details/L10n78_0_0_2cd3938a.json

FL expansions

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

Braid

Braid word Components Crossings Strands
[-1, 2, -1, -2, 1, -2, -2, -2, -2, -2] 3 10 3

Multivariable Alexander polynomial

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

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) yes
(1, 1, 3) yes
(-1, -1, -1) yes
(-1, 3, 1) yes
(1, -1, -1) yes
(-1, -1, -3) yes
(1, 1, 1) yes
(1, -3, -1) yes
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HFL polytope

Poincaré polynomial
m^(-3)*A1^(-1)*A2^(-1)*A3^(-2) + 2*m^(-2)*A1^(-1)*A2^(-1)*A3^(-1) + m^(-2)*A1^(-1)*A3^(-2) + m^(-2)*A2^(-2)*A3^(-1) + m^(-2)*A2^(-1)*A3^(-2) + m^(-1)*A1^(-1)*A2^(-1) + 3*m^(-1)*A1^(-1)*A3^(-1) + m^(-1)*A2^(-2) + 4*m^(-1)*A2^(-1)*A3^(-1) + m^(-1)*A3^(-2) + m^(-1)*A1*A2^(-2)*A3^(-1) + 3*A1^(-1) + A1^(-1)*A2*A3^(-1) + 4*A2^(-1) + 4*A3^(-1) + A1*A2^(-2) + 2*A1*A2^(-1)*A3^(-1) + m*A1^(-1)*A3 + 3*m*A1^(-1)*A2 + m*A2^(-1)*A3 + 6*m + m*A2*A3^(-1) + 3*m*A1*A2^(-1) + m*A1*A3^(-1) + 2*m^2*A1^(-1)*A2*A3 + m^2*A1^(-1)*A2^2 + 4*m^2*A3 + 4*m^2*A2 + m^2*A1*A2^(-1)*A3 + 3*m^2*A1 + m^3*A1^(-1)*A2^2*A3 + m^3*A3^2 + 4*m^3*A2*A3 + m^3*A2^2 + 3*m^3*A1*A3 + m^3*A1*A2 + m^4*A2*A3^2 + m^4*A2^2*A3 + m^4*A1*A3^2 + 2*m^4*A1*A2*A3 + m^5*A1*A2*A3^2
VertexMaslovRank
(-1, -1, -2)-31
(-1, -1, 0)-11
(-1, 0, -2)-21
(-1, 0, 1)11
(-1, 2, 0)21
(-1, 2, 1)31
(0, -2, -1)-21
(0, -2, 0)-11
(0, -1, -2)-21
(0, 0, -2)-11
(0, 0, 2)31
(0, 1, 2)41
(0, 2, 0)31
(0, 2, 1)41
(1, -2, -1)-11
(1, -2, 0)01
(1, 0, -1)11
(1, 0, 2)41
(1, 1, 0)31
(1, 1, 2)51
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Record

FL/HFL Links

orderOption(int) 2217
namestring L10n78{0;0}
statusstring success
slugstring L10n78_0_0_2cd3938a
result_filestring details/L10n78_0_0_2cd3938a.json
complexity_scoreOption(int) 300
strandsOption(int) null
crossingsOption(int) 10
component_countOption(int) 3
girthOption(int) 6
total_rankOption(int) 80
wall_secondsOption(float) 0.001873
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 3
support_sizeOption(int) 41
vertex_countOption(int) 20
fibered_vertex_countOption(int) 8
polytope_statusstring computed
alexander_support_sizeOption(int) 10
alexander_vertex_countOption(int) 8
alexander_relationstring not_computed
fk_countint 3
detailsRowRef(FLHFLLinks) 
{
  "dataset": "FLHFLLinks",
  "key": "L10n78_0_0_2cd3938a"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L10n78_0_0_2cd3938a