details/L8a20_0_1_b347a7e5.json

FL expansions

Newt(ΔL) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle FL
(1/2, -3/2, -1/2) (1/2, 1, 1) x1^(-1/2)x2^(3/2)x3^(1/2) q^(-2) 
{"0": [-1, -1, -1, -1, -1, -1, -1, -1], "1": [-1, -1, -1, -1, -1, -1, -1, -1], "2": [-1, -1, -1, -1, -1, -1]}
 
(-5*q^(8) - 3*q^(7) - 4*q^(6) - 3*q^(5) - q^(4))*x1^(-9/2)*x2^(11/2)*x3^(1/2) + (4*q^(7) + 6*q^(6) + 8*q^(5) + 8*q^(4) + 4*q^(3) + 2*q^(2))*x1^(-9/2)*x2^(11/2)*x3^(3/2) + (-3*q^(5) - 4*q^(4) - 7*q^(3) - 5*q^(2) - 4*q - 1)*x1^(-9/2)*x2^(11/2)*x3^(5/2) + (2*q^(2) + 2*q + 2*1 + 2*q^(-1))*x1^(-9/2)*x2^(11/2)*x3^(7/2) + (-q^(-2))*x1^(-9/2)*x2^(11/2)*x3^(9/2) + (4*q^(4) + 2*q^(3) + 2*q^(2))*x1^(-7/2)*x2^(9/2)*x3^(1/2) + (-3*q^(3) - 4*q^(2) - 4*q - 1)*x1^(-7/2)*x2^(9/2)*x3^(3/2) + (2*q + 2*1 + 2*q^(-1))*x1^(-7/2)*x2^(9/2)*x3^(5/2) + (-q^(-2))*x1^(-7/2)*x2^(9/2)*x3^(7/2) + (2*q^(7) + 4*q^(6) + 8*q^(5) + 14*q^(4) + 8*q^(3) + 4*q^(2))*x1^(-7/2)*x2^(11/2)*x3^(1/2) + (-2*q^(6) - 6*q^(5) - 14*q^(4) - 28*q^(3) - 28*q^(2) - 22*q - 10*1 - 2*q^(-1))*x1^(-7/2)*x2^(11/2)*x3^(3/2) + (2*q^(4) + 6*q^(3) + 16*q^(2) + 26*q + 28*1 + 22*q^(-1) + 10*q^(-2) + 4*q^(-3))*x1^(-7/2)*x2^(11/2)*x3^(5/2) + (-2*q - 6*1 - 10*q^(-1) - 14*q^(-2) - 10*q^(-3) - 6*q^(-4) - 2*q^(-5))*x1^(-7/2)*x2^(11/2)*x3^(7/2) + (2*q^(-3) + 2*q^(-4) + 2*q^(-5) + 2*q^(-6))*x1^(-7/2)*x2^(11/2)*x3^(9/2) + (-3*q - 1)*x1^(-5/2)*x2^(7/2)*x3^(1/2) + (2*1 + 2*q^(-1))*x1^(-5/2)*x2^(7/2)*x3^(3/2) + (-q^(-2))*x1^(-5/2)*x2^(7/2)*x3^(5/2) + (-2*q^(3) - 4*q^(2) - 8*q - 2*1)*x1^(-5/2)*x2^(9/2)*x3^(1/2) + (2*q^(2) + 6*q + 14*1 + 10*q^(-1) + 4*q^(-2))*x1^(-5/2)*x2^(9/2)*x3^(3/2) + (-2*1 - 6*q^(-1) - 10*q^(-2) - 6*q^(-3) - 2*q^(-4))*x1^(-5/2)*x2^(9/2)*x3^(5/2) + (2*q^(-3) + 2*q^(-4) + 2*q^(-5))*x1^(-5/2)*x2^(9/2)*x3^(7/2) + (-2*q^(5) - 2*q^(4) - 9*q^(3) - 11*q^(2) - 13*q - 