L10n74{0;1} - HFL and FL

details/L10n74_0_1_5b9686fe.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^(1)`	`{"0": [-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)x1^(1/2)x2^(3/2)x3^(-1/2) + (-q)x1^(1/2)x2^(5/2)x3^(-1/2) + (-q)x1^(1/2)x2^(7/2)x3^(-1/2) + (-q)x1^(1/2)x2^(9/2)x3^(-1/2) + (-q)x1^(1/2)x2^(11/2)x3^(-1/2) + (q^(2))x1^(1/2)x2^(5/2)x3^(1/2) + (q^(3) + q^(2))x1^(1/2)x2^(7/2)x3^(1/2) + (q^(4) + q^(3) + q^(2))x1^(1/2)x2^(9/2)x3^(1/2) + (q^(5) + q^(4) + q^(3) + q^(2))x1^(1/2)x2^(11/2)x3^(1/2) + (-q^(4))x1^(1/2)x2^(7/2)x3^(3/2) + (-q^(6) - q^(5) - q^(4))x1^(1/2)x2^(9/2)x3^(3/2) + (-q^(8) - q^(7) - 2q^(6) - q^(5) - q^(4))x1^(1/2)x2^(11/2)x3^(3/2) + (q^(7))x1^(1/2)x2^(9/2)x3^(5/2) + (q^(10) + q^(9) + q^(8) + q^(7))x1^(1/2)x2^(11/2)x3^(5/2) + (-q^(11))x1^(1/2)x2^(11/2)x3^(7/2) + (-q^(-3))x1^(3/2)x2^(7/2)x3^(-5/2) + (-q^(-3) - q^(-4))x1^(3/2)x2^(9/2)x3^(-5/2) + (-q^(-3) - q^(-4) - q^(-5))x1^(3/2)x2^(11/2)x3^(-5/2) + (q^(-2))x1^(3/2)x2^(7/2)x3^(-3/2) + (2q^(-2) + q^(-3))x1^(3/2)x2^(9/2)x3^(-3/2) + (q^(-1) + 3q^(-2) + 2q^(-3) + q^(-4))x1^(3/2)x2^(11/2)x3^(-3/2) + (-1 - q^(-1))x1^(3/2)x2^(9/2)x3^(-1/2) + (-q - 31 - 2q^(-1) - q^(-2))x1^(3/2)x2^(11/2)x3^(-1/2) + (q^(3) + q^(2) + q)x1^(3/2)x2^(11/2)x3^(1/2) + (-q^(-11))x1^(5/2)x2^(11/2)x3^(-9/2) + (q^(-9) + q^(-10))x1^(5/2)x2^(11/2)x3^(-7/2) + (-q^(-8))x1^(5/2)x2^(11/2)*x3^(-5/2)
`(-1/2, -3/2, 1/2)`	`(1, 1, 1)`	`x1^(1/2)x2^(3/2)x3^(-1/2)`	`q^(1)`	`{"0": [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)x1^(1/2)x2^(3/2)x3^(-1/2) + (-q)x1^(1/2)x2^(5/2)x3^(-1/2) + (-q)x1^(1/2)x2^(7/2)x3^(-1/2) + (-q)x1^(1/2)x2^(9/2)x3^(-1/2) + (-q)x1^(1/2)x2^(11/2)x3^(-1/2) + (q^(2))x1^(1/2)x2^(5/2)x3^(1/2) + (q^(3) + q^(2))x1^(1/2)x2^(7/2)x3^(1/2) + (q^(4) + q^(3) + q^(2))x1^(1/2)x2^(9/2)x3^(1/2) + (q^(5) + q^(4) + q^(3) + q^(2))x1^(1/2)x2^(11/2)x3^(1/2) + (-q^(4))x1^(1/2)x2^(7/2)x3^(3/2) + (-q^(6) - q^(5) - q^(4))x1^(1/2)x2^(9/2)x3^(3/2) + (-q^(8) - q^(7) - 