L10n38{1} - HFL and FL

details/L10n38_1_4d057513.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, -5/2)`	`(1, 1)`	`x1^(1/2)x2^(5/2)`	`q^(3/2)`	`{"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^(3/2))x1^(1/2)x2^(5/2) + (-2q^(3/2))x1^(1/2)x2^(7/2) + (q^(5/2))x1^(3/2)x2^(7/2) + (q^(5/2) - 3q^(3/2) + q^(1/2))x1^(1/2)x2^(9/2) + (2q^(5/2))x1^(3/2)x2^(9/2) + (-q^(9/2))x1^(5/2)x2^(9/2) + (2q^(5/2) - 4q^(3/2) + 2q^(1/2) + 2q^(-1/2))x1^(1/2)x2^(11/2) + (q^(9/2) - q^(7/2) + 3q^(5/2) - q^(3/2) - q^(1/2))x1^(3/2)x2^(11/2) + (-2q^(9/2))x1^(5/2)x2^(11/2) + (q^(15/2))x1^(7/2)x2^(11/2) + (-q^(9/2) + 3q^(5/2) - 6q^(3/2) + 2q^(1/2) + 4q^(-1/2) + 2q^(-3/2))x1^(1/2)x2^(13/2) + (2q^(11/2) + 2q^(9/2) - 2q^(7/2) + 4q^(5/2) - 2q^(3/2) - 4q^(1/2) - 2q^(-1/2))x1^(3/2)x2^(13/2) + (-q^(13/2) - 3q^(9/2) + q^(7/2) + q^(5/2) + q^(3/2))x1^(5/2)x2^(13/2) + (2q^(15/2))x1^(7/2)x2^(13/2) + (-q^(23/2))x1^(9/2)x2^(13/2) + (-2q^(9/2) + 4q^(5/2) - 8q^(3/2) + 4q^(-1/2) + 4q^(-3/2) + 2q^(-5/2) - 2q^(-7/2))x1^(1/2)x2^(15/2) + (-q^(15/2) + q^(13/2) + 5q^(11/2) + 3q^(9/2) - 4q^(7/2) + 7q^(5/2) - q^(3/2) - 7q^(1/2) - 6q^(-1/2) - 2q^(-3/2) + q^(-5/2))x1^(3/2)x2^(15/2) + (-2q^(15/2) - 4q^(13/2) - 4q^(9/2) + 2q^(7/2) + 4q^(5/2) + 4q^(3/2) + 2q^(1/2))x1^(5/2)x2^(15/2) + (q^(19/2) + 4q^(15/2) - q^(13/2) - q^(11/2) - q^(9/2) - q^(7/2))x1^(7/2)x2^(15/2) + (-2q^(23/2))x1^(9/2)x2^(15/2) + (q^(33/2))x1^(11/2)x2^(15/2) + (q^(15/2) - 3q^(9/2) + q^(7/2) + 6q^(5/2) - 9q^(3/2) - 2q^(1/2) + 2q^(-1/2) + 4q^(-3/2) + 5q^(-5/2) - 2q^(-7/2) - 3q^(-9/2) - 3q^(-11/2))x1^(1/2)x2^(17/2) + (-2q^(17/2) - 2q^(15/2) + 2q^(13/2) + 8q^(11/2) + 2q^(9/2) - 8q^(7/2) + 8q^(5/2) + 4q^(3/2) - 6q^(1/2) - 10q^(-1/2) - 6q^(-3/2) + 2q^(-5/2) + 4q^(-7/2) + 2q^(-9/2))x1^(3/2)x2^(17/2) + (-q^(21/2) + 2q^(19/2) - 7q^(15/2) - 7q^(13/2) - 5q^(9/2) + 2q^(7/2) + 6q^(5/2) + 9q^(3/2) + 6q^(1/2) + q^(-1/2) - q^(-3/2) - q^(-5/2))x1^(5/2)x2^(17/2) + (2q^(21/2) + 4q^(19/2) + 2q^(17/2) + 6q^(15/2) - 2q^(13/2) - 4q^(11/2) - 4q^(9/2) - 4q^(7/2) - 2q^(5/2))x1^(7/2)x2^(17/2) + (-q^(27/2) - 4q^(23/2) + q^(19/2) + q^(17/2) + q^(15/2) + q^(13/2))x1^(9/2)x2^(17/2) + (2q^(33/2))x1^(11/2)x2^(17/2) + (-q^(45/2))x1^(13/2)x2^(17/2) + (2q^(15/2) - 4q^(9/2) + 2q^(7/2) + 10q^(5/2) - 8q^(3/2) - 2q^(1/2) + 2q^(-3/2) + 8q^(-5/2) + 2q^(-7/2) - 2q^(-9/2) - 10q^(-11/2) - 4q^(-13/2) - 2q^(-15/2))x1^(1/2)x2^(19/2) + (q^(23/2) + q^(21/2) - q^(19/2) - 5q^(17/2) - 3q^(15/2) + 4q^(13/2) + 