details/L11a541_1_1_1_f983d755.json

Multivariable Alexander polynomial

ΔL
2*A1^(1/2)*A2^(1/2)*A3^(3/2)*A4^(1/2) - 2*A1^(1/2)*A2^(1/2)*A3^(3/2)*A4^(-1/2) - 5*A1^(1/2)*A2^(1/2)*A3^(1/2)*A4^(1/2) + 5*A1^(1/2)*A2^(1/2)*A3^(1/2)*A4^(-1/2) + 4*A1^(1/2)*A2^(1/2)*A3^(-1/2)*A4^(1/2) - 4*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) - 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) - 3*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) + 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) - 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) - 3*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) + 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) + A1^(-1/2)*A2^(-1/2)*A3^(3/2)*A4^(1/2) - A1^(-1/2)*A2^(-1/2)*A3^(3/2)*A4^(-1/2) - 4*A1^(-1/2)*A2^(-1/2)*A3^(1/2)*A4^(1/2) + 4*A1^(-1/2)*A2^(-1/2)*A3^(1/2)*A4^(-1/2) + 5*A1^(-1/2)*A2^(-1/2)*A3^(-1/2)*A4^(1/2) - 5*A1^(-1/2)*A2^(-1/2)*A3^(-1/2)*A4^(-1/2) - 2*A1^(-1/2)*A2^(-1/2)*A3^(-3/2)*A4^(1/2) + 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
2*m^(-8)*A1^(-1)*A2^(-1)*A3^(-2)*A4^(-1) + 4*m^(-7)*A1^(-1)*A2^(-1)*A3^(-2) + 7*m^(-7)*A1^(-1)*A2^(-1)*A3^(-1)*A4^(-1) + 3*m^(-7)*A1^(-1)*A3^(-2)*A4^(-1) + 3*m^(-7)*A2^(-1)*A3^(-2)*A4^(-1) + 2*m^(-6)*A1^(-1)*A2^(-1)*A3^(-2)*A4 + 14*m^(-6)*A1^(-1)*A2^(-1)*A3^(-1) + 9*m^(-6)*A1^(-1)*A2^(-1)*A4^(-1) + 6*m^(-6)*A1^(-1)*A3^(-2) + 11*m^(-6)*A1^(-1)*A3^(-1)*A4^(-1) + m^(-6)*A1^(-1)*A2*A3^(-2)*A4^(-1) + 6*m^(-6)*A2^(-1)*A3^(-2) + 11*m^(-6)*A2^(-1)*A3^(-1)*A4^(-1) + 5*m^(-6)*A3^(-2)*A4^(-1) + m^(-6)*A1*A2^(-1)*A3^(-2)*A4^(-1) + 7*m^(-5)*A1^(-1)*A2^(-1)*A3^(-1)*A4 + 18*m^(-5)*A1^(-1)*A2^(-1) + 5*m^(-5)*A1^(-1)*A2^(-1)*A3*A4^(-1) + 3*m^(-5)*A1^(-1)*A3^(-2)*A4 + 22*m^(-5)*A1^(-1)*A3^(-1) + 15*m^(-5)*A1^(-1)*A4^(-1) + 2*m^(-5)*A1^(-1)*A2*A3^(-2) + 4*m^(-5)*A1^(-1)*A2*A3^(-1)*A4^(-1) + 3*m^(-5)*A2^(-1)*A3^(-2)*A4 + 22*m^(-5)*A2^(-1)*A3^(-1) + 15*m^(-5)*A2^(-1)*A4^(-1) + 10*m^(-5)*A3^(-2) + 