2q^(6) - q^(5) - q^(4))x1^(1/2)x2^(11/2)x3^(3/2) + (q^(7))x1^(1/2)x2^(9/2)x3^(5/2) + (q^(10) + q^(9) + q^(8) + q^(7))x1^(1/2)x2^(11/2)x3^(5/2) + (-q^(11))x1^(1/2)x2^(11/2)x3^(7/2) + (-q^(-3))x1^(3/2)x2^(7/2)x3^(-5/2) + (-q^(-3) - q^(-4))x1^(3/2)x2^(9/2)x3^(-5/2) + (-q^(-3) - q^(-4) - q^(-5))x1^(3/2)x2^(11/2)x3^(-5/2) + (q^(-2))x1^(3/2)x2^(7/2)x3^(-3/2) + (2q^(-2) + q^(-3))x1^(3/2)x2^(9/2)x3^(-3/2) + (q^(-1) + 3q^(-2) + 2q^(-3) + q^(-4))x1^(3/2)x2^(11/2)x3^(-3/2) + (-1 - q^(-1))x1^(3/2)x2^(9/2)x3^(-1/2) + (-q - 31 - 2q^(-1) - q^(-2))x1^(3/2)x2^(11/2)x3^(-1/2) + (q^(3) + q^(2) + q)x1^(3/2)x2^(11/2)x3^(1/2) + (-q^(-11))x1^(5/2)x2^(11/2)x3^(-9/2) + (q^(-9) + q^(-10))x1^(5/2)x2^(11/2)x3^(-7/2) + (-q^(-8))x1^(5/2)x2^(11/2)*x3^(-5/2)
`(1/2, 3/2, -1/2)`		`x1^(-1/2)x2^(-3/2)x3^(1/2)`	`q^(1)`		(-q)x1^(-1/2)x2^(-3/2)x3^(1/2) + (-q)x1^(-1/2)x2^(-5/2)x3^(1/2) + (-q)x1^(-1/2)x2^(-7/2)x3^(1/2) + (-q)x1^(-1/2)x2^(-9/2)x3^(1/2) + (-q)x1^(-1/2)x2^(-11/2)x3^(1/2) + (q^(2))x1^(-1/2)x2^(-5/2)x3^(-1/2) + (q^(3) + q^(2))x1^(-1/2)x2^(-7/2)x3^(-1/2) + (q^(4) + q^(3) + q^(2))x1^(-1/2)x2^(-9/2)x3^(-1/2) + (q^(5) + q^(4) + q^(3) + q^(2))x1^(-1/2)x2^(-11/2)x3^(-1/2) + (-q^(4))x1^(-1/2)x2^(-7/2)x3^(-3/2) + (-q^(6) - q^(5) - q^(4))x1^(-1/2)x2^(-9/2)x3^(-3/2) + (-q^(8) - q^(7) - 2q^(6) - q^(5) - q^(4))x1^(-1/2)x2^(-11/2)x3^(-3/2) + (q^(7))x1^(-1/2)x2^(-9/2)x3^(-5/2) + (q^(10) + q^(9) + q^(8) + q^(7))x1^(-1/2)x2^(-11/2)x3^(-5/2) + (-q^(11))x1^(-1/2)x2^(-11/2)x3^(-7/2) + (-q^(-3))x1^(-3/2)x2^(-7/2)x3^(5/2) + (-q^(-3) - q^(-4))x1^(-3/2)x2^(-9/2)x3^(5/2) + (-q^(-3) - q^(-4) - q^(-5))x1^(-3/2)x2^(-11/2)x3^(5/2) + (q^(-2))x1^(-3/2)x2^(-7/2)x3^(3/2) + (2q^(-2) + q^(-3))x1^(-3/2)x2^(-9/2)x3^(3/2) + (q^(-1) + 3q^(-2) + 2q^(-3) + q^(-4))x1^(-3/2)x2^(-11/2)x3^(3/2) + (-1 - q^(-1))x1^(-3/2)x2^(-9/2)x3^(1/2) + (-q - 31 - 2q^(-1) - q^(-2))x1^(-3/2)x2^(-11/2)x3^(1/2) + (q^(3) + q^(2) + q)x1^(-3/2)x2^(-11/2)x3^(-1/2) + (-q^(-11))x1^(-5/2)x2^(-11/2)x3^(9/2) + (q^(-9) + q^(-10))x1^(-5/2)x2^(-11/2)x3^(7/2) + (-q^(-8))x1^(-5/2)x2^(-11/2)*x3^(5/2)