11q^(11/2) - 2q^(9/2) - 19q^(7/2) + 4q^(5/2) + 7q^(3/2) - q^(1/2) - 11q^(-1/2) - 13q^(-3/2) + 9q^(-7/2) + 13q^(-9/2) + 6q^(-11/2) + 2q^(-13/2))x1^(3/2)x2^(19/2) + (-2q^(25/2) - 2q^(23/2) + 2q^(21/2) + 6q^(19/2) - 2q^(17/2) - 12q^(15/2) - 8q^(13/2) + 6q^(11/2) - 2q^(9/2) + 2q^(7/2) + 6q^(5/2) + 12q^(3/2) + 12q^(1/2) + 2q^(-1/2) - 4q^(-3/2) - 8q^(-5/2) - 4q^(-7/2) - 2q^(-9/2))x1^(5/2)x2^(19/2) + (-q^(25/2) + q^(23/2) + 6q^(21/2) + 10q^(19/2) + 4q^(17/2) + 8q^(15/2) - 4q^(13/2) - 8q^(11/2) - 9q^(9/2) - 9q^(7/2) - 5q^(5/2) - q^(3/2) + 2q^(1/2) + q^(-1/2) + q^(-3/2))x1^(7/2)x2^(19/2) + (-2q^(29/2) - 4q^(27/2) - 2q^(25/2) - 8q^(23/2) + 4q^(19/2) + 4q^(17/2) + 4q^(15/2) + 4q^(13/2) + 2q^(11/2))x1^(9/2)x2^(19/2) + (q^(37/2) + 4q^(33/2) - q^(27/2) - q^(25/2) - q^(23/2) - q^(21/2))x1^(11/2)x2^(19/2) + (-2q^(45/2))x1^(13/2)x2^(19/2) + (q^(59/2))x1^(15/2)*x2^(19/2)
`(-1/2, -5/2)`	`(1, 1)`	`x1^(1/2)x2^(5/2)`	`q^(3/2)`	`{"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^(3/2))x1^(1/2)x2^(5/2) + (-2q^(3/2))x1^(1/2)x2^(7/2) + (q^(5/2))x1^(3/2)x2^(7/2) + (q^(5/2) - 3q^(3/2) + q^(1/2))x1^(1/2)x2^(9/2) + (2q^(5/2))x1^(3/2)x2^(9/2) + (-q^(9/2))x1^(5/2)x2^(9/2) + (2q^(5/2) - 4q^(3/2) + 2q^(1/2) + 2q^(-1/2))x1^(1/2)x2^(11/2) + (q^(9/2) - q^(7/2) + 3q^(5/2) - q^(3/2) - q^(1/2))x1^(3/2)x2^(11/2) + (-2q^(9/2))x1^(5/2)x2^(11/2) + (q^(15/2))x1^(7/2)x2^(11/2) + (-q^(9/2) + 3q^(5/2) - 6q^(3/2) + 2q^(1/2) + 4q^(-1/2) + 2q^(-3/2))x1^(1/2)x2^(13/2) + (2q^(11/2) + 2q^(9/2) - 2q^(7/2) + 4q^(5/2) - 2q^(3/2) - 4q^(1/2) - 2q^(-1/2))x1^(3/2)x2^(13/2) + (-q^(13/2) - 3q^(9/2) + q^(7/2) + q^(5/2) + q^(3/2))x1^(5/2)x2^(13/2) + (2q^(15/2))x1^(7/2)x2^(13/2) + (-q^(23/2))x1^(9/2)x2^(13/2) + (-2q^(9/2) + 4q^(5/2) - 8q^(3/2) + 4q^(-1/2) + 4q^(-3/2) + 2q^(-5/2) - 2q^(-7/2))x1^(1/2)x2^(15/2) + (-q^(15/2) + q^(13/2) + 5q^(11/2) + 3q^(9/2) - 4q^(7/2) + 7q^(5/2) - q^(3/2) - 7q^(1/2) - 6q^(-1/2) - 2q^(-3/2) + q^(-5/2))x1^(3/2)x2^(15/2) + (-2q^(15/2) - 4q^(13/2) - 4q^(9/2) + 2q^(7/2) + 4q^(5/2) + 4q^(3/2) + 2q^(1/2))x1^(5/2)x2^(15/2) + (q^(19/2) + 4q^(15/2) - q^(13/2) - q^(11/2) - q^(9/2) - q^(7/2))x1^(7/2)x2^(15/2) + (-2q^(23/2))x1^(9/2)x2^(15/2) + (q^(33/2))x1^(11/2)x2^(15/2) + (q^(15/2) - 3q^(9/2) + q^(7/2) + 6q^(5/2) - 9q^(3/2) - 2q^(1/2) + 2q^(-1/2) + 4q^(-3/2) + 5q^(-5/2) - 2q^(-7/2) - 3q^(-9/2) - 3q^(-11/2))x1^(1/2)x2^(17/2) + (-2q^(17/2) - 2q^(15/2) + 2q^(13/2) + 8q^(11/2) + 2q^(9/2) - 8q^(7/2) + 8q^(5/2) + 4q^(3/2) - 