details/L10n81_1_0_6743fa2d.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, 1, 0) x1^(1/2)x2^(3/2)x3^(-1/2) q^(-8)
{"0": [1, 1, 1, 1, 1, 1], "1": [1, 1, 1, 1, 1, 1, 1, 1], "2": [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}
(-q^(2))*x1^(1/2)*x2^(3/2)*x3^(-1/2) + (2*q)*x1^(1/2)*x2^(5/2)*x3^(-3/2) + (-2*q^(2))*x1^(1/2)*x2^(5/2)*x3^(-1/2) + (-1 - 2*q^(-1))*x1^(1/2)*x2^(7/2)*x3^(-5/2) + (4*q + 2*1)*x1^(1/2)*x2^(7/2)*x3^(-3/2) + (-3*q^(2))*x1^(1/2)*x2^(7/2)*x3^(-1/2) + (2*q^(-2) + 2*q^(-4))*x1^(1/2)*x2^(9/2)*x3^(-7/2) + (-2*1 - 6*q^(-1) - 2*q^(-2) - 2*q^(-3))*x1^(1/2)*x2^(9/2)*x3^(-5/2) + (6*q + 4*1 + 2*q^(-1))*x1^(1/2)*x2^(9/2)*x3^(-3/2) + (-4*q^(2))*x1^(1/2)*x2^(9/2)*x3^(-1/2) + (-q^(-4) - 2*q^(-5) - 2*q^(-8))*x1^(1/2)*x2^(11/2)*x3^(-9/2) + (4*q^(-2) + 4*q^(-3) + 6*q^(-4) + 2*q^(-5) + 2*q^(-6) + 2*q^(-7))*x1^(1/2)*x2^(11/2)*x3^(-7/2) + (-3*1 - 10*q^(-1) - 7*q^(-2) - 6*q^(-3) - 2*q^(-4) - 2*q^(-5))*x1^(1/2)*x2^(11/2)*x3^(-5/2) + (8*q + 6*1 + 4*q^(-1) + 2*q^(-2))*x1^(1/2)*x2^(11/2)*x3^(-3/2) + (-5*q^(2))*x1^(1/2)*x2^(11/2)*x3^(-1/2) + (-q^(2))*x1^(3/2)*x2^(5/2)*x3^(-3/2) + (2*q^(3))*x1^(3/2)*x2^(5/2)*x3^(-1/2) + (-q^(4))*x1^(3/2)*x2^(5/2)*x3^(1/2) + (2*q + 2*1)*x1^(3/2)*x2^(7/2)*x3^(-5/2) + (-2*q^(3) - 6*q^(2) - 2*q)*x1^(3/2)*x2^(7/2)*x3^(-3/2) + (4*q^(4) + 6*q^(3))*x1^(3/2)*x2^(7/2)*x3^(-1/2) + (-2*q^(5) - 2*q^(4))*x1^(3/2)*x2^(7/2)*x3^(1/2) + (-1 - 4*q^(-1) - 3*q^(-2) - 2*q^(-3))*x1^(3/2)*x2^(9/2)*x3^(-7/2) + (4*q^(2) + 10*q + 12*1 + 4*q^(-1) + 2*q^(-2))*x1^(3/2)*x2^(9/2)*x3^(-5/2) + (-3*q^(4) - 12*q^(3) - 18*q^(2) - 10*q - 2*1)*x1^(3/2)*x2^(9/2)*x3^(-3/2) + (6*q^(5) + 12*q^(4) + 12*q^(3) + 2*q^(2))*x1^(3/2)*x2^(9/2)*x3^(-1/2) + (-3*q^(6) - 4*q^(5) - 3*q^(4))*x1^(3/2)*x2^(9/2)*x3^(1/2) + (2*q^(-2) + 4*q^(-3) + 6*q^(-4) + 4*q^(-5) + 2*q^(-6) + 2*q^(-7))*x1^(3/2)*x2^(11/2)*x3^(-9/2) + (-2*q - 10*1 - 20*q^(-1) - 20*q^(-2) - 16*q^(-3) - 6*q^(-4) - 4*q^(-5) - 2*q^(-6))*x1^(3/2)*x2^(11/2)*x3^(-7/2) + (6*q^(3) + 18*q^(2) + 36*q + 40*1 + 24*q^(-1) + 14*q^(-2) + 4*q^(-3) + 2*q^(-4))*x1^(3/2)*x2^(11/2)*x3^(-5/2) + (-4*q^(5) - 18*q^(4) - 34*q^(3) - 44*q^(2) - 28*q - 12*1 - 4*q^(-1))*x1^(3/2)*x2^(11/2)*x3^(-3/2) + (8*q^(6) + 18*q^(5) + 24*q^(4) + 22*q^(3) + 6*q^(2) + 2*q)*x1^(3/2)*x2^(11/2)*x3^(-1/2) + (-4*q^(7) - 6*q^(6) - 6*q^(5) - 4*q^(4))*x1^(3/2)*x2^(11/2)*x3^(1/2) + (-q^(2))*x1^(5/2)*x2^(7/2)*x3^(-5/2) + (2*q^(4) + 2*q^(3))*x1^(5/2)*x2^(7/2)*x3^(-3/2) + (-q^(6) - 4*q^(5) - q^(4))*x1^(5/2)*x2^(7/2)*x3^(-1/2) + (2*q^(7) + 