% SOLVELIDARCALIBRATIONOPT Solve LIDAR-Camera calibration problem instance. % % SOLVELIDARCALIBRATIONOPT(n,x) Computes up to four pose matrices % from six plane normal to 3D point correspondences n(i,:) <-> % x(i,:) for i from 1 to 6. % % This function solves the equation n' * (R x + T) = 0 % assuming that the first component of x is 0. function P = SolveLidarCalibrationOpt(n,x) n11 = n(1,1); n21 = n(2,1); n31 = n(3,1); n41 = n(4,1); n51 = n(5,1); n61 = n(6,1); n12 = n(1,2); n22 = n(2,2); n32 = n(3,2); n42 = n(4,2); n52 = n(5,2); n62 = n(6,2); n13 = n(1,3); n23 = n(2,3); n33 = n(3,3); n43 = n(4,3); n53 = n(5,3); n63 = n(6,3); x11 = x(1,1); x21 = x(2,1); x31 = x(3,1); x41 = x(4,1); x51 = x(5,1); x61 = x(6,1); x12 = x(1,2); x22 = x(2,2); x32 = x(3,2); x42 = x(4,2); x52 = x(5,2); x62 = x(6,2); x13 = x(1,3); x23 = x(2,3); x33 = x(3,3); x43 = x(4,3); x53 = x(5,3); x63 = x(6,3); a11 = n11*x12; a21 = n21*x22; a31 = n31*x32; a41 = n41*x42; a51 = n51*x52; a61 = n61*x62; a12 = n12*x12; a22 = n22*x22; a32 = n32*x32; a42 = n42*x42; a52 = n52*x52; a62 = n62*x62; a13 = n13*x12; a23 = n23*x22; a33 = n33*x32; a43 = n43*x42; a53 = n53*x52; a63 = n63*x62; a14 = n11*x13; a24 = n21*x23; a34 = n31*x33; a44 = n41*x43; a54 = n51*x53; a64 = n61*x63; a15 = n12*x13; a25 = n22*x23; a35 = n32*x33; a45 = n42*x43; a55 = n52*x53; a65 = n62*x63; a16 = n13*x13; a26 = n23*x23; a36 = n33*x33; a46 = n43*x43; a56 = n53*x53; a66 = n63*x63; a17 = n11; a27 = n21; a37 = n31; a47 = n41; a57 = n51; a67 = n61; a18 = n12; a28 = n22; a38 = n32; a48 = n42; a58 = n52; a68 = n62; a19 = n13; a29 = n23; a39 = n33; a49 = n43; a59 = n53; a69 = n63; d = (a37*a18*a29-a37*a19*a28-a27*a18*a39+a27*a19*a38+a17*a28*a39- ... a17*a29*a38); b11 = -(a28*a39-a29*a38)/d*a11+ (a18*a39-a19*a38)/d*a21-(a18* ... a29-a19*a28)/ d*a31; b12 = -(a12*a28*a39-a12*a29*a38-a22*a18*a39+a22*a19*a38+a32*a18* ... a29-a32*a19*a28)/d; b13 = -(a13*a28*a39-a13*a29*a38-a23*a18*a39+a23*a19*a38+a33*a18* ... a29-a33*a19*a28)/d; b14 = -(a14*a28*a39-a14*a29*a38-a24*a18*a39+a24*a19*a38+a34*a18* ... a29-a34*a19*a28)/d; b15 = -(a15*a28*a39-a15*a29*a38-a25*a18*a39+a25*a19*a38+a35*a18* ... a29-a35*a19*a28)/d; b16 = -(a16*a28*a39-a16*a29*a38-a26*a18*a39+a26*a19*a38+a36*a18* ... a29-a36*a19*a28)/d; b21 = (-a37*a29+a27*a39)/d*a11-(- a37*a19+a17*a39)/ d*a21+(-a27* ... a19+a17*a29)/d*a31; b22 = (-a12*a37*a29+a12*a27*a39+a22*a37*a19-a22*a17*a39-a32*a27* ... a19+a32*a17*a29)/d; b23 = (-a13*a37*a29+a13*a27*a39+a23*a37*a19-a23*a17*a39-a33*a27* ... a19+a33*a17*a29)/d; b24 = (-a14*a37*a29+a14*a27*a39+a24*a37*a19-a24*a17*a39-a34*a27* ... a19+a34*a17*a29)/d; b25 = (-a15*a37*a29+a15*a27*a39+a25*a37*a19-a25*a17*a39-a35*a27* ... a19+a35*a17*a29)/d; b26 = (-a16*a37*a29+a16*a27*a39+a26*a37*a19-a26*a17*a39-a36*a27* ... a19+a36*a17*a29)/d; b31 = -(-a37*a28+a27*a38)/d* a11+(-a37*a18+a17*a38)/d* a21-(-a27* ... a18+a17*a28)/d*a31; b32 = -(-a12*a37*a28+a12*a27*a38+a22*a37*a18-a22*a17*a38-a32*a27* ... a18+a32*a17*a28)/d; b33 = -(-a13*a37*a28+a13*a27*a38+a23*a37*a18-a23*a17*a38-a33*a27* ... a18+a33*a17*a28)/d; b34 = -(-a14*a37*a28+a14*a27*a38+a24*a37*a18-a24*a17*a38-a34*a27* ... a18+a34*a17*a28)/d; b35 = -(-a15*a37*a28+a15*a27*a38+a25*a37*a18-a25*a17*a38-a35*a27* ... a18+a35*a17*a28)/d; b36 = -(-a16*a37*a28+a16*a27*a38+a26*a37*a18-a26*a17*a38-a36*a27* ... a18+a36*a17*a28)/d; c41 = a41+a47*b11+a48*b21+a49*b31; c42 = a49*b32+a42+a48*b22+a47*b12; c43 = a43+a47*b13+a49*b33+a48*b23; c44 = a47*b14+a44+a49*b34+a48*b24; c45 = a47*b15+a49*b35+a45+a48*b25; c46 = a49*b36+a48*b26+a46+a47*b16; c51 = a51+a57*b11+a58*b21+a59*b31; c52 = a59*b32+a52+a58*b22+a57*b12; c53 = a53+a57*b13+a59*b33+a58*b23; c54 = a57*b14+a54+a59*b34+a58*b24; c55 = a57*b15+a59*b35+a55+a58*b25; c56 = a59*b36+a58*b26+a56+a57*b16; c61 = a61+a67*b11+a68*b21+a69*b31; c62 = a69*b32+a62+a68*b22+a67*b12; c63 = a63+a67*b13+a69*b33+a68*b23; c64 = a67*b14+a64+a69*b34+a68*b24; c65 = a67*b15+a69*b35+a65+a68*b25; c66 = a69*b36+a68*b26+a66+a67*b16; d2 = (c61*c42*c53-c61*c43*c52-c51*c42*c63+c51*c43*c62+c41*c52* ... c63-c41*c53*c62); d = d2^2; e11 = 1/d*(-2*c52*c63^2*c44*c42*c54-2*c52^2*c63* ... c44*c43*c64-2*c43^2*c62*c54*c52*c64-2* ... c53*c62^2*c44*c43*c54-2*c53^2*c62*c44* ... c42*c64-2*c42*c63*c54^2*c43*c62-2* ... c42^2*c63*c54*c53*c64-2*c52*c63*c44^2* ... c53*c62-2*c61*c53*c44^2*c51*c63-2* ... c61^2*c53*c44*c43*c54-2*c61*c53^2*c44* ... c41*c64-2*c42*c53*c64^2*c43*c52-2* ... c41^2*c63*c54*c53*c64-2*c51*c63^2*c44* ... c41*c54-2*c51^2*c63*c44*c43*c64-2*c51* ... c42*c64^2*c41*c52-2*c51*c43*c64^2*c41* ... c53-2*c61*c43*c54^2*c41*c63-2*c61* ... c43^2*c54*c51*c64-2*c61*c42*c54^2*c41* ... c62-2*c61*c42^2*c54*c51*c64-2*c41^2* ... c62*c54*c52*c64-2*c51*c62^2*c44*c41* ... c54-2*c51^2*c62*c44*c42*c64-2*c61*c52* ... c44^2*c51*c62-2*c61^2*c52*c44*c42*c54- ... 2*c61*c52^2*c44*c41*c64+2*c51*c62*c44* ... c61*c42*c54+2*c51*c62*c44*c41*c52*c64+ ... 2*c61*c42*c54*c41*c52*c64+2*c41*c62* ... c54*c51*c42*c64+2*c61*c52*c44*c41*c62* ... c54+2*c61*c52*c44*c51*c42*c64+2*c61* ... c53*c44*c41*c63*c54+2*c61*c53*c44*c51* ... c43*c64+2*c51*c63*c44*c61*c43*c54+2* ... c51*c63*c44*c41*c53*c64+2*c61*c43*c54* ... c41*c53*c64+2*c41*c63*c54*c51*c43*c64+ ... 2*c43*c62*c54*c42*c53*c64+2*c52*c63* ... c44*c43*c62*c54+2*c52*c63*c44*c42*c53* ... c64+2*c53*c62*c44*c42*c63*c54+2*c53* ... c62*c44*c43*c52*c64+2*c42*c63*c54*c43* ... c52*c64+c61^2*c52^2*c44^2+c51^2*c62^2* ... c44^2+c61^2*c42^2*c54^2+c41^2*c62^2* ... c54^2+c51^2*c42^2*c64^2+c41^2*c52^2* ... c64^2+c61^2*c53^2*c44^2+c51^2*c63^2* ... c44^2+c61^2*c43^2*c54^2+c41^2*c63^2* ... c54^2+c51^2*c43^2*c64^2+c41^2*c53^2* ... c64^2+c52^2*c63^2*c44^2+c53^2*c62^2* ... c44^2+c42^2*c63^2*c54^2+c43^2*c62^2* ... c54^2+c42^2*c53^2*c64^2+c43^2*c52^2*c64^2); e12 = -(-2*c43^2*c62^2*c54*c55-2*c42^2*c53^2*c64*c65-2*c53^2* ... c62^2*c44*c45-2*c42^2*c63^2*c54*c55-2*c52^2*c63^2*c44*c45- ... 