details/L10n84_1_1_74c3f12d.json

FL expansions

Newt(ΔL) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle FL
(1/2, -1, -1) (1/3, 1/3, 1) x1^(-1/2)x2^(1)x3^(1) q^(-1) 
{"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]}
 
(-q^(5))*x1^(-9/2)*x2^(-3)*x3^(5) + (q^(4) + q^(3) + q^(2) + q)*x1^(-9/2)*x2^(-2)*x3^(5) + (-q^(2) - q - 3*1 - 2*q^(-1) - 2*q^(-2) - q^(-3) - q^(-4))*x1^(-9/2)*x2^(-1)*x3^(5) + (2*q^(-1) + 3*q^(-2) + 4*q^(-3) + 5*q^(-4) + 4*q^(-5) + 3*q^(-6) + 2*q^(-7) + q^(-8))*x1^(-9/2)*x3^(5) + (-q^(-3) - 2*q^(-4) - 6*q^(-5) - 6*q^(-6) - 8*q^(-7) - 7*q^(-8) - 7*q^(-9) - 4*q^(-10) - 3*q^(-11) - q^(-12) - q^(-13))*x1^(-9/2)*x2*x3^(5) + (2*q^(-6) + 4*q^(-7) + 7*q^(-8) + 10*q^(-9) + 12*q^(-10) + 12*q^(-11) + 11*q^(-12) + 9*q^(-13) + 6*q^(-14) + 4*q^(-15) + 2*q^(-16) + q^(-17))*x1^(-9/2)*x2^(2)*x3^(5) + (-q^(-8) - 2*q^(-9) - 7*q^(-10) - 9*q^(-11) - 14*q^(-12) - 16*q^(-13) - 19*q^(-14) - 16*q^(-15) - 16*q^(-16) - 11*q^(-17) - 9*q^(-18) - 5*q^(-19) - 3*q^(-20) - q^(-21) - q^(-22))*x1^(-9/2)*x2^(3)*x3^(5) + (2*q^(-11) + 4*q^(-12) + 8*q^(-13) + 13*q^(-14) + 18*q^(-15) + 22*q^(-16) + 25*q^(-17) + 25*q^(-18) + 23*q^(-19) + 20*q^(-20) + 15*q^(-21) + 11*q^(-22) + 7*q^(-23) + 4*q^(-24) + 2*q^(-25) + q^(-26))*x1^(-9/2)*x2^(4)*x3^(5) + (-q^(-13) - 2*q^(-14) - 7*q^(-15) - 10*q^(-16) - 17*q^(-17) - 22*q^(-18) - 30*q^(-19) - 31*q^(-20) - 35*q^(-21) - 32*q^(-22) - 31*q^(-23) - 24*q^(-24) - 20*q^(-25) - 13*q^(-26) - 10*q^(-27) - 5*q^(-28) - 3*q^(-29) - q^(-30) - q^(-31))*x1^(-9/2)*x2^(5)*x3^(5) + (q^(2))*x1^(-7/2)*x2^(-2)*x3^(4) + (-q - 1 - q^(-1))*x1^(-7/2)*x2^(-1)*x3^(4) + (1 + q^(-1) + q^(-2))*x1^(-7/2)*x2^(-1)*x3^(5) + (q^(-1) + 2*q^(-2) + 2*q^(-3) + q^(-4) + q^(-5))*x1^(-7/2)*x3^(4) + (-q^(-2) - 3*q^(-3) - 3*q^(-4) - 2*q^(-5) - q^(-6))*x1^(-7/2)*x3^(5) + (-q^(-3) - 3*q^(-4) - 3*q^(-5) - 3*q^(-6) - 2*q^(-7) - q^(-8))*x1^(-7/2)*x2*x3^(4) + (q^(-4) + 4*q^(-5) + 6*q^(-6) + 8*q^(-7) + 5*q^(-8) + 3*q^(-9) + q^(-10))*x1^(-7/2)*x2*x3^(5) + (q^(-5) + 3*q^(-6) + 4*q^(-7) + 5*q^(-8) + 4*q^(-9) + 3*q^(-10) + q^(-11) + q^(-12))*x1^(-7/2)*x2^(2)*x3^(4) + (-q^(-6) - 4*q^(-7) - 9*q^(-8) - 13*q^(-9) - 14*q^(-10) - 11*q^(-11) - 6*q^(-12) - 3*q^(-13) - q^(-14))*x1^(-7/2)*x2^(2)*x3^(5) + (-q^(-7) - 3*q^(-8) - 5*q^(-9) - 6*q^(-10) - 7*q^(-11) - 5*q^(-12) - 4*q^(-13) - 2*q^(-14) - q^(-15))*x1^(-7/2)*x2^(3)*x3^(4) + (q^(-8) + 4*q^(-9) + 10*q^(-10) + 17*q^(-11) + 24*q^(-12) + 23*q^(-13) + 20*q^(-14) + 13*q^(-15) + 7*q^(-16) + 3*q^(-17) + q^(-18))*x1^(-7/2)*x2^(3)*x3^(5) + (q^(-9) + 3*q^(-10) + 5*q^(-11) + 7*q^(-12) + 9*q^(-13) + 8*q^(-14) + 