2^(9/2)*x3^(5/2) + (-q^(-4) - 3*q^(-5) - q^(-6))*x1^(3/2)*x2^(11/2)*x3^(5/2) + (q^(-6) + q^(-7) + q^(-8))*x1^(3/2)*x2^(11/2)*x3^(7/2) + (-q^(4))*x1^(5/2)*x2^(7/2)*x3^(-3/2) + (-q^(6) - q^(5) - q^(4))*x1^(5/2)*x2^(9/2)*x3^(-3/2) + (-q^(8) - q^(7) - 2*q^(6) - q^(5) - q^(4))*x1^(5/2)*x2^(11/2)*x3^(-3/2) + (q^(3) + q^(2))*x1^(5/2)*x2^(7/2)*x3^(-1/2) + (q^(5) + 2*q^(4) + 3*q^(3) + q^(2))*x1^(5/2)*x2^(9/2)*x3^(-1/2) + (q^(7) + 2*q^(6) + 4*q^(5) + 4*q^(4) + 3*q^(3) + q^(2))*x1^(5/2)*x2^(11/2)*x3^(-1/2) + (-q)*x1^(5/2)*x2^(7/2)*x3^(1/2) + (-q^(3) - 2*q^(2) - 2*q)*x1^(5/2)*x2^(9/2)*x3^(1/2) + (-q^(5) - 2*q^(4) - 4*q^(3) - 3*q^(2) - 2*q)*x1^(5/2)*x2^(11/2)*x3^(1/2) + (1)*x1^(5/2)*x2^(9/2)*x3^(3/2) + (q^(2) + q + 1 - q^(-1) - q^(-2))*x1^(5/2)*x2^(11/2)*x3^(3/2) + (q^(-3) + q^(-4))*x1^(5/2)*x2^(11/2)*x3^(5/2) + (-q^(10))*x1^(7/2)*x2^(9/2)*x3^(-5/2) + (-q^(13) - q^(12) - q^(11) - q^(10))*x1^(7/2)*x2^(11/2)*x3^(-5/2) + (q^(9) + q^(8) + q^(7))*x1^(7/2)*x2^(9/2)*x3^(-3/2) + (q^(12) + 2*q^(11) + 3*q^(10) + 4*q^(9) + 2*q^(8) + q^(7))*x1^(7/2)*x2^(11/2)*x3^(-3/2) + (-q^(7) - q^(6) - q^(5))*x1^(7/2)*x2^(9/2)*x3^(-1/2) + (-q^(10) - 2*q^(9) - 4*q^(8) - 4*q^(7) - 3*q^(6) - q^(5))*x1^(7/2)*x2^(11/2)*x3^(-1/2) + (q^(4))*x1^(7/2)*x2^(9/2)*x3^(1/2) + (q^(7) + 2*q^(6) + 2*q^(5) + 2*q^(4))*x1^(7/2)*x2^(11/2)*x3^(1/2) + (-q^(3))*x1^(7/2)*x2^(11/2)*x3^(3/2) + (-q^(18))*x1^(9/2)*x2^(11/2)*x3^(-7/2) + (q^(17) + q^(16) + q^(15) + q^(14))*x1^(9/2)*x2^(11/2)*x3^(-5/2) + (-q^(15) - q^(14) - 2*q^(13) - q^(12) - q^(11))*x1^(9/2)*x2^(11/2)*x3^(-3/2) + (q^(12) + q^(11) + q^(10) + q^(9))*x1^(9/2)*x2^(11/2)*x3^(-1/2) + (-q^(8))*x1^(9/2)*x2^(11/2)*x3^(1/2)

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

(1, 1, 1)

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

q^(-2)