6q^(1/2) - 10q^(-1/2) - 6q^(-3/2) + 2q^(-5/2) + 4q^(-7/2) + 2q^(-9/2))x1^(3/2)x2^(17/2) + (-q^(21/2) + 2q^(19/2) - 7q^(15/2) - 7q^(13/2) - 5q^(9/2) + 2q^(7/2) + 6q^(5/2) + 9q^(3/2) + 6q^(1/2) + q^(-1/2) - q^(-3/2) - q^(-5/2))x1^(5/2)x2^(17/2) + (2q^(21/2) + 4q^(19/2) + 2q^(17/2) + 6q^(15/2) - 2q^(13/2) - 4q^(11/2) - 4q^(9/2) - 4q^(7/2) - 2q^(5/2))x1^(7/2)x2^(17/2) + (-q^(27/2) - 4q^(23/2) + q^(19/2) + q^(17/2) + q^(15/2) + q^(13/2))x1^(9/2)x2^(17/2) + (2q^(33/2))x1^(11/2)x2^(17/2) + (-q^(45/2))x1^(13/2)x2^(17/2) + (2q^(15/2) - 4q^(9/2) + 2q^(7/2) + 10q^(5/2) - 8q^(3/2) - 2q^(1/2) + 2q^(-3/2) + 8q^(-5/2) + 2q^(-7/2) - 2q^(-9/2) - 10q^(-11/2) - 4q^(-13/2) - 2q^(-15/2))x1^(1/2)x2^(19/2) + (q^(23/2) + q^(21/2) - q^(19/2) - 5q^(17/2) - 3q^(15/2) + 4q^(13/2) + 11q^(11/2) - 2q^(9/2) - 19q^(7/2) + 4q^(5/2) + 7q^(3/2) - q^(1/2) - 11q^(-1/2) - 13q^(-3/2) + 9q^(-7/2) + 13q^(-9/2) + 6q^(-11/2) + 2q^(-13/2))x1^(3/2)x2^(19/2) + (-2q^(25/2) - 2q^(23/2) + 2q^(21/2) + 6q^(19/2) - 2q^(17/2) - 12q^(15/2) - 8q^(13/2) + 6q^(11/2) - 2q^(9/2) + 2q^(7/2) + 6q^(5/2) + 12q^(3/2) + 12q^(1/2) + 2q^(-1/2) - 4q^(-3/2) - 8q^(-5/2) - 4q^(-7/2) - 2q^(-9/2))x1^(5/2)x2^(19/2) + (-q^(25/2) + q^(23/2) + 6q^(21/2) + 10q^(19/2) + 4q^(17/2) + 8q^(15/2) - 4q^(13/2) - 8q^(11/2) - 9q^(9/2) - 9q^(7/2) - 5q^(5/2) - q^(3/2) + 2q^(1/2) + q^(-1/2) + q^(-3/2))x1^(7/2)x2^(19/2) + (-2q^(29/2) - 4q^(27/2) - 2q^(25/2) - 8q^(23/2) + 4q^(19/2) + 4q^(17/2) + 4q^(15/2) + 4q^(13/2) + 2q^(11/2))x1^(9/2)x2^(19/2) + (q^(37/2) + 4q^(33/2) - q^(27/2) - q^(25/2) - q^(23/2) - q^(21/2))x1^(11/2)x2^(19/2) + (-2q^(45/2))x1^(13/2)x2^(19/2) + (q^(59/2))x1^(15/2)*x2^(19/2)
`(1/2, 5/2)`		`x1^(-1/2)x2^(-5/2)`	`q^(3/2)`		(-q^(3/2))x1^(-1/2)x2^(-5/2) + (-2q^(3/2))x1^(-1/2)x2^(-7/2) + (q^(5/2))x1^(-3/2)x2^(-7/2) + (q^(5/2) - 3q^(3/2) + q^(1/2))x1^(-1/2)x2^(-9/2) + (2q^(5/2))x1^(-3/2)x2^(-9/2) + (-q^(9/2))x1^(-5/2)x2^(-9/2) + (2q^(5/2) - 4q^(3/2) + 2q^(1/2) + 2q^(-1/2))x1^(-1/2)x2^(-11/2) + (q^(9/2) - q^(7/2) + 3q^(5/2) - q^(3/2) - q^(1/2))x1^(-3/2)x2^(-11/2) + (-2q^(9/2))x1^(-5/2)x2^(-11/2) + (q^(15/2))x1^(-7/2)x2^(-11/2) + (-q^(9/2) + 3q^(5/2) - 6q^(3/2) + 2q^(1/2) + 4q^(-1/2) + 2q^(-3/2))x1^(-1/2)x2^(-13/2) + (2q^(11/2) + 2q^(9/2) - 2q^(7/2) + 4q^(5/2) - 2q^(3/2) - 4q^(1/2) - 2q^(-1/2))x1^(-3/2)x2^(-13/2) + (-q^(13/2) - 3q^(9/2) + q^(7/2) + q^(5/2) + q^(3/2))x1^(-5/2)x2^(-13/2) + (2q^(15/2))x1^(-7/2)x2^(-13/2) + (-q^(23/2))x1^(-9/2)x2^(-13/2) + (-2q^(9/2) + 