7*q^(-15) + 5*q^(-16) + 3*q^(-17) + q^(-18) + q^(-19))*x1^(-7/2)*x2^(4)*x3^(4) + (-q^(-10) - 4*q^(-11) - 10*q^(-12) - 20*q^(-13) - 30*q^(-14) - 37*q^(-15) - 38*q^(-16) - 32*q^(-17) - 23*q^(-18) - 14*q^(-19) - 7*q^(-20) - 3*q^(-21) - q^(-22))*x1^(-7/2)*x2^(4)*x3^(5) + (-q^(-11) - 3*q^(-12) - 5*q^(-13) - 8*q^(-14) - 10*q^(-15) - 11*q^(-16) - 10*q^(-17) - 9*q^(-18) - 6*q^(-19) - 4*q^(-20) - 2*q^(-21) - q^(-22))*x1^(-7/2)*x2^(5)*x3^(4) + (q^(-12) + 4*q^(-13) + 10*q^(-14) + 21*q^(-15) + 34*q^(-16) + 48*q^(-17) + 55*q^(-18) + 57*q^(-19) + 49*q^(-20) + 38*q^(-21) + 25*q^(-22) + 15*q^(-23) + 7*q^(-24) + 3*q^(-25) + q^(-26))*x1^(-7/2)*x2^(5)*x3^(5) + (-1)*x1^(-5/2)*x2^(-1)*x3^(3) + (q^(-1) + q^(-2))*x1^(-5/2)*x3^(3) + (-q^(-2) - q^(-3))*x1^(-5/2)*x3^(4) + (-2*q^(-3) - q^(-4) - q^(-5))*x1^(-5/2)*x2*x3^(3) + (2*q^(-4) + 2*q^(-5) + q^(-6))*x1^(-5/2)*x2*x3^(4) + (-q^(-6))*x1^(-5/2)*x2*x3^(5) + (q^(-4) + 2*q^(-5) + 2*q^(-6) + q^(-7))*x1^(-5/2)*x2^(2)*x3^(3) + (-q^(-5) - 3*q^(-6) - 5*q^(-7) - 3*q^(-8) - q^(-9))*x1^(-5/2)*x2^(2)*x3^(4) + (q^(-7) + 2*q^(-8) + 2*q^(-9) + q^(-10))*x1^(-5/2)*x2^(2)*x3^(5) + (-2*q^(-6) - 2*q^(-7) - 3*q^(-8) - q^(-9) - q^(-10))*x1^(-5/2)*x2^(3)*x3^(3) + (2*q^(-7) + 5*q^(-8) + 8*q^(-9) + 6*q^(-10) + 3*q^(-11) + q^(-12))*x1^(-5/2)*x2^(3)*x3^(4) + (-2*q^(-9) - 4*q^(-10) - 7*q^(-11) - 4*q^(-12) - 2*q^(-13))*x1^(-5/2)*x2^(3)*x3^(5) + (q^(-7) + 2*q^(-8) + 3*q^(-9) + 3*q^(-10) + 2*q^(-11) + q^(-12))*x1^(-5/2)*x2^(4)*x3^(3) + (-q^(-8) - 3*q^(-9) - 8*q^(-10) - 11*q^(-11) - 11*q^(-12) - 7*q^(-13) - 3*q^(-14) - q^(-15))*x1^(-5/2)*x2^(4)*x3^(4) + (q^(-10) + 3*q^(-11) + 8*q^(-12) + 12*q^(-13) + 12*q^(-14) + 8*q^(-15) + 3*q^(-16) + q^(-17))*x1^(-5/2)*x2^(4)*x3^(5) + (-2*q^(-9) - 2*q^(-10) - 4*q^(-11) - 3*q^(-12) - 3*q^(-13) - q^(-14) - q^(-15))*x1^(-5/2)*x2^(5)*x3^(3) + (2*q^(-10) + 5*q^(-11) + 11*q^(-12) + 15*q^(-13) + 16*q^(-14) + 12*q^(-15) + 7*q^(-16) + 3*q^(-17) + q^(-18))*x1^(-5/2)*x2^(5)*x3^(4) + (-2*q^(-12) - 5*q^(-13) - 13*q^(-14) - 19*q^(-15) - 25*q^(-16) - 19*q^(-17) - 13*q^(-18) - 5*q^(-19) - 2*q^(-20))*x1^(-5/2)*x2^(5)*x3^(5) + (q^(-1))*x1^(-3/2)*x3^(2) + (-q^(-2))*x1^(-3/2)*x2*x3^(2) + (q^(-3))*x1^(-3/2)*x2*x3^(3) + (q^(-3) + q^(-4))*x1^(-3/2)*x2^(2)*x3^(2) + (-q^(-4) - q^(-5))*x1^(-3/2)*x2^(2)*x3^(3) + (-q^(-4) - q^(-5))*x1^(-3/2)*x2^(3)*x3^(2) + (q^(-5) + 3*q^(-6) + q^(-7))*x1^(-3/2)*x2^(3)*x3^(3) + (-q^(-7) - q^(-8))*x1^(-3/2)*x2^(3)*x3^(4) + (q^(-5) + q^(-6) + q^(-7))*x1^(-3/2)*x2^(4)*x3^(2) + (-q^(-6) - 3*q^(-7) - 3*q^(-8) - q^(-9))*x1^(-3/2)*x2^(4)*x3^(3) + (q^(-8) + 2*q^(-9) + 