2*q^(6))*x1^(5/2)*x2^(7/2)*x3^(1/2) + (-q^(8))*x1^(5/2)*x2^(7/2)*x3^(3/2) + (2*q + 2*1 + 2*q^(-1))*x1^(5/2)*x2^(9/2)*x3^(-7/2) + (-2*q^(4) - 6*q^(3) - 10*q^(2) - 6*q - 2*1)*x1^(5/2)*x2^(9/2)*x3^(-5/2) + (4*q^(6) + 10*q^(5) + 18*q^(4) + 12*q^(3) + 4*q^(2))*x1^(5/2)*x2^(9/2)*x3^(-3/2) + (-2*q^(8) - 10*q^(7) - 16*q^(6) - 16*q^(5) - 4*q^(4))*x1^(5/2)*x2^(9/2)*x3^(-1/2) + (4*q^(9) + 8*q^(8) + 10*q^(7) + 4*q^(6))*x1^(5/2)*x2^(9/2)*x3^(1/2) + (-2*q^(10) - 2*q^(9) - 2*q^(8))*x1^(5/2)*x2^(9/2)*x3^(3/2) + (-1 - 4*q^(-1) - 5*q^(-2) - 6*q^(-3) - 3*q^(-4) - 2*q^(-5))*x1^(5/2)*x2^(11/2)*x3^(-9/2) + (4*q^(3) + 10*q^(2) + 22*q + 26*1 + 22*q^(-1) + 12*q^(-2) + 4*q^(-3) + 2*q^(-4))*x1^(5/2)*x2^(11/2)*x3^(-7/2) + (-3*q^(6) - 12*q^(5) - 32*q^(4) - 50*q^(3) - 59*q^(2) - 40*q - 21*1 - 6*q^(-1) - 2*q^(-2))*x1^(5/2)*x2^(11/2)*x3^(-5/2) + (6*q^(8) + 18*q^(7) + 46*q^(6) + 68*q^(5) + 74*q^(4) + 50*q^(3) + 20*q^(2) + 6*q)*x1^(5/2)*x2^(11/2)*x3^(-3/2) + (-3*q^(10) - 16*q^(9) - 34*q^(8) - 58*q^(7) - 57*q^(6) - 42*q^(5) - 13*q^(4) - 2*q^(3))*x1^(5/2)*x2^(11/2)*x3^(-1/2) + (6*q^(11) + 14*q^(10) + 26*q^(9) + 28*q^(8) + 20*q^(7) + 8*q^(6))*x1^(5/2)*x2^(11/2)*x3^(1/2) + (-3*q^(12) - 4*q^(11) - 7*q^(10) - 4*q^(9) - 3*q^(8))*x1^(5/2)*x2^(11/2)*x3^(3/2) + (-q^(2))*x1^(7/2)*x2^(9/2)*x3^(-7/2) + (2*q^(5) + 2*q^(4) + 2*q^(3))*x1^(7/2)*x2^(9/2)*x3^(-5/2) + (-q^(8) - 4*q^(7) - 5*q^(6) - 4*q^(5) - q^(4))*x1^(7/2)*x2^(9/2)*x3^(-3/2) + (2*q^(10) + 4*q^(9) + 8*q^(8) + 4*q^(7) + 2*q^(6))*x1^(7/2)*x2^(9/2)*x3^(-1/2) + (-q^(12) - 4*q^(11) - 5*q^(10) - 4*q^(9) - q^(8))*x1^(7/2)*x2^(9/2)*x3^(1/2) + (2*q^(13) + 2*q^(12) + 2*q^(11))*x1^(7/2)*x2^(9/2)*x3^(3/2) + (-q^(14))*x1^(7/2)*x2^(9/2)*x3^(5/2) + (2*q + 2*1 + 2*q^(-1) + 2*q^(-2))*x1^(7/2)*x2^(11/2)*x3^(-9/2) + (-2*q^(5) - 6*q^(4) - 10*q^(3) - 14*q^(2) - 10*q - 6*1 - 2*q^(-1))*x1^(7/2)*x2^(11/2)*x3^(-7/2) + (4*q^(8) + 10*q^(7) + 22*q^(6) + 32*q^(5) + 32*q^(4) + 24*q^(3) + 10*q^(2) + 4*q)*x1^(7/2)*x2^(11/2)*x3^(-5/2) + (-2*q^(11) - 10*q^(10) - 24*q^(9) - 40*q^(8) - 54*q^(7) - 46*q^(6) - 30*q^(5) - 12*q^(4) - 2*q^(3))*x1^(7/2)*x2^(11/2)*x3^(-3/2) + (4*q^(13) + 12*q^(12) + 30*q^(11) + 46*q^(10) + 52*q^(9) + 46*q^(8) + 22*q^(7) + 8*q^(6))*x1^(7/2)*x2^(11/2)*x3^(-1/2) + (-2*q^(15) - 10*q^(14) - 20*q^(13) - 32*q^(12) - 34*q^(11) - 26*q^(10) - 12*q^(9) - 2*q^(8))*x1^(7/2)*x2^(11/2)*x3^(1/2) + (4*q^(16) + 8*q^(15) + 12*q^(14) + 14*q^(13) + 8*q^(12) + 4*q^(11))*x1^(7/2)*x2^(11/2)*x3^(3/2) + (-2*q^(17) - 2*q^(16) - 2*q^(15) - 