details/L10a168_1_1_0_d9627465.json

Multivariable Alexander polynomial

ΔL
A1^(1/2)*A2^(1/2)*A3^(3/2)*A4^(1/2) - 3*A1^(1/2)*A2^(1/2)*A3^(1/2)*A4^(1/2) + 2*A1^(1/2)*A2^(1/2)*A3^(1/2)*A4^(-1/2) + 2*A1^(1/2)*A2^(1/2)*A3^(-1/2)*A4^(1/2) - 3*A1^(1/2)*A2^(1/2)*A3^(-1/2)*A4^(-1/2) + A1^(1/2)*A2^(1/2)*A3^(-3/2)*A4^(-1/2) - A1^(1/2)*A2^(-1/2)*A3^(3/2)*A4^(1/2) + 2*A1^(1/2)*A2^(-1/2)*A3^(1/2)*A4^(1/2) - 2*A1^(1/2)*A2^(-1/2)*A3^(1/2)*A4^(-1/2) - A1^(1/2)*A2^(-1/2)*A3^(-1/2)*A4^(1/2) + 2*A1^(1/2)*A2^(-1/2)*A3^(-1/2)*A4^(-1/2) + 2*A1^(-1/2)*A2^(1/2)*A3^(1/2)*A4^(1/2) - A1^(-1/2)*A2^(1/2)*A3^(1/2)*A4^(-1/2) - 2*A1^(-1/2)*A2^(1/2)*A3^(-1/2)*A4^(1/2) + 2*A1^(-1/2)*A2^(1/2)*A3^(-1/2)*A4^(-1/2) - A1^(-1/2)*A2^(1/2)*A3^(-3/2)*A4^(-1/2) + A1^(-1/2)*A2^(-1/2)*A3^(3/2)*A4^(1/2) - 3*A1^(-1/2)*A2^(-1/2)*A3^(1/2)*A4^(1/2) + 2*A1^(-1/2)*A2^(-1/2)*A3^(1/2)*A4^(-1/2) + 2*A1^(-1/2)*A2^(-1/2)*A3^(-1/2)*A4^(1/2) - 3*A1^(-1/2)*A2^(-1/2)*A3^(-1/2)*A4^(-1/2) + A1^(-1/2)*A2^(-1/2)*A3^(-3/2)*A4^(-1/2)

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

Newton Projection of Alexander-0.500.5-0.500.5A1A2

Dual Thurston polytope

VertexDual to fibered face
(-1, -1) no
(1, -1) no
(1, 1) no
(-1, 1) no
Dual Thurston slice-101-101h1h2