2*q^(-10))*x1^(-3/2)*x2^(4)*x3^(4) + (-q^(-6) - q^(-7) - q^(-8))*x1^(-3/2)*x2^(5)*x3^(2) + (q^(-7) + 3*q^(-8) + 5*q^(-9) + 3*q^(-10) + q^(-11))*x1^(-3/2)*x2^(5)*x3^(3) + (-q^(-9) - 3*q^(-10) - 5*q^(-11) - 3*q^(-12) - q^(-13))*x1^(-3/2)*x2^(5)*x3^(4) + (q^(-12) + q^(-13) + q^(-14))*x1^(-3/2)*x2^(5)*x3^(5) + (-q^(-1))*x1^(-1/2)*x2*x3 + (-q^(-2))*x1^(-1/2)*x2^(3)*x3 + (q^(-3))*x1^(-1/2)*x2^(3)*x3^(2) + (-q^(-4))*x1^(-1/2)*x2^(4)*x3^(2) + (-q^(-3))*x1^(-1/2)*x2^(5)*x3 + (q^(-4) + q^(-5))*x1^(-1/2)*x2^(5)*x3^(2) + (-q^(-6))*x1^(-1/2)*x2^(5)*x3^(3)
(-1/2, -2, 0) (1, 1, 1) x1^(1/2)x2^(2)x3^(0) q^(0) 
{"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]}
 
(-1)*x1^(1/2)*x2^(2) + (-1)*x1^(1/2)*x2^(3) + (q^(-1))*x1^(1/2)*x2^(3)*x3 + (-1)*x1^(1/2)*x2^(4) + (q^(-1) + q^(-2))*x1^(1/2)*x2^(4)*x3 + (-q^(-3))*x1^(1/2)*x2^(4)*x3^(2) + (-1)*x1^(1/2)*x2^(5) + (q^(-2) + q^(-3))*x1^(1/2)*x2^(5)*x3 + (-q^(-3) - q^(-4) - q^(-5))*x1^(1/2)*x2^(5)*x3^(2) + (q^(-6))*x1^(1/2)*x2^(5)*x3^(3) + (q^(2))*x1^(3/2)*x2^(3)*x3^(-1) + (q^(3) + q^(2))*x1^(3/2)*x2^(4)*x3^(-1) + (-q^(2) - q)*x1^(3/2)*x2^(4) + (q^(3) + q^(2))*x1^(3/2)*x2^(5)*x3^(-1) + (-2*q^(2) - 2*q - 1)*x1^(3/2)*x2^(5) + (q + 1 + q^(-1))*x1^(3/2)*x2^(5)*x3 + (-q^(5))*x1^(5/2)*x2^(4)*x3^(-2) + (-q^(7) - q^(6) - q^(5))*x1^(5/2)*x2^(5)*x3^(-2) + (q^(6) + q^(5) + q^(4))*x1^(5/2)*x2^(5)*x3^(-1) + (q^(9))*x1^(7/2)*x2^(5)*x3^(-3)
(1/2, -1, -1) (1/3, 1/3, 1) x1^(-1/2)x2^(1)x3^(1) q^(-1) 
{"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]}
 
(-q^(5))*x1^(-9/2)*x2^(-3)*x3^(5) + (q^(4) + q^(3) + q^(2) + q)*x1^(-9/2)*x2^(-2)*x3^(5) + (-q^(2) - q - 3*1 - 2*q^(-1) - 2*q^(-2) - q^(-3) - q^(-4))*x1^(-9/2)*x2^(-1)*x3^(5) + (2*q^(-1) + 3*q^(-2) + 4*q^(-3) + 5*q^(-4) + 4*q^(-5) + 3*q^(-6) + 2*q^(-7) + q^(-8))*x1^(-9/2)*x3^(5) + (-q^(-3) - 2*q^(-4) - 6*q^(-5) - 6*q^(-6) - 8*q^(-7) - 7*q^(-8) - 7*q^(-9) - 4*q^(-10) - 3*q^(-11) - q^(-12) - q^(-13))*x1^(-9/2)*x2*x3^(5) + (2*q^(-6) + 4*q^(-7) + 7*q^(-8) + 10*q^(-9) + 12*q^(-10) + 12*q^(-11) + 11*q^(-12) + 9*q^(-13) + 6*q^(-14) + 4*q^(-15) + 2*q^(-16) + q^(-17))*x1^(-9/2)*x2^(2)*x3^(5) + (-q^(-8) - 2*q^(-9) - 7*q^(-10) - 9*q^(-11) - 14*q^(-12) - 16*q^(-13) - 19*q^(-14) - 16*q^(-15) - 16*q^(-16) - 11*q^(-17) - 9*q^(-18) - 5*q^(-19) - 3*q^(-20) - q^(-21) - q^(-22))*x1^(-9/2)*x2^(3)*x3^(5) + (2*q^(-11) + 4*q^(-12) + 8*q^(-13) + 13*q^(-14) + 18*q^(-15) + 22*q^(-16) + 25*q^(-17) + 25*q^(-18) + 23*q^(-19) + 20*q^(-20) + 15*q^(-21) + 11*q^(-22) + 7*q^(-23) + 4*q^(-24) + 2*q^(-25) + q^(-26))*x1^(-9/2)*x2^(4)*x3^(5) + (-q^(-13) - 2*q^(-14) - 7*q^(-15) - 10*q^(-16) - 17*q^(-17) - 22*q^(-18) - 30*q^(-19) - 