details/L8n4_0_0_58fb8970.json

FL expansions

Newt(ΔL) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle FL
(-1/2, 0, -1) (1, 1, 1) x1^(1/2)x2^(0)x3^(1) q^(-1) 
{"0": [-1, -1, 1, 1], "1": [-1, -1, -1, -1, 1, -1], "2": [1, -1, -1, 1, -1, 1]}
 
(-q^(-1))*x1^(1/2)*x3 + (-q^(-1))*x1^(1/2)*x3^(2) + (-q^(-1))*x1^(1/2)*x3^(3) + (-q^(-1))*x1^(1/2)*x3^(4) + (-q^(-1))*x1^(1/2)*x3^(5) + (q^(-2))*x1^(1/2)*x2*x3^(2) + (q^(-2) + q^(-3))*x1^(1/2)*x2*x3^(3) + (q^(-2) + q^(-3) + q^(-4))*x1^(1/2)*x2*x3^(4) + (q^(-2) + q^(-3) + q^(-4) + q^(-5))*x1^(1/2)*x2*x3^(5) + (-q^(-4))*x1^(1/2)*x2^(2)*x3^(3) + (-q^(-4) - q^(-5) - q^(-6))*x1^(1/2)*x2^(2)*x3^(4) + (-q^(-4) - q^(-5) - 2*q^(-6) - q^(-7) - q^(-8))*x1^(1/2)*x2^(2)*x3^(5) + (q^(-7))*x1^(1/2)*x2^(3)*x3^(4) + (q^(-7) + q^(-8) + q^(-9) + q^(-10))*x1^(1/2)*x2^(3)*x3^(5) + (-q^(-11))*x1^(1/2)*x2^(4)*x3^(5) + (-q)*x1^(3/2)*x2^(-1)*x3^(2) + (-q^(2) - q)*x1^(3/2)*x2^(-1)*x3^(3) + (-q^(3) - q^(2) - q)*x1^(3/2)*x2^(-1)*x3^(4) + (-q^(4) - q^(3) - q^(2) - q)*x1^(3/2)*x2^(-1)*x3^(5) + (1)*x1^(3/2)*x3^(2) + (q + 2*1)*x1^(3/2)*x3^(3) + (q^(2) + 2*q + 3*1 + q^(-1))*x1^(3/2)*x3^(4) + (q^(3) + 2*q^(2) + 3*q + 4*1 + 2*q^(-1) + q^(-2))*x1^(3/2)*x3^(5) + (-q^(-1) - q^(-2))*x1^(3/2)*x2*x3^(3) + (-1 - 2*q^(-1) - 3*q^(-2) - q^(-3))*x1^(3/2)*x2*x3^(4) + (-q - 2*1 - 4*q^(-1) - 5*q^(-2) - 4*q^(-3) - 2*q^(-4))*x1^(3/2)*x2*x3^(5) + (q^(-3) + q^(-4) + q^(-5))*x1^(3/2)*x2^(2)*x3^(4) + (q^(-2) + 2*q^(-3) + 3*q^(-4) + 4*q^(-5) + 2*q^(-6) + q^(-7))*x1^(3/2)*x2^(2)*x3^(5) + (-q^(-6) - q^(-7) - q^(-8) - q^(-9))*x1^(3/2)*x2^(3)*x3^(5) + (-q^(5))*x1^(5/2)*x2^(-2)*x3^(3) + (-q^(7) - q^(6) - q^(5))*x1^(5/2)*x2^(-2)*x3^(4) + (-q^(9) - q^(8) - 2*q^(7) - q^(6) - q^(5))*x1^(5/2)*x2^(-2)*x3^(5) + (q^(4) + q^(3))*x1^(5/2)*x2^(-1)*x3^(3) + (q^(6) + 2*q^(5) + 3*q^(4) + q^(3))*x1^(5/2)*x2^(-1)*x3^(4) + (q^(8) + 2*q^(7) + 4*q^(6) + 5*q^(5) + 4*q^(4) + 2*q^(3))*x1^(5/2)*x2^(-1)*x3^(5) + (-q^(2))*x1^(5/2)*x3^(3) + (-q^(4) - 2*q^(3) - 3*q^(2) - q)*x1^(5/2)*x3^(4) + (-q^(6) - 2*q^(5) - 5*q^(4) - 6*q^(3) - 7*q^(2) - 3*q - 1)*x1^(5/2)*x3^(5) + (q + 1 + q^(-1))*x1^(5/2)*x2*x3^(4) + (q^(3) + 2*q^(2) + 4*q + 5*1 + 4*q^(-1) + 2*q^(-2))*x1^(5/2)*x2*x3^(5) + (-q^(-1) - q^(-2) - 2*q^(-3) - q^(-4) - q^(-5))*x1^(5/2)*x2^(2)*x3^(5) + (-q^(11))*x1^(7/2)*x2^(-3)*x3^(4) + (-q^(14) - q^(13) - q^(12) - q^(11))*x1^(7/2)*x2^(-3)*x3^(5) + (q^(10) + q^(9) + q^(8))*x1^(7/2)*x2^(-2)*x3^(4) + (q^(13) + 2*q^(12) + 3*q^(11) + 4*q^(10) + 2*q^(9) + q^(8))*x1^(7/2)*x2^(-2)*x3^(5) + (-q^(8) - q^(7) - q^(6))*x1^(7/2)*x2^(-1)*x3^(4) + (-q^(11) - 2*q^(10) - 4*q^(9) - 5*q^(8) - 4*q^(7) - 2*q^(6))*x1^(7/2)*x2^(-1)*x3^(5) + (q^(5))*x1^(7/2)*x3^(4) + (q^(8) + 2*q^(7) + 3*q^(6) + 4*q^(5) + 2*q^(4) + q^(3))*x1^(7/2)*x3^(5) + (-q^(4) - q^(3) - q^(2) - q)*x1^(7/2)*x2*x3^(5) + (-q^(19))*x1^(9/2)*x2^(-4)*x3^(5) + (q^(18) + q^(17) + q^(16) + q^(15))*x1^(9/2)*x2^(-3)*x3^(5) + (-q^(16) - q^(15) - 2*q^(14) - q^(13) - q^(12))*x1^(9/2)*x2^(-2)*x3^(5) + (q^(13) + q^(12) + q^(11) + q^(10))*x1^(9/2)*x2^(-1)*x3^(5) + (-q^(9))*x1^(9/2)*x3^(5)
(1/2, -1, 0) (1/3, 1, 1/3) x1^(-1/2)x2^(1)x3^(0) q^(-1) 
{"0": [1, -1, -1, 1], "1": [-1, 1, 1, -1, -1, -1], "2": [-1, -1, -1, -1, -1, -1]}
 
(-q^(19))*x1^(-9/2)*x2^(5)*x3^(-4) + (q^(18) + q^(17) + q^(16) + q^(15))*x1^(-9/2)*x2^(5)*x3^(-3) + (-q^(16) - q^(15) - 2*q^(14) - q^(13) - q^(12))*x1^(-9/2)*x2^(5)*x3^(-2) + (q^(13) + q^(12) + q^(11) + q^(10))*x1^(-9/2)*x2^(5)*x3^(-1) + (-q^(9))*x1^(-9/2)*x2^(5) + (-q^(11))*x1^(-7/2)*x2^(4)*x3^(-3) + (q^(10) + q^(9) + q^(8))*x1^(-7/2)*x2^(4)*x3^(-2) + (-q^(8) - q^(7) - q^(6))*x1^(-7/2)*x2^(4)*x3^(-1) + (q^(5))*x1^(-7/2)*x2^(4) + (-q^(14) - q^(13) - q^(12) - q^(11))*x1^(-7/2)*x2^(5)*x3^(-3) + (q^(13) + 2*q^(12) + 3*q^(11) + 4*q^(10) + 2*q^(9) + q^(8))*x1^(-7/2)*x2^(5)*x3^(-2) + (-q^(11) - 2*q^(10) - 4*q^(9) - 5*q^(8) - 4*q^(7) - 2*q^(6))*x1^(-7/2)*x2^(5)*x3^(-1) + (q^(8) + 2*q^(7) + 3*q^(6) + 4*q^(5) + 2*q^(4) + q^(3))*x1^(-7/2)*x2^(5) + (-q^(4) - q^(3) - q^(2) - q)*x1^(-7/2)*x2^(5)*x3 + (-q^(5))*x1^(-5/2)*x2^(3)*x3^(-2) + (q^(4) + q^(3))*x1^(-5/2)*x2^(3)*x3^(-1) + (-q^(2))*x1^(-5/2)*x2^(3) + (-q^(7) - q^(6) - q^(5))*x1^(-5/2)*x2^(4)*x3^(-2) + (q^(6) + 2*q^(5) + 3*q^(4) + q^(3))*x1^(-5/2)*x2^(4)*x3^(-1) + (-q^(4) - 2*q^(3) - 3*q^(2) - q)*x1^(-5/2)*x2^(4) + (q + 1 + q^(-1))*x1^(-5/2)*x2^(4)*x3 + (-q^(9) - q^(8) - 2*q^(7) - q^(6) - q^(5))*x1^(-5/2)*x2^(5)*x3^(-2) + (q^(8) + 2*q^(7) + 4*q^(6) + 5*q^(5) + 4*q^(4) + 2*q^(3))*x1^(-5/2)*x2^(5)*x3^(-1) + (-q^(6) - 2*q^(5) - 5*q^(4) - 6*q^(3) - 7*q^(2) - 3*q - 1)*x1^(-5/2)*x2^(5) + (q^(3) + 2*q^(2) + 4*q + 5*1 + 4*q^(-1) + 2*q^(-2))*x1^(-5/2)*x2^(5)*x3 + (-q^(-1) - q^(-2) - 2*q^(-3) - q^(-4) - q^(-5))*x1^(-5/2)*x2^(5)*x3^(2) + (-q)*x1^(-3/2)*x2^(2)*x3^(-1) + (1)*x1^(-3/2)*x2^(2) + (-q^(2) - q)*x1^(-3/2)*x2^(3)*x3^(-1) + (q + 2*1)*x1^(-3/2)*x2^(3) + (-q^(-1) - q^(-2))*x1^(-3/2)*x2^(3)*x3 + (-q^(3) - q^(2) - q)*x1^(-3/2)*x2^(4)*x3^(-1) + (q^(2) + 2*q + 3*1 + q^(-1))*x1^(-3/2)*x2^(4) + (-1 - 2*q^(-1) - 3*q^(-2) - q^(-3))*x1^(-3/2)*x2^(4)*x3 + (q^(-3) + q^(-4) + q^(-5))*x1^(-3/2)*x2^(4)*x3^(2) + (-q^(4) - q^(3) - q^(2) - q)*x1^(-3/2)*x2^(5)*x3^(-1) + (q^(3) + 2*q^(2) + 3*q + 4*1 + 2*q^(-1) + q^(-2))*x1^(-3/2)*x2^(5) + (-q - 2*1 - 4*q^(-1) - 5*q^(-2) - 4*q^(-3) - 2*q^(-4))*x1^(-3/2)*x2^(5)*x3 + (q^(-2) + 2*q^(-3) + 3*q^(-4) + 4*q^(-5) + 2*q^(-6) + q^(-7))*x1^(-3/2)*x2^(5)*x3^(2) + (-q^(-6) - q^(-7) - q^(-8) - q^(-9))*x1^(-3/2)*x2^(5)*x3^(3) + (-q^(-1))*x1^(-1/2)*x2 + (-q^(-1))*x1^(-1/2)*x2^(2) + (q^(-2))*x1^(-1/2)*x2^(2)*x3 + (-q^(-1))*x1^(-1/2)*x2^(3) + (q^(-2) + q^(-3))*x1^(-1/2)*x2^(3)*x3 + (-q^(-4))*x1^(-1/2)*x2^(3)*x3^(2) + (-q^(-1))*x1^(-1/2)*x2^(4) + (q^(-2) + q^(-3) + q^(-4))*x1^(-1/2)*x2^(4)*x3 + (-q^(-4) - q^(-5) - q^(-6))*x1^(-1/2)*x2^(4)*x3^(2) + (q^(-7))*x1^(-1/2)*x2^(4)*x3^(3) + (-q^(-1))*x1^(-1/2)*x2^(5) + (q^(-2) + q^(-3) + q^(-4) + q^(-5))*x1^(-1/2)*x2^(5)*x3 + (-q^(-4) - q^(-5) - 2*q^(-6) - q^(-7) - q^(-8))*x1^(-1/2)*x2^(5)*x3^(2) + (q^(-7) + q^(-8) + q^(-9) + q^(-10))*x1^(-1/2)*x2^(5)*x3^(3) + (-q^(-11))*x1^(-1/2)*x2^(5)*x3^(4)
(-1/2, 0, -1) (1, 1, 1) x1^(1/2)x2^(0)x3^(1) q^(-1) 
{"0": [1, -1, 1, 1], "1": [-1, 1, -1, -1, 1, -1], "2": [1, -1, 1, 1, -1, 1]}
 