HFL polytope

Poincaré polynomial
m^(-6)*A1^(-1)*A2^(-1)*A3^(-2)*A4^(-1) + m^(-5)*A1^(-1)*A2^(-1)*A3^(-2) + 4*m^(-5)*A1^(-1)*A2^(-1)*A3^(-1)*A4^(-1) + 2*m^(-5)*A1^(-1)*A3^(-2)*A4^(-1) + m^(-5)*A2^(-1)*A3^(-2)*A4^(-1) + 6*m^(-4)*A1^(-1)*A2^(-1)*A3^(-1) + 5*m^(-4)*A1^(-1)*A2^(-1)*A4^(-1) + 2*m^(-4)*A1^(-1)*A3^(-2) + 7*m^(-4)*A1^(-1)*A3^(-1)*A4^(-1) + m^(-4)*A1^(-1)*A2*A3^(-2)*A4^(-1) + m^(-4)*A2^(-1)*A3^(-2) + 6*m^(-4)*A2^(-1)*A3^(-1)*A4^(-1) + 3*m^(-4)*A3^(-2)*A4^(-1) + 2*m^(-3)*A1^(-1)*A2^(-1)*A3^(-1)*A4 + 10*m^(-3)*A1^(-1)*A2^(-1) + 2*m^(-3)*A1^(-1)*A2^(-1)*A3*A4^(-1) + 11*m^(-3)*A1^(-1)*A3^(-1) + 8*m^(-3)*A1^(-1)*A4^(-1) + m^(-3)*A1^(-1)*A2*A3^(-2) + 3*m^(-3)*A1^(-1)*A2*A3^(-1)*A4^(-1) + 9*m^(-3)*A2^(-1)*A3^(-1) + 9*m^(-3)*A2^(-1)*A4^(-1) + 3*m^(-3)*A3^(-2) + 13*m^(-3)*A3^(-1)*A4^(-1) + 2*m^(-3)*A2*A3^(-2)*A4^(-1) + 2*m^(-3)*A1*A2^(-1)*A3^(-1)*A4^(-1) + m^(-3)*A1*A3^(-2)*A4^(-1) + 5*m^(-2)*A1^(-1)*A2^(-1)*A4 + 6*m^(-2)*A1^(-1)*A2^(-1)*A3 + 4*m^(-2)*A1^(-1)*A3^(-1)*A4 + 17*m^(-2)*A1^(-1) + 3*m^(-2)*A1^(-1)*A3*A4^(-1) + 5*m^(-2)*A1^(-1)*A2*A3^(-1) + 3*m^(-2)*A1^(-1)*A2*A4^(-1) + 3*m^(-2)*A2^(-1)*A3^(-1)*A4 + 17*m^(-2)*A2^(-1) + 4*m^(-2)*A2^(-1)*A3*A4^(-1) + 20*m^(-2)*A3^(-1) + 17*m^(-2)*A4^(-1) + 2*m^(-2)*A2*A3^(-2) + 7*m^(-2)*A2*A3^(-1)*A4^(-1) + 3*m^(-2)*A1*A2^(-1)*A3^(-1) + 4*m^(-2)*A1*A2^(-1)*A4^(-1) + m^(-2)*A1*A3^(-2) + 6*m^(-2)*A1*A3^(-1)*A4^(-1) + m^(-2)*A1*A2*A3^(-2)*A4^(-1) + 4*m^(-1)*A1^(-1)*A2^(-1)*A3*A4 + m^(-1)*A1^(-1)*A2^(-1)*A3^2 + 9*m^(-1)*A1^(-1)*A4 + 9*m^(-1)*A1^(-1)*A3 + 2*m^(-1)*A1^(-1)*A2*A3^(-1)*A4 + 7*m^(-1)*A1^(-1)*A2 + m^(-1)*A1^(-1)*A2*A3*A4^(-1) + 8*m^(-1)*A2^(-1)*A4 + 11*m^(-1)*A2^(-1)*A3 + 7*m^(-1)*A3^(-1)*A4 + 34*m^(-1) + 7*m^(-1)*A3*A4^(-1) + 11*m^(-1)*A2*A3^(-1) + 8*m^(-1)*A2*A4^(-1) + m^(-1)*A1*A2^(-1)*A3^(-1)*A4 + 7*m^(-1)*A1*A2^(-1) + 2*m^(-1)*A1*A2^(-1)*A3*A4^(-1) + 9*m^(-1)*A1*A3^(-1) + 9*m^(-1)*A1*A4^(-1) + m^(-1)*A1*A2*A3^(-2) + 4*m^(-1)*A1*A2*A3^(-1)*A4^(-1) + A1^(-1)*A2^(-1)*A3^2*A4 + 6*A1^(-1)*A3*A4 + A1^(-1)*A3^2 + 4*A1^(-1)*A2*A4 + 3*A1^(-1)*A2*A3 + 7*A2^(-1)*A3*A4 + 2*A2^(-1)*A3^2 + 17*A4 + 20*A3 + 4*A2*A3^(-1)*A4 + 17*A2 + 3*A2*A3*A4^(-1) + 3*A1*A2^(-1)*A4 + 5*A1*A2^(-1)*A3 + 3*A1*A3^(-1)*A4 + 17*A1 + 4*A1*A3*A4^(-1) + 6*A1*A2*A3^(-1) + 5*A1*A2*A4^(-1) + m*A1^(-1)*A3^2*A4 + 2*m*A1^(-1)*A2*A3*A4 + 2*m*A2^(-1)*A3^2*A4 + 13*m*A3*A4 + 3*m*A3^2 + 9*m*A2*A4 + 9*m*A2*A3 + 3*m*A1*A2^(-1)*A3*A4 + m*A1*A2^(-1)*A3^2 + 8*m*A1*A4 + 11*m*A1*A3 + 2*m*A1*A2*A3^(-1)*A4 + 10*m*A1*A2 + 2*m*A1*A2*A3*A4^(-1) + 3*m^2*A3^2*A4 + 6*m^2*A2*A3*A4 + m^2*A2*A3^2 + m^2*A1*A2^(-1)*A3^2*A4 + 7*m^2*A1*A3*A4 + 2*m^2*A1*A3^2 + 5*m^2*A1*A2*A4 + 6*m^2*A1*A2*A3 + m^3*A2*A3^2*A4 + 2*m^3*A1*A3^2*A4 + 4*m^3*A1*A2*A3*A4 + m^3*A1*A2*A3^2 + m^4*A1*A2*A3^2*A4
VertexMaslovRank
(-1, -1, -2, -1)-61
(-1, -1, -2, 0)-51
(-1, -1, -1, 1)-32
(-1, -1, 1, -1)-32
(-1, -1, 2, 0)-11
(-1, -1, 2, 1)01
(-1, 0, 2, 0)01
(-1, 0, 2, 1)11
(-1, 1, -2, -1)-41
(-1, 1, -2, 0)-31
(-1, 1, -1, 1)-12
(-1, 1, 1, -1)-11
(-1, 1, 1, 1)12
(0, -1, -2, -1)-51
(0, -1, -2, 0)-41
(0, 1, 2, 0)21
(0, 1, 2, 1)31
(1, -1, -1, -1)-32
(1, -1, -1, 1)-11
(1, -1, 1, -1)-12
(1, -1, 2, 0)11
(1, -1, 2, 1)21
(1, 0, -2, -1)-31
(1, 0, -2, 0)-21
(1, 1, -2, -1)-21
(1, 1, -2, 0)-11
(1, 1, -1, 1)12
(1, 1, 1, -1)12
(1, 1, 2, 0)31
(1, 1, 2, 1)41
HFL projection-101-101A1A2

Record

FL/HFL Links

orderOption(int) 3643
namestring L10a168{1;1;0}
statusstring success
slugstring L10a168_1_1_0_d9627465
result_filestring details/L10a168_1_1_0_d9627465.json
complexity_scoreOption(int) 400
strandsOption(int) null
crossingsOption(int) 10
component_countOption(int) 4
girthOption(int) 6
total_rankOption(int) 640
wall_secondsOption(float) 0.004173
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 4
support_sizeOption(int) 113
vertex_countOption(int) 30
fibered_vertex_countOption(int) 0
polytope_statusstring computed
alexander_support_sizeOption(int) 22
alexander_vertex_countOption(int) 16
alexander_relationstring not_computed
fk_countint 0
detailsRowRef(FLHFLLinks) 
{
  "dataset": "FLHFLLinks",
  "key": "L10a168_1_1_0_d9627465"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L10a168_1_1_0_d9627465