3*1)*x1^(-5/2)*x2^(11/2)*x3^(1/2) + (2*q^(4) + 4*q^(3) + 16*q^(2) + 30*q + 42*1 + 32*q^(-1) + 14*q^(-2) + 4*q^(-3))*x1^(-5/2)*x2^(11/2)*x3^(3/2) + (-2*q^(2) - 7*q - 23*1 - 39*q^(-1) - 53*q^(-2) - 39*q^(-3) - 23*q^(-4) - 7*q^(-5) - 2*q^(-6))*x1^(-5/2)*x2^(11/2)*x3^(5/2) + (4*q^(-1) + 10*q^(-2) + 22*q^(-3) + 28*q^(-4) + 26*q^(-5) + 16*q^(-6) + 6*q^(-7) + 2*q^(-8))*x1^(-5/2)*x2^(11/2)*x3^(7/2) + (-q^(-4) - 4*q^(-5) - 5*q^(-6) - 7*q^(-7) - 4*q^(-8) - 3*q^(-9))*x1^(-5/2)*x2^(11/2)*x3^(9/2) + (2*q^(-1))*x1^(-3/2)*x2^(5/2)*x3^(1/2) + (-q^(-2))*x1^(-3/2)*x2^(5/2)*x3^(3/2) + (2*1 + 4*q^(-1))*x1^(-3/2)*x2^(7/2)*x3^(1/2) + (-2*q^(-1) - 6*q^(-2) - 2*q^(-3))*x1^(-3/2)*x2^(7/2)*x3^(3/2) + (2*q^(-3) + 2*q^(-4))*x1^(-3/2)*x2^(7/2)*x3^(5/2) + (2*q + 4*1 + 6*q^(-1))*x1^(-3/2)*x2^(9/2)*x3^(1/2) + (-2*1 - 8*q^(-1) - 15*q^(-2) - 8*q^(-3) - 2*q^(-4))*x1^(-3/2)*x2^(9/2)*x3^(3/2) + (4*q^(-2) + 10*q^(-3) + 14*q^(-4) + 6*q^(-5) + 2*q^(-6))*x1^(-3/2)*x2^(9/2)*x3^(5/2) + (-q^(-4) - 4*q^(-5) - 4*q^(-6) - 3*q^(-7))*x1^(-3/2)*x2^(9/2)*x3^(7/2) + (2*q^(2) + 4*q + 6*1 + 8*q^(-1))*x1^(-3/2)*x2^(11/2)*x3^(1/2) + (-2*q - 8*1 - 18*q^(-1) - 28*q^(-2) - 18*q^(-3) - 8*q^(-4) - 2*q^(-5))*x1^(-3/2)*x2^(11/2)*x3^(3/2) + (4*q^(-1) + 14*q^(-2) + 32*q^(-3) + 42*q^(-4) + 30*q^(-5) + 16*q^(-6) + 4*q^(-7) + 2*q^(-8))*x1^(-3/2)*x2^(11/2)*x3^(5/2) + (-2*q^(-3) - 10*q^(-4) - 22*q^(-5) - 28*q^(-6) - 28*q^(-7) - 14*q^(-8) - 6*q^(-9) - 2*q^(-10))*x1^(-3/2)*x2^(11/2)*x3^(7/2) + (2*q^(-6) + 4*q^(-7) + 8*q^(-8) + 8*q^(-9) + 6*q^(-10) + 4*q^(-11))*x1^(-3/2)*x2^(11/2)*x3^(9/2) + (-q^(-2))*x1^(-1/2)*x2^(3/2)*x3^(1/2) + (-2*q^(-2))*x1^(-1/2)*x2^(5/2)*x3^(1/2) + (2*q^(-3))*x1^(-1/2)*x2^(5/2)*x3^(3/2) + (-3*q^(-2))*x1^(-1/2)*x2^(7/2)*x3^(1/2) + (4*q^(-3) + 2*q^(-4))*x1^(-1/2)*x2^(7/2)*x3^(3/2) + (-q^(-4) - 3*q^(-5))*x1^(-1/2)*x2^(7/2)*x3^(5/2) + (-4*q^(-2))*x1^(-1/2)*x2^(9/2)*x3^(1/2) + (6*q^(-3) + 