details/L10a152_1_1_fecd72a0.json

FL expansions

Newt(ΔL) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle FL
(-1/2, -2, 0) (1, 1, 1/2) x1^(1/2)x2^(2)x3^(0) q^(3) 
{"0": [-1, 1, -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^(3))*x1^(1/2)*x2^(2) + (2*q^(2))*x1^(1/2)*x2^(3)*x3^(-1) + (-3*q^(3))*x1^(1/2)*x2^(3) + (q^(4))*x1^(1/2)*x2^(3)*x3 + (-q^(3))*x1^(3/2)*x2^(3)*x3^(-1) + (2*q^(4))*x1^(3/2)*x2^(3) + (-q - 3*1)*x1^(1/2)*x2^(4)*x3^(-2) + (6*q^(2) + 4*q)*x1^(1/2)*x2^(4)*x3^(-1) + (-8*q^(3) - q^(2))*x1^(1/2)*x2^(4) + (q^(5) + 3*q^(4))*x1^(1/2)*x2^(4)*x3 + (-q^(6))*x1^(1/2)*x2^(4)*x3^(2) + (2*q^(2) + 2*q)*x1^(3/2)*x2^(4)*x3^(-2) + (-2*q^(4) - 7*q^(3) - 3*q^(2))*x1^(3/2)*x2^(4)*x3^(-1) + (2*q^(5) + 7*q^(4) + q^(3))*x1^(3/2)*x2^(4) + (-2*q^(5))*x1^(3/2)*x2^(4)*x3 + (-q^(3))*x1^(5/2)*x2^(4)*x3^(-2) + (2*q^(5) + 2*q^(4))*x1^(5/2)*x2^(4)*x3^(-1) + (-3*q^(6) - q^(5))*x1^(5/2)*x2^(4) + (2*q^(-1) + 2*q^(-2) + 4*q^(-3))*x1^(1/2)*x2^(5)*x3^(-3) + (-3*q - 12*1 - 8*q^(-1) - 5*q^(-2))*x1^(1/2)*x2^(5)*x3^(-2) + (13*q^(2) + 16*q + 8*1 + q^(-1))*x1^(1/2)*x2^(5)*x3^(-1) + (-2*q^(4) - 18*q^(3) - 7*q^(2) - 2*q)*x1^(1/2)*x2^(5) + (q^(6) + 5*q^(5) + 7*q^(4) + q^(3))*x1^(1/2)*x2^(5)*x3 + (-q^(8) - q^(7) - 3*q^(6))*x1^(1/2)*x2^(5)*x3^(2) + (q^(9))*x1^(1/2)*x2^(5)*x3^(3) + (-q - 4*1 - 4*q^(-1) - 3*q^(-2))*x1^(3/2)*x2^(5)*x3^(-3) + (4*q^(3) + 12*q^(2) + 18*q + 10*1 + 4*q^(-1))*x1^(3/2)*x2^(5)*x3^(-2) + (-2*q^(5) - 10*q^(4) - 26*q^(3) - 21*q^(2) - 8*q - 1)*x1^(3/2)*x2^(5)*x3^(-1) + (2*q^(6) + 9*q^(5) + 22*q^(4) + 8*q^(3) + 2*q^(2))*x1^(3/2)*x2^(5) + (-5*q^(6) - 7*q^(5) - q^(4))*x1^(3/2)*x2^(5)*x3 + (2*q^(7))*x1^(3/2)*x2^(5)*x3^(2) + (2*q^(2) + 2*q + 2*1)*x1^(5/2)*x2^(5)*x3^(-3) + (-2*q^(5) - 6*q^(4) - 11*q^(3) - 7*q^(2) - 3*q)*x1^(5/2)*x2^(5)*x3^(-2) + (2*q^(7) + 6*q^(6) + 16*q^(5) + 15*q^(4) + 7*q^(3) + q^(2))*x1^(5/2)*x2^(5)*x3^(-1) + (-2*q^(8) - 4*q^(7) - 13*q^(6) - 7*q^(5) - 2*q^(4))*x1^(5/2)*x2^(5) + (3*q^(7) + q^(6))*x1^(5/2)*x2^(5)*x3 + (-q^(3))*x1^(7/2)*x2^(5)*x3^(-3) + (2*q^(6) + 2*q^(5) + 2*q^(4))*x1^(7/2)*x2^(5)*x3^(-2) + (-3*q^(8) - 4*q^(7) - 4*q^(6) - q^(5))*x1^(7/2)*x2^(5)*x3^(-1) + (4*q^(9) + 2*q^(8) + 2*q^(7))*x1^(7/2)*x2^(5)