{"0": [1, -1, 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^(3/2)*x3^(1/2) + (-q^(-2))*x1^(1/2)*x2^(5/2)*x3^(1/2) + (-q^(-2))*x1^(1/2)*x2^(7/2)*x3^(1/2) + (-q^(-2))*x1^(1/2)*x2^(9/2)*x3^(1/2) + (-q^(-2))*x1^(1/2)*x2^(11/2)*x3^(1/2) + (q^(-3))*x1^(1/2)*x2^(5/2)*x3^(3/2) + (q^(-3))*x1^(1/2)*x2^(7/2)*x3^(3/2) + (q^(-3))*x1^(1/2)*x2^(9/2)*x3^(3/2) + (q^(-3))*x1^(1/2)*x2^(11/2)*x3^(3/2) + (q^(-6))*x1^(1/2)*x2^(9/2)*x3^(5/2) + (q^(-6) + q^(-7))*x1^(1/2)*x2^(11/2)*x3^(5/2) + (-q^(-7))*x1^(1/2)*x2^(9/2)*x3^(7/2) + (-q^(-7) - q^(-8) - q^(-9))*x1^(1/2)*x2^(11/2)*x3^(7/2) + (q^(-10))*x1^(1/2)*x2^(11/2)*x3^(9/2) + (-1)*x1^(3/2)*x2^(5/2)*x3^(-1/2) + (-q - 1)*x1^(3/2)*x2^(7/2)*x3^(-1/2) + (-q^(2) - q - 1)*x1^(3/2)*x2^(9/2)*x3^(-1/2) + (-q^(3) - q^(2) - q - 1)*x1^(3/2)*x2^(11/2)*x3^(-1/2) + (q^(-1))*x1^(3/2)*x2^(5/2)*x3^(1/2) + (1 + 2*q^(-1))*x1^(3/2)*x2^(7/2)*x3^(1/2) + (q + 2*1 + 2*q^(-1))*x1^(3/2)*x2^(9/2)*x3^(1/2) + (q^(2) + 2*q + 2*1 + 2*q^(-1))*x1^(3/2)*x2^(11/2)*x3^(1/2) + (-q^(-2))*x1^(3/2)*x2^(7/2)*x3^(3/2) + (-q^(-1) - q^(-2))*x1^(3/2)*x2^(9/2)*x3^(3/2) + (-1 - q^(-1) - q^(-2) + q^(-3) + q^(-4))*x1^(3/2)*x2^(11/2)*x3^(3/2) + (-q^(-5))*x1^(3/2)*x2^(9/2)*x3^(5/2) + (-q^(-4) - 3*q^(-5) - q^(-6))*x1^(3/2)*x2^(11/2)*x3^(5/2) + (q^(-6) + q^(-7) + q^(-8))*x1^(3/2)*x2^(11/2)*x3^(7/2) + (-q^(4))*x1^(5/2)*x2^(7/2)*x3^(-3/2) + (-q^(6) - q^(5) - q^(4))*x1^(5/2)*x2^(9/2)*x3^(-3/2) + (-q^(8) - q^(7) - 2*q^(6) - q^(5) - q^(4))*x1^(5/2)*x2^(11/2)*x3^(-3/2) + (q^(3) + q^(2))*x1^(5/2)*x2^(7/2)*x3^(-1/2) + (q^(5) + 2*q^(4) + 3*q^(3) + q^(2))*x1^(5/2)*x2^(9/2)*x3^(-1/2) + (q^(7) + 2*q^(6) + 4*q^(5) + 4*q^(4) + 3*q^(3) + q^(2))*x1^(5/2)*x2^(11/2)*x3^(-1/2) + (-q)*x1^(5/2)*x2^(7/2)*x3^(1/2) + (-q^(3) - 2*q^(2) - 2*q)*x1^(5/2)*x2^(9/2)*x3^(1/2) + (-q^(5) - 2*q^(4) - 4*q^(3) - 3*q^(2) - 2*q)*x1^(5/2)*x2^(11/2)*x3^(1/2) + (1)*x1^(5/2)*x2^(9/2)*x3^(3/2) + (q^(2) + q + 1 - q^(-1) - q^(-2))*x1^(5/2)*x2^(11/2)*x3^(3/2) + (q^(-3) + q^(-4))*x1^(5/2)*x2^(11/2)*x3^(5/2) + (-q^(10))*x1^(7/2)*x2^(9/2)*x3^(-5/2) + (-q^(13) - q^(12) - q^(11) - q^(10))*x1^(7/2)*x2^(11/2)*x3^(-5/2) + (q^(9) + q^(8) + q^(7))*x1^(7/2)*x2^(9/2)*x3^(-3/2) + (q^(12) + 2*q^(11) + 3*q^(10) + 4*q^(9) + 2*q^(8) + q^(7))*x1^(7/2)*x2^(11/2)*x3^(-3/2) + (-q^(7) - q^(6) - q^(5))*x1^(7/2)*x2^(9/2)*x3^(-1/2) + (-q^(10) - 2*q^(9) - 4*q^(8) - 4*q^(7) - 3*q^(6) - q^(5))*x1^(7/2)*x2^(11/2)*x3^(-1/2) + (q^(4))*x1^(7/2)*x2^(9/2)*x3^(1/2) + (q^(7) + 2*q^(6) + 2*q^(5) + 2*q^(4))*x1^(7/2)*x2^(11/2)*x3^(1/2) + (-q^(3))*x1^(7/2)*x2^(11/2)*x3^(3/2) + (-q^(18))*x1^(9/2)*x2^(11/2)*x3^(-7/2) + (q^(17) + q^(16) + q^(15) + q^(14))*x1^(9/2)*x2^(11/2)*x3^(-5/2) + (-q^(15) - q^(14) - 2*q^(13) - q^(12) - q^(11))*x1^(9/2)*x2^(11/2)*x3^(-3/2) + (q^(12) + q^(11) + q^(10) + q^(9))*x1^(9/2)*x2^(11/2)*x3^(-1/2) + (-q^(8))*x1^(9/2)*x2^(11/2)*x3^(1/2)