2*q^(14))*x1^(7/2)*x2^(11/2)*x3^(5/2) + (-q^(2))*x1^(9/2)*x2^(11/2)*x3^(-9/2) + (2*q^(6) + 2*q^(5) + 2*q^(4) + 2*q^(3))*x1^(9/2)*x2^(11/2)*x3^(-7/2) + (-q^(10) - 4*q^(9) - 5*q^(8) - 8*q^(7) - 5*q^(6) - 4*q^(5) - q^(4))*x1^(9/2)*x2^(11/2)*x3^(-5/2) + (2*q^(13) + 4*q^(12) + 10*q^(11) + 12*q^(10) + 12*q^(9) + 10*q^(8) + 4*q^(7) + 2*q^(6))*x1^(9/2)*x2^(11/2)*x3^(-3/2) + (-q^(16) - 4*q^(15) - 9*q^(14) - 12*q^(13) - 18*q^(12) - 12*q^(11) - 9*q^(10) - 4*q^(9) - q^(8))*x1^(9/2)*x2^(11/2)*x3^(-1/2) + (2*q^(18) + 4*q^(17) + 10*q^(16) + 12*q^(15) + 12*q^(14) + 10*q^(13) + 4*q^(12) + 2*q^(11))*x1^(9/2)*x2^(11/2)*x3^(1/2) + (-q^(20) - 4*q^(19) - 5*q^(18) - 8*q^(17) - 5*q^(16) - 4*q^(15) - q^(14))*x1^(9/2)*x2^(11/2)*x3^(3/2) + (2*q^(21) + 2*q^(20) + 2*q^(19) + 2*q^(18))*x1^(9/2)*x2^(11/2)*x3^(5/2) + (-q^(22))*x1^(9/2)*x2^(11/2)*x3^(7/2)
(-1/2, -3/2, 1/2) (1, 1, 0) x1^(1/2)x2^(3/2)x3^(-1/2) q^(-8)
{"0": [1, 1, 1, 1, 1, 1], "1": [1, 1, 1, 1, 1, 1, 1, 1], "2": [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}
(-q^(2))*x1^(1/2)*x2^(3/2)*x3^(-1/2) + (2*q)*x1^(1/2)*x2^(5/2)*x3^(-3/2) + (-2*q^(2))*x1^(1/2)*x2^(5/2)*x3^(-1/2) + (-1 - 2*q^(-1))*x1^(1/2)*x2^(7/2)*x3^(-5/2) + (4*q + 2*1)*x1^(1/2)*x2^(7/2)*x3^(-3/2) + (-3*q^(2))*x1^(1/2)*x2^(7/2)*x3^(-1/2) + (2*q^(-2) + 2*q^(-4))*x1^(1/2)*x2^(9/2)*x3^(-7/2) + (-2*1 - 6*q^(-1) - 2*q^(-2) - 2*q^(-3))*x1^(1/2)*x2^(9/2)*x3^(-5/2) + (6*q + 4*1 + 2*q^(-1))*x1^(1/2)*x2^(9/2)*x3^(-3/2) + (-4*q^(2))*x1^(1/2)*x2^(9/2)*x3^(-1/2) + (-q^(-4) - 2*q^(-5) - 2*q^(-8))*x1^(1/2)*x2^(11/2)*x3^(-9/2) + (4*q^(-2) + 4*q^(-3) + 6*q^(-4) + 2*q^(-5) + 2*q^(-6) + 2*q^(-7))*x1^(1/2)*x2^(11/2)*x3^(-7/2) + (-3*1 - 10*q^(-1) - 7*q^(-2) - 6*q^(-3) - 2*q^(-4) - 2*q^(-5))*x1^(1/2)*x2^(11/2)*x3^(-5/2) + (8*q + 6*1 + 4*q^(-1) + 2*q^(-2))*x1^(1/2)*x2^(11/2)*x3^(-3/2) + (-5*q^(2))*x1^(1/2)*x2^(11/2)*x3^(-1/2) + (-q^(2))*x1^(3/2)*x2^(5/2)*x3^(-3/2) + (2*q^(3))*x1^(3/2)*x2^(5/2)*x3^(-1/2) + (-q^(4))*x1^(3/2)*x2^(5/2)*x3^(1/2) + (2*q + 2*1)*x1^(3/2)*x2^(7/2)*x3^(-5/2) + (-2*q^(3) - 6*q^(2) - 2*q)*x1^(3/2)*x2^(7/2)*x3^(-3/2) + (4*q^(4) + 6*q^(3))*x1^(3/2)*x2^(7/2)*x3^(-1/2) + (-2*q^(5) - 2*q^(4))*x1^(3/2)*x2^(7/2)*x3^(1/2) + (-1 - 4*q^(-1) - 3*q^(-2) - 2*q^(-3))*x1^(3/2)*x2^(9/2)*x3^(-7/2) + (4*q^(2) + 10*q + 12*1 + 4*q^(-1) + 2*q^(-2))*x1^(3/2)*x2^(9/2)*x3^(-5/2) + (-3*q^(4) - 12*q^(3) - 18*q^(2) - 10*q - 2*1)*x1^(3/2)*x2^(9/2)*x3^(-3/2) + (6*q^(5) + 12*q^(4) + 12*q^(3) + 2*q^(2))*x1^(3/2)*x2^(9/2)*x3^(-1/2) + (-3*q^(6) - 4*q^(5) - 