(-q^(-1))*x1^(1/2)*x3 + (-q^(-1))*x1^(1/2)*x3^(2) + (-q^(-1))*x1^(1/2)*x3^(3) + (-q^(-1))*x1^(1/2)*x3^(4) + (-q^(-1))*x1^(1/2)*x3^(5) + (q^(-2))*x1^(1/2)*x2*x3^(2) + (q^(-2) + q^(-3))*x1^(1/2)*x2*x3^(3) + (q^(-2) + q^(-3) + q^(-4))*x1^(1/2)*x2*x3^(4) + (q^(-2) + q^(-3) + q^(-4) + q^(-5))*x1^(1/2)*x2*x3^(5) + (-q^(-4))*x1^(1/2)*x2^(2)*x3^(3) + (-q^(-4) - q^(-5) - q^(-6))*x1^(1/2)*x2^(2)*x3^(4) + (-q^(-4) - q^(-5) - 2*q^(-6) - q^(-7) - q^(-8))*x1^(1/2)*x2^(2)*x3^(5) + (q^(-7))*x1^(1/2)*x2^(3)*x3^(4) + (q^(-7) + q^(-8) + q^(-9) + q^(-10))*x1^(1/2)*x2^(3)*x3^(5) + (-q^(-11))*x1^(1/2)*x2^(4)*x3^(5) + (-q)*x1^(3/2)*x2^(-1)*x3^(2) + (-q^(2) - q)*x1^(3/2)*x2^(-1)*x3^(3) + (-q^(3) - q^(2) - q)*x1^(3/2)*x2^(-1)*x3^(4) + (-q^(4) - q^(3) - q^(2) - q)*x1^(3/2)*x2^(-1)*x3^(5) + (1)*x1^(3/2)*x3^(2) + (q + 2*1)*x1^(3/2)*x3^(3) + (q^(2) + 2*q + 3*1 + q^(-1))*x1^(3/2)*x3^(4) + (q^(3) + 2*q^(2) + 3*q + 4*1 + 2*q^(-1) + q^(-2))*x1^(3/2)*x3^(5) + (-q^(-1) - q^(-2))*x1^(3/2)*x2*x3^(3) + (-1 - 2*q^(-1) - 3*q^(-2) - q^(-3))*x1^(3/2)*x2*x3^(4) + (-q - 2*1 - 4*q^(-1) - 5*q^(-2) - 4*q^(-3) - 2*q^(-4))*x1^(3/2)*x2*x3^(5) + (q^(-3) + q^(-4) + q^(-5))*x1^(3/2)*x2^(2)*x3^(4) + (q^(-2) + 2*q^(-3) + 3*q^(-4) + 4*q^(-5) + 2*q^(-6) + q^(-7))*x1^(3/2)*x2^(2)*x3^(5) + (-q^(-6) - q^(-7) - q^(-8) - q^(-9))*x1^(3/2)*x2^(3)*x3^(5) + (-q^(5))*x1^(5/2)*x2^(-2)*x3^(3) + (-q^(7) - q^(6) - q^(5))*x1^(5/2)*x2^(-2)*x3^(4) + (-q^(9) - q^(8) - 2*q^(7) - q^(6) - q^(5))*x1^(5/2)*x2^(-2)*x3^(5) + (q^(4) + q^(3))*x1^(5/2)*x2^(-1)*x3^(3) + (q^(6) + 2*q^(5) + 3*q^(4) + q^(3))*x1^(5/2)*x2^(-1)*x3^(4) + (q^(8) + 2*q^(7) + 4*q^(6) + 5*q^(5) + 4*q^(4) + 2*q^(3))*x1^(5/2)*x2^(-1)*x3^(5) + (-q^(2))*x1^(5/2)*x3^(3) + (-q^(4) - 2*q^(3) - 3*q^(2) - q)*x1^(5/2)*x3^(4) + (-q^(6) - 2*q^(5) - 5*q^(4) - 6*q^(3) - 7*q^(2) - 3*q - 1)*x1^(5/2)*x3^(5) + (q + 1 + q^(-1))*x1^(5/2)*x2*x3^(4) + (q^(3) + 2*q^(2) + 4*q + 5*1 + 4*q^(-1) + 2*q^(-2))*x1^(5/2)*x2*x3^(5) + (-q^(-1) - q^(-2) - 2*q^(-3) - q^(-4) - q^(-5))*x1^(5/2)*x2^(2)*x3^(5) + (-q^(11))*x1^(7/2)*x2^(-3)*x3^(4) + (-q^(14) - q^(13) - q^(12) - q^(11))*x1^(7/2)*x2^(-3)*x3^(5) + (q^(10) + q^(9) + q^(8))*x1^(7/2)*x2^(-2)*x3^(4) + (q^(13) + 2*q^(12) + 3*q^(11) + 4*q^(10) + 2*q^(9) + q^(8))*x1^(7/2)*x2^(-2)*x3^(5) + (-q^(8) - q^(7) - q^(6))*x1^(7/2)*x2^(-1)*x3^(4) + (-q^(11) - 2*q^(10) - 4*q^(9) - 5*q^(8) - 4*q^(7) - 