(-1/2, -2, 0) (1, 1, 1/2) x1^(1/2)x2^(2)x3^(0) q^(3) 
{"0": [1, 1, 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^(3))*x1^(1/2)*x2^(2) + (2*q^(2))*x1^(1/2)*x2^(3)*x3^(-1) + (-3*q^(3))*x1^(1/2)*x2^(3) + (q^(4))*x1^(1/2)*x2^(3)*x3 + (-q^(3))*x1^(3/2)*x2^(3)*x3^(-1) + (2*q^(4))*x1^(3/2)*x2^(3) + (-q - 3*1)*x1^(1/2)*x2^(4)*x3^(-2) + (6*q^(2) + 4*q)*x1^(1/2)*x2^(4)*x3^(-1) + (-8*q^(3) - q^(2))*x1^(1/2)*x2^(4) + (q^(5) + 3*q^(4))*x1^(1/2)*x2^(4)*x3 + (-q^(6))*x1^(1/2)*x2^(4)*x3^(2) + (2*q^(2) + 2*q)*x1^(3/2)*x2^(4)*x3^(-2) + (-2*q^(4) - 7*q^(3) - 3*q^(2))*x1^(3/2)*x2^(4)*x3^(-1) + (2*q^(5) + 7*q^(4) + q^(3))*x1^(3/2)*x2^(4) + (-2*q^(5))*x1^(3/2)*x2^(4)*x3 + (-q^(3))*x1^(5/2)*x2^(4)*x3^(-2) + (2*q^(5) + 2*q^(4))*x1^(5/2)*x2^(4)*x3^(-1) + (-3*q^(6) - q^(5))*x1^(5/2)*x2^(4) + (2*q^(-1) + 2*q^(-2) + 4*q^(-3))*x1^(1/2)*x2^(5)*x3^(-3) + (-3*q - 12*1 - 8*q^(-1) - 5*q^(-2))*x1^(1/2)*x2^(5)*x3^(-2) + (13*q^(2) + 16*q + 8*1 + q^(-1))*x1^(1/2)*x2^(5)*x3^(-1) + (-2*q^(4) - 18*q^(3) - 7*q^(2) - 2*q)*x1^(1/2)*x2^(5) + (q^(6) + 5*q^(5) + 7*q^(4) + q^(3))*x1^(1/2)*x2^(5)*x3 + (-q^(8) - q^(7) - 3*q^(6))*x1^(1/2)*x2^(5)*x3^(2) + (q^(9))*x1^(1/2)*x2^(5)*x3^(3) + (-q - 4*1 - 4*q^(-1) - 3*q^(-2))*x1^(3/2)*x2^(5)*x3^(-3) + (4*q^(3) + 12*q^(2) + 18*q + 10*1 + 4*q^(-1))*x1^(3/2)*x2^(5)*x3^(-2) + (-2*q^(5) - 10*q^(4) - 26*q^(3) - 21*q^(2) - 8*q - 1)*x1^(3/2)*x2^(5)*x3^(-1) + (2*q^(6) + 9*q^(5) + 22*q^(4) + 8*q^(3) + 2*q^(2))*x1^(3/2)*x2^(5) + (-5*q^(6) - 7*q^(5) - q^(4))*x1^(3/2)*x2^(5)*x3 + (2*q^(7))*x1^(3/2)*x2^(5)*x3^(2) + (2*q^(2) + 2*q + 2*1)*x1^(5/2)*x2^(5)*x3^(-3) + (-2*q^(5) - 6*q^(4) - 11*q^(3) - 7*q^(2) - 3*q)*x1^(5/2)*x2^(5)*x3^(-2) + (2*q^(7) + 6*q^(6) + 16*q^(5) + 15*q^(4) + 7*q^(3) + q^(2))*x1^(5/2)*x2^(5)*x3^(-1) + (-2*q^(8) - 4*q^(7) - 13*q^(6) - 7*q^(5) - 2*q^(4))*x1^(5/2)*x2^(5) + (3*q^(7) + q^(6))*x1^(5/2)*x2^(5)*x3 + (-q^(3))*x1^(7/2)*x2^(5)*x3^(-3) + (2*q^(6) + 2*q^(5) + 2*q^(4))*x1^(7/2)*x2^(5)*x3^(-2) + (-3*q^(8) - 4*q^(7) - 4*q^(6) - q^(5))*x1^(7/2)*x2^(5)*x3^(-1) + (4*q^(9) + 2*q^(8) + 2*q^(7))*x1^(7/2)*x2^(5)