4*q^(-4) + 2*q^(-5))*x1^(-1/2)*x2^(9/2)*x3^(3/2) + (-2*q^(-4) - 8*q^(-5) - 4*q^(-6) - 2*q^(-7))*x1^(-1/2)*x2^(9/2)*x3^(5/2) + (2*q^(-6) + 2*q^(-7) + 4*q^(-8))*x1^(-1/2)*x2^(9/2)*x3^(7/2) + (-5*q^(-2))*x1^(-1/2)*x2^(11/2)*x3^(1/2) + (8*q^(-3) + 6*q^(-4) + 4*q^(-5) + 2*q^(-6))*x1^(-1/2)*x2^(11/2)*x3^(3/2) + (-3*q^(-4) - 13*q^(-5) - 11*q^(-6) - 9*q^(-7) - 2*q^(-8) - 2*q^(-9))*x1^(-1/2)*x2^(11/2)*x3^(5/2) + (4*q^(-6) + 8*q^(-7) + 14*q^(-8) + 8*q^(-9) + 4*q^(-10) + 2*q^(-11))*x1^(-1/2)*x2^(11/2)*x3^(7/2) + (-q^(-8) - 3*q^(-9) - 4*q^(-10) - 3*q^(-11) - 5*q^(-12))*x1^(-1/2)*x2^(11/2)*x3^(9/2)
(1/2, -3/2, -1/2) (1/2, 1, 1) x1^(-1/2)x2^(3/2)x3^(1/2) q^(-2) 
{"0": [1, -1, -1, -1, -1, -1, -1, -1], "1": [-1, -1, -1, -1, -1, -1, -1, 1], "2": [-1, -1, -1, -1, -1, -1]}
 
(-5*q^(8) - 3*q^(7) - 4*q^(6) - 3*q^(5) - q^(4))*x1^(-9/2)*x2^(11/2)*x3^(1/2) + (4*q^(7) + 6*q^(6) + 8*q^(5) + 8*q^(4) + 4*q^(3) + 2*q^(2))*x1^(-9/2)*x2^(11/2)*x3^(3/2) + (-3*q^(5) - 4*q^(4) - 7*q^(3) - 5*q^(2) - 4*q - 1)*x1^(-9/2)*x2^(11/2)*x3^(5/2) + (2*q^(2) + 2*q + 2*1 + 2*q^(-1))*x1^(-9/2)*x2^(11/2)*x3^(7/2) + (-q^(-2))*x1^(-9/2)*x2^(11/2)*x3^(9/2) + (4*q^(4) + 2*q^(3) + 2*q^(2))*x1^(-7/2)*x2^(9/2)*x3^(1/2) + (-3*q^(3) - 4*q^(2) - 4*q - 1)*x1^(-7/2)*x2^(9/2)*x3^(3/2) + (2*q + 2*1 + 2*q^(-1))*x1^(-7/2)*x2^(9/2)*x3^(5/2) + (-q^(-2))*x1^(-7/2)*x2^(9/2)*x3^(7/2) + (2*q^(7) + 4*q^(6) + 8*q^(5) + 14*q^(4) + 8*q^(3) + 4*q^(2))*x1^(-7/2)*x2^(11/2)*x3^(1/2) + (-2*q^(6) - 6*q^(5) - 14*q^(4) - 28*q^(3) - 28*q^(2) - 22*q - 10*1 - 2*q^(-1))*x1^(-7/2)*x2^(11/2)*x3^(3/2) + (2*q^(4) + 6*q^(3) + 16*q^(2) + 26*q + 28*1 + 22*q^(-1) + 10*q^(-2) + 4*q^(-3))*x1^(-7/2)*x2^(11/2)*x3^(5/2) + (-2*q - 6*1 - 10*q^(-1) - 14*q^(-2) - 10*q^(-3) - 6*q^(-4) - 2*q^(-5))*x1^(-7/2)*x2^(11/2)*x3^(7/2) + (2*q^(-3) + 2*q^(-4) + 2*q^(-5) + 2*q^(-6))*x1^(-7/2)*x2^(11/2)*x3^(9/2) + (-3*q - 1)*x1^(-5/2)*x2^(7/2)*x3^(1/2) + (2*1 + 2*q^(-1))*x1^(-5/2)*x2^(7/2)*x3^(3/2) + (-q^(-2))*x1^(-5/2)*x2^(7/2)*x3^(5/2) + (-2*q^(3) - 4*q^(2) - 8*q - 2*1)*x1^(-5/2)*x2^(9/2)*x3^(1/2) + (2*q^(2) + 6*q + 14*1 + 10*q^(-1) + 4*q^(-2))*x1^(-5/2)*x2^(9/2)*x3^(3/2) + (-2*1 - 6*q^(-1) - 10*q^(-2) - 6*q^(-3) - 2*q^(-4))*x1^(-5/2)*x2^(9/2)*x3^(5/2) + (2*q^(-3) + 2*q^(-4) + 2*q^(-5))*x1^(-5/2)*x2^(9/2)*x3^(7/2) + (-2*q^(5) - 2*q^(4) - 9*q^(3) - 11*q^(2) - 13*q - 3*1)*x1^(-5/2)*x2^(11/2)*x3^(1/2) + (2*q^(4) + 4*q^(3) + 16*q^(2) + 30*q + 42*1 + 32*q^(-1) + 14*q^(-2) + 4*q^(-3))*x1^(-5/2)*x2^(11/2)*x3^(3/2) + (-2*q^(2) - 7*q - 23*1 - 39*q^(-1) - 53*q^(-2) - 39*q^(-3) - 23*q^(-4) - 7*q^(-5) - 2*q^(-6))*x1^(-5/2)*x2^(11/2)*x3^(5/2) + (4*q^(-1) + 10*q^(-2) + 22*q^(-3) + 28*q^(-4) + 26*q^(-5) + 16*q^(-6) + 6*q^(-7) + 2*q^(-8))*x1^(-5/2)*x2^(11/2)*x3^(7/2) + (-q^(-4) - 4*q^(-5) - 5*q^(-6) - 7*q^(-7) - 4*q^(-8) - 3*q^(-9))*x1^(-5/2)*x2^(11/2)*x3^(9/2) + (2*q^(-1))*x1^(-3/2)*x2^(5/2)*x3^(1/2) + (-q^(-2))*x1^(-3/2)*x2^(5/2)*x3^(3/2) + (2*1 + 4*q^(-1))*x1^(-3/2)*x2^(7/2)*x3^(1/2) + (-2*q^(-1) - 6*q^(-2) - 2*q^(-3))*x1^(-3/2)*x2^(7/2)*x3^(3/2) + (2*q^(-3) + 2*q^(-4))*x1^(-3/2)*x2^(7/2)*x3^(5/2) + (2*q + 4*1 + 6*q^(-1))*x1^(-3/2)*x2^(9/2)*x3^(1/2) + (-2*1 - 8*q^(-1) - 15*q^(-2) - 8*q^(-3) - 2*q^(-4))*x1^(-3/2)*x2^(9/2)*x3^(3/2) + (4*q^(-2) + 10*q^(-3) + 14*q^(-4) + 6*q^(-5) + 2*q^(-6))*x1^(-3/2)*x2^(9/2)*x3^(5/2) + (-q^(-4) - 4*q^(-5) - 4*q^(-6) - 3*q^(-7))*x1^(-3/2)*x2^(9/2)*x3^(7/2) + (2*q^(2) + 4*q + 6*1 + 8*q^(-1))*x1^(-3/2)*x2^(11/2)*x3^(1/2) + (-2*q - 8*1 - 18*q^(-1) - 28*q^(-2) - 18*q^(-3) - 8*q^(-4) - 2*q^(-5))*x1^(-3/2)*x2^(11/2)*x3^(3/2) + (4*q^(-1) + 14*q^(-2) + 32*q^(-3) + 42*q^(-4) + 30*q^(-5) + 16*q^(-6) + 4*q^(-7) + 2*q^(-8))*x1^(-3/2)*x2^(11/2)*x3^(5/2) + (-2*q^(-3) - 10*q^(-4) - 22*q^(-5) - 