2*q^(6))*x1^(7/2)*x2^(-1)*x3^(5) + (q^(5))*x1^(7/2)*x3^(4) + (q^(8) + 2*q^(7) + 3*q^(6) + 4*q^(5) + 2*q^(4) + q^(3))*x1^(7/2)*x3^(5) + (-q^(4) - q^(3) - q^(2) - q)*x1^(7/2)*x2*x3^(5) + (-q^(19))*x1^(9/2)*x2^(-4)*x3^(5) + (q^(18) + q^(17) + q^(16) + q^(15))*x1^(9/2)*x2^(-3)*x3^(5) + (-q^(16) - q^(15) - 2*q^(14) - q^(13) - q^(12))*x1^(9/2)*x2^(-2)*x3^(5) + (q^(13) + q^(12) + q^(11) + q^(10))*x1^(9/2)*x2^(-1)*x3^(5) + (-q^(9))*x1^(9/2)*x3^(5)
(1/2, 0, 1) x1^(-1/2)x2^(0)x3^(-1) q^(-1) 
(-q^(-1))*x1^(-1/2)*x3^(-1) + (-q^(-1))*x1^(-1/2)*x3^(-2) + (-q^(-1))*x1^(-1/2)*x3^(-3) + (-q^(-1))*x1^(-1/2)*x3^(-4) + (-q^(-1))*x1^(-1/2)*x3^(-5) + (q^(-2))*x1^(-1/2)*x2^(-1)*x3^(-2) + (q^(-2) + q^(-3))*x1^(-1/2)*x2^(-1)*x3^(-3) + (q^(-2) + q^(-3) + q^(-4))*x1^(-1/2)*x2^(-1)*x3^(-4) + (q^(-2) + q^(-3) + q^(-4) + q^(-5))*x1^(-1/2)*x2^(-1)*x3^(-5) + (-q^(-4))*x1^(-1/2)*x2^(-2)*x3^(-3) + (-q^(-4) - q^(-5) - q^(-6))*x1^(-1/2)*x2^(-2)*x3^(-4) + (-q^(-4) - q^(-5) - 2*q^(-6) - q^(-7) - q^(-8))*x1^(-1/2)*x2^(-2)*x3^(-5) + (q^(-7))*x1^(-1/2)*x2^(-3)*x3^(-4) + (q^(-7) + q^(-8) + q^(-9) + q^(-10))*x1^(-1/2)*x2^(-3)*x3^(-5) + (-q^(-11))*x1^(-1/2)*x2^(-4)*x3^(-5) + (-q)*x1^(-3/2)*x2*x3^(-2) + (-q^(2) - q)*x1^(-3/2)*x2*x3^(-3) + (-q^(3) - q^(2) - q)*x1^(-3/2)*x2*x3^(-4) + (-q^(4) - q^(3) - q^(2) - q)*x1^(-3/2)*x2*x3^(-5) + (1)*x1^(-3/2)*x3^(-2) + (q + 2*1)*x1^(-3/2)*x3^(-3) + (q^(2) + 2*q + 3*1 + q^(-1))*x1^(-3/2)*x3^(-4) + (q^(3) + 2*q^(2) + 3*q + 4*1 + 2*q^(-1) + q^(-2))*x1^(-3/2)*x3^(-5) + (-q^(-1) - q^(-2))*x1^(-3/2)*x2^(-1)*x3^(-3) + (-1 - 2*q^(-1) - 3*q^(-2) - q^(-3))*x1^(-3/2)*x2^(-1)*x3^(-4) + (-q - 2*1 - 4*q^(-1) - 5*q^(-2) - 4*q^(-3) - 2*q^(-4))*x1^(-3/2)*x2^(-1)*x3^(-5) + (q^(-3) + q^(-4) + q^(-5))*x1^(-3/2)*x2^(-2)*x3^(-4) + (q^(-2) + 2*q^(-3) + 3*q^(-4) + 4*q^(-5) + 2*q^(-6) + q^(-7))*x1^(-3/2)*x2^(-2)*x3^(-5) + (-q^(-6) - q^(-7) - q^(-8) - q^(-9))*x1^(-3/2)*x2^(-3)*x3^(-5) + (-q^(5))*x1^(-5/2)*x2^(2)*x3^(-3) + (-q^(7) - q^(6) - q^(5))*x1^(-5/2)*x2^(2)*x3^(-4) + (-q^(9) - q^(8) - 2*q^(7) - q^(6) - q^(5))*x1^(-5/2)*x2^(2)*x3^(-5) + (q^(4) + q^(3))*x1^(-5/2)*x2*x3^(-3) + (q^(6) + 2*q^(5) + 3*q^(4) + q^(3))*x1^(-5/2)*x2*x3^(-4) + (q^(8) + 