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

(1, 1, 1)

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

q^(1)

{"0": [-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)*x1^(1/2)*x2^(3/2)*x3^(-1/2) + (-q)*x1^(1/2)*x2^(5/2)*x3^(-1/2) + (-q)*x1^(1/2)*x2^(7/2)*x3^(-1/2) + (-q)*x1^(1/2)*x2^(9/2)*x3^(-1/2) + (-q)*x1^(1/2)*x2^(11/2)*x3^(-1/2) + (q^(2))*x1^(1/2)*x2^(5/2)*x3^(1/2) + (q^(3) + q^(2))*x1^(1/2)*x2^(7/2)*x3^(1/2) + (q^(4) + q^(3) + q^(2))*x1^(1/2)*x2^(9/2)*x3^(1/2) + (q^(5) + q^(4) + q^(3) + q^(2))*x1^(1/2)*x2^(11/2)*x3^(1/2) + (-q^(4))*x1^(1/2)*x2^(7/2)*x3^(3/2) + (-q^(6) - q^(5) - q^(4))*x1^(1/2)*x2^(9/2)*x3^(3/2) + (-q^(8) - q^(7) - 2*q^(6) - q^(5) - q^(4))*x1^(1/2)*x2^(11/2)*x3^(3/2) + (q^(7))*x1^(1/2)*x2^(9/2)*x3^(5/2) + (q^(10) + q^(9) + q^(8) + q^(7))*x1^(1/2)*x2^(11/2)*x3^(5/2) + (-q^(11))*x1^(1/2)*x2^(11/2)*x3^(7/2) + (-q^(-3))*x1^(3/2)*x2^(7/2)*x3^(-5/2) + (-q^(-3) - q^(-4))*x1^(3/2)*x2^(9/2)*x3^(-5/2) + (-q^(-3) - q^(-4) - q^(-5))*x1^(3/2)*x2^(11/2)*x3^(-5/2) + (q^(-2))*x1^(3/2)*x2^(7/2)*x3^(-3/2) + (2*q^(-2) + q^(-3))*x1^(3/2)*x2^(9/2)*x3^(-3/2) + (q^(-1) + 3*q^(-2) + 2*q^(-3) + q^(-4))*x1^(3/2)*x2^(11/2)*x3^(-3/2) + (-1 - q^(-1))*x1^(3/2)*x2^(9/2)*x3^(-1/2) + (-q - 3*1 - 2*q^(-1) - q^(-2))*x1^(3/2)*x2^(11/2)*x3^(-1/2) + (q^(3) + q^(2) + q)*x1^(3/2)*x2^(11/2)*x3^(1/2) + (-q^(-11))*x1^(5/2)*x2^(11/2)*x3^(-9/2) + (q^(-9) + q^(-10))*x1^(5/2)*x2^(11/2)*x3^(-7/2) + (-q^(-8))*x1^(5/2)*x2^(11/2)*x3^(-5/2)

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

(1, 1, 1)

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

q^(1)

