L10a169{0;0;0} - HFL and FL

details/L10a169_0_0_0_9323ab36.json

Multivariable Alexander polynomial

Δ_L
A1^(1/2)A2A3^(1/2)A4 - 2A1^(1/2)A2A3^(1/2) + A1^(1/2)A2A3^(1/2)A4^(-1) - A1^(1/2)A2A3^(-1/2)A4 + 2A1^(1/2)A2A3^(-1/2) - A1^(1/2)A2A3^(-1/2)A4^(-1) - 2A1^(1/2)A3^(1/2)A4 + 4A1^(1/2)A3^(1/2) - 2A1^(1/2)A3^(1/2)A4^(-1) + 2A1^(1/2)A3^(-1/2)A4 - 4A1^(1/2)A3^(-1/2) + 2A1^(1/2)A3^(-1/2)A4^(-1) + A1^(1/2)A2^(-1)A3^(1/2)A4 - 2A1^(1/2)A2^(-1)A3^(1/2) + A1^(1/2)A2^(-1)A3^(1/2)A4^(-1) - A1^(1/2)A2^(-1)A3^(-1/2)A4 + 2A1^(1/2)A2^(-1)A3^(-1/2) - A1^(1/2)A2^(-1)A3^(-1/2)A4^(-1) - A1^(-1/2)A2A3^(1/2)A4 + 2A1^(-1/2)A2A3^(1/2) - A1^(-1/2)A2A3^(1/2)A4^(-1) + A1^(-1/2)A2A3^(-1/2)A4 - 2A1^(-1/2)A2A3^(-1/2) + A1^(-1/2)A2A3^(-1/2)A4^(-1) + 2A1^(-1/2)A3^(1/2)A4 - 4A1^(-1/2)A3^(1/2) + 2A1^(-1/2)A3^(1/2)A4^(-1) - 2A1^(-1/2)A3^(-1/2)A4 + 4A1^(-1/2)A3^(-1/2) - 2A1^(-1/2)A3^(-1/2)A4^(-1) - A1^(-1/2)A2^(-1)A3^(1/2)A4 + 2A1^(-1/2)A2^(-1)A3^(1/2) - A1^(-1/2)A2^(-1)A3^(1/2)A4^(-1) + A1^(-1/2)A2^(-1)A3^(-1/2)A4 - 2A1^(-1/2)A2^(-1)A3^(-1/2) + A1^(-1/2)A2^(-1)A3^(-1/2)A4^(-1)

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, -2)`	no
`(1, -2)`	no
`(1, 2)`	no
`(-1, 2)`	no