3*q^(4))*x1^(3/2)*x2^(9/2)*x3^(1/2) + (2*q^(-2) + 4*q^(-3) + 6*q^(-4) + 4*q^(-5) + 2*q^(-6) + 2*q^(-7))*x1^(3/2)*x2^(11/2)*x3^(-9/2) + (-2*q - 10*1 - 20*q^(-1) - 20*q^(-2) - 16*q^(-3) - 6*q^(-4) - 4*q^(-5) - 2*q^(-6))*x1^(3/2)*x2^(11/2)*x3^(-7/2) + (6*q^(3) + 18*q^(2) + 36*q + 40*1 + 24*q^(-1) + 14*q^(-2) + 4*q^(-3) + 2*q^(-4))*x1^(3/2)*x2^(11/2)*x3^(-5/2) + (-4*q^(5) - 18*q^(4) - 34*q^(3) - 44*q^(2) - 28*q - 12*1 - 4*q^(-1))*x1^(3/2)*x2^(11/2)*x3^(-3/2) + (8*q^(6) + 18*q^(5) + 24*q^(4) + 22*q^(3) + 6*q^(2) + 2*q)*x1^(3/2)*x2^(11/2)*x3^(-1/2) + (-4*q^(7) - 6*q^(6) - 6*q^(5) - 4*q^(4))*x1^(3/2)*x2^(11/2)*x3^(1/2) + (-q^(2))*x1^(5/2)*x2^(7/2)*x3^(-5/2) + (2*q^(4) + 2*q^(3))*x1^(5/2)*x2^(7/2)*x3^(-3/2) + (-q^(6) - 4*q^(5) - q^(4))*x1^(5/2)*x2^(7/2)*x3^(-1/2) + (2*q^(7) + 2*q^(6))*x1^(5/2)*x2^(7/2)*x3^(1/2) + (-q^(8))*x1^(5/2)*x2^(7/2)*x3^(3/2) + (2*q + 2*1 + 2*q^(-1))*x1^(5/2)*x2^(9/2)*x3^(-7/2) + (-2*q^(4) - 6*q^(3) - 10*q^(2) - 6*q - 2*1)*x1^(5/2)*x2^(9/2)*x3^(-5/2) + (4*q^(6) + 10*q^(5) + 18*q^(4) + 12*q^(3) + 4*q^(2))*x1^(5/2)*x2^(9/2)*x3^(-3/2) + (-2*q^(8) - 10*q^(7) - 16*q^(6) - 16*q^(5) - 4*q^(4))*x1^(5/2)*x2^(9/2)*x3^(-1/2) + (4*q^(9) + 8*q^(8) + 10*q^(7) + 4*q^(6))*x1^(5/2)*x2^(9/2)*x3^(1/2) + (-2*q^(10) - 2*q^(9) - 2*q^(8))*x1^(5/2)*x2^(9/2)*x3^(3/2) + (-1 - 4*q^(-1) - 5*q^(-2) - 6*q^(-3) - 3*q^(-4) - 2*q^(-5))*x1^(5/2)*x2^(11/2)*x3^(-9/2) + (4*q^(3) + 10*q^(2) + 22*q + 26*1 + 22*q^(-1) + 12*q^(-2) + 4*q^(-3) + 2*q^(-4))*x1^(5/2)*x2^(11/2)*x3^(-7/2) + (-3*q^(6) - 12*q^(5) - 32*q^(4) - 50*q^(3) - 59*q^(2) - 40*q - 21*1 - 6*q^(-1) - 2*q^(-2))*x1^(5/2)*x2^(11/2)*x3^(-5/2) + (6*q^(8) + 18*q^(7) + 46*q^(6) + 68*q^(5) + 74*q^(4) + 50*q^(3) + 20*q^(2) + 6*q)*x1^(5/2)*x2^(11/2)*x3^(-3/2) + (-3*q^(10) - 16*q^(9) - 34*q^(8) - 58*q^(7) - 57*q^(6) - 42*q^(5) - 13*q^(4) - 2*q^(3))*x1^(5/2)*x2^(11/2)*x3^(-1/2) + (6*q^(11) + 14*q^(10) + 26*q^(9) + 28*q^(8) + 20*q^(7) + 8*q^(6))*x1^(5/2)*x2^(11/2)*x3^(1/2) + (-3*q^(12) - 4*q^(11) - 7*q^(10) - 4*q^(9) - 3*q^(8))*x1^(5/2)*x2^(11/2)*x3^(3/2) + (-q^(2))*x1^(7/2)*x2^(9/2)*x3^(-7/2) + (2*q^(5) + 2*q^(4) + 2*q^(3))*x1^(7/2)*x2^(9/2)*x3^(-5/2) + (-q^(8) - 4*q^(7) - 5*q^(6) - 4*q^(5) - q^(4))*x1^(7/2)*x2^(9/2)*x3^(-3/2) + (2*q^(10) + 4*q^(9) + 8*q^(8) + 4*q^(7) + 2*q^(6))*x1^(7/2)*x2^(9/2)*x3^(-1/2) + (-q^(12) - 4*q^(11) - 5*q^(10) - 4*q^(9) - q^(8))*x1^(7/2)*x2^(9/2)*x3^(1/2) + (2*q^(13) + 2*q^(12) + 2*q^(11))*x1^(7/2)*x2^(9/2)*x3^(3/2) + (-q^(14))*x1^(7/2)*x2^(9/2)*x3^(5/2) + (2*q + 2*1 + 2*q^(-1) + 