31*q^(-20) - 35*q^(-21) - 32*q^(-22) - 31*q^(-23) - 24*q^(-24) - 20*q^(-25) - 13*q^(-26) - 10*q^(-27) - 5*q^(-28) - 3*q^(-29) - q^(-30) - q^(-31))*x1^(-9/2)*x2^(5)*x3^(5) + (q^(2))*x1^(-7/2)*x2^(-2)*x3^(4) + (-q - 1 - q^(-1))*x1^(-7/2)*x2^(-1)*x3^(4) + (1 + q^(-1) + q^(-2))*x1^(-7/2)*x2^(-1)*x3^(5) + (q^(-1) + 2*q^(-2) + 2*q^(-3) + q^(-4) + q^(-5))*x1^(-7/2)*x3^(4) + (-q^(-2) - 3*q^(-3) - 3*q^(-4) - 2*q^(-5) - q^(-6))*x1^(-7/2)*x3^(5) + (-q^(-3) - 3*q^(-4) - 3*q^(-5) - 3*q^(-6) - 2*q^(-7) - q^(-8))*x1^(-7/2)*x2*x3^(4) + (q^(-4) + 4*q^(-5) + 6*q^(-6) + 8*q^(-7) + 5*q^(-8) + 3*q^(-9) + q^(-10))*x1^(-7/2)*x2*x3^(5) + (q^(-5) + 3*q^(-6) + 4*q^(-7) + 5*q^(-8) + 4*q^(-9) + 3*q^(-10) + q^(-11) + q^(-12))*x1^(-7/2)*x2^(2)*x3^(4) + (-q^(-6) - 4*q^(-7) - 9*q^(-8) - 13*q^(-9) - 14*q^(-10) - 11*q^(-11) - 6*q^(-12) - 3*q^(-13) - q^(-14))*x1^(-7/2)*x2^(2)*x3^(5) + (-q^(-7) - 3*q^(-8) - 5*q^(-9) - 6*q^(-10) - 7*q^(-11) - 5*q^(-12) - 4*q^(-13) - 2*q^(-14) - q^(-15))*x1^(-7/2)*x2^(3)*x3^(4) + (q^(-8) + 4*q^(-9) + 10*q^(-10) + 17*q^(-11) + 24*q^(-12) + 23*q^(-13) + 20*q^(-14) + 13*q^(-15) + 7*q^(-16) + 3*q^(-17) + q^(-18))*x1^(-7/2)*x2^(3)*x3^(5) + (q^(-9) + 3*q^(-10) + 5*q^(-11) + 7*q^(-12) + 9*q^(-13) + 8*q^(-14) + 7*q^(-15) + 5*q^(-16) + 3*q^(-17) + q^(-18) + q^(-19))*x1^(-7/2)*x2^(4)*x3^(4) + (-q^(-10) - 4*q^(-11) - 10*q^(-12) - 20*q^(-13) - 30*q^(-14) - 37*q^(-15) - 38*q^(-16) - 32*q^(-17) - 23*q^(-18) - 14*q^(-19) - 7*q^(-20) - 3*q^(-21) - q^(-22))*x1^(-7/2)*x2^(4)*x3^(5) + (-q^(-11) - 3*q^(-12) - 5*q^(-13) - 8*q^(-14) - 10*q^(-15) - 11*q^(-16) - 10*q^(-17) - 9*q^(-18) - 6*q^(-19) - 4*q^(-20) - 2*q^(-21) - q^(-22))*x1^(-7/2)*x2^(5)*x3^(4) + (q^(-12) + 4*q^(-13) + 10*q^(-14) + 21*q^(-15) + 34*q^(-16) + 48*q^(-17) + 55*q^(-18) + 57*q^(-19) + 49*q^(-20) + 38*q^(-21) + 25*q^(-22) + 15*q^(-23) + 7*q^(-24) + 3*q^(-25) + q^(-26))*x1^(-7/2)*x2^(5)*x3^(5) + (-1)*x1^(-5/2)*x2^(-1)*x3^(3) + (q^(-1) + q^(-2))*x1^(-5/2)*x3^(3) + (-q^(-2) - q^(-3))*x1^(-5/2)*x3^(4) + (-2*q^(-3) - q^(-4) - q^(-5))*x1^(-5/2)*x2*x3^(3) + (2*q^(-4) + 2*q^(-5) + q^(-6))*x1^(-5/2)*x2*x3^(4) + (-q^(-6))*x1^(-5/2)*x2*x3^(5) + (q^(-4) + 2*q^(-5) + 2*q^(-6) + q^(-7))*x1^(-5/2)*x2^(2)*x3^(3) + (-q^(-5) - 3*q^(-6) - 5*q^(-7) - 3*q^(-8) - q^(-9))*x1^(-5/2)*x2^(2)*x3^(4) + (q^(-7) + 2*q^(-8) + 2*q^(-9) + q^(-10))*x1^(-5/2)*x2^(2)*x3^(5) + (-2*q^(-6) - 2*q^(-7) - 3*q^(-8) - q^(-9) - q^(-10))*x1^(-5/2)*x2^(3)*x3^(3) + (2*q^(-7) + 5*q^(-8) + 8*q^(-9) + 6*q^(-10) + 3*q^(-11) + q^(-12))*x1^(-5/2)*x2^(3)*x3^(4) + (-2*q^(-9) - 4*q^(-10) - 7*q^(-11) - 4*q^(-12) - 