4q^(5/2) - 8q^(3/2) + 4q^(-1/2) + 4q^(-3/2) + 2q^(-5/2) - 2q^(-7/2))x1^(-1/2)x2^(-15/2) + (-q^(15/2) + q^(13/2) + 5q^(11/2) + 3q^(9/2) - 4q^(7/2) + 7q^(5/2) - q^(3/2) - 7q^(1/2) - 6q^(-1/2) - 2q^(-3/2) + q^(-5/2))x1^(-3/2)x2^(-15/2) + (-2q^(15/2) - 4q^(13/2) - 4q^(9/2) + 2q^(7/2) + 4q^(5/2) + 4q^(3/2) + 2q^(1/2))x1^(-5/2)x2^(-15/2) + (q^(19/2) + 4q^(15/2) - q^(13/2) - q^(11/2) - q^(9/2) - q^(7/2))x1^(-7/2)x2^(-15/2) + (-2q^(23/2))x1^(-9/2)x2^(-15/2) + (q^(33/2))x1^(-11/2)x2^(-15/2) + (q^(15/2) - 3q^(9/2) + q^(7/2) + 6q^(5/2) - 9q^(3/2) - 2q^(1/2) + 2q^(-1/2) + 4q^(-3/2) + 5q^(-5/2) - 2q^(-7/2) - 3q^(-9/2) - 3q^(-11/2))x1^(-1/2)x2^(-17/2) + (-2q^(17/2) - 2q^(15/2) + 2q^(13/2) + 8q^(11/2) + 2q^(9/2) - 8q^(7/2) + 8q^(5/2) + 4q^(3/2) - 6q^(1/2) - 10q^(-1/2) - 6q^(-3/2) + 2q^(-5/2) + 4q^(-7/2) + 2q^(-9/2))x1^(-3/2)x2^(-17/2) + (-q^(21/2) + 2q^(19/2) - 7q^(15/2) - 7q^(13/2) - 5q^(9/2) + 2q^(7/2) + 6q^(5/2) + 9q^(3/2) + 6q^(1/2) + q^(-1/2) - q^(-3/2) - q^(-5/2))x1^(-5/2)x2^(-17/2) + (2q^(21/2) + 4q^(19/2) + 2q^(17/2) + 6q^(15/2) - 2q^(13/2) - 4q^(11/2) - 4q^(9/2) - 4q^(7/2) - 2q^(5/2))x1^(-7/2)x2^(-17/2) + (-q^(27/2) - 4q^(23/2) + q^(19/2) + q^(17/2) + q^(15/2) + q^(13/2))x1^(-9/2)x2^(-17/2) + (2q^(33/2))x1^(-11/2)x2^(-17/2) + (-q^(45/2))x1^(-13/2)x2^(-17/2) + (2q^(15/2) - 4q^(9/2) + 2q^(7/2) + 10q^(5/2) - 8q^(3/2) - 2q^(1/2) + 2q^(-3/2) + 8q^(-5/2) + 2q^(-7/2) - 2q^(-9/2) - 10q^(-11/2) - 4q^(-13/2) - 2q^(-15/2))x1^(-1/2)x2^(-19/2) + (q^(23/2) + q^(21/2) - q^(19/2) - 5q^(17/2) - 3q^(15/2) + 4q^(13/2) + 11q^(11/2) - 2q^(9/2) - 19q^(7/2) + 4q^(5/2) + 7q^(3/2) - q^(1/2) - 11q^(-1/2) - 13q^(-3/2) + 9q^(-7/2) + 13q^(-9/2) + 6q^(-11/2) + 2q^(-13/2))x1^(-3/2)x2^(-19/2) + (-2q^(25/2) - 2q^(23/2) + 2q^(21/2) + 6q^(19/2) - 2q^(17/2) - 12q^(15/2) - 8q^(13/2) + 6q^(11/2) - 2q^(9/2) + 2q^(7/2) + 6q^(5/2) + 12q^(3/2) + 12q^(1/2) + 2q^(-1/2) - 4q^(-3/2) - 8q^(-5/2) - 4q^(-7/2) - 2q^(-9/2))x1^(-5/2)x2^(-19/2) + (-q^(25/2) + q^(23/2) + 6q^(21/2) + 10q^(19/2) + 4q^(17/2) + 8q^(15/2) - 4q^(13/2) - 8q^(11/2) - 9q^(9/2) - 9q^(7/2) - 5q^(5/2) - q^(3/2) + 2q^(1/2) + q^(-1/2) + q^(-3/2))x1^(-7/2)x2^(-19/2) + (-2q^(29/2) - 4q^(27/2) - 2q^(25/2) - 8q^(23/2) + 4q^(19/2) + 4q^(17/2) + 4q^(15/2) + 4q^(13/2) + 2q^(11/2))x1^(-9/2)x2^(-19/2) + (q^(37/2) + 4q^(33/2) - q^(27/2) - q^(25/2) - q^(23/2) - q^(21/2))x1^(-11/2)x2^(-19/2) + (-2q^(45/2))x1^(-13/2)x2^(-19/2) + (q^(59/2))x1^(-15/2)*x2^(-19/2)