2*q^(-2))*x1^(7/2)*x2^(11/2)*x3^(-9/2) + (-2*q^(5) - 6*q^(4) - 10*q^(3) - 14*q^(2) - 10*q - 6*1 - 2*q^(-1))*x1^(7/2)*x2^(11/2)*x3^(-7/2) + (4*q^(8) + 10*q^(7) + 22*q^(6) + 32*q^(5) + 32*q^(4) + 24*q^(3) + 10*q^(2) + 4*q)*x1^(7/2)*x2^(11/2)*x3^(-5/2) + (-2*q^(11) - 10*q^(10) - 24*q^(9) - 40*q^(8) - 54*q^(7) - 46*q^(6) - 30*q^(5) - 12*q^(4) - 2*q^(3))*x1^(7/2)*x2^(11/2)*x3^(-3/2) + (4*q^(13) + 12*q^(12) + 30*q^(11) + 46*q^(10) + 52*q^(9) + 46*q^(8) + 22*q^(7) + 8*q^(6))*x1^(7/2)*x2^(11/2)*x3^(-1/2) + (-2*q^(15) - 10*q^(14) - 20*q^(13) - 32*q^(12) - 34*q^(11) - 26*q^(10) - 12*q^(9) - 2*q^(8))*x1^(7/2)*x2^(11/2)*x3^(1/2) + (4*q^(16) + 8*q^(15) + 12*q^(14) + 14*q^(13) + 8*q^(12) + 4*q^(11))*x1^(7/2)*x2^(11/2)*x3^(3/2) + (-2*q^(17) - 2*q^(16) - 2*q^(15) - 2*q^(14))*x1^(7/2)*x2^(11/2)*x3^(5/2) + (-q^(2))*x1^(9/2)*x2^(11/2)*x3^(-9/2) + (2*q^(6) + 2*q^(5) + 2*q^(4) + 2*q^(3))*x1^(9/2)*x2^(11/2)*x3^(-7/2) + (-q^(10) - 4*q^(9) - 5*q^(8) - 8*q^(7) - 5*q^(6) - 4*q^(5) - q^(4))*x1^(9/2)*x2^(11/2)*x3^(-5/2) + (2*q^(13) + 4*q^(12) + 10*q^(11) + 12*q^(10) + 12*q^(9) + 10*q^(8) + 4*q^(7) + 2*q^(6))*x1^(9/2)*x2^(11/2)*x3^(-3/2) + (-q^(16) - 4*q^(15) - 9*q^(14) - 12*q^(13) - 18*q^(12) - 12*q^(11) - 9*q^(10) - 4*q^(9) - q^(8))*x1^(9/2)*x2^(11/2)*x3^(-1/2) + (2*q^(18) + 4*q^(17) + 10*q^(16) + 12*q^(15) + 12*q^(14) + 10*q^(13) + 4*q^(12) + 2*q^(11))*x1^(9/2)*x2^(11/2)*x3^(1/2) + (-q^(20) - 4*q^(19) - 5*q^(18) - 8*q^(17) - 5*q^(16) - 4*q^(15) - q^(14))*x1^(9/2)*x2^(11/2)*x3^(3/2) + (2*q^(21) + 2*q^(20) + 2*q^(19) + 2*q^(18))*x1^(9/2)*x2^(11/2)*x3^(5/2) + (-q^(22))*x1^(9/2)*x2^(11/2)*x3^(7/2)
(1/2, 3/2, -1/2) x1^(-1/2)x2^(-3/2)x3^(1/2) q^(-8)
(-q^(2))*x1^(-1/2)*x2^(-3/2)*x3^(1/2) + (2*q)*x1^(-1/2)*x2^(-5/2)*x3^(3/2) + (-2*q^(2))*x1^(-1/2)*x2^(-5/2)*x3^(1/2) + (-1 - 2*q^(-1))*x1^(-1/2)*x2^(-7/2)*x3^(5/2) + (4*q + 2*1)*x1^(-1/2)*x2^(-7/2)*x3^(3/2) + (-3*q^(2))*x1^(-1/2)*x2^(-7/2)*x3^(1/2) + (2*q^(-2) + 2*q^(-4))*x1^(-1/2)*x2^(-9/2)*x3^(7/2) + (-2*1 - 6*q^(-1) - 2*q^(-2) - 2*q^(-3))*x1^(-1/2)*x2^(-9/2)*x3^(5/2) + (6*q + 4*1 + 2*q^(-1))*x1^(-1/2)*x2^(-9/2)*x3^(3/2) + (-4*q^(2))*x1^(-1/2)*x2^(-9/2)*x3^(1/2) + (-q^(-4) - 2*q^(-5) - 2*q^(-8))*x1^(-1/2)*x2^(-11/2)*x3^(9/2) + (4*q^(-2) + 4*q^(-3) + 6*q^(-4) + 2*q^(-5) + 2*q^(-6) + 2*q^(-7))*x1^(-1/2)*x2^(-11/2)*x3^(7/2) + (-3*1 - 10*q^(-1) - 7*q^(-2) - 6*q^(-3) - 2*q^(-4) - 2*q^(-5))*x1^(-1/2)*x2^(-11/2)*x3^(5/2) + (8*q + 6*1 + 4*q^(-1) + 