2*c61^2*c53^2*c44*c45-2*c43^2*c52^2*c64*c65-2*c51^2*c63^2* ... c44*c45-2*c51^2*c42^2*c64*c65-2*c41^2*c52^2*c64*c65-2* ... c51^2*c43^2*c64*c65-2*c41^2*c53^2*c64*c65-2*c61^2*c43^2* ... c54*c55-2*c41^2*c63^2*c54*c55-2*c41^2*c62^2*c54*c55-2* ... c51^2*c62^2*c44*c45-2*c61^2*c42^2*c54*c55-2*c61^2*c52^2* ... c44*c45+2*c51*c62^2*c44*c41*c55+2*c51^2*c62*c44*c42*c65+2* ... c51*c62^2*c45*c41*c54+2*c51^2*c62*c45*c42*c64+2*c61*c42^2* ... c54*c51*c65+2*c61*c42^2*c55*c51*c64+2*c41^2*c62*c54*c52* ... c65+2*c41^2*c62*c55*c52*c64+2*c61^2*c52*c44*c42*c55+2*c61* ... c52^2*c44*c41*c65+2*c61^2*c52*c45*c42*c54+2*c61*c52^2*c45* ... c41*c64+2*c61^2*c53*c44*c43*c55+2*c61*c53^2*c44*c41*c65+2* ... c61^2*c53*c45*c43*c54+2*c61*c53^2*c45*c41*c64+2*c51*c63^2* ... c44*c41*c55+2*c51^2*c63*c44*c43*c65+2*c51*c63^2*c45*c41* ... c54+2*c51^2*c63*c45*c43*c64+2*c61*c43^2*c54*c51*c65+2*c61* ... c43^2*c55*c51*c64+2*c41^2*c63*c54*c53*c65+2*c41^2*c63*c55* ... c53*c64+2*c43^2*c62*c54*c52*c65+2*c43^2*c62*c55*c52*c64+2* ... c52*c63^2*c44*c42*c55+2*c52^2*c63*c44*c43*c65+2*c52*c63^2* ... c45*c42*c54+2*c52^2*c63*c45*c43*c64+2*c53*c62^2*c44*c43* ... c55+2*c53^2*c62*c44*c42*c65+2*c53*c62^2*c45*c43*c54+2* ... c53^2*c62*c45*c42*c64+2*c42^2*c63*c54*c53*c65+2*c42^2*c63* ... c55*c53*c64-2*c52*c63*c45*c43*c62*c54-2*c52*c63*c45*c42* ... c53*c64-2*c53*c62*c44*c42*c63*c55-2*c53*c62*c44*c43*c52* ... c65-2*c53*c62*c45*c42*c63*c54-2*c53*c62*c45*c43*c52*c64+4* ... c42*c63*c54*c43*c62*c55-2*c42*c63*c54*c43*c52*c65-2*c42* ... c63*c55*c43*c52*c64-2*c43*c62*c54*c42*c53*c65-2*c43*c62* ... c55*c42*c53*c64+4*c42*c53*c64*c43*c52*c65-2*c51*c62*c44* ... c61*c42*c55-2*c51*c62*c44*c41*c52*c65+4*c51*c43*c64*c41* ... c53*c65-2*c41*c63*c55*c51*c43*c64-2*c41*c63*c54*c51*c43* ... c65-2*c61*c43*c55*c41*c53*c64-2*c61*c43*c54*c41*c53*c65+4* ... c61*c43*c54*c41*c63*c55-2*c51*c63*c45*c61*c43*c54-2*c51* ... c63*c45*c41*c53*c64-2*c51*c63*c44*c61*c43*c55-2*c51*c63* ... c44*c41*c53*c65-2*c61*c53*c45*c41*c63*c54-2*c61*c53*c45* ... c51*c43*c64-2*c61*c53*c44*c51*c43*c65+4*c61*c53*c44*c51* ... c63*c45-2*c61*c53*c44*c41*c63*c55-2*c52*c63*c44*c43*c62* ... c55-2*c52*c63*c44*c42*c53*c65+4*c51*c42*c64*c41*c52*c65+4* ... c52*c63*c44*c53*c62*c45-2*c41*c62*c54*c51*c42*c65-2*c41* ... c62*c55*c51*c42*c64+4*c61*c42*c54*c41*c62*c55-2*c61*c42* ... c54*c41*c52*c65-2*c61*c42*c55*c41*c52*c64-2*c51*c62*c45* ... c61*c42*c54-2*c51*c62*c45*c41*c52*c64+4*c61*c52*c44*c51* ... c62*c45-2*c61*c52*c44*c41*c62*c55-2*c61*c52*c44*c51*c42* ... c65-2*c61*c52*c45*c41*c62*c54-2*c61*c52*c45*c51*c42*c64)/d; e13 = -(2*c52*c63*c45^2*c53*c62+2*c52*c63^2*c45*c42*c55+2*c52^2* ... c63*c45*c43*c65+2*c43^2*c62*c55*c52*c65+2*c53*c62^2*c45* ... c43*c55+2*c53^2*c62*c45*c42*c65+2*c42*c63*c55^2*c43*c62+2* ... c42^2*c63*c55*c53*c65+2*c42*c53*c65^2*c43*c52+2*c41^2*c63* ... c55*c53*c65+2*c61*c53*c45^2*c51*c63+2*c61^2*c53*c45*c43* ... c55+2*c61*c53^2*c45*c41*c65+2*c51*c63^2*c45*c41*c55+2* ... c51^2*c63*c45*c43*c65+2*c41^2*c62*c55*c52*c65+2*c51*c42* ... c65^2*c41*c52+2*c51*c43*c65^2*c41*c53+2*c61*c43*c55^2*c41* ... c63+2*c61*c43^2*c55*c51*c65+2*c61*c42*c55^2*c41*c62+2*c61* ... c42^2*c55*c51*c65+2*c61^2*c52*c45*c42*c55+2*c61*c52^2*c45* ... c41*c65+2*c51*c62^2*c45*c41*c55+2*c51^2*c62*c45*c42*c65+2* ... c61*c52*c45^2*c51*c62-2*c51*c62*c45*c61*c42*c55-2*c51*c62* ... c45*c41*c52*c65-2*c61*c42*c55*c41*c52*c65-2*c41*c62*c55* ... c51*c42*c65-2*c61*c52*c45*c41*c62*c55-2*c61*c52*c45*c51* ... c42*c65-2*c61*c53*c45*c41*c63*c55-2*c61*c53*c45*c51*c43* ... c65-2*c51*c63*c45*c61*c43*c55-2*c51*c63*c45*c41*c53*c65-2* ... c61*c43*c55*c41*c53*c65-2*c41*c63*c55*c51*c43*c65-2*c43* ... c62*c55*c42*c53*c65-2*c52*c63*c45*c43*c62*c55-2*c52*c63* ... c45*c42*c53*c65-2*c53*c62*c45*c42*c63*c55-2*c53*c62*c45* ... c43*c52*c65-2*c42*c63*c55*c43*c52*c65-c61^2*c52^2*c45^2- ... c51^2*c62^2*c45^2-c61^2*c42^2*c55^2-c41^2*c62^2*c55^2- ... c51^2*c42^2*c65^2-c41^2*c52^2*c65^2-c61^2*c53^2*c45^2- ... c51^2*c63^2*c45^2-c61^2*c43^2*c55^2-c41^2*c63^2*c55^2- ... c51^2*c43^2*c65^2-c41^2*c53^2*c65^2-c52^2*c63^2*c45^2- ... c53^2*c62^2*c45^2-c42^2*c63^2*c55^2-c43^2*c62^2*c55^2- ... c42^2*c53^2*c65^2-c43^2*c52^2*c65^2)/d; e14 = -(-2*c43^2*c52^2*c64*c66-2*c43^2*c62^2*c54*c56-2*c53^2* ... c62^2*c44*c46-2*c42^2*c63^2*c54*c56-2*c52^2*c63^2*c44*c46- ... 2*c61^2*c53^2*c44*c46-2*c42^2*c53^2*c64*c66-2*c41^2*c63^2* ... c54*c56-2*c51^2*c63^2*c44*c46-2*c51^2*c42^2*c64*c66-2* ... c41^2*c52^2*c64*c66-2*c41^2*c53^2*c64*c66-2*c51^2*c43^2* ... c64*c66-2*c61^2*c43^2*c54*c56-2*c41^2*c62^2*c54*c56-2* ... c51^2*c62^2*c44*c46-2*c61^2*c42^2*c54*c56-2*c61^2*c52^2* ... c44*c46+2*c51*c62^2*c44*c41*c56+2*c51^2*c62*c44*c42*c66+2* ... c51*c62^2*c46*c41*c54+2*c51^2*c62*c46*c42*c64+2*c61*c42^2* ... c54*c51*c66+2*c61*c42^2*c56*c51*c64+2*c41^2*c62*c54*c52* ... c66+2*c41^2*c62*c56*c52*c64+2*c61^2*c52*c44*c42*c56+2*c61* ... c52^2*c44*c41*c66+2*c61^2*c52*c46*c42*c54+2*c61*c52^2*c46* ... c41*c64+2*c61^2*c53*c44*c43*c56+2*c61*c53^2*c44*c41*c66+2* ... c61^2*c53*c46*c43*c54+2*c61*c53^2*c46*c41*c64+2*c51*c63^2* ... c44*c41*c56+2*c51^2*c63*c44*c43*c66+2*c51*c63^2*c46*c41* ... c54+2*c51^2*c63*c46*c43*c64+2*c61*c43^2*c54*c51*c66+2*c61* ... c43^2*c56*c51*c64+2*c41^2*c63*c54*c53*c66+2*c41^2*c63*c56* ... c53*c64+2*c42^2*c63*c56*c53*c64+2*c43^2*c62*c54*c52*c66+2* ... c43^2*c62*c56*c52*c64+2*c52*