HFL polytope

Poincaré polynomial
m^(-6)A1^(-1)A2^(-3/2)A3^(-1)A4^(-3/2) + 3m^(-5)A1^(-1)A2^(-3/2)A3^(-1)A4^(-1/2) + 2m^(-5)A1^(-1)A2^(-3/2)A4^(-3/2) + 3m^(-5)A1^(-1)A2^(-1/2)A3^(-1)A4^(-3/2) + 2m^(-5)A2^(-3/2)A3^(-1)A4^(-3/2) + 3m^(-4)A1^(-1)A2^(-3/2)A3^(-1)A4^(1/2) + 6m^(-4)A1^(-1)A2^(-3/2)A4^(-1/2) + m^(-4)A1^(-1)A2^(-3/2)A3A4^(-3/2) + 9m^(-4)A1^(-1)A2^(-1/2)A3^(-1)A4^(-1/2) + 6m^(-4)A1^(-1)A2^(-1/2)A4^(-3/2) + 3m^(-4)A1^(-1)A2^(1/2)A3^(-1)A4^(-3/2) + 6m^(-4)A2^(-3/2)A3^(-1)A4^(-1/2) + 4m^(-4)A2^(-3/2)A4^(-3/2) + 6m^(-4)A2^(-1/2)A3^(-1)A4^(-3/2) + m^(-4)A1A2^(-3/2)A3^(-1)A4^(-3/2) + m^(-3)A1^(-1)A2^(-3/2)A3^(-1)A4^(3/2) + 6m^(-3)A1^(-1)A2^(-3/2)A4^(1/2) + 3m^(-3)A1^(-1)A2^(-3/2)A3A4^(-1/2) + 9m^(-3)A1^(-1)A2^(-1/2)A3^(-1)A4^(1/2) + 18m^(-3)A1^(-1)A2^(-1/2)A4^(-1/2) + 3m^(-3)A1^(-1)A2^(-1/2)A3A4^(-3/2) + 9m^(-3)A1^(-1)A2^(1/2)A3^(-1)A4^(-1/2) + 6m^(-3)A1^(-1)A2^(1/2)A4^(-3/2) + m^(-3)A1^(-1)A2^(3/2)A3^(-1)A4^(-3/2) + 6m^(-3)A2^(-3/2)A3^(-1)A4^(1/2) + 12m^(-3)A2^(-3/2)A4^(-1/2) + 2m^(-3)A2^(-3/2)A3A4^(-3/2) + 18m^(-3)A2^(-1/2)A3^(-1)A4^(-1/2) + 12m^(-3)A2^(-1/2)A4^(-3/2) + 6m^(-3)A2^(1/2)A3^(-1)A4^(-3/2) + 3m^(-3)A1A2^(-3/2)A3^(-1)A4^(-1/2) + 2m^(-3)A1A2^(-3/2)A4^(-3/2) + 3m^(-3)A1A2^(-1/2)A3^(-1)A4^(-3/2) + 2m^(-2)A1^(-1)A2^(-3/2)A4^(3/2) + 3m^(-2)A1^(-1)A2^(-3/2)A3A4^(1/2) + 3m^(-2)A1^(-1)A2^(-1/2)A3^(-1)A4^(3/2) + 18m^(-2)A1^(-1)A2^(-1/2)A4^(1/2) + 9m^(-2)A1^(-1)A2^(-1/2)A3A4^(-1/2) + 9m^(-2)A1^(-1)A2^(1/2)A3^(-1)A4^(1/2) + 18m^(-2)A1^(-1)A2^(1/2)A4^(-1/2) + 3m^(-2)A1^(-1)A2^(1/2)A3A4^(-3/2) + 3m^(-2)A1^(-1)A2^(3/2)A3^(-1)A4^(-1/2) + 2m^(-2)A1^(-1)A2^(3/2)A4^(-3/2) + 2m^(-2)A2^(-3/2)A3^(-1)A4^(3/2) + 12m^(-2)A2^(-3/2)A4^(1/2) + 6m^(-2)A2^(-3/2)A3A4^(-1/2) + 18m^(-2)A2^(-1/2)A3^(-1)A4^(1/2) + 36m^(-2)A2^(-1/2)A4^(-1/2) + 6m^(-2)A2^(-1/2)A3A4^(-3/2) + 18m^(-2)A2^(1/2)A3^(-1)A4^(-1/2) + 12m^(-2)A2^(1/2)A4^(-3/2) + 2m^(-2)A2^(3/2)A3^(-1)A4^(-3/2) + 3m^(-2)A1A2^(-3/2)A3^(-1)A4^(1/2) + 6m^(-2)A1A2^(-3/2)A4^(-1/2) + m^(-2)A1A2^(-3/2)A3A4^(-3/2) + 9m^(-2)A1A2^(-1/2)A3^(-1)A4^(-1/2) + 6m^(-2)A1A2^(-1/2)A4^(-3/2) + 3m^(-2)A1A2^(1/2)A3^(-1)A4^(-3/2) + m^(-1)A1^(-1)A2^(-3/2)A3A4^(3/2) + 6m^(-1)A1^(-1)A2^(-1/2)A4^(3/2) + 9m^(-1)A1^(-1)A2^(-1/2)A3A4^(1/2) + 3m^(-1)A1^(-1)A2^(1/2)A3^(-1)A4^(3/2) + 18m^(-1)A1^(-1)A2^(1/2)A4^(1/2) + 