(-1/2, -5/2)

(1, 1)

x1^(1/2)x2^(5/2)

q^(3/2)

{"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^(3/2))*x1^(1/2)*x2^(5/2) + (-2*q^(3/2))*x1^(1/2)*x2^(7/2) + (q^(5/2))*x1^(3/2)*x2^(7/2) + (q^(5/2) - 3*q^(3/2) + q^(1/2))*x1^(1/2)*x2^(9/2) + (2*q^(5/2))*x1^(3/2)*x2^(9/2) + (-q^(9/2))*x1^(5/2)*x2^(9/2) + (2*q^(5/2) - 4*q^(3/2) + 2*q^(1/2) + 2*q^(-1/2))*x1^(1/2)*x2^(11/2) + (q^(9/2) - q^(7/2) + 3*q^(5/2) - q^(3/2) - q^(1/2))*x1^(3/2)*x2^(11/2) + (-2*q^(9/2))*x1^(5/2)*x2^(11/2) + (q^(15/2))*x1^(7/2)*x2^(11/2) + (-q^(9/2) + 3*q^(5/2) - 6*q^(3/2) + 2*q^(1/2) + 4*q^(-1/2) + 2*q^(-3/2))*x1^(1/2)*x2^(13/2) + (2*q^(11/2) + 2*q^(9/2) - 2*q^(7/2) + 4*q^(5/2) - 2*q^(3/2) - 4*q^(1/2) - 2*q^(-1/2))*x1^(3/2)*x2^(13/2) + (-q^(13/2) - 3*q^(9/2) + q^(7/2) + q^(5/2) + q^(3/2))*x1^(5/2)*x2^(13/2) + (2*q^(15/2))*x1^(7/2)*x2^(13/2) + (-q^(23/2))*x1^(9/2)*x2^(13/2) + (-2*q^(9/2) + 4*q^(5/2) - 8*q^(3/2) + 4*q^(-1/2) + 4*q^(-3/2) + 2*q^(-5/2) - 2*q^(-7/2))*x1^(1/2)*x2^(15/2) + (-q^(15/2) + q^(13/2) + 5*q^(11/2) + 3*q^(9/2) - 4*q^(7/2) + 7*q^(5/2) - q^(3/2) - 7*q^(1/2) - 6*q^(-1/2) - 2*q^(-3/2) + q^(-5/2))*x1^(3/2)*x2^(15/2) + (-2*q^(15/2) - 4*q^(13/2) - 4*q^(9/2) + 2*q^(7/2) + 4*q^(5/2) + 4*q^(3/2) + 2*q^(1/2))*x1^(5/2)*x2^(15/2) + (q^(19/2) + 4*q^(15/2) - q^(13/2) - q^(11/2) - q^(9/2) - q^(7/2))*x1^(7/2)*x2^(15/2) + (-2*q^(23/2))*x1^(9/2)*x2^(15/2) + (q^(33/2))*x1^(11/2)*x2^(15/2) + (q^(15/2) - 3*q^(9/2) + q^(7/2) + 6*q^(5/2) - 9*q^(3/2) - 2*q^(1/2) + 2*q^(-1/2) + 4*q^(-3/2) + 5*q^(-5/2) - 2*q^(-7/2) - 3*q^(-9/2) - 3*q^(-11/2))*x1^(1/2)*x2^(17/2) + (-2*q^(17/2) - 2*q^(15/2) + 2*q^(13/2) + 8*q^(11/2) + 2*q^(9/2) - 8*q^(7/2) + 8*q^(5/2) + 4*q^(3/2) - 6*q^(1/2) - 10*q^(-1/2) - 6*q^(-3/2) + 2*q^(-5/2) + 4*q^(-7/2) + 2*q^(-9/2))*x1^(3/2)*x2^(17/2) + (-q^(21/2) + 2*q^(19/2) - 7*q^(15/2) - 7*q^(13/2) - 5*q^(9/2) + 2*q^(7/2) + 6*q^(5/2) + 9*q^(3/2) + 6*q^(1/2) + q^(-1/2) - q^(-3/2) - q^(-5/2))*x1^(5/2)*x2^(17/2) + (2*q^(21/2) + 4*q^(19/2) + 2*q^(17/2) + 6*q^(15/2) - 2*q^(13/2) - 4*q^(11/2) - 4*q^(9/2) - 4*q^(7/2) - 2*q^(5/2))*x1^(7/2)*x2^(17/2) + (-q^(27/2) - 4*q^(23/2) + q^(19/2) + q^(17/2) + q^(15/2) + q^(13/2))*x1^(9/2)*x2^(17/2) + (2*q^(33/2))*x1^(11/2)*x2^(17/2) + (-q^(45/2))*x1^(13/2)*x2^(17/2) + (2*q^(15/2) - 4*q^(9/2) + 2*q^(7/2) + 10*q^(5/2) - 8*q^(3/2) - 2*q^(1/2) + 2*q^(-3/2) + 8*q^(-5/2) + 2*q^(-7/2) - 2*q^(-9/2) - 10*q^(-11/2) - 4*q^(-13/2) - 2*q^(-15/2))*x1^(1/2)*x2^(19/2) + (q^(23/2) + q^(21/2) - q^(19/2) - 5*q^(17/2) - 3*q^(15/2) + 4*q^(13/2) + 11*q^(11/2) - 2*q^(9/2) - 19*q^(7/2) + 4*q^(5/2) + 7*q^(3/2) - q^(1/2) - 11*q^(-1/2) - 13*q^(-3/2) + 9*q^(-7/2) + 13*q^(-9/2) + 6*q^(-11/2) + 2*q^(-13/2))*x1^(3/2)*x2^(19/2) + (-2*q^(25/2) - 2*q^(23/2) + 2*q^(21/2) + 6*q^(19/2) - 2*q^(17/2) - 12*q^(15/2) - 8*q^(13/2) + 6*q^(11/2) - 2*q^(9/2) + 2*q^(7/2) + 6*q^(5/2) + 12*q^(3/2) + 12*q^(1/2) + 2*q^(-1/2) - 4*q^(-3/2) - 8*q^(-5/2) - 4*q^(-7/2) - 2*q^(-9/2))*x1^(5/2)*x2^(19/2) + (-q^(25/2) + q^(23/2) + 6*q^(21/2) + 10*q^(19/2) + 4*q^(17/2) + 8*q^(15/2) - 4*q^(13/2) - 8*q^(11/2) - 9*q^(9/2) - 9*q^(7/2) - 5*q^(5/2) - q^(3/2) + 2*q^(1/2) + q^(-1/2) + q^(-3/2))*x1^(7/2)*x2^(19/2) + (-2*q^(29/2) - 4*q^(27/2) - 2*q^(25/2) - 8*q^(23/2) + 4*q^(19/2) + 4*q^(17/2) + 4*q^(15/2) + 4*q^(13/2) + 2*q^(11/2))*x1^(9/2)*x2^(19/2) + (q^(37/2) + 4*q^(33/2) - q^(27/2) - q^(25/2) - q^(23/2) - q^(21/2))*x1^(11/2)*x2^(19/2) + (-2*q^(45/2))*x1^(13/2)*x2^(19/2) + (q^(59/2))*x1^(15/2)*x2^(19/2)

(-1/2, -5/2)

(1, 1)

x1^(1/2)x2^(5/2)

q^(3/2)