{"0": [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)*x1^(1/2)*x2^(3/2)*x3^(-1/2) + (-q)*x1^(1/2)*x2^(5/2)*x3^(-1/2) + (-q)*x1^(1/2)*x2^(7/2)*x3^(-1/2) + (-q)*x1^(1/2)*x2^(9/2)*x3^(-1/2) + (-q)*x1^(1/2)*x2^(11/2)*x3^(-1/2) + (q^(2))*x1^(1/2)*x2^(5/2)*x3^(1/2) + (q^(3) + q^(2))*x1^(1/2)*x2^(7/2)*x3^(1/2) + (q^(4) + q^(3) + q^(2))*x1^(1/2)*x2^(9/2)*x3^(1/2) + (q^(5) + q^(4) + q^(3) + q^(2))*x1^(1/2)*x2^(11/2)*x3^(1/2) + (-q^(4))*x1^(1/2)*x2^(7/2)*x3^(3/2) + (-q^(6) - q^(5) - q^(4))*x1^(1/2)*x2^(9/2)*x3^(3/2) + (-q^(8) - q^(7) - 2*q^(6) - q^(5) - q^(4))*x1^(1/2)*x2^(11/2)*x3^(3/2) + (q^(7))*x1^(1/2)*x2^(9/2)*x3^(5/2) + (q^(10) + q^(9) + q^(8) + q^(7))*x1^(1/2)*x2^(11/2)*x3^(5/2) + (-q^(11))*x1^(1/2)*x2^(11/2)*x3^(7/2) + (-q^(-3))*x1^(3/2)*x2^(7/2)*x3^(-5/2) + (-q^(-3) - q^(-4))*x1^(3/2)*x2^(9/2)*x3^(-5/2) + (-q^(-3) - q^(-4) - q^(-5))*x1^(3/2)*x2^(11/2)*x3^(-5/2) + (q^(-2))*x1^(3/2)*x2^(7/2)*x3^(-3/2) + (2*q^(-2) + q^(-3))*x1^(3/2)*x2^(9/2)*x3^(-3/2) + (q^(-1) + 3*q^(-2) + 2*q^(-3) + q^(-4))*x1^(3/2)*x2^(11/2)*x3^(-3/2) + (-1 - q^(-1))*x1^(3/2)*x2^(9/2)*x3^(-1/2) + (-q - 3*1 - 2*q^(-1) - q^(-2))*x1^(3/2)*x2^(11/2)*x3^(-1/2) + (q^(3) + q^(2) + q)*x1^(3/2)*x2^(11/2)*x3^(1/2) + (-q^(-11))*x1^(5/2)*x2^(11/2)*x3^(-9/2) + (q^(-9) + q^(-10))*x1^(5/2)*x2^(11/2)*x3^(-7/2) + (-q^(-8))*x1^(5/2)*x2^(11/2)*x3^(-5/2)

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

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

q^(1)

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

Braid

Braid word	Components	Crossings	Strands
`[2, -3, 2, 1, -2, -2, 3, 3, 3, 3, 1]`	3	11	4

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

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HFL polytope

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

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

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Record

FL/HFL Links

`orderOption(int)`	`2202`
`namestring`	`L10n74{0;1}`
`statusstring`	`success`
`slugstring`	`L10n74_0_1_5b9686fe`
`result_filestring`	`details/L10n74_0_1_5b9686fe.json`
`complexity_scoreOption(int)`	`300`
`strandsOption(int)`	`null`
`crossingsOption(int)`	`10`
`component_countOption(int)`	`3`
`girthOption(int)`	`6`
`total_rankOption(int)`	`64`
`wall_secondsOption(float)`	`0.001649`
`backend_secondsOption(float)`	`0.0`
`errorstring`
`dimensionOption(int)`	`3`
`support_sizeOption(int)`	`33`
`vertex_countOption(int)`	`18`
`fibered_vertex_countOption(int)`	`6`
`polytope_statusstring`	`computed`
`alexander_support_sizeOption(int)`	`6`
`alexander_vertex_countOption(int)`	`6`
`alexander_relationstring`	`not_computed`
`fk_countint`	`4`
`detailsRowRef(FLHFLLinks)`	{ "dataset": "FLHFLLinks", "key": "L10n74_0_1_5b9686fe" }
`detail_assetstring`	`/api/v1/datasets/FLHFLLinks/assets/L10n74_0_1_5b9686fe`

FL expansions

Braid

Multivariable Alexander polynomial

Dual Thurston polytope

HFL polytope

Record

F_L expansions