2*q^(-13))*x1^(-5/2)*x2^(3)*x3^(5) + (q^(-7) + 2*q^(-8) + 3*q^(-9) + 3*q^(-10) + 2*q^(-11) + q^(-12))*x1^(-5/2)*x2^(4)*x3^(3) + (-q^(-8) - 3*q^(-9) - 8*q^(-10) - 11*q^(-11) - 11*q^(-12) - 7*q^(-13) - 3*q^(-14) - q^(-15))*x1^(-5/2)*x2^(4)*x3^(4) + (q^(-10) + 3*q^(-11) + 8*q^(-12) + 12*q^(-13) + 12*q^(-14) + 8*q^(-15) + 3*q^(-16) + q^(-17))*x1^(-5/2)*x2^(4)*x3^(5) + (-2*q^(-9) - 2*q^(-10) - 4*q^(-11) - 3*q^(-12) - 3*q^(-13) - q^(-14) - q^(-15))*x1^(-5/2)*x2^(5)*x3^(3) + (2*q^(-10) + 5*q^(-11) + 11*q^(-12) + 15*q^(-13) + 16*q^(-14) + 12*q^(-15) + 7*q^(-16) + 3*q^(-17) + q^(-18))*x1^(-5/2)*x2^(5)*x3^(4) + (-2*q^(-12) - 5*q^(-13) - 13*q^(-14) - 19*q^(-15) - 25*q^(-16) - 19*q^(-17) - 13*q^(-18) - 5*q^(-19) - 2*q^(-20))*x1^(-5/2)*x2^(5)*x3^(5) + (q^(-1))*x1^(-3/2)*x3^(2) + (-q^(-2))*x1^(-3/2)*x2*x3^(2) + (q^(-3))*x1^(-3/2)*x2*x3^(3) + (q^(-3) + q^(-4))*x1^(-3/2)*x2^(2)*x3^(2) + (-q^(-4) - q^(-5))*x1^(-3/2)*x2^(2)*x3^(3) + (-q^(-4) - q^(-5))*x1^(-3/2)*x2^(3)*x3^(2) + (q^(-5) + 3*q^(-6) + q^(-7))*x1^(-3/2)*x2^(3)*x3^(3) + (-q^(-7) - q^(-8))*x1^(-3/2)*x2^(3)*x3^(4) + (q^(-5) + q^(-6) + q^(-7))*x1^(-3/2)*x2^(4)*x3^(2) + (-q^(-6) - 3*q^(-7) - 3*q^(-8) - q^(-9))*x1^(-3/2)*x2^(4)*x3^(3) + (q^(-8) + 2*q^(-9) + 2*q^(-10))*x1^(-3/2)*x2^(4)*x3^(4) + (-q^(-6) - q^(-7) - q^(-8))*x1^(-3/2)*x2^(5)*x3^(2) + (q^(-7) + 3*q^(-8) + 5*q^(-9) + 3*q^(-10) + q^(-11))*x1^(-3/2)*x2^(5)*x3^(3) + (-q^(-9) - 3*q^(-10) - 5*q^(-11) - 3*q^(-12) - q^(-13))*x1^(-3/2)*x2^(5)*x3^(4) + (q^(-12) + q^(-13) + q^(-14))*x1^(-3/2)*x2^(5)*x3^(5) + (-q^(-1))*x1^(-1/2)*x2*x3 + (-q^(-2))*x1^(-1/2)*x2^(3)*x3 + (q^(-3))*x1^(-1/2)*x2^(3)*x3^(2) + (-q^(-4))*x1^(-1/2)*x2^(4)*x3^(2) + (-q^(-3))*x1^(-1/2)*x2^(5)*x3 + (q^(-4) + q^(-5))*x1^(-1/2)*x2^(5)*x3^(2) + (-q^(-6))*x1^(-1/2)*x2^(5)*x3^(3)
(-1/2, -2, 0) (1, 1, 1) x1^(1/2)x2^(2)x3^(0) q^(0) 
{"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]}
 
(-1)*x1^(1/2)*x2^(2) + (-1)*x1^(1/2)*x2^(3) + (q^(-1))*x1^(1/2)*x2^(3)*x3 + (-1)*x1^(1/2)*x2^(4) + (q^(-1) + q^(-2))*x1^(1/2)*x2^(4)*x3 + (-q^(-3))*x1^(1/2)*x2^(4)*x3^(2) + (-1)*x1^(1/2)*x2^(5) + (q^(-2) + q^(-3))*x1^(1/2)*x2^(5)*x3 + (-q^(-3) - q^(-4) - q^(-5))*x1^(1/2)*x2^(5)*x3^(2) + (q^(-6))*x1^(1/2)*x2^(5)*x3^(3) + (q^(2))*x1^(3/2)*x2^(3)*x3^(-1) + (q^(3) + q^(2))*x1^(3/2)*x2^(4)*x3^(-1) + (-q^(2) - q)*x1^(3/2)*x2^(4) + (q^(3) + q^(2))*x1^(3/2)*x2^(5)*x3^(-1) + (-2*q^(2) - 2*q - 1)*x1^(3/2)*x2^(5) + (q + 1 + q^(-1))*x1^(3/2)*x2^(5)*x3 + (-q^(5))*x1^(5/2)*x2^(4)*x3^(-2) + (-q^(7) - q^(6) - q^(5))*x1^(5/2)*x2^(5)*x3^(-2) + (q^(6) + q^(5) + q^(4))*x1^(5/2)*x2^(5)*x3^(-1) + (q^(9))*x1^(7/2)*x2^(5)*x3^(-3)