2*q^(-2))*x1^(-1/2)*x2^(-11/2)*x3^(3/2) + (-5*q^(2))*x1^(-1/2)*x2^(-11/2)*x3^(1/2) + (-q^(2))*x1^(-3/2)*x2^(-5/2)*x3^(3/2) + (2*q^(3))*x1^(-3/2)*x2^(-5/2)*x3^(1/2) + (-q^(4))*x1^(-3/2)*x2^(-5/2)*x3^(-1/2) + (2*q + 2*1)*x1^(-3/2)*x2^(-7/2)*x3^(5/2) + (-2*q^(3) - 6*q^(2) - 2*q)*x1^(-3/2)*x2^(-7/2)*x3^(3/2) + (4*q^(4) + 6*q^(3))*x1^(-3/2)*x2^(-7/2)*x3^(1/2) + (-2*q^(5) - 2*q^(4))*x1^(-3/2)*x2^(-7/2)*x3^(-1/2) + (-1 - 4*q^(-1) - 3*q^(-2) - 2*q^(-3))*x1^(-3/2)*x2^(-9/2)*x3^(7/2) + (4*q^(2) + 10*q + 12*1 + 4*q^(-1) + 2*q^(-2))*x1^(-3/2)*x2^(-9/2)*x3^(5/2) + (-3*q^(4) - 12*q^(3) - 18*q^(2) - 10*q - 2*1)*x1^(-3/2)*x2^(-9/2)*x3^(3/2) + (6*q^(5) + 12*q^(4) + 12*q^(3) + 2*q^(2))*x1^(-3/2)*x2^(-9/2)*x3^(1/2) + (-3*q^(6) - 4*q^(5) - 3*q^(4))*x1^(-3/2)*x2^(-9/2)*x3^(-1/2) + (2*q^(-2) + 4*q^(-3) + 6*q^(-4) + 4*q^(-5) + 2*q^(-6) + 2*q^(-7))*x1^(-3/2)*x2^(-11/2)*x3^(9/2) + (-2*q - 10*1 - 20*q^(-1) - 20*q^(-2) - 16*q^(-3) - 6*q^(-4) - 4*q^(-5) - 2*q^(-6))*x1^(-3/2)*x2^(-11/2)*x3^(7/2) + (6*q^(3) + 18*q^(2) + 36*q + 40*1 + 24*q^(-1) + 14*q^(-2) + 4*q^(-3) + 2*q^(-4))*x1^(-3/2)*x2^(-11/2)*x3^(5/2) + (-4*q^(5) - 18*q^(4) - 34*q^(3) - 44*q^(2) - 28*q - 12*1 - 4*q^(-1))*x1^(-3/2)*x2^(-11/2)*x3^(3/2) + (8*q^(6) + 18*q^(5) + 24*q^(4) + 22*q^(3) + 6*q^(2) + 2*q)*x1^(-3/2)*x2^(-11/2)*x3^(1/2) + (-4*q^(7) - 6*q^(6) - 6*q^(5) - 4*q^(4))*x1^(-3/2)*x2^(-11/2)*x3^(-1/2) + (-q^(2))*x1^(-5/2)*x2^(-7/2)*x3^(5/2) + (2*q^(4) + 2*q^(3))*x1^(-5/2)*x2^(-7/2)*x3^(3/2) + (-q^(6) - 4*q^(5) - q^(4))*x1^(-5/2)*x2^(-7/2)*x3^(1/2) + (2*q^(7) + 2*q^(6))*x1^(-5/2)*x2^(-7/2)*x3^(-1/2) + (-q^(8))*x1^(-5/2)*x2^(-7/2)*x3^(-3/2) + (2*q + 2*1 + 2*q^(-1))*x1^(-5/2)*x2^(-9/2)*x3^(7/2) + (-2*q^(4) - 6*q^(3) - 10*q^(2) - 6*q - 2*1)*x1^(-5/2)*x2^(-9/2)*x3^(5/2) + (4*q^(6) + 10*q^(5) + 18*q^(4) + 12*q^(3) + 4*q^(2))*x1^(-5/2)*x2^(-9/2)*x3^(3/2) + (-2*q^(8) - 10*q^(7) - 16*q^(6) - 16*q^(5) - 4*q^(4))*x1^(-5/2)*x2^(-9/2)*x3^(1/2) + (4*q^(9) + 8*q^(8) + 10*q^(7) + 4*q^(6))*x1^(-5/2)*x2^(-9/2)*x3^(-1/2) + (-2*q^(10) - 2*q^(9) - 2*q^(8))*x1^(-5/2)*x2^(-9/2)*x3^(-3/2) + (-1 - 4*q^(-1) - 5*q^(-2) - 6*q^(-3) - 3*q^(-4) - 2*q^(-5))*x1^(-5/2)*x2^(-11/2)*x3^(9/2) + (4*q^(3) + 10*q^(2) + 22*q + 26*1 + 22*q^(-1) + 12*q^(-2) + 4*q^(-3) + 2*q^(-4))*x1^(-5/2)*x2^(-11/2)*x3^(7/2) + (-3*q^(6) - 12*q^(5) - 32*q^(4) - 50*q^(3) - 59*q^(2) - 40*q - 21*1 - 6*q^(-1) - 2*q^(-2))*x1^(-5/2)*x2^(-11/2)*x3^(5/2) + (6*q^(8) + 18*q^(7) + 46*q^(6) + 68*q^(5) + 74*q^(4) + 50*q^(3) + 20*q^(2) + 6*q)*x1^(-5/2)*x2^(-11/2)*x3^(3/2) + (-3*q^(10) - 16*q^(9) - 34*q^(8) - 58*q^(7) - 57*q^(6) - 