{"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^(3/2))*x1^(1/2)*x2^(5/2) + (-2*q^(3/2))*x1^(1/2)*x2^(7/2) + (q^(5/2))*x1^(3/2)*x2^(7/2) + (q^(5/2) - 3*q^(3/2) + q^(1/2))*x1^(1/2)*x2^(9/2) + (2*q^(5/2))*x1^(3/2)*x2^(9/2) + (-q^(9/2))*x1^(5/2)*x2^(9/2) + (2*q^(5/2) - 4*q^(3/2) + 2*q^(1/2) + 2*q^(-1/2))*x1^(1/2)*x2^(11/2) + (q^(9/2) - q^(7/2) + 3*q^(5/2) - q^(3/2) - q^(1/2))*x1^(3/2)*x2^(11/2) + (-2*q^(9/2))*x1^(5/2)*x2^(11/2) + (q^(15/2))*x1^(7/2)*x2^(11/2) + (-q^(9/2) + 3*q^(5/2) - 6*q^(3/2) + 2*q^(1/2) + 4*q^(-1/2) + 2*q^(-3/2))*x1^(1/2)*x2^(13/2) + (2*q^(11/2) + 2*q^(9/2) - 2*q^(7/2) + 4*q^(5/2) - 2*q^(3/2) - 4*q^(1/2) - 2*q^(-1/2))*x1^(3/2)*x2^(13/2) + (-q^(13/2) - 3*q^(9/2) + q^(7/2) + q^(5/2) + q^(3/2))*x1^(5/2)*x2^(13/2) + (2*q^(15/2))*x1^(7/2)*x2^(13/2) + (-q^(23/2))*x1^(9/2)*x2^(13/2) + (-2*q^(9/2) + 4*q^(5/2) - 8*q^(3/2) + 4*q^(-1/2) + 4*q^(-3/2) + 2*q^(-5/2) - 2*q^(-7/2))*x1^(1/2)*x2^(15/2) + (-q^(15/2) + q^(13/2) + 5*q^(11/2) + 3*q^(9/2) - 4*q^(7/2) + 7*q^(5/2) - q^(3/2) - 7*q^(1/2) - 6*q^(-1/2) - 2*q^(-3/2) + q^(-5/2))*x1^(3/2)*x2^(15/2) + (-2*q^(15/2) - 4*q^(13/2) - 4*q^(9/2) + 2*q^(7/2) + 4*q^(5/2) + 4*q^(3/2) + 2*q^(1/2))*x1^(5/2)*x2^(15/2) + (q^(19/2) + 4*q^(15/2) - q^(13/2) - q^(11/2) - q^(9/2) - q^(7/2))*x1^(7/2)*x2^(15/2) + (-2*q^(23/2))*x1^(9/2)*x2^(15/2) + (q^(33/2))*x1^(11/2)*x2^(15/2) + (q^(15/2) - 3*q^(9/2) + q^(7/2) + 6*q^(5/2) - 9*q^(3/2) - 2*q^(1/2) + 2*q^(-1/2) + 4*q^(-3/2) + 5*q^(-5/2) - 2*q^(-7/2) - 3*q^(-9/2) - 3*q^(-11/2))*x1^(1/2)*x2^(17/2) + (-2*q^(17/2) - 2*q^(15/2) + 2*q^(13/2) + 8*q^(11/2) + 2*q^(9/2) - 8*q^(7/2) + 8*q^(5/2) + 4*q^(3/2) - 6*q^(1/2) - 10*q^(-1/2) - 6*q^(-3/2) + 2*q^(-5/2) + 4*q^(-7/2) + 2*q^(-9/2))*x1^(3/2)*x2^(17/2) + (-q^(21/2) + 2*q^(19/2) - 7*q^(15/2) - 7*q^(13/2) - 5*q^(9/2) + 2*q^(7/2) + 6*q^(5/2) + 9*q^(3/2) + 6*q^(1/2) + q^(-1/2) - q^(-3/2) - q^(-5/2))*x1^(5/2)*x2^(17/2) + (2*q^(21/2) + 4*q^(19/2) + 2*q^(17/2) + 6*q^(15/2) - 2*q^(13/2) - 4*q^(11/2) - 4*q^(9/2) - 4*q^(7/2) - 2*q^(5/2))*x1^(7/2)*x2^(17/2) + (-q^(27/2) - 4*q^(23/2) + q^(19/2) + q^(17/2) + q^(15/2) + q^(13/2))*x1^(9/2)*x2^(17/2) + (2*q^(33/2))*x1^(11/2)*x2^(17/2) + (-q^(45/2))*x1^(13/2)*x2^(17/2) + (2*q^(15/2) - 4*q^(9/2) + 2*q^(7/2) + 10*q^(5/2) - 8*q^(3/2) - 2*q^(1/2) + 2*q^(-3/2) + 8*q^(-5/2) + 2*q^(-7/2) - 2*q^(-9/2) - 10*q^(-11/2) - 4*q^(-13/2) - 2*q^(-15/2))*x1^(1/2)*x2^(19/2) + (q^(23/2) + q^(21/2) - q^(19/2) - 5*q^(17/2) - 3*q^(15/2) + 4*q^(13/2) + 11*q^(11/2) - 2*q^(9/2) - 19*q^(7/2) + 4*q^(5/2) + 7*q^(3/2) - q^(1/2) - 11*q^(-1/2) - 13*q^(-3/2) + 9*q^(-7/2) + 13*q^(-9/2) + 6*q^(-11/2) + 2*q^(-13/2))*x1^(3/2)*x2^(19/2) + (-2*q^(25/2) - 2*q^(23/2) + 2*q^(21/2) + 6*q^(19/2) - 2*q^(17/2) - 12*q^(15/2) - 8*q^(13/2) + 6*q^(11/2) - 2*q^(9/2) + 2*q^(7/2) + 6*q^(5/2) + 12*q^(3/2) + 12*q^(1/2) + 2*q^(-1/2) - 4*q^(-3/2) - 8*q^(-5/2) - 4*q^(-7/2) - 2*q^(-9/2))*x1^(5/2)*x2^(19/2) + (-q^(25/2) + q^(23/2) + 6*q^(21/2) + 10*q^(19/2) + 4*q^(17/2) + 8*q^(15/2) - 4*q^(13/2) - 8*q^(11/2) - 9*q^(9/2) - 9*q^(7/2) - 5*q^(5/2) - q^(3/2) + 2*q^(1/2) + q^(-1/2) + q^(-3/2))*x1^(7/2)*x2^(19/2) + (-2*q^(29/2) - 4*q^(27/2) - 2*q^(25/2) - 8*q^(23/2) + 4*q^(19/2) + 4*q^(17/2) + 4*q^(15/2) + 4*q^(13/2) + 2*q^(11/2))*x1^(9/2)*x2^(19/2) + (q^(37/2) + 4*q^(33/2) - q^(27/2) - q^(25/2) - q^(23/2) - q^(21/2))*x1^(11/2)*x2^(19/2) + (-2*q^(45/2))*x1^(13/2)*x2^(19/2) + (q^(59/2))*x1^(15/2)*x2^(19/2)