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

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

q^(-2)

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

Braid

Braid word	Components	Crossings	Strands
`[-1, 2, -1, -2, 1, -2, -2, -2, -2, -2]`	3	10	3

Multivariable Alexander polynomial

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

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HFL polytope

Poincaré polynomial
m^(-3)A1^(-1)A2^(-2)A3^(-1) + m^(-2)A1^(-1)A2^(-2) + 2m^(-2)A1^(-1)A2^(-1)A3^(-1) + m^(-2)A2^(-2)A3^(-1) + m^(-2)A2^(-1)A3^(-2) + 3m^(-1)A1^(-1)A2^(-1) + m^(-1)A1^(-1)A3^(-1) + m^(-1)A2^(-2) + 4m^(-1)A2^(-1)A3^(-1) + m^(-1)A3^(-2) + m^(-1)A1A2^(-1)A3^(-2) + A1^(-1)A2^(-1)A3 + 3A1^(-1) + 4A2^(-1) + 4A3^(-1) + 2A1A2^(-1)A3^(-1) + A1A3^(-2) + 3mA1^(-1)A3 + mA1^(-1)A2 + mA2^(-1)A3 + 6m + mA2A3^(-1) + mA1A2^(-1) + 3mA1A3^(-1) + m^2A1^(-1)A3^2 + 2m^2A1^(-1)A2A3 + 4m^2A3 + 4m^2A2 + 3m^2A1 + m^2A1A2A3^(-1) + m^3A1^(-1)A2A3^2 + m^3A3^2 + 4m^3A2A3 + m^3A2^2 + m^3A1A3 + 3m^3A1A2 + m^4A2A3^2 + m^4A2^2A3 + 2m^4A1A2A3 + m^4A1A2^2 + m^5A1A2^2*A3

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

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Record

FL/HFL Links

`orderOption(int)`	`2220`
`namestring`	`L10n78{1;1}`
`statusstring`	`success`
`slugstring`	`L10n78_1_1_31b7275a`
`result_filestring`	`details/L10n78_1_1_31b7275a.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)`	`0.001864`
`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`	`3`
`detailsRowRef(FLHFLLinks)`	{ "dataset": "FLHFLLinks", "key": "L10n78_1_1_31b7275a" }
`detail_assetstring`	`/api/v1/datasets/FLHFLLinks/assets/L10n78_1_1_31b7275a`

FL expansions

Braid

Multivariable Alexander polynomial

Dual Thurston polytope

HFL polytope

Record

F_L expansions