42*q^(5) - 13*q^(4) - 2*q^(3))*x1^(-5/2)*x2^(-11/2)*x3^(1/2) + (6*q^(11) + 14*q^(10) + 26*q^(9) + 28*q^(8) + 20*q^(7) + 8*q^(6))*x1^(-5/2)*x2^(-11/2)*x3^(-1/2) + (-3*q^(12) - 4*q^(11) - 7*q^(10) - 4*q^(9) - 3*q^(8))*x1^(-5/2)*x2^(-11/2)*x3^(-3/2) + (-q^(2))*x1^(-7/2)*x2^(-9/2)*x3^(7/2) + (2*q^(5) + 2*q^(4) + 2*q^(3))*x1^(-7/2)*x2^(-9/2)*x3^(5/2) + (-q^(8) - 4*q^(7) - 5*q^(6) - 4*q^(5) - q^(4))*x1^(-7/2)*x2^(-9/2)*x3^(3/2) + (2*q^(10) + 4*q^(9) + 8*q^(8) + 4*q^(7) + 2*q^(6))*x1^(-7/2)*x2^(-9/2)*x3^(1/2) + (-q^(12) - 4*q^(11) - 5*q^(10) - 4*q^(9) - q^(8))*x1^(-7/2)*x2^(-9/2)*x3^(-1/2) + (2*q^(13) + 2*q^(12) + 2*q^(11))*x1^(-7/2)*x2^(-9/2)*x3^(-3/2) + (-q^(14))*x1^(-7/2)*x2^(-9/2)*x3^(-5/2) + (2*q + 2*1 + 2*q^(-1) + 2*q^(-2))*x1^(-7/2)*x2^(-11/2)*x3^(9/2) + (-2*q^(5) - 6*q^(4) - 10*q^(3) - 14*q^(2) - 10*q - 6*1 - 2*q^(-1))*x1^(-7/2)*x2^(-11/2)*x3^(7/2) + (4*q^(8) + 10*q^(7) + 22*q^(6) + 32*q^(5) + 32*q^(4) + 24*q^(3) + 10*q^(2) + 4*q)*x1^(-7/2)*x2^(-11/2)*x3^(5/2) + (-2*q^(11) - 10*q^(10) - 24*q^(9) - 40*q^(8) - 54*q^(7) - 46*q^(6) - 30*q^(5) - 12*q^(4) - 2*q^(3))*x1^(-7/2)*x2^(-11/2)*x3^(3/2) + (4*q^(13) + 12*q^(12) + 30*q^(11) + 46*q^(10) + 52*q^(9) + 46*q^(8) + 22*q^(7) + 8*q^(6))*x1^(-7/2)*x2^(-11/2)*x3^(1/2) + (-2*q^(15) - 10*q^(14) - 20*q^(13) - 32*q^(12) - 34*q^(11) - 26*q^(10) - 12*q^(9) - 2*q^(8))*x1^(-7/2)*x2^(-11/2)*x3^(-1/2) + (4*q^(16) + 8*q^(15) + 12*q^(14) + 14*q^(13) + 8*q^(12) + 4*q^(11))*x1^(-7/2)*x2^(-11/2)*x3^(-3/2) + (-2*q^(17) - 2*q^(16) - 2*q^(15) - 2*q^(14))*x1^(-7/2)*x2^(-11/2)*x3^(-5/2) + (-q^(2))*x1^(-9/2)*x2^(-11/2)*x3^(9/2) + (2*q^(6) + 2*q^(5) + 2*q^(4) + 2*q^(3))*x1^(-9/2)*x2^(-11/2)*x3^(7/2) + (-q^(10) - 4*q^(9) - 5*q^(8) - 8*q^(7) - 5*q^(6) - 4*q^(5) - q^(4))*x1^(-9/2)*x2^(-11/2)*x3^(5/2) + (2*q^(13) + 4*q^(12) + 10*q^(11) + 12*q^(10) + 12*q^(9) + 10*q^(8) + 4*q^(7) + 2*q^(6))*x1^(-9/2)*x2^(-11/2)*x3^(3/2) + (-q^(16) - 4*q^(15) - 9*q^(14) - 12*q^(13) - 18*q^(12) - 12*q^(11) - 9*q^(10) - 4*q^(9) - q^(8))*x1^(-9/2)*x2^(-11/2)*x3^(1/2) + (2*q^(18) + 4*q^(17) + 10*q^(16) + 12*q^(15) + 12*q^(14) + 10*q^(13) + 4*q^(12) + 2*q^(11))*x1^(-9/2)*x2^(-11/2)*x3^(-1/2) + (-q^(20) - 4*q^(19) - 5*q^(18) - 8*q^(17) - 5*q^(16) - 4*q^(15) - q^(14))*x1^(-9/2)*x2^(-11/2)*x3^(-3/2) + (2*q^(21) + 2*q^(20) + 2*q^(19) + 2*q^(18))*x1^(-9/2)*x2^(-11/2)*x3^(-5/2) + (-q^(22))*x1^(-9/2)*x2^(-11/2)*x3^(-7/2)

Braid

Braid word Components Crossings Strands
[2, 3, 4, 4, 3, 2, 3, 1, -2, 3, 3, -4, 2, -3, -4, 1] 3 16 5