2*q^(7) + 4*q^(6) + 5*q^(5) + 4*q^(4) + 2*q^(3))*x1^(-5/2)*x2*x3^(-5) + (-q^(2))*x1^(-5/2)*x3^(-3) + (-q^(4) - 2*q^(3) - 3*q^(2) - q)*x1^(-5/2)*x3^(-4) + (-q^(6) - 2*q^(5) - 5*q^(4) - 6*q^(3) - 7*q^(2) - 3*q - 1)*x1^(-5/2)*x3^(-5) + (q + 1 + q^(-1))*x1^(-5/2)*x2^(-1)*x3^(-4) + (q^(3) + 2*q^(2) + 4*q + 5*1 + 4*q^(-1) + 2*q^(-2))*x1^(-5/2)*x2^(-1)*x3^(-5) + (-q^(-1) - q^(-2) - 2*q^(-3) - q^(-4) - q^(-5))*x1^(-5/2)*x2^(-2)*x3^(-5) + (-q^(11))*x1^(-7/2)*x2^(3)*x3^(-4) + (-q^(14) - q^(13) - q^(12) - q^(11))*x1^(-7/2)*x2^(3)*x3^(-5) + (q^(10) + q^(9) + q^(8))*x1^(-7/2)*x2^(2)*x3^(-4) + (q^(13) + 2*q^(12) + 3*q^(11) + 4*q^(10) + 2*q^(9) + q^(8))*x1^(-7/2)*x2^(2)*x3^(-5) + (-q^(8) - q^(7) - q^(6))*x1^(-7/2)*x2*x3^(-4) + (-q^(11) - 2*q^(10) - 4*q^(9) - 5*q^(8) - 4*q^(7) - 2*q^(6))*x1^(-7/2)*x2*x3^(-5) + (q^(5))*x1^(-7/2)*x3^(-4) + (q^(8) + 2*q^(7) + 3*q^(6) + 4*q^(5) + 2*q^(4) + q^(3))*x1^(-7/2)*x3^(-5) + (-q^(4) - q^(3) - q^(2) - q)*x1^(-7/2)*x2^(-1)*x3^(-5) + (-q^(19))*x1^(-9/2)*x2^(4)*x3^(-5) + (q^(18) + q^(17) + q^(16) + q^(15))*x1^(-9/2)*x2^(3)*x3^(-5) + (-q^(16) - q^(15) - 2*q^(14) - q^(13) - q^(12))*x1^(-9/2)*x2^(2)*x3^(-5) + (q^(13) + q^(12) + q^(11) + q^(10))*x1^(-9/2)*x2*x3^(-5) + (-q^(9))*x1^(-9/2)*x3^(-5)
(-1/2, 1, 0) x1^(1/2)x2^(-1)x3^(0) q^(-1) 
(-q^(19))*x1^(9/2)*x2^(-5)*x3^(4) + (q^(18) + q^(17) + q^(16) + q^(15))*x1^(9/2)*x2^(-5)*x3^(3) + (-q^(16) - q^(15) - 2*q^(14) - q^(13) - q^(12))*x1^(9/2)*x2^(-5)*x3^(2) + (q^(13) + q^(12) + q^(11) + q^(10))*x1^(9/2)*x2^(-5)*x3 + (-q^(9))*x1^(9/2)*x2^(-5) + (-q^(11))*x1^(7/2)*x2^(-4)*x3^(3) + (q^(10) + q^(9) + q^(8))*x1^(7/2)*x2^(-4)*x3^(2) + (-q^(8) - q^(7) - q^(6))*x1^(7/2)*x2^(-4)*x3 + (q^(5))*x1^(7/2)*x2^(-4) + (-q^(14) - q^(13) - q^(12) - q^(11))*x1^(7/2)*x2^(-5)*x3^(3) + (q^(13) + 2*q^(12) + 3*q^(11) + 4*q^(10) + 2*q^(9) + q^(8))*x1^(7/2)*x2^(-5)*x3^(2) + (-q^(11) - 2*q^(10) - 4*q^(9) - 5*q^(8) - 4*q^(7) - 2*q^(6))*x1^(7/2)*x2^(-5)*x3 + (q^(8) + 2*q^(7) + 3*q^(6) + 4*q^(5) + 2*q^(4) + q^(3))*x1^(7/2)*x2^(-5) + (-q^(4) - q^(3) - q^(2) - q)*x1^(7/2)*x2^(-5)*x3^(-1) + (-q^(5))*x1^(5/2)*x2^(-3)*x3^(2) + (q^(4) + q^(3))*x1^(5/2)*x2^(-3)*x3 + (-q^(2))*x1^(5/2)*x2^(-3) + (-q^(7) - q^(6) - q^(5))*x1^(5/2)*x2^(-4)*x3^(2) + (q^(6) + 2*q^(5) + 3*q^(4) + q^(3))*x1^(5/2)*x2^(-4)*x3 + (-q^(4) - 2*q^(3) - 3*q^(2) - q)*x1^(5/2)*x2^(-4) + (q + 1 + q^(-1))*x1^(5/2)*x2^(-4)*x3^(-1) + (-q^(9) - q^(8) - 2*q^(7) - q^(6) - q^(5))*x1^(5/2)*x2^(-5)*x3^(2) + (q^(8) + 2*q^(7) + 4*q^(6) + 5*q^(5) + 4*q^(4) + 2*q^(3))*x1^(5/2)*x2^(-5)*x3 + (-q^(6) - 2*q^(5) - 5*q^(4) - 6*q^(3) - 7*q^(2) - 3*q - 1)*x1^(5/2)*x2^(-5) + (q^(3) + 2*q^(2) + 4*q + 5*1 + 4*q^(-1) + 2*q^(-2))*x1^(5/2)*x2^(-5)*x3^(-1) + (-q^(-1) - q^(-2) - 2*q^(-3) - q^(-4) - q^(-5))*x1^(5/2)*x2^(-5)*x3^(-2) + (-q)*x1^(3/2)*x2^(-2)*x3 + (1)*x1^(3/2)*x2^(-2) + (-q^(2) - q)*x1^(3/2)*x2^(-3)*x3 + (q + 2*1)*x1^(3/2)*x2^(-3) + (-q^(-1) - q^(-2))*x1^(3/2)*x2^(-3)*x3^(-1) + (-q^(3) - q^(2) - q)*x1^(3/2)*x2^(-4)*x3 + (q^(2) + 2*q + 3*1 + q^(-1))*x1^(3/2)*x2^(-4) + (-1 - 2*q^(-1) - 3*q^(-2) - q^(-3))*x1^(3/2)*x2^(-4)*x3^(-1) + (q^(-3) + q^(-4) + q^(-5))*x1^(3/2)*x2^(-4)*x3^(-2) + (-q^(4) - q^(3) - q^(2) - q)*x1^(3/2)*x2^(-5)*x3 + (q^(3) + 2*q^(2) + 3*q + 4*1 + 2*q^(-1) + q^(-2))*x1^(3/2)*x2^(-5) + (-q - 2*1 - 4*q^(-1) - 5*q^(-2) - 4*q^(-3) - 2*q^(-4))*x1^(3/2)*x2^(-5)*x3^(-1) + (q^(-2) + 2*q^(-3) + 3*q^(-4) + 4*q^(-5) + 2*q^(-6) + q^(-7))*x1^(3/2)*x2^(-5)*x3^(-2) + (-q^(-6) - q^(-7) - q^(-8) - q^(-9))*x1^(3/2)*x2^(-5)*x3^(-3) + (-q^(-1))*x1^(1/2)*x2^(-1) + (-q^(-1))*x1^(1/2)*x2^(-2) + (q^(-2))*x1^(1/2)*x2^(-2)*x3^(-1) + (-q^(-1))*x1^(1/2)*x2^(-3) + (q^(-2) + q^(-3))*x1^(1/2)*x2^(-3)*x3^(-1) + (-q^(-4))*x1^(1/2)*x2^(-3)*x3^(-2) + (-q^(-1))*x1^(1/2)*x2^(-4) + (q^(-2) + q^(-3) + q^(-4))*x1^(1/2)*x2^(-4)*x3^(-1) + (-q^(-4) - q^(-5) - q^(-6))*x1^(1/2)*x2^(-4)*x3^(-2) + (q^(-7))*x1^(1/2)*x2^(-4)*x3^(-3) + (-q^(-1))*x1^(1/2)*x2^(-5) + (q^(-2) + q^(-3) + q^(-4) + q^(-5))*x1^(1/2)*x2^(-5)*x3^(-1) + (-q^(-4) - q^(-5) - 2*q^(-6) - q^(-7) - q^(-8))*x1^(1/2)*x2^(-5)*x3^(-2) + (q^(-7) + q^(-8) + q^(-9) + q^(-10))*x1^(1/2)*x2^(-5)*x3^(-3) + (-q^(-11))*x1^(1/2)*x2^(-5)*x3^(-4)

Braid

Braid word Components Crossings Strands
[-1, 2, -1, -2, 1, -2, -2, -2] 3 8 3

Multivariable Alexander polynomial