(1/2, 5/2)

x1^(-1/2)x2^(-5/2)

q^(3/2)

(-q^(3/2))*x1^(-1/2)*x2^(-5/2) + (-2*q^(3/2))*x1^(-1/2)*x2^(-7/2) + (q^(5/2))*x1^(-3/2)*x2^(-7/2) + (q^(5/2) - 3*q^(3/2) + q^(1/2))*x1^(-1/2)*x2^(-9/2) + (2*q^(5/2))*x1^(-3/2)*x2^(-9/2) + (-q^(9/2))*x1^(-5/2)*x2^(-9/2) + (2*q^(5/2) - 4*q^(3/2) + 2*q^(1/2) + 2*q^(-1/2))*x1^(-1/2)*x2^(-11/2) + (q^(9/2) - q^(7/2) + 3*q^(5/2) - q^(3/2) - q^(1/2))*x1^(-3/2)*x2^(-11/2) + (-2*q^(9/2))*x1^(-5/2)*x2^(-11/2) + (q^(15/2))*x1^(-7/2)*x2^(-11/2) + (-q^(9/2) + 3*q^(5/2) - 6*q^(3/2) + 2*q^(1/2) + 4*q^(-1/2) + 2*q^(-3/2))*x1^(-1/2)*x2^(-13/2) + (2*q^(11/2) + 2*q^(9/2) - 2*q^(7/2) + 4*q^(5/2) - 2*q^(3/2) - 4*q^(1/2) - 2*q^(-1/2))*x1^(-3/2)*x2^(-13/2) + (-q^(13/2) - 3*q^(9/2) + q^(7/2) + q^(5/2) + q^(3/2))*x1^(-5/2)*x2^(-13/2) + (2*q^(15/2))*x1^(-7/2)*x2^(-13/2) + (-q^(23/2))*x1^(-9/2)*x2^(-13/2) + (-2*q^(9/2) + 4*q^(5/2) - 8*q^(3/2) + 4*q^(-1/2) + 4*q^(-3/2) + 2*q^(-5/2) - 2*q^(-7/2))*x1^(-1/2)*x2^(-15/2) + (-q^(15/2) + q^(13/2) + 5*q^(11/2) + 3*q^(9/2) - 4*q^(7/2) + 7*q^(5/2) - q^(3/2) - 7*q^(1/2) - 6*q^(-1/2) - 2*q^(-3/2) + q^(-5/2))*x1^(-3/2)*x2^(-15/2) + (-2*q^(15/2) - 4*q^(13/2) - 4*q^(9/2) + 2*q^(7/2) + 4*q^(5/2) + 4*q^(3/2) + 2*q^(1/2))*x1^(-5/2)*x2^(-15/2) + (q^(19/2) + 4*q^(15/2) - q^(13/2) - q^(11/2) - q^(9/2) - q^(7/2))*x1^(-7/2)*x2^(-15/2) + (-2*q^(23/2))*x1^(-9/2)*x2^(-15/2) + (q^(33/2))*x1^(-11/2)*x2^(-15/2) + (q^(15/2) - 3*q^(9/2) + q^(7/2) + 6*q^(5/2) - 9*q^(3/2) - 2*q^(1/2) + 2*q^(-1/2) + 4*q^(-3/2) + 5*q^(-5/2) - 2*q^(-7/2) - 3*q^(-9/2) - 3*q^(-11/2))*x1^(-1/2)*x2^(-17/2) + (-2*q^(17/2) - 2*q^(15/2) + 2*q^(13/2) + 8*q^(11/2) + 2*q^(9/2) - 8*q^(7/2) + 8*q^(5/2) + 4*q^(3/2) - 6*q^(1/2) - 10*q^(-1/2) - 6*q^(-3/2) + 2*q^(-5/2) + 4*q^(-7/2) + 2*q^(-9/2))*x1^(-3/2)*x2^(-17/2) + (-q^(21/2) + 2*q^(19/2) - 7*q^(15/2) - 7*q^(13/2) - 5*q^(9/2) + 2*q^(7/2) + 6*q^(5/2) + 9*q^(3/2) + 6*q^(1/2) + q^(-1/2) - q^(-3/2) - q^(-5/2))*x1^(-5/2)*x2^(-17/2) + (2*q^(21/2) + 4*q^(19/2) + 2*q^(17/2) + 6*q^(15/2) - 2*q^(13/2) - 4*q^(11/2) - 4*q^(9/2) - 4*q^(7/2) - 2*q^(5/2))*x1^(-7/2)*x2^(-17/2) + (-q^(27/2) - 4*q^(23/2) + q^(19/2) + q^(17/2) + q^(15/2) + q^(13/2))*x1^(-9/2)*x2^(-17/2) + (2*q^(33/2))*x1^(-11/2)*x2^(-17/2) + (-q^(45/2))*x1^(-13/2)*x2^(-17/2) + (2*q^(15/2) - 4*q^(9/2) + 2*q^(7/2) + 10*q^(5/2) - 8*q^(3/2) - 2*q^(1/2) + 2*q^(-3/2) + 8*q^(-5/2) + 2*q^(-7/2) - 2*q^(-9/2) - 10*q^(-11/2) - 4*q^(-13/2) - 2*q^(-15/2))*x1^(-1/2)*x2^(-19/2) + (q^(23/2) + q^(21/2) - q^(19/2) - 5*q^(17/2) - 3*q^(15/2) + 4*q^(13/2) + 11*q^(11/2) - 2*q^(9/2) - 19*q^(7/2) + 4*q^(5/2) + 7*q^(3/2) - q^(1/2) - 11*q^(-1/2) - 13*q^(-3/2) + 9*q^(-7/2) + 13*q^(-9/2) + 6*q^(-11/2) + 2*q^(-13/2))*x1^(-3/2)*x2^(-19/2) + (-2*q^(25/2) - 2*q^(23/2) + 2*q^(21/2) + 6*q^(19/2) - 2*q^(17/2) - 12*q^(15/2) - 8*q^(13/2) + 6*q^(11/2) - 2*q^(9/2) + 2*q^(7/2) + 6*q^(5/2) + 12*q^(3/2) + 12*q^(1/2) + 2*q^(-1/2) - 4*q^(-3/2) - 8*q^(-5/2) - 4*q^(-7/2) - 2*q^(-9/2))*x1^(-5/2)*x2^(-19/2) + (-q^(25/2) + q^(23/2) + 6*q^(21/2) + 10*q^(19/2) + 4*q^(17/2) + 8*q^(15/2) - 4*q^(13/2) - 8*q^(11/2) - 9*q^(9/2) - 9*q^(7/2) - 5*q^(5/2) - q^(3/2) + 2*q^(1/2) + q^(-1/2) + q^(-3/2))*x1^(-7/2)*x2^(-19/2) + (-2*q^(29/2) - 4*q^(27/2) - 2*q^(25/2) - 8*q^(23/2) + 4*q^(19/2) + 4*q^(17/2) + 4*q^(15/2) + 4*q^(13/2) + 2*q^(11/2))*x1^(-9/2)*x2^(-19/2) + (q^(37/2) + 4*q^(33/2) - q^(27/2) - q^(25/2) - q^(23/2) - q^(21/2))*x1^(-11/2)*x2^(-19/2) + (-2*q^(45/2))*x1^(-13/2)*x2^(-19/2) + (q^(59/2))*x1^(-15/2)*x2^(-19/2)