(1/2, 2, 0) x1^(-1/2)x2^(-2)x3^(0) q^(3) 
(-q^(3))*x1^(-1/2)*x2^(-2) + (2*q^(2))*x1^(-1/2)*x2^(-3)*x3 + (-3*q^(3))*x1^(-1/2)*x2^(-3) + (q^(4))*x1^(-1/2)*x2^(-3)*x3^(-1) + (-q^(3))*x1^(-3/2)*x2^(-3)*x3 + (2*q^(4))*x1^(-3/2)*x2^(-3) + (-q - 3*1)*x1^(-1/2)*x2^(-4)*x3^(2) + (6*q^(2) + 4*q)*x1^(-1/2)*x2^(-4)*x3 + (-8*q^(3) - q^(2))*x1^(-1/2)*x2^(-4) + (q^(5) + 3*q^(4))*x1^(-1/2)*x2^(-4)*x3^(-1) + (-q^(6))*x1^(-1/2)*x2^(-4)*x3^(-2) + (2*q^(2) + 2*q)*x1^(-3/2)*x2^(-4)*x3^(2) + (-2*q^(4) - 7*q^(3) - 3*q^(2))*x1^(-3/2)*x2^(-4)*x3 + (2*q^(5) + 7*q^(4) + q^(3))*x1^(-3/2)*x2^(-4) + (-2*q^(5))*x1^(-3/2)*x2^(-4)*x3^(-1) + (-q^(3))*x1^(-5/2)*x2^(-4)*x3^(2) + (2*q^(5) + 2*q^(4))*x1^(-5/2)*x2^(-4)*x3 + (-3*q^(6) - q^(5))*x1^(-5/2)*x2^(-4) + (2*q^(-1) + 2*q^(-2) + 4*q^(-3))*x1^(-1/2)*x2^(-5)*x3^(3) + (-3*q - 12*1 - 8*q^(-1) - 5*q^(-2))*x1^(-1/2)*x2^(-5)*x3^(2) + (13*q^(2) + 16*q + 8*1 + q^(-1))*x1^(-1/2)*x2^(-5)*x3 + (-2*q^(4) - 18*q^(3) - 7*q^(2) - 2*q)*x1^(-1/2)*x2^(-5) + (q^(6) + 5*q^(5) + 7*q^(4) + q^(3))*x1^(-1/2)*x2^(-5)*x3^(-1) + (-q^(8) - q^(7) - 3*q^(6))*x1^(-1/2)*x2^(-5)*x3^(-2) + (q^(9))*x1^(-1/2)*x2^(-5)*x3^(-3) + (-q - 4*1 - 4*q^(-1) - 3*q^(-2))*x1^(-3/2)*x2^(-5)*x3^(3) + (4*q^(3) + 12*q^(2) + 18*q + 10*1 + 4*q^(-1))*x1^(-3/2)*x2^(-5)*x3^(2) + (-2*q^(5) - 10*q^(4) - 26*q^(3) - 21*q^(2) - 8*q - 1)*x1^(-3/2)*x2^(-5)*x3 + (2*q^(6) + 9*q^(5) + 22*q^(4) + 8*q^(3) + 2*q^(2))*x1^(-3/2)*x2^(-5) + (-5*q^(6) - 7*q^(5) - q^(4))*x1^(-3/2)*x2^(-5)*x3^(-1) + (2*q^(7))*x1^(-3/2)*x2^(-5)*x3^(-2) + (2*q^(2) + 2*q + 2*1)*x1^(-5/2)*x2^(-5)*x3^(3) + (-2*q^(5) - 6*q^(4) - 11*q^(3) - 7*q^(2) - 3*q)*x1^(-5/2)*x2^(-5)*x3^(2) + (2*q^(7) + 6*q^(6) + 16*q^(5) + 15*q^(4) + 7*q^(3) + q^(2))*x1^(-5/2)*x2^(-5)*x3 + (-2*q^(8) - 4*q^(7) - 13*q^(6) - 7*q^(5) - 2*q^(4))*x1^(-5/2)*x2^(-5) + (3*q^(7) + q^(6))*x1^(-5/2)*x2^(-5)*x3^(-1) + (-q^(3))*x1^(-7/2)*x2^(-5)*x3^(3) + (2*q^(6) + 2*q^(5) + 2*q^(4))*x1^(-7/2)*x2^(-5)*x3^(2) + (-3*q^(8) - 4*q^(7) - 4*q^(6) - q^(5))*x1^(-7/2)*x2^(-5)*x3 + (4*q^(9) + 2*q^(8) + 2*q^(7))*x1^(-7/2)*x2^(-5)