20*m^(-5)*A3^(-1)*A4^(-1) + 2*m^(-5)*A2*A3^(-2)*A4^(-1) + 2*m^(-5)*A1*A2^(-1)*A3^(-2) + 4*m^(-5)*A1*A2^(-1)*A3^(-1)*A4^(-1) + 2*m^(-5)*A1*A3^(-2)*A4^(-1) + 9*m^(-4)*A1^(-1)*A2^(-1)*A4 + 10*m^(-4)*A1^(-1)*A2^(-1)*A3 + m^(-4)*A1^(-1)*A2^(-1)*A3^2*A4^(-1) + 11*m^(-4)*A1^(-1)*A3^(-1)*A4 + 30*m^(-4)*A1^(-1) + 9*m^(-4)*A1^(-1)*A3*A4^(-1) + m^(-4)*A1^(-1)*A2*A3^(-2)*A4 + 8*m^(-4)*A1^(-1)*A2*A3^(-1) + 6*m^(-4)*A1^(-1)*A2*A4^(-1) + 11*m^(-4)*A2^(-1)*A3^(-1)*A4 + 30*m^(-4)*A2^(-1) + 9*m^(-4)*A2^(-1)*A3*A4^(-1) + 5*m^(-4)*A3^(-2)*A4 + 40*m^(-4)*A3^(-1) + 30*m^(-4)*A4^(-1) + 4*m^(-4)*A2*A3^(-2) + 9*m^(-4)*A2*A3^(-1)*A4^(-1) + m^(-4)*A1*A2^(-1)*A3^(-2)*A4 + 8*m^(-4)*A1*A2^(-1)*A3^(-1) + 6*m^(-4)*A1*A2^(-1)*A4^(-1) + 4*m^(-4)*A1*A3^(-2) + 9*m^(-4)*A1*A3^(-1)*A4^(-1) + m^(-4)*A1*A2*A3^(-2)*A4^(-1) + 5*m^(-3)*A1^(-1)*A2^(-1)*A3*A4 + 2*m^(-3)*A1^(-1)*A2^(-1)*A3^2 + 15*m^(-3)*A1^(-1)*A4 + 18*m^(-3)*A1^(-1)*A3 + 2*m^(-3)*A1^(-1)*A3^2*A4^(-1) + 4*m^(-3)*A1^(-1)*A2*A3^(-1)*A4 + 12*m^(-3)*A1^(-1)*A2 + 4*m^(-3)*A1^(-1)*A2*A3*A4^(-1) + 15*m^(-3)*A2^(-1)*A4 + 18*m^(-3)*A2^(-1)*A3 + 2*m^(-3)*A2^(-1)*A3^2*A4^(-1) + 20*m^(-3)*A3^(-1)*A4 + 60*m^(-3) + 20*m^(-3)*A3*A4^(-1) + 2*m^(-3)*A2*A3^(-2)*A4 + 18*m^(-3)*A2*A3^(-1) + 15*m^(-3)*A2*A4^(-1) + 4*m^(-3)*A1*A2^(-1)*A3^(-1)*A4 + 12*m^(-3)*A1*A2^(-1) + 4*m^(-3)*A1*A2^(-1)*A3*A4^(-1) + 2*m^(-3)*A1*A3^(-2)*A4 + 18*m^(-3)*A1*A3^(-1) + 15*m^(-3)*A1*A4^(-1) + 2*m^(-3)*A1*A2*A3^(-2) + 5*m^(-3)*A1*A2*A3^(-1)*A4^(-1) + m^(-2)*A1^(-1)*A2^(-1)*A3^2*A4 + 9*m^(-2)*A1^(-1)*A3*A4 + 4*m^(-2)*A1^(-1)*A3^2 + 6*m^(-2)*A1^(-1)*A2*A4 + 8*m^(-2)*A1^(-1)*A2*A3 + m^(-2)*A1^(-1)*A2*A3^2*A4^(-1) + 9*m^(-2)*A2^(-1)*A3*A4 + 4*m^(-2)*A2^(-1)*A3^2 + 30*m^(-2)*A4 + 40*m^(-2)*A3 + 5*m^(-2)*A3^2*A4^(-1) + 9*m^(-2)*A2*A3^(-1)*A4 + 30*m^(-2)*A2 + 11*m^(-2)*A2*A3*A4^(-1) + 6*m^(-2)*A1*A2^(-1)*A4 + 8*m^(-2)*A1*A2^(-1)*A3 + m^(-2)*A1*A2^(-1)*A3^2*A4^(-1) + 9*m^(-2)*A1*A3^(-1)*A4 + 30*m^(-2)*A1 + 11*m^(-2)*A1*A3*A4^(-1) + m^(-2)*A1*A2*A3^(-2)*A4 + 10*m^(-2)*A1*A2*A3^(-1) + 9*m^(-2)*A1*A2*A4^(-1) + 2*m^(-1)*A1^(-1)*A3^2*A4 + 4*m^(-1)*A1^(-1)*A2*A3*A4 + 2*m^(-1)*A1^(-1)*A2*A3^2 + 2*m^(-1)*A2^(-1)*A3^2*A4 + 20*m^(-1)*A3*A4 + 10*m^(-1)*A3^2 + 15*m^(-1)*A2*A4 + 22*m^(-1)*A2*A3 + 3*m^(-1)*A2*A3^2*A4^(-1) + 4*m^(-1)*A1*A2^(-1)*A3*A4 + 2*m^(-1)*A1*A2^(-1)*A3^2 + 15*m^(-1)*A1*A4 + 22*m^(-1)*A1*A3 + 3*m^(-1)*A1*A3^2*A4^(-1) + 5*m^(-1)*A1*A2*A3^(-1)*A4 + 18*m^(-1)*A1*A2 + 7*m^(-1)*A1*A2*A3*A4^(-1) + A1^(-1)*A2*A3^2*A4 + 5*A3^2*A4 + 11*A2*A3*A4 + 6*A2*A3^2 + A1*A2^(-1)*A3^2*A4 + 11*A1*A3*A4 + 6*A1*A3^2 + 9*A1*A2*A4 + 14*A1*A2*A3 + 2*A1*A2*A3^2*A4^(-1) + 3*m*A2*A3^2*A4 + 3*m*A1*A3^2*A4 + 7*m*A1*A2*A3*A4 + 4*m*A1*A2*A3^2 + 2*m^2*A1*A2*A3^2*A4
VertexMaslovRank
(-1, -1, -2, -1)-82
(-1, -1, -2, 1)-62
(-1, -1, 2, -1)-41
(-1, -1, 2, 1)-21
(-1, 1, -2, -1)-61
(-1, 1, -2, 1)-41
(-1, 1, 2, -1)-21
(-1, 1, 2, 1)01
(1, -1, -2, -1)-61
(1, -1, -2, 1)-41
(1, -1, 2, -1)-21
(1, -1, 2, 1)01
(1, 1, -2, -1)-41
(1, 1, -2, 1)-21
(1, 1, 2, -1)02
(1, 1, 2, 1)22
HFL projection-101-101A1A2

Record

FL/HFL Links

orderOption(int) 3900
namestring L11a541{1;1;1}
statusstring success
slugstring L11a541_1_1_1_f983d755
result_filestring details/L11a541_1_1_1_f983d755.json
complexity_scoreOption(int) 484
strandsOption(int) null
crossingsOption(int) 11
component_countOption(int) 4
girthOption(int) 6
total_rankOption(int) 1280
wall_secondsOption(float) 0.007521
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 4
support_sizeOption(int) 135
vertex_countOption(int) 16
fibered_vertex_countOption(int) 0
polytope_statusstring computed
alexander_support_sizeOption(int) 32
alexander_vertex_countOption(int) 16
alexander_relationstring not_computed
fk_countint 0
detailsRowRef(FLHFLLinks) 
{
  "dataset": "FLHFLLinks",
  "key": "L11a541_1_1_1_f983d755"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L11a541_1_1_1_f983d755