9m^(-1)A1^(-1)A2^(1/2)A3A4^(-1/2) + 3m^(-1)A1^(-1)A2^(3/2)A3^(-1)A4^(1/2) + 6m^(-1)A1^(-1)A2^(3/2)A4^(-1/2) + m^(-1)A1^(-1)A2^(3/2)A3A4^(-3/2) + 4m^(-1)A2^(-3/2)A4^(3/2) + 6m^(-1)A2^(-3/2)A3A4^(1/2) + 6m^(-1)A2^(-1/2)A3^(-1)A4^(3/2) + 36m^(-1)A2^(-1/2)A4^(1/2) + 18m^(-1)A2^(-1/2)A3A4^(-1/2) + 18m^(-1)A2^(1/2)A3^(-1)A4^(1/2) + 36m^(-1)A2^(1/2)A4^(-1/2) + 6m^(-1)A2^(1/2)A3A4^(-3/2) + 6m^(-1)A2^(3/2)A3^(-1)A4^(-1/2) + 4m^(-1)A2^(3/2)A4^(-3/2) + m^(-1)A1A2^(-3/2)A3^(-1)A4^(3/2) + 6m^(-1)A1A2^(-3/2)A4^(1/2) + 3m^(-1)A1A2^(-3/2)A3A4^(-1/2) + 9m^(-1)A1A2^(-1/2)A3^(-1)A4^(1/2) + 18m^(-1)A1A2^(-1/2)A4^(-1/2) + 3m^(-1)A1A2^(-1/2)A3A4^(-3/2) + 9m^(-1)A1A2^(1/2)A3^(-1)A4^(-1/2) + 6m^(-1)A1A2^(1/2)A4^(-3/2) + m^(-1)A1A2^(3/2)A3^(-1)A4^(-3/2) + 3A1^(-1)A2^(-1/2)A3A4^(3/2) + 6A1^(-1)A2^(1/2)A4^(3/2) + 9A1^(-1)A2^(1/2)A3A4^(1/2) + A1^(-1)A2^(3/2)A3^(-1)A4^(3/2) + 6A1^(-1)A2^(3/2)A4^(1/2) + 3A1^(-1)A2^(3/2)A3A4^(-1/2) + 2A2^(-3/2)A3A4^(3/2) + 12A2^(-1/2)A4^(3/2) + 18A2^(-1/2)A3A4^(1/2) + 6A2^(1/2)A3^(-1)A4^(3/2) + 36A2^(1/2)A4^(1/2) + 18A2^(1/2)A3A4^(-1/2) + 6A2^(3/2)A3^(-1)A4^(1/2) + 12A2^(3/2)A4^(-1/2) + 2A2^(3/2)A3A4^(-3/2) + 2A1A2^(-3/2)A4^(3/2) + 3A1A2^(-3/2)A3A4^(1/2) + 3A1A2^(-1/2)A3^(-1)A4^(3/2) + 18A1A2^(-1/2)A4^(1/2) + 9A1A2^(-1/2)A3A4^(-1/2) + 9A1A2^(1/2)A3^(-1)A4^(1/2) + 18A1A2^(1/2)A4^(-1/2) + 3A1A2^(1/2)A3A4^(-3/2) + 3A1A2^(3/2)A3^(-1)A4^(-1/2) + 2A1A2^(3/2)A4^(-3/2) + 3mA1^(-1)A2^(1/2)A3A4^(3/2) + 2mA1^(-1)A2^(3/2)A4^(3/2) + 3mA1^(-1)A2^(3/2)A3A4^(1/2) + 6mA2^(-1/2)A3A4^(3/2) + 12mA2^(1/2)A4^(3/2) + 18mA2^(1/2)A3A4^(1/2) + 2mA2^(3/2)A3^(-1)A4^(3/2) + 12mA2^(3/2)A4^(1/2) + 6mA2^(3/2)A3A4^(-1/2) + mA1A2^(-3/2)A3A4^(3/2) + 6mA1A2^(-1/2)A4^(3/2) + 9mA1A2^(-1/2)A3A4^(1/2) + 3mA1A2^(1/2)A3^(-1)A4^(3/2) + 18mA1A2^(1/2)A4^(1/2) + 9mA1A2^(1/2)A3A4^(-1/2) + 3mA1A2^(3/2)A3^(-1)A4^(1/2) + 6mA1A2^(3/2)A4^(-1/2) + mA1A2^(3/2)A3A4^(-3/2) + m^2A1^(-1)A2^(3/2)A3A4^(3/2) + 6m^2A2^(1/2)A3A4^(3/2) + 4m^2A2^(3/2)A4^(3/2) + 6m^2A2^(3/2)A3A4^(1/2) + 3m^2A1A2^(-1/2)A3A4^(3/2) + 6m^2A1A2^(1/2)A4^(3/2) + 9m^2A1A2^(1/2)A3A4^(1/2) + m^2A1A2^(3/2)A3^(-1)A4^(3/2) + 6m^2A1A2^(3/2)A4^(1/2) + 3m^2A1A2^(3/2)A3A4^(-1/2) + 2m^3A2^(3/2)A3A4^(3/2) + 3m^3A1A2^(1/2)A3A4^(3/2) + 2m^3A1A2^(3/2)A4^(3/2) + 3m^3A1A2^(3/2)A3A4^(1/2) + m^4A1A2^(3/2)A3*A4^(3/2)