Braid

Braid word Components Crossings Strands
[2, 2, -3, 2, 3, 1, 1, 2, 3, 3, 3, 2, -1] 3 13 4

Multivariable Alexander polynomial

ΔL
A1^(1/2)*A2^(2) + 2*A1^(1/2)*A2*A3 - 3*A1^(1/2)*A2 + A1^(1/2)*A2*A3^(-1) - 2*A1^(1/2)*A3 + 4*A1^(1/2) - 2*A1^(1/2)*A3^(-1) - 2*A1^(1/2)*A2^(-1) + A1^(1/2)*A2^(-1)*A3^(-1) - A1^(-1/2)*A2*A3 + 2*A1^(-1/2)*A2 + 2*A1^(-1/2)*A3 - 4*A1^(-1/2) + 2*A1^(-1/2)*A3^(-1) - A1^(-1/2)*A2^(-1)*A3 + 3*A1^(-1/2)*A2^(-1) - 2*A1^(-1/2)*A2^(-1)*A3^(-1) - A1^(-1/2)*A2^(-2)

Warning: the A1, A2, … basis used for the HFL and Alexander data might not match the x1, x2, … basis used for FL.

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Dual Thurston polytope

VertexDual to fibered face
(-1, 2, 2) yes
(-1, -2, 2) yes
(-1, 0, -2) no
(-1, -2, -2) no
(1, 4, 0) yes
(1, -2, -2) yes
(1, 2, 2) no
(-1, -4, 0) yes
(-1, 2, 0) no
(1, -2, 0) no
(1, 0, 2) no
(1, 2, -2) yes
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HFL polytope