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

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, 0, -2) yes
(1, 0, 0) yes
(-1, 0, 0) yes
(-1, 2, 0) yes
(1, -2, 0) yes
(1, 0, 2) yes
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HFL polytope

Poincaré polynomial
m^(-3)*A1^(-1)*A2^(-1/2)*A3^(-3/2) + 2*m^(-2)*A1^(-1)*A2^(-1/2)*A3^(-1/2) + m^(-2)*A1^(-1)*A2^(1/2)*A3^(-3/2) + m^(-2)*A2^(-3/2)*A3^(-1/2) + m^(-2)*A2^(-1/2)*A3^(-3/2) + m^(-1)*A1^(-1)*A2^(-1/2)*A3^(1/2) + 3*m^(-1)*A1^(-1)*A2^(1/2)*A3^(-1/2) + m^(-1)*A2^(-3/2)*A3^(1/2) + 4*m^(-1)*A2^(-1/2)*A3^(-1/2) + m^(-1)*A2^(1/2)*A3^(-3/2) + m^(-1)*A1*A2^(-3/2)*A3^(-1/2) + 2*A1^(-1)*A2^(1/2)*A3^(1/2) + A1^(-1)*A2^(3/2)*A3^(-1/2) + 4*A2^(-1/2)*A3^(1/2) + 4*A2^(1/2)*A3^(-1/2) + A1*A2^(-3/2)*A3^(1/2) + 2*A1*A2^(-1/2)*A3^(-1/2) + m*A1^(-1)*A2^(3/2)*A3^(1/2) + m*A2^(-1/2)*A3^(3/2) + 4*m*A2^(1/2)*A3^(1/2) + m*A2^(3/2)*A3^(-1/2) + 3*m*A1*A2^(-1/2)*A3^(1/2) + m*A1*A2^(1/2)*A3^(-1/2) + m^2*A2^(1/2)*A3^(3/2) + m^2*A2^(3/2)*A3^(1/2) + m^2*A1*A2^(-1/2)*A3^(3/2) + 2*m^2*A1*A2^(1/2)*A3^(1/2) + m^3*A1*A2^(1/2)*A3^(3/2)
VertexMaslovRank
(-1, -1/2, -3/2)-31
(-1, -1/2, 1/2)-11
(-1, 1/2, -3/2)-21
(-1, 3/2, -1/2)01
(-1, 3/2, 1/2)11
(0, -3/2, -1/2)-21
(0, -3/2, 1/2)-11
(0, -1/2, -3/2)-21
(0, -1/2, 3/2)11
(0, 1/2, -3/2)-11
(0, 1/2, 3/2)21
(0, 3/2, -1/2)11
(0, 3/2, 1/2)21
(1, -3/2, -1/2)-11
(1, -3/2, 1/2)01
(1, -1/2, 3/2)21
(1, 1/2, -1/2)11
(1, 1/2, 3/2)31
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Record

FL/HFL Links

orderOption(int) 227
namestring L8n4{0;0}
statusstring success
slugstring L8n4_0_0_58fb8970
result_filestring details/L8n4_0_0_58fb8970.json
complexity_scoreOption(int) 192
strandsOption(int) null
crossingsOption(int) 8
component_countOption(int) 3
girthOption(int) 6
total_rankOption(int) 48
wall_secondsOption(float) 0.002788
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 3
support_sizeOption(int) 28
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 3
detailsRowRef(FLHFLLinks) 
{
  "dataset": "FLHFLLinks",
  "key": "L8n4_0_0_58fb8970"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L8n4_0_0_58fb8970