Vertex	Maslov	Rank
`(-1, -3/2, -1, -3/2)`	-6	1
`(-1, -3/2, -1, 3/2)`	-3	1
`(-1, -3/2, 1, -3/2)`	-4	1
`(-1, -3/2, 1, 3/2)`	-1	1
`(-1, 3/2, -1, -3/2)`	-3	1
`(-1, 3/2, -1, 3/2)`	0	1
`(-1, 3/2, 1, -3/2)`	-1	1
`(-1, 3/2, 1, 3/2)`	2	1
`(1, -3/2, -1, -3/2)`	-4	1
`(1, -3/2, -1, 3/2)`	-1	1
`(1, -3/2, 1, -3/2)`	-2	1
`(1, -3/2, 1, 3/2)`	1	1
`(1, 3/2, -1, -3/2)`	-1	1
`(1, 3/2, -1, 3/2)`	2	1
`(1, 3/2, 1, -3/2)`	1	1
`(1, 3/2, 1, 3/2)`	4	1

Record

FL/HFL Links

`orderOption(int)`	`3645`
`namestring`	`L10a169{0;0;0}`
`statusstring`	`success`
`slugstring`	`L10a169_0_0_0_9323ab36`
`result_filestring`	`details/L10a169_0_0_0_9323ab36.json`
`complexity_scoreOption(int)`	`400`
`strandsOption(int)`	`null`
`crossingsOption(int)`	`10`
`component_countOption(int)`	`4`
`girthOption(int)`	`6`
`total_rankOption(int)`	`1024`
`wall_secondsOption(float)`	`0.009458`
`backend_secondsOption(float)`	`0.0`
`errorstring`
`dimensionOption(int)`	`4`
`support_sizeOption(int)`	`144`
`vertex_countOption(int)`	`16`
`fibered_vertex_countOption(int)`	`0`
`polytope_statusstring`	`computed`
`alexander_support_sizeOption(int)`	`36`
`alexander_vertex_countOption(int)`	`16`
`alexander_relationstring`	`not_computed`
`fk_countint`	`0`
`detailsRowRef(FLHFLLinks)`	{ "dataset": "FLHFLLinks", "key": "L10a169_0_0_0_9323ab36" }
`detail_assetstring`	`/api/v1/datasets/FLHFLLinks/assets/L10a169_0_0_0_9323ab36`