28*q^(-6) - 28*q^(-7) - 14*q^(-8) - 6*q^(-9) - 2*q^(-10))*x1^(-3/2)*x2^(11/2)*x3^(7/2) + (2*q^(-6) + 4*q^(-7) + 8*q^(-8) + 8*q^(-9) + 6*q^(-10) + 4*q^(-11))*x1^(-3/2)*x2^(11/2)*x3^(9/2) + (-q^(-2))*x1^(-1/2)*x2^(3/2)*x3^(1/2) + (-2*q^(-2))*x1^(-1/2)*x2^(5/2)*x3^(1/2) + (2*q^(-3))*x1^(-1/2)*x2^(5/2)*x3^(3/2) + (-3*q^(-2))*x1^(-1/2)*x2^(7/2)*x3^(1/2) + (4*q^(-3) + 2*q^(-4))*x1^(-1/2)*x2^(7/2)*x3^(3/2) + (-q^(-4) - 3*q^(-5))*x1^(-1/2)*x2^(7/2)*x3^(5/2) + (-4*q^(-2))*x1^(-1/2)*x2^(9/2)*x3^(1/2) + (6*q^(-3) + 4*q^(-4) + 2*q^(-5))*x1^(-1/2)*x2^(9/2)*x3^(3/2) + (-2*q^(-4) - 8*q^(-5) - 4*q^(-6) - 2*q^(-7))*x1^(-1/2)*x2^(9/2)*x3^(5/2) + (2*q^(-6) + 2*q^(-7) + 4*q^(-8))*x1^(-1/2)*x2^(9/2)*x3^(7/2) + (-5*q^(-2))*x1^(-1/2)*x2^(11/2)*x3^(1/2) + (8*q^(-3) + 6*q^(-4) + 4*q^(-5) + 2*q^(-6))*x1^(-1/2)*x2^(11/2)*x3^(3/2) + (-3*q^(-4) - 13*q^(-5) - 11*q^(-6) - 9*q^(-7) - 2*q^(-8) - 2*q^(-9))*x1^(-1/2)*x2^(11/2)*x3^(5/2) + (4*q^(-6) + 8*q^(-7) + 14*q^(-8) + 8*q^(-9) + 4*q^(-10) + 2*q^(-11))*x1^(-1/2)*x2^(11/2)*x3^(7/2) + (-q^(-8) - 3*q^(-9) - 4*q^(-10) - 3*q^(-11) - 5*q^(-12))*x1^(-1/2)*x2^(11/2)*x3^(9/2)
(-1/2, 3/2, 1/2) x1^(1/2)x2^(-3/2)x3^(-1/2) q^(-2) 
(-5*q^(8) - 3*q^(7) - 4*q^(6) - 3*q^(5) - q^(4))*x1^(9/2)*x2^(-11/2)*x3^(-1/2) + (4*q^(7) + 6*q^(6) + 8*q^(5) + 8*q^(4) + 4*q^(3) + 2*q^(2))*x1^(9/2)*x2^(-11/2)*x3^(-3/2) + (-3*q^(5) - 4*q^(4) - 7*q^(3) - 5*q^(2) - 4*q - 1)*x1^(9/2)*x2^(-11/2)*x3^(-5/2) + (2*q^(2) + 2*q + 2*1 + 2*q^(-1))*x1^(9/2)*x2^(-11/2)*x3^(-7/2) + (-q^(-2))*x1^(9/2)*x2^(-11/2)*x3^(-9/2) + (4*q^(4) + 2*q^(3) + 2*q^(2))*x1^(7/2)*x2^(-9/2)*x3^(-1/2) + (-3*q^(3) - 4*q^(2) - 4*q - 1)*x1^(7/2)*x2^(-9/2)*x3^(-3/2) + (2*q + 2*1 + 2*q^(-1))*x1^(7/2)*x2^(-9/2)*x3^(-5/2) + (-q^(-2))*x1^(7/2)*x2^(-9/2)*x3^(-7/2) + (2*q^(7) + 4*q^(6) + 8*q^(5) + 14*q^(4) + 8*q^(3) + 4*q^(2))*x1^(7/2)*x2^(-11/2)*x3^(-1/2) + (-2*q^(6) - 