c63^2*c44*c42*c56+2*c52^2*c63* ... c44*c43*c66+2*c52*c63^2*c46*c42*c54+2*c52^2*c63*c46*c43* ... c64+2*c53*c62^2*c44*c43*c56+2*c53^2*c62*c44*c42*c66+2*c53* ... c62^2*c46*c43*c54+2*c53^2*c62*c46*c42*c64+2*c42^2*c63*c54* ... c53*c66-2*c52*c63*c46*c43*c62*c54-2*c52*c63*c46*c42*c53* ... c64-2*c53*c62*c44*c42*c63*c56-2*c53*c62*c44*c43*c52*c66-2* ... c53*c62*c46*c42*c63*c54-2*c53*c62*c46*c43*c52*c64+4*c42* ... c63*c54*c43*c62*c56-2*c42*c63*c54*c43*c52*c66-2*c42*c63* ... c56*c43*c52*c64-2*c43*c62*c54*c42*c53*c66-2*c43*c62*c56* ... c42*c53*c64+4*c42*c53*c64*c43*c52*c66-2*c61*c52*c46*c41* ... c62*c54-2*c61*c52*c46*c51*c42*c64-2*c51*c62*c44*c61*c42* ... c56-2*c51*c62*c44*c41*c52*c66+4*c51*c43*c64*c41*c53*c66-2* ... c41*c63*c56*c51*c43*c64-2*c41*c63*c54*c51*c43*c66-2*c61* ... c43*c56*c41*c53*c64-2*c61*c43*c54*c41*c53*c66+4*c61*c43* ... c54*c41*c63*c56-2*c51*c63*c46*c61*c43*c54-2*c51*c63*c46* ... c41*c53*c64-2*c51*c63*c44*c41*c53*c66-2*c51*c63*c44*c61* ... c43*c56-2*c61*c53*c46*c51*c43*c64-2*c61*c53*c46*c41*c63* ... c54-2*c61*c53*c44*c41*c63*c56-2*c61*c53*c44*c51*c43*c66+4* ... c61*c53*c44*c51*c63*c46+4*c52*c63*c44*c53*c62*c46-2*c52* ... c63*c44*c43*c62*c56-2*c52*c63*c44*c42*c53*c66+4*c51*c42* ... c64*c41*c52*c66-2*c61*c42*c56*c41*c52*c64-2*c41*c62*c54* ... c51*c42*c66-2*c41*c62*c56*c51*c42*c64+4*c61*c42*c54*c41* ... c62*c56-2*c61*c42*c54*c41*c52*c66-2*c51*c62*c46*c61*c42* ... c54-2*c51*c62*c46*c41*c52*c64+4*c61*c52*c44*c51*c62*c46-2* ... c61*c52*c44*c41*c62*c56-2*c61*c52*c44*c51*c42*c66)/d; e15 = -(-2*c52^2*c63^2*c45*c46-2*c43^2*c62^2*c55*c56-2*c53^2* ... c62^2*c45*c46-2*c42^2*c63^2*c55*c56-2*c43^2*c52^2*c65*c66- ... 2*c42^2*c53^2*c65*c66-2*c41^2*c63^2*c55*c56-2*c61^2*c53^2* ... c45*c46-2*c51^2*c63^2*c45*c46-2*c51^2*c42^2*c65*c66-2* ... c41^2*c52^2*c65*c66-2*c41^2*c53^2*c65*c66-2*c51^2*c43^2* ... c65*c66-2*c61^2*c43^2*c55*c56-2*c61^2*c42^2*c55*c56-2* ... c41^2*c62^2*c55*c56-2*c51^2*c62^2*c45*c46-2*c61^2*c52^2* ... c45*c46+2*c61*c52^2*c46*c41*c65+2*c51*c62^2*c45*c41*c56+2* ... c51^2*c62*c45*c42*c66+2*c51*c62^2*c46*c41*c55+2*c51^2*c62* ... c46*c42*c65+2*c61*c42^2*c55*c51*c66+2*c61*c42^2*c56*c51* ... c65+2*c41^2*c62*c55*c52*c66+2*c41^2*c62*c56*c52*c65+2* ... c61^2*c52*c45*c42*c56+2*c61*c52^2*c45*c41*c66+2*c61^2*c52* ... c46*c42*c55+2*c61^2*c53*c45*c43*c56+2*c61*c53^2*c45*c41* ... c66+2*c61^2*c53*c46*c43*c55+2*c61*c53^2*c46*c41*c65+2*c51* ... c63^2*c45*c41*c56+2*c51^2*c63*c45*c43*c66+2*c51*c63^2*c46* ... c41*c55+2*c51^2*c63*c46*c43*c65+2*c61*c43^2*c55*c51*c66+2* ... c61*c43^2*c56*c51*c65+2*c41^2*c63*c55*c53*c66+2*c41^2*c63* ... c56*c53*c65+2*c42^2*c63*c56*c53*c65+2*c43^2*c62*c55*c52* ... c66+2*c43^2*c62*c56*c52*c65+2*c52*c63^2*c45*c42*c56+2* ... c52^2*c63*c45*c43*c66+2*c52*c63^2*c46*c42*c55+2*c52^2*c63* ... c46*c43*c65+2*c53*c62^2*