(-1/2, 1, 1) x1^(1/2)x2^(-1)x3^(-1) q^(-1) 
(-q^(5))*x1^(9/2)*x2^(3)*x3^(-5) + (q^(4) + q^(3) + q^(2) + q)*x1^(9/2)*x2^(2)*x3^(-5) + (-q^(2) - q - 3*1 - 2*q^(-1) - 2*q^(-2) - q^(-3) - q^(-4))*x1^(9/2)*x2*x3^(-5) + (2*q^(-1) + 3*q^(-2) + 4*q^(-3) + 5*q^(-4) + 4*q^(-5) + 3*q^(-6) + 2*q^(-7) + q^(-8))*x1^(9/2)*x3^(-5) + (-q^(-3) - 2*q^(-4) - 6*q^(-5) - 6*q^(-6) - 8*q^(-7) - 7*q^(-8) - 7*q^(-9) - 4*q^(-10) - 3*q^(-11) - q^(-12) - q^(-13))*x1^(9/2)*x2^(-1)*x3^(-5) + (2*q^(-6) + 4*q^(-7) + 7*q^(-8) + 10*q^(-9) + 12*q^(-10) + 12*q^(-11) + 11*q^(-12) + 9*q^(-13) + 6*q^(-14) + 4*q^(-15) + 2*q^(-16) + q^(-17))*x1^(9/2)*x2^(-2)*x3^(-5) + (-q^(-8) - 2*q^(-9) - 7*q^(-10) - 9*q^(-11) - 14*q^(-12) - 16*q^(-13) - 19*q^(-14) - 16*q^(-15) - 16*q^(-16) - 11*q^(-17) - 9*q^(-18) - 5*q^(-19) - 3*q^(-20) - q^(-21) - q^(-22))*x1^(9/2)*x2^(-3)*x3^(-5) + (2*q^(-11) + 4*q^(-12) + 8*q^(-13) + 13*q^(-14) + 18*q^(-15) + 22*q^(-16) + 25*q^(-17) + 25*q^(-18) + 23*q^(-19) + 20*q^(-20) + 15*q^(-21) + 11*q^(-22) + 7*q^(-23) + 4*q^(-24) + 2*q^(-25) + q^(-26))*x1^(9/2)*x2^(-4)*x3^(-5) + (-q^(-13) - 2*q^(-14) - 7*q^(-15) - 10*q^(-16) - 17*q^(-17) - 22*q^(-18) - 30*q^(-19) - 31*q^(-20) - 35*q^(-21) - 32*q^(-22) - 31*q^(-23) - 24*q^(-24) - 20*q^(-25) - 13*q^(-26) - 10*q^(-27) - 5*q^(-28) - 3*q^(-29) - q^(-30) - q^(-31))*x1^(9/2)*x2^(-5)*x3^(-5) + (q^(2))*x1^(7/2)*x2^(2)*x3^(-4) + (-q - 1 - q^(-1))*x1^(7/2)*x2*x3^(-4) + (1 + q^(-1) + q^(-2))*x1^(7/2)*x2*x3^(-5) + (q^(-1) + 2*q^(-2) + 2*q^(-3) + q^(-4) + q^(-5))*x1^(7/2)*x3^(-4) + (-q^(-2) - 3*q^(-3) - 3*q^(-4) - 2*q^(-5) - q^(-6))*x1^(7/2)*x3^(-5) + (-q^(-3) - 3*q^(-4) - 3*q^(-5) - 3*q^(-6) - 2*q^(-7) - q^(-8))*x1^(7/2)*x2^(-1)*x3^(-4) + (q^(-4) + 4*q^(-5) + 6*q^(-6) + 8*q^(-7) + 5*q^(-8) + 3*q^(-9) + q^(-10))*x1^(7/2)*x2^(-1)*x3^(-5) + (q^(-5) + 3*q^(-6) + 4*q^(-7) + 5*q^(-8) + 4*q^(-9) + 3*q^(-10) + q^(-11) + q^(-12))*x1^(7/2)*x2^(-2)*x3^(-4) + (-q^(-6) - 4*q^(-7) - 9*q^(-8) - 13*q^(-9) - 14*q^(-10) - 11*q^(-11) - 6*q^(-12) - 3*q^(-13) - q^(-14))*x1^(7/2)*x2^(-2)*x3^(-5) + (-q^(-7) - 3*q^(-8) - 5*q^(-9) - 6*q^(-10) - 7*q^(-11) - 5*q^(-12) - 4*q^(-13) - 2*q^(-14) - q^(-15))*x1^(7/2)*x2^(-3)*x3^(-4) + (q^(-8) + 4*q^(-9) + 10*q^(-10) + 17*q^(-11) + 24*q^(-12) + 23*q^(-13) + 20*q^(-14) + 13*q^(-15) + 7*q^(-16) + 3*q^(-17) + q^(-18))*x1^(7/2)*x2^(-3)*x3^(-5) + (q^(-9) + 3*q^(-10) + 5*q^(-11) + 7*q^(-12) + 9*q^(-13) + 8*q^(-14) + 7*q^(-15) + 5*q^(-16) + 3*q^(-17) + q^(-18) + q^(-19))*x1^(7/2)*x2^(-4)*x3^(-4) + (-q^(-10) - 4*q^(-11) - 10*q^(-12) - 20*q^(-13) - 30*q^(-14) - 37*q^(-15) - 38*q^(-16) - 32*q^(-17) - 