6*q^(5) - 14*q^(4) - 28*q^(3) - 28*q^(2) - 22*q - 10*1 - 2*q^(-1))*x1^(7/2)*x2^(-11/2)*x3^(-3/2) + (2*q^(4) + 6*q^(3) + 16*q^(2) + 26*q + 28*1 + 22*q^(-1) + 10*q^(-2) + 4*q^(-3))*x1^(7/2)*x2^(-11/2)*x3^(-5/2) + (-2*q - 6*1 - 10*q^(-1) - 14*q^(-2) - 10*q^(-3) - 6*q^(-4) - 2*q^(-5))*x1^(7/2)*x2^(-11/2)*x3^(-7/2) + (2*q^(-3) + 2*q^(-4) + 2*q^(-5) + 2*q^(-6))*x1^(7/2)*x2^(-11/2)*x3^(-9/2) + (-3*q - 1)*x1^(5/2)*x2^(-7/2)*x3^(-1/2) + (2*1 + 2*q^(-1))*x1^(5/2)*x2^(-7/2)*x3^(-3/2) + (-q^(-2))*x1^(5/2)*x2^(-7/2)*x3^(-5/2) + (-2*q^(3) - 4*q^(2) - 8*q - 2*1)*x1^(5/2)*x2^(-9/2)*x3^(-1/2) + (2*q^(2) + 6*q + 14*1 + 10*q^(-1) + 4*q^(-2))*x1^(5/2)*x2^(-9/2)*x3^(-3/2) + (-2*1 - 6*q^(-1) - 10*q^(-2) - 6*q^(-3) - 2*q^(-4))*x1^(5/2)*x2^(-9/2)*x3^(-5/2) + (2*q^(-3) + 2*q^(-4) + 2*q^(-5))*x1^(5/2)*x2^(-9/2)*x3^(-7/2) + (-2*q^(5) - 2*q^(4) - 9*q^(3) - 11*q^(2) - 13*q - 3*1)*x1^(5/2)*x2^(-11/2)*x3^(-1/2) + (2*q^(4) + 4*q^(3) + 16*q^(2) + 30*q + 42*1 + 32*q^(-1) + 14*q^(-2) + 4*q^(-3))*x1^(5/2)*x2^(-11/2)*x3^(-3/2) + (-2*q^(2) - 7*q - 23*1 - 39*q^(-1) - 53*q^(-2) - 39*q^(-3) - 23*q^(-4) - 7*q^(-5) - 2*q^(-6))*x1^(5/2)*x2^(-11/2)*x3^(-5/2) + (4*q^(-1) + 10*q^(-2) + 22*q^(-3) + 28*q^(-4) + 26*q^(-5) + 16*q^(-6) + 6*q^(-7) + 2*q^(-8))*x1^(5/2)*x2^(-11/2)*x3^(-7/2) + (-q^(-4) - 4*q^(-5) - 5*q^(-6) - 7*q^(-7) - 4*q^(-8) - 3*q^(-9))*x1^(5/2)*x2^(-11/2)*x3^(-9/2) + (2*q^(-1))*x1^(3/2)*x2^(-5/2)*x3^(-1/2) + (-q^(-2))*x1^(3/2)*x2^(-5/2)*x3^(-3/2) + (2*1 + 4*q^(-1))*x1^(3/2)*x2^(-7/2)*x3^(-1/2) + (-2*q^(-1) - 6*q^(-2) - 2*q^(-3))*x1^(3/2)*x2^(-7/2)*x3^(-3/2) + (2*q^(-3) + 2*q^(-4))*x1^(3/2)*x2^(-7/2)*x3^(-5/2) + (2*q + 4*1 + 6*q^(-1))*x1^(3/2)*x2^(-9/2)*x3^(-1/2) + (-2*1 - 8*q^(-1) - 15*q^(-2) - 8*q^(-3) - 2*q^(-4))*x1^(3/2)*x2^(-9/2)*x3^(-3/2) + (4*q^(-2) + 10*q^(-3) + 14*q^(-4) + 6*q^(-5) + 2*q^(-6))*x1^(3/2)*x2^(-9/2)*x3^(-5/2) + (-q^(-4) - 