Poincaré polynomial
m^(-8)*A1^(-1)*A2^(-5/2)*A3^(-1/2) + 2*m^(-8)*A1^(-1)*A2^(-3/2)*A3^(-3/2) + m^(-7)*A1^(-1)*A2^(-5/2)*A3^(1/2) + 6*m^(-7)*A1^(-1)*A2^(-3/2)*A3^(-1/2) + 4*m^(-7)*A1^(-1)*A2^(-1/2)*A3^(-3/2) + m^(-7)*A2^(-5/2)*A3^(-1/2) + 3*m^(-7)*A2^(-3/2)*A3^(-3/2) + 5*m^(-6)*A1^(-1)*A2^(-3/2)*A3^(1/2) + 11*m^(-6)*A1^(-1)*A2^(-1/2)*A3^(-1/2) + 2*m^(-6)*A1^(-1)*A2^(1/2)*A3^(-3/2) + m^(-6)*A2^(-5/2)*A3^(1/2) + 9*m^(-6)*A2^(-3/2)*A3^(-1/2) + 7*m^(-6)*A2^(-1/2)*A3^(-3/2) + m^(-6)*A1*A2^(-3/2)*A3^(-3/2) + m^(-5)*A1^(-1)*A2^(-3/2)*A3^(3/2) + 10*m^(-5)*A1^(-1)*A2^(-1/2)*A3^(1/2) + 8*m^(-5)*A1^(-1)*A2^(1/2)*A3^(-1/2) + 7*m^(-5)*A2^(-3/2)*A3^(1/2) + 20*m^(-5)*A2^(-1/2)*A3^(-1/2) + 5*m^(-5)*A2^(1/2)*A3^(-3/2) + 3*m^(-5)*A1*A2^(-3/2)*A3^(-1/2) + 3*m^(-5)*A1*A2^(-1/2)*A3^(-3/2) + 3*m^(-4)*A1^(-1)*A2^(-1/2)*A3^(3/2) + 9*m^(-4)*A1^(-1)*A2^(1/2)*A3^(1/2) + 2*m^(-4)*A1^(-1)*A2^(3/2)*A3^(-1/2) + m^(-4)*A2^(-3/2)*A3^(3/2) + 18*m^(-4)*A2^(-1/2)*A3^(1/2) + 18*m^(-4)*A2^(1/2)*A3^(-1/2) + m^(-4)*A2^(3/2)*A3^(-3/2) + 2*m^(-4)*A1*A2^(-3/2)*A3^(1/2) + 9*m^(-4)*A1*A2^(-1/2)*A3^(-1/2) + 3*m^(-4)*A1*A2^(1/2)*A3^(-3/2) + 3*m^(-3)*A1^(-1)*A2^(1/2)*A3^(3/2) + 3*m^(-3)*A1^(-1)*A2^(3/2)*A3^(1/2) + 5*m^(-3)*A2^(-1/2)*A3^(3/2) + 20*m^(-3)*A2^(1/2)*A3^(1/2) + 7*m^(-3)*A2^(3/2)*A3^(-1/2) + 8*m^(-3)*A1*A2^(-1/2)*A3^(1/2) + 10*m^(-3)*A1*A2^(1/2)*A3^(-1/2) + m^(-3)*A1*A2^(3/2)*A3^(-3/2) + m^(-2)*A1^(-1)*A2^(3/2)*A3^(3/2) + 7*m^(-2)*A2^(1/2)*A3^(3/2) + 9*m^(-2)*A2^(3/2)*A3^(1/2) + m^(-2)*A2^(5/2)*A3^(-1/2) + 2*m^(-2)*A1*A2^(-1/2)*A3^(3/2) + 11*m^(-2)*A1*A2^(1/2)*A3^(1/2) + 5*m^(-2)*A1*A2^(3/2)*A3^(-1/2) + 3*m^(-1)*A2^(3/2)*A3^(3/2) + m^(-1)*A2^(5/2)*A3^(1/2) + 4*m^(-1)*A1*A2^(1/2)*A3^(3/2) + 6*m^(-1)*A1*A2^(3/2)*A3^(1/2) + m^(-1)*A1*A2^(5/2)*A3^(-1/2) + 2*A1*A2^(3/2)*A3^(3/2) + A1*A2^(5/2)*A3^(1/2)
VertexMaslovRank
(-1, -5/2, -1/2)-81
(-1, -5/2, 1/2)-71
(-1, -3/2, -3/2)-82
(-1, -3/2, 3/2)-51
(-1, 1/2, -3/2)-62
(-1, 3/2, -1/2)-42
(-1, 3/2, 3/2)-21
(0, -5/2, -1/2)-71
(0, -5/2, 1/2)-61
(0, -3/2, 3/2)-41
(0, 3/2, -3/2)-41
(0, 5/2, -1/2)-21
(0, 5/2, 1/2)-11
(1, -3/2, -3/2)-61
(1, -3/2, 1/2)-42
(1, -1/2, 3/2)-22
(1, 3/2, -3/2)-31
(1, 3/2, 3/2)02
(1, 5/2, -1/2)-11
(1, 5/2, 1/2)01
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Record

FL/HFL Links

orderOption(int) 2116
namestring L10a152{1;1}
statusstring success
slugstring L10a152_1_1_fecd72a0
result_filestring details/L10a152_1_1_fecd72a0.json
complexity_scoreOption(int) 300
strandsOption(int) null
crossingsOption(int) 10
component_countOption(int) 3
girthOption(int) 6
total_rankOption(int) 288
wall_secondsOption(float) 0.002647
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 3
support_sizeOption(int) 54
vertex_countOption(int) 20
fibered_vertex_countOption(int) 6
polytope_statusstring computed
alexander_support_sizeOption(int) 18
alexander_vertex_countOption(int) 12
alexander_relationstring not_computed
fk_countint 2
detailsRowRef(FLHFLLinks) 
{
  "dataset": "FLHFLLinks",
  "key": "L10a152_1_1_fecd72a0"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L10a152_1_1_fecd72a0