23*q^(-18) - 14*q^(-19) - 7*q^(-20) - 3*q^(-21) - q^(-22))*x1^(7/2)*x2^(-4)*x3^(-5) + (-q^(-11) - 3*q^(-12) - 5*q^(-13) - 8*q^(-14) - 10*q^(-15) - 11*q^(-16) - 10*q^(-17) - 9*q^(-18) - 6*q^(-19) - 4*q^(-20) - 2*q^(-21) - q^(-22))*x1^(7/2)*x2^(-5)*x3^(-4) + (q^(-12) + 4*q^(-13) + 10*q^(-14) + 21*q^(-15) + 34*q^(-16) + 48*q^(-17) + 55*q^(-18) + 57*q^(-19) + 49*q^(-20) + 38*q^(-21) + 25*q^(-22) + 15*q^(-23) + 7*q^(-24) + 3*q^(-25) + q^(-26))*x1^(7/2)*x2^(-5)*x3^(-5) + (-1)*x1^(5/2)*x2*x3^(-3) + (q^(-1) + q^(-2))*x1^(5/2)*x3^(-3) + (-q^(-2) - q^(-3))*x1^(5/2)*x3^(-4) + (-2*q^(-3) - q^(-4) - q^(-5))*x1^(5/2)*x2^(-1)*x3^(-3) + (2*q^(-4) + 2*q^(-5) + q^(-6))*x1^(5/2)*x2^(-1)*x3^(-4) + (-q^(-6))*x1^(5/2)*x2^(-1)*x3^(-5) + (q^(-4) + 2*q^(-5) + 2*q^(-6) + q^(-7))*x1^(5/2)*x2^(-2)*x3^(-3) + (-q^(-5) - 3*q^(-6) - 5*q^(-7) - 3*q^(-8) - q^(-9))*x1^(5/2)*x2^(-2)*x3^(-4) + (q^(-7) + 2*q^(-8) + 2*q^(-9) + q^(-10))*x1^(5/2)*x2^(-2)*x3^(-5) + (-2*q^(-6) - 2*q^(-7) - 3*q^(-8) - q^(-9) - q^(-10))*x1^(5/2)*x2^(-3)*x3^(-3) + (2*q^(-7) + 5*q^(-8) + 8*q^(-9) + 6*q^(-10) + 3*q^(-11) + q^(-12))*x1^(5/2)*x2^(-3)*x3^(-4) + (-2*q^(-9) - 4*q^(-10) - 7*q^(-11) - 4*q^(-12) - 2*q^(-13))*x1^(5/2)*x2^(-3)*x3^(-5) + (q^(-7) + 2*q^(-8) + 3*q^(-9) + 3*q^(-10) + 2*q^(-11) + q^(-12))*x1^(5/2)*x2^(-4)*x3^(-3) + (-q^(-8) - 3*q^(-9) - 8*q^(-10) - 11*q^(-11) - 11*q^(-12) - 7*q^(-13) - 3*q^(-14) - q^(-15))*x1^(5/2)*x2^(-4)*x3^(-4) + (q^(-10) + 3*q^(-11) + 8*q^(-12) + 12*q^(-13) + 12*q^(-14) + 8*q^(-15) + 3*q^(-16) + q^(-17))*x1^(5/2)*x2^(-4)*x3^(-5) + (-2*q^(-9) - 2*q^(-10) - 4*q^(-11) - 3*q^(-12) - 3*q^(-13) - q^(-14) - q^(-15))*x1^(5/2)*x2^(-5)*x3^(-3) + (2*q^(-10) + 5*q^(-11) + 11*q^(-12) + 15*q^(-13) + 16*q^(-14) + 12*q^(-15) + 7*q^(-16) + 3*q^(-17) + q^(-18))*x1^(5/2)*x2^(-5)*x3^(-4) + (-2*q^(-12) - 5*q^(-13) - 13*q^(-14) - 19*q^(-15) - 25*q^(-16) - 19*q^(-17) - 13*q^(-18) - 5*q^(-19) - 2*q^(-20))*x1^(5/2)*x2^(-5)*x3^(-5) + (q^(-1))*x1^(3/2)*x3^(-2) + (-q^(-2))*x1^(3/2)*x2^(-1)*x3^(-2) + (q^(-3))*x1^(3/2)*x2^(-1)*x3^(-3) + (q^(-3) + q^(-4))*x1^(3/2)*x2^(-2)*x3^(-2) + (-q^(-4) - q^(-5))*x1^(3/2)*x2^(-2)*x3^(-3) + (-q^(-4) - q^(-5))*x1^(3/2)*x2^(-3)*x3^(-2) + (q^(-5) + 3*q^(-6) + q^(-7))*x1^(3/2)*x2^(-3)*x3^(-3) + (-q^(-7) - q^(-8))*x1^(3/2)*x2^(-3)*x3^(-4) + (q^(-5) + q^(-6) + q^(-7))*x1^(3/2)*x2^(-4)*x3^(-2) + (-q^(-6) - 3*q^(-7) - 3*q^(-8) - q^(-9))*x1^(3/2)*x2^(-4)*x3^(-3) + (q^(-8) + 2*q^(-9) + 2*q^(-10))*x1^(3/2)*x2^(-4)*x3^(-4) + (-q^(-6) - q^(-7) - q^(-8))*x1^(3/2)*x2^(-5)*x3^(-2) + (q^(-7) + 3*q^(-8) + 5*q^(-9) + 3*q^(-10) + q^(-11))*x1^(3/2)*x2^(-5)*x3^(-3) + (-q^(-9) - 