4*q^(-5) - 4*q^(-6) - 3*q^(-7))*x1^(3/2)*x2^(-9/2)*x3^(-7/2) + (2*q^(2) + 4*q + 6*1 + 8*q^(-1))*x1^(3/2)*x2^(-11/2)*x3^(-1/2) + (-2*q - 8*1 - 18*q^(-1) - 28*q^(-2) - 18*q^(-3) - 8*q^(-4) - 2*q^(-5))*x1^(3/2)*x2^(-11/2)*x3^(-3/2) + (4*q^(-1) + 14*q^(-2) + 32*q^(-3) + 42*q^(-4) + 30*q^(-5) + 16*q^(-6) + 4*q^(-7) + 2*q^(-8))*x1^(3/2)*x2^(-11/2)*x3^(-5/2) + (-2*q^(-3) - 10*q^(-4) - 22*q^(-5) - 28*q^(-6) - 28*q^(-7) - 14*q^(-8) - 6*q^(-9) - 2*q^(-10))*x1^(3/2)*x2^(-11/2)*x3^(-7/2) + (2*q^(-6) + 4*q^(-7) + 8*q^(-8) + 8*q^(-9) + 6*q^(-10) + 4*q^(-11))*x1^(3/2)*x2^(-11/2)*x3^(-9/2) + (-q^(-2))*x1^(1/2)*x2^(-3/2)*x3^(-1/2) + (-2*q^(-2))*x1^(1/2)*x2^(-5/2)*x3^(-1/2) + (2*q^(-3))*x1^(1/2)*x2^(-5/2)*x3^(-3/2) + (-3*q^(-2))*x1^(1/2)*x2^(-7/2)*x3^(-1/2) + (4*q^(-3) + 2*q^(-4))*x1^(1/2)*x2^(-7/2)*x3^(-3/2) + (-q^(-4) - 3*q^(-5))*x1^(1/2)*x2^(-7/2)*x3^(-5/2) + (-4*q^(-2))*x1^(1/2)*x2^(-9/2)*x3^(-1/2) + (6*q^(-3) + 4*q^(-4) + 2*q^(-5))*x1^(1/2)*x2^(-9/2)*x3^(-3/2) + (-2*q^(-4) - 8*q^(-5) - 4*q^(-6) - 2*q^(-7))*x1^(1/2)*x2^(-9/2)*x3^(-5/2) + (2*q^(-6) + 2*q^(-7) + 4*q^(-8))*x1^(1/2)*x2^(-9/2)*x3^(-7/2) + (-5*q^(-2))*x1^(1/2)*x2^(-11/2)*x3^(-1/2) + (8*q^(-3) + 6*q^(-4) + 4*q^(-5) + 2*q^(-6))*x1^(1/2)*x2^(-11/2)*x3^(-3/2) + (-3*q^(-4) - 13*q^(-5) - 11*q^(-6) - 9*q^(-7) - 2*q^(-8) - 2*q^(-9))*x1^(1/2)*x2^(-11/2)*x3^(-5/2) + (4*q^(-6) + 8*q^(-7) + 14*q^(-8) + 8*q^(-9) + 4*q^(-10) + 2*q^(-11))*x1^(1/2)*x2^(-11/2)*x3^(-7/2) + (-q^(-8) - 3*q^(-9) - 4*q^(-10) - 3*q^(-11) - 5*q^(-12))*x1^(1/2)*x2^(-11/2)*x3^(-9/2)

Braid

Braid word Components Crossings Strands
[-2, -2, 3, -2, -3, -3, -2, -1, 2, -3, -1] 3 11 4

Multivariable Alexander polynomial

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

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, 1, -1) no
(-1, -1, -1) no
(1, -1, 1) no
(-1, 3, 1) yes
(-1, -1, 1) yes