Braid

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

Multivariable Alexander polynomial

Δ_L
`A1^(1/2)A2^(5/2) - 2A1^(1/2)A2^(3/2) + 3A1^(1/2)A2^(1/2) - 2A1^(1/2)A2^(-1/2) + A1^(1/2)A2^(-3/2) + A1^(-1/2)A2^(3/2) - 2A1^(-1/2)A2^(1/2) + 3A1^(-1/2)A2^(-1/2) - 2A1^(-1/2)A2^(-3/2) + A1^(-1/2)A2^(-5/2)`

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
`(-1, -5)`	yes
`(1, -3)`	yes
`(1, 5)`	yes
`(-1, 3)`	yes

HFL polytope

Poincaré polynomial
`m^(-6)A1^(-1)A2^(-3) + 3m^(-5)A1^(-1)A2^(-2) + m^(-5)A2^(-3) + 5m^(-4)A1^(-1)A2^(-1) + 4m^(-4)A2^(-2) + 5m^(-3)A1^(-1) + 8m^(-3)A2^(-1) + m^(-3)A1A2^(-2) + 3m^(-2)A1^(-1)A2 + 10m^(-2) + 3m^(-2)A1A2^(-1) + m^(-1)A1^(-1)A2^2 + 8m^(-1)A2 + 5m^(-1)A1 + 4A2^2 + 5A1A2 + mA2^3 + 3mA1A2^2 + m^2A1*A2^3`

Vertex	Maslov	Rank
`(-1, -3)`	-6	1
`(0, -3)`	-5	1
`(1, -2)`	-3	1
`(1, 3)`	2	1
`(0, 3)`	1	1
`(-1, 2)`	-1	1

Record

FL/HFL Links

`orderOption(int)`	`542`
`namestring`	`L10n38{1}`
`statusstring`	`success`
`slugstring`	`L10n38_1_4d057513`
`result_filestring`	`details/L10n38_1_4d057513.json`
`complexity_scoreOption(int)`	`200`
`strandsOption(int)`	`null`
`crossingsOption(int)`	`10`
`component_countOption(int)`	`2`
`girthOption(int)`	`6`
`total_rankOption(int)`	`72`
`wall_secondsOption(float)`	`0.002195`
`backend_secondsOption(float)`	`0.0`
`errorstring`
`dimensionOption(int)`	`2`
`support_sizeOption(int)`	`19`
`vertex_countOption(int)`	`6`
`fibered_vertex_countOption(int)`	`4`
`polytope_statusstring`	`computed`
`alexander_support_sizeOption(int)`	`10`
`alexander_vertex_countOption(int)`	`4`
`alexander_relationstring`	`not_computed`
`fk_countint`	`2`
`detailsRowRef(FLHFLLinks)`	{ "dataset": "FLHFLLinks", "key": "L10n38_1_4d057513" }
`detail_assetstring`	`/api/v1/datasets/FLHFLLinks/assets/L10n38_1_4d057513`

FL expansions

Braid

Multivariable Alexander polynomial

Dual Thurston polytope

HFL polytope

Record

F_L expansions