3*q^(-10) - 5*q^(-11) - 3*q^(-12) - q^(-13))*x1^(3/2)*x2^(-5)*x3^(-4) + (q^(-12) + q^(-13) + q^(-14))*x1^(3/2)*x2^(-5)*x3^(-5) + (-q^(-1))*x1^(1/2)*x2^(-1)*x3^(-1) + (-q^(-2))*x1^(1/2)*x2^(-3)*x3^(-1) + (q^(-3))*x1^(1/2)*x2^(-3)*x3^(-2) + (-q^(-4))*x1^(1/2)*x2^(-4)*x3^(-2) + (-q^(-3))*x1^(1/2)*x2^(-5)*x3^(-1) + (q^(-4) + q^(-5))*x1^(1/2)*x2^(-5)*x3^(-2) + (-q^(-6))*x1^(1/2)*x2^(-5)*x3^(-3)
(1/2, 2, 0) x1^(-1/2)x2^(-2)x3^(0) q^(0) 
(-1)*x1^(-1/2)*x2^(-2) + (-1)*x1^(-1/2)*x2^(-3) + (q^(-1))*x1^(-1/2)*x2^(-3)*x3^(-1) + (-1)*x1^(-1/2)*x2^(-4) + (q^(-1) + q^(-2))*x1^(-1/2)*x2^(-4)*x3^(-1) + (-q^(-3))*x1^(-1/2)*x2^(-4)*x3^(-2) + (-1)*x1^(-1/2)*x2^(-5) + (q^(-2) + q^(-3))*x1^(-1/2)*x2^(-5)*x3^(-1) + (-q^(-3) - q^(-4) - q^(-5))*x1^(-1/2)*x2^(-5)*x3^(-2) + (q^(-6))*x1^(-1/2)*x2^(-5)*x3^(-3) + (q^(2))*x1^(-3/2)*x2^(-3)*x3 + (q^(3) + q^(2))*x1^(-3/2)*x2^(-4)*x3 + (-q^(2) - q)*x1^(-3/2)*x2^(-4) + (q^(3) + q^(2))*x1^(-3/2)*x2^(-5)*x3 + (-2*q^(2) - 2*q - 1)*x1^(-3/2)*x2^(-5) + (q + 1 + q^(-1))*x1^(-3/2)*x2^(-5)*x3^(-1) + (-q^(5))*x1^(-5/2)*x2^(-4)*x3^(2) + (-q^(7) - q^(6) - q^(5))*x1^(-5/2)*x2^(-5)*x3^(2) + (q^(6) + q^(5) + q^(4))*x1^(-5/2)*x2^(-5)*x3 + (q^(9))*x1^(-7/2)*x2^(-5)*x3^(3)

Braid

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

Multivariable Alexander polynomial

ΔL
-A1^(1/2)*A2^(2) + A1^(1/2)*A2 - A1^(1/2)*A2*A3^(-1) + A1^(1/2)*A2^(-1)*A3^(-1) - A1^(-1/2)*A2*A3 + A1^(-1/2)*A2^(-1)*A3 - A1^(-1/2)*A2^(-1) + A1^(-1/2)*A2^(-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, 2, 2) yes
(-1, -2, 2) yes
(1, 2, 0) yes
(1, 4, 0) yes
(1, -2, -2) yes
(-1, -4, 0) yes
(-1, -2, 0) yes
(1, 2, -2) yes
Interactive 3D view · hover a vertex for coordinates

HFL polytope

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

FL/HFL Links

orderOption(int) 2244
namestring L10n84{1;1}
statusstring success
slugstring L10n84_1_1_74c3f12d
result_filestring details/L10n84_1_1_74c3f12d.json
complexity_scoreOption(int) 300
strandsOption(int) null
crossingsOption(int) 10
component_countOption(int) 3
girthOption(int) 6
total_rankOption(int) 72
wall_secondsOption(float) 0.001994
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 3
support_sizeOption(int) 44
vertex_countOption(int) 20
fibered_vertex_countOption(int) 8
polytope_statusstring computed
alexander_support_sizeOption(int) 8
alexander_vertex_countOption(int) 8
alexander_relationstring not_computed
fk_countint 4
detailsRowRef(FLHFLLinks) 
{
  "dataset": "FLHFLLinks",
  "key": "L10n84_1_1_74c3f12d"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L10n84_1_1_74c3f12d