(1, 1, -1) yes
(1, 1, 1) no
(1, -3, -1) yes
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HFL polytope

Poincaré polynomial
2*m^(-2)*A1^(-1)*A2^(-1)*A3^(-1) + m^(-2)*A2^(-2)*A3^(-1) + 3*m^(-1)*A1^(-1)*A2^(-1) + 4*m^(-1)*A1^(-1)*A3^(-1) + m^(-1)*A2^(-2) + 5*m^(-1)*A2^(-1)*A3^(-1) + m^(-1)*A1*A2^(-2)*A3^(-1) + A1^(-1)*A2^(-1)*A3 + 7*A1^(-1) + 2*A1^(-1)*A2*A3^(-1) + 8*A2^(-1) + 7*A3^(-1) + A1*A2^(-2) + 3*A1*A2^(-1)*A3^(-1) + 3*m*A1^(-1)*A3 + 5*m*A1^(-1)*A2 + 3*m*A2^(-1)*A3 + 14*m + 3*m*A2*A3^(-1) + 5*m*A1*A2^(-1) + 3*m*A1*A3^(-1) + 3*m^2*A1^(-1)*A2*A3 + m^2*A1^(-1)*A2^2 + 7*m^2*A3 + 8*m^2*A2 + 2*m^2*A1*A2^(-1)*A3 + 7*m^2*A1 + m^2*A1*A2*A3^(-1) + m^3*A1^(-1)*A2^2*A3 + 5*m^3*A2*A3 + m^3*A2^2 + 4*m^3*A1*A3 + 3*m^3*A1*A2 + m^4*A2^2*A3 + 2*m^4*A1*A2*A3
VertexMaslovRank
(-1, -1, -1)-22
(-1, -1, 1)01
(-1, 1, -1)02
(-1, 2, 0)21
(-1, 2, 1)31
(0, -2, -1)-21
(0, -2, 0)-11
(0, 2, 0)31
(0, 2, 1)41
(1, -2, -1)-11
(1, -2, 0)01
(1, -1, 1)22
(1, 1, -1)21
(1, 1, 1)42
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Record

FL/HFL Links

orderOption(int) 220
namestring L8a20{0;1}
statusstring success
slugstring L8a20_0_1_b347a7e5
result_filestring details/L8a20_0_1_b347a7e5.json
complexity_scoreOption(int) 192
strandsOption(int) null
crossingsOption(int) 8
component_countOption(int) 3
girthOption(int) 6
total_rankOption(int) 128
wall_secondsOption(float) 0.002189
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 3
support_sizeOption(int) 35
vertex_countOption(int) 14
fibered_vertex_countOption(int) 4
polytope_statusstring computed
alexander_support_sizeOption(int) 10
alexander_vertex_countOption(int) 8
alexander_relationstring not_computed
fk_countint 2
detailsRowRef(FLHFLLinks) 
{
  "dataset": "FLHFLLinks",
  "key": "L8a20_0_1_b347a7e5"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L8a20_0_1_b347a7e5