Multivariable Alexander polynomial

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

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

Interactive 3D view · hover a vertex for coordinates

Dual Thurston polytope

VertexDual to fibered face
(-1, 1, 1) yes
(1, 3, -1) yes
(1, -1, -1) yes
(-1, 1, -3) yes
(1, -1, 3) yes
(-1, -3, 1) yes
Interactive 3D view · hover a vertex for coordinates

HFL polytope

Poincaré polynomial
m^(-6)*A1^(-1)*A2^(-2) + 2*m^(-6)*A1^(-1)*A2^(-1)*A3^(-1) + m^(-6)*A1^(-1)*A3^(-2) + m^(-5)*A1^(-1)*A2^(-2)*A3 + 5*m^(-5)*A1^(-1)*A2^(-1) + 5*m^(-5)*A1^(-1)*A3^(-1) + m^(-5)*A1^(-1)*A2*A3^(-2) + m^(-5)*A2^(-2) + 3*m^(-5)*A2^(-1)*A3^(-1) + m^(-5)*A3^(-2) + 3*m^(-4)*A1^(-1)*A2^(-1)*A3 + 7*m^(-4)*A1^(-1) + 3*m^(-4)*A1^(-1)*A2*A3^(-1) + m^(-4)*A2^(-2)*A3 + 8*m^(-4)*A2^(-1) + 8*m^(-4)*A3^(-1) + m^(-4)*A2*A3^(-2) + m^(-4)*A1*A2^(-1)*A3^(-1) + 3*m^(-3)*A1^(-1)*A3 + 3*m^(-3)*A1^(-1)*A2 + 6*m^(-3)*A2^(-1)*A3 + 14*m^(-3) + 6*m^(-3)*A2*A3^(-1) + 3*m^(-3)*A1*A2^(-1) + 3*m^(-3)*A1*A3^(-1) + m^(-2)*A1^(-1)*A2*A3 + m^(-2)*A2^(-1)*A3^2 + 8*m^(-2)*A3 + 8*m^(-2)*A2 + m^(-2)*A2^2*A3^(-1) + 3*m^(-2)*A1*A2^(-1)*A3 + 7*m^(-2)*A1 + 3*m^(-2)*A1*A2*A3^(-1) + m^(-1)*A3^2 + 3*m^(-1)*A2*A3 + m^(-1)*A2^2 + m^(-1)*A1*A2^(-1)*A3^2 + 5*m^(-1)*A1*A3 + 5*m^(-1)*A1*A2 + m^(-1)*A1*A2^2*A3^(-1) + A1*A3^2 + 2*A1*A2*A3 + A1*A2^2
VertexMaslovRank
(-1, -2, 0)-61
(-1, -2, 1)-51
(-1, 0, -2)-61
(-1, 1, -2)-51
(-1, 1, 1)-21
(0, -2, 0)-51
(0, -2, 1)-41
(0, -1, 2)-21
(0, 0, -2)-51
(0, 0, 2)-11
(0, 1, -2)-41
(0, 2, -1)-21
(0, 2, 0)-11
(1, -1, -1)-41
(1, -1, 2)-11
(1, 0, 2)01
(1, 2, -1)-11
(1, 2, 0)01
Interactive 3D view · hover a vertex for coordinates

Record

FL/HFL Links

orderOption(int) 2231
namestring L10n81{1;0}
statusstring success
slugstring L10n81_1_0_6743fa2d
result_filestring details/L10n81_1_0_6743fa2d.json
complexity_scoreOption(int) 300
strandsOption(int) null
crossingsOption(int) 10
component_countOption(int) 3
girthOption(int) 6
total_rankOption(int) 144
wall_secondsOption(float) 0.002161
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 3
support_sizeOption(int) 43
vertex_countOption(int) 18
fibered_vertex_countOption(int) 6
polytope_statusstring computed
alexander_support_sizeOption(int) 12
alexander_vertex_countOption(int) 6
alexander_relationstring not_computed
fk_countint 2
detailsRowRef(FLHFLLinks)
{
  "dataset": "FLHFLLinks",
  "key": "L10n81_1_0_6743fa2d"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L10n81_1_0_6743fa2d