c45*c43*c56+2*c53^2*c62*c45*c42* ... c66+2*c53*c62^2*c46*c43*c55+2*c53^2*c62*c46*c42*c65+2* ... c42^2*c63*c55*c53*c66+4*c52*c63*c45*c53*c62*c46-2*c52*c63* ... c45*c43*c62*c56-2*c52*c63*c45*c42*c53*c66-2*c52*c63*c46* ... c43*c62*c55-2*c52*c63*c46*c42*c53*c65-2*c53*c62*c45*c42* ... c63*c56-2*c53*c62*c45*c43*c52*c66-2*c53*c62*c46*c42*c63* ... c55-2*c53*c62*c46*c43*c52*c65+4*c42*c63*c55*c43*c62*c56-2* ... c42*c63*c55*c43*c52*c66-2*c42*c63*c56*c43*c52*c65-2*c43* ... c62*c55*c42*c53*c66-2*c43*c62*c56*c42*c53*c65+4*c42*c53* ... c65*c43*c52*c66-2*c61*c52*c46*c41*c62*c55-2*c61*c52*c46* ... c51*c42*c65+4*c51*c43*c65*c41*c53*c66-2*c41*c63*c56*c51* ... c43*c65-2*c41*c63*c55*c51*c43*c66-2*c61*c43*c56*c41*c53* ... c65+4*c61*c43*c55*c41*c63*c56-2*c61*c43*c55*c41*c53*c66-2* ... c51*c63*c46*c61*c43*c55-2*c51*c63*c46*c41*c53*c65-2*c51* ... c63*c45*c61*c43*c56-2*c51*c63*c45*c41*c53*c66-2*c61*c53* ... c46*c41*c63*c55-2*c61*c53*c46*c51*c43*c65-2*c61*c53*c45* ... c41*c63*c56-2*c61*c53*c45*c51*c43*c66+4*c61*c53*c45*c51* ... c63*c46+4*c51*c42*c65*c41*c52*c66-2*c61*c42*c56*c41*c52* ... c65-2*c41*c62*c55*c51*c42*c66-2*c41*c62*c56*c51*c42*c65+4* ... c61*c42*c55*c41*c62*c56-2*c61*c42*c55*c41*c52*c66-2*c51* ... c62*c45*c61*c42*c56-2*c51*c62*c45*c41*c52*c66-2*c51*c62* ... c46*c61*c42*c55-2*c51*c62*c46*c41*c52*c65+4*c61*c52*c45* ... c51*c62*c46-2*c61*c52*c45*c41*c62*c56-2*c61*c52*c45*c51* ... c42*c66)/d; e16 = -(2*c42^2*c63*c56*c53*c66+2*c43^2*c62*c56*c52*c66+2*c52^2* ... c63*c46*c43*c66+2*c53*c62^2*c46*c43*c56+2*c53^2*c62*c46* ... c42*c66+2*c42*c63*c56^2*c43*c62+2*c51*c63^2*c46*c41*c56+2* ... c51^2*c63*c46*c43*c66+2*c42*c53*c66^2*c43*c52+2*c61*c53* ... c46^2*c51*c63+2*c61^2*c53*c46*c43*c56+2*c61*c53^2*c46*c41* ... c66+2*c41^2*c62*c56*c52*c66+2*c51*c42*c66^2*c41*c52+2* ... c41^2*c63*c56*c53*c66+2*c51*c43*c66^2*c41*c53+2*c61*c43* ... c56^2*c41*c63+2*c61*c43^2*c56*c51*c66+2*c61*c42*c56^2*c41* ... c62+2*c61*c42^2*c56*c51*c66+2*c61*c52*c46^2*c51*c62+2* ... c61^2*c52*c46*c42*c56+2*c61*c52^2*c46*c41*c66+2*c51*c62^2* ... c46*c41*c56+2*c51^2*c62*c46*c42*c66-2*c51*c62*c46*c61*c42* ... c56-2*c51*c62*c46*c41*c52*c66-2*c61*c42*c56*c41*c52*c66-2* ... c41*c62*c56*c51*c42*c66-2*c61*c52*c46*c41*c62*c56-2*c61* ... c52*c46*c51*c42*c66-2*c61*c53*c46*c41*c63*c56-2*c61*c53* ... c46*c51*c43*c66-2*c51*c63*c46*c61*c43*c56-2*c51*c63*c46* ... c41*c53*c66-2*c61*c43*c56*c41*c53*c66-2*c41*c63*c56*c51* ... c43*c66-2*c42*c63*c56*c43*c52*c66-2*c43*c62*c56*c42*c53* ... c66-2*c52*c63*c46*c43*c62*c56-2*c52*c63*c46*c42*c53*c66-2* ... c53*c62*c46*c42*c63*c56-2*c53*c62*c46*c43*c52*c66-c61^2* ... c52^2*c46^2-c51^2*c62^2*c46^2-c61^2*c42^2*c56^2-c41^2* ... c62^2*c56^2-c51^2*c42^2*c66^2-c41^2*c52^2*c66^2-c61^2* ... c53^2*c46^2-c51^2*c63^2*c46^2-c61^2*c43^2*c56^2-c41^2* ... c63^2*c56^2-c51^2*c43^2*c66^2-c41^2*c53^2*c66^2-c52^2* ... c63^2*c46^2-c53^2*c62^2*c46^2-c42^2*c63^2*c56^2-c43^2* ... c62^2*c56^2-c42^2*c53^2*c66^2-c43^2*c52^2*c66^2+2*c52*c63* ... c46^2*c53*c62+2*c52*c63^2*c46*c42*c56)/d; d2 = (c61*c42*c53-c61*c43*c52-c51*c42*c63+c51*c43*c62+c41*c52* ... c63-c41*c53*c62); e31 = 1/d2*(-c43*c62*c54+c43*c52*c64-c52*c63*c44- ... c42*c53*c64+c42*c63*c54+c53*c62*c44); e32 = -(c43*c62*c55-c42*c63*c55-c53*c62*c45+c52*c63*c45+c42*c53* ... c65-c43*c52*c65-c61*c43*c54-c51*c63*c44+c41*c63*c54-c41* ... c53*c64+c61*c53*c44+c51*c43*c64)/d2; e33 = -(-c41*c53*c65+c41*c63*c55-c51*c63*c45+c51*c43*c65+c61*c53* ... c45-c61*c43*c55)/d2; e34 = -(-c42*c63*c56+c43*c62*c56+c52*c63*c46-c53*c62*c46-c61*c52* ... c44+c61*c42*c54-c41*c62*c54-c43*c52*c66+c42*c53*c66+c41* ... c52*c64-c51*c42*c64+c51*c62*c44)/d2; e35 = -(c41*c63*c56+c61*c53*c46+c61*c42*c55+c51*c43*c66-c41*c53* ... c66-c51*c63*c46-c61*c43*c56+c51*c62*c45+c41*c52*c65-c41* ... c62*c55-c61*c52*c45-c51*c42*c65)/d2; e36 = -(-c61*c52*c46+c51*c62*c46+c61*c42*c56-c41*c62*c56-c51*c42*c66+c41*c52*c66)/d2; e112 = e11^2; e113 = e112*e11; e114 = e113*e11; e122 = e12^2; e123 = e122*e12; e124 = e123*e12; e132 = e13^2; e133 = e132*e13; e134 = e133*e13; e142 = e14^2; e143 = e142*e14; e144 = e143*e14; e152 = e15^2; e153 = e152*e15; e154 = e153*e15; e162 = e16^2; e163 = e162*e16; e164 = e163*e16; e312 = e31^2; e313 = e312*e31; e314 = e313*e31; e322 = e32^2; e323 = e322*e32; e324 = e323*e32; e332 = e33^2; e333 = e332*e33; e334 = e333*e33; e342 = e34^2; e343 = e342*e34; e344 = e343*e34; e352 = e35^2; e353 = e352*e35; e354 = e353*e35; e362 = e36^2; e363 = e362*e36; e364 = e363*e36; g1 = 6*e132*e162*e322*e312-2*e133*e16*e322*e312-6*e133* ... e16*e342*e312+e122*e132*e342*e312-4*e13*e152*e16* ... e314+2*e133*e34*e14*e313+e312*e132*e322*e152-2*e13* ... e324*e16*e142+e132*e322*e312*e142+e132*e322*e122* ... e342+2*e132*e16*e34*e15*e32*e312+4*e13*e32*e16*e14*e15* ... e313+4*e12*e34*e13*e15*e16*e313+4*e13*e323*e16*e14*e15*e31- ... 10*e132*e322*e16*e34*e14*e31+2*e133*e31*e343*e14+e132* ... e322*e342*e142+e132*e342*e312*e142+8*e13*e322*e34*e14* ... e162*e31-4*e132*e322*e162*e342-2*e122*e13*e16*e344-2* ... e133*e15*e32*e343+2*e133*e16*e322*e342+3*e312*e132* ... e152*e342-6*e312*e13*e322*e163+6*e132*e312*e342*e162+ ... 4*e12*e16*e34*e323*e13*e14-10*e12*e32*e31*e13*e162*e342+8* ... e132*e32*e16*e12*e31*e342-2*e12*e32*e152*e13*e31*e342+4* ... e31*e12*e13*e15*e16*e343+4*e13*e32*e14*e12*e16*e343-6*e12* ... e32*e162*e13*e313-2*e132*e32*e15*e14*e313+2*e312*e13*e32* ... e15*e162*e34+6*e12*e32*e16*e132*e313-6*e132*e16*e34*e14* ... e313-2*e12*e32*e152*e13*e313-4*e13*e322*e152*e16*e312-2* ... e133*e15*e32*e34*e312-2*e122*e16*e13*e342*e312-2*e132* ... e34*e15*e12*e313-2*e122*e322*e16*e13*e312-4*e12*e323* ... e162*e13*e31+6*e13*e34*e313*e14*e162+e122*e152*e312* ... e352+e122*e152*e362*e352-2*e31*e124*e36*e352-2*e123* ... e14*e36*e353+2*e122*e342*e162*e352+e332*e142*e162* ... e352+e322*e142*e162*e352+e312*e142*e162*e352+e122* ... e322*e162*e352+2*e332*e122*e312*e152+e122*e322*e312* ... e152-2*e12*e34*e313*e153+e332*e322*e142*e152-2*e323* ... e14*e31*e153-2*e32*e14*e313*e153+2*e313*e35*e15*e163+2* ... e313*e142*e36*e162-4*e31*e322*e164*e33+2*e12*e323*e163* ... e33-6*e313*e152*e162*e33+2*e313*e152*e142*e33-2*e323* ... e15*e143*e33-2*e313*e162*e142*e33-2*e322*e36*e144*e33-2* ... e312*e36*e144*e33+2*e333*e36*e122*e142-2*e333*e31*e122* ... e142-2*e333*e35*e12*e143-2*e333*e15*e32*e143-2*e333*e36* ... e152*e142+2*e333*e31*e152*e142-4*e312*e332*e152*e142+ ... 2*e333*e34*e16*e143+4*e332*e31*e36*e144+2*e333*e12*e32* ... e163+2*e333*e31*e122*e162-2*e333*e36*e122*e162-3*e122* ... e332*e342*e162-2*e33*e31*e144*e352+e122*e152*e342* ... e352+e122*e142*e342*e352-2*e33*e12*e143*e353+2*e31*e12* ... e143*e353+2*e123*e14*e31*e353+e122*e322*e142*e352+6* ... e312*e152*e332*e162+2*e333*e34*e14*e163-2*e333*e35*e15* ... e163+2*e333*e36*e152*e162-2*e333*e31*e152*e162-6*e333* ... e31*e142*e162+6*e312*e332*e142*e162+3*e322*e142*e332* ... e162-2*e333*e142*e36*e162+2*e123*e34*e16*e353+e322* ... e312*e152*e142-2*e313*e36*e152*e142+e322*e312*e162* ... e142-2*e313*e36*e152*e162+3*e322*e312*e152*e162-2*e34* ... e313*e14*e163+2*e143*e35*e323*e13+e342*e152*e322*e132+ ... e362*e152*e322*e132+e362*e132*e322*e122-2*e163*e322* ... e13*e332+2*e162*e352*e322*e132+e122*e322*e342*e162-2* ... e323*e15*e163*e34+e122*e142*e362*e342+e332*e152*e162* ... e342+e312*e152*e162*e342+e322*e152*e162*e342+e122* ... e352*e362*e142-2*e33*e31*e362*e144+e342*e332*e162* ... e142+e342*e312*e162*e142+e322*e342*e162*e142+2*e323* ... e36*e143*e15+2*e33*e123*e343*e15-2*e323*e34*e16*e153+2* ... e313*e35*e16*e153+e322*e352*e162*e152+e332*e352*e162* ... e152+e312*e352*e162*e152+e332*e322*e162*e152+e122* ... e322*e362*e152-2*e31*e33*e362*e154+e122*e342*e362* ... e152+2*e332*e122*e362*e152+2*e322*e142*e362*e152+2* ... e332*e142*e362*e152+2*e312*e142*e362*e152+4*e312*e33* ... e36*e154-2*e322*e31*e36*e154-2*e332*e31*e36*e154+2*e323* ... e14*e36*e153+e322*e342*e142*e152+e342*e332*e142*e152+ ... e342*e312*e142*e152+e332*e352*e142*e152+e312*e352* ... e142*e152+e322*e352*e142*e152+2*e332*e122*e342*e152- ... 2*e31*e12*e343*e153+2*e33*e12*e343*e153-2*e31*e33*e342* ... e154+e122*e322*e342*e152+2*e123*e16*e343*e35-2*e323* ... e16*e143*e35-2*e323*e14*e163*e35+e332*e122*e352*e162+ ... e322*e122*e332*e162-2*e31*e124*e332*e36+e122*e332* ... e352*e142+e322*e332*e122*e142-4*e36*e163*e323*e12-12* ... e36*e162*e132*e313-2*e36*e162*e122*e313+12*e36*e16* ... e133*e313-4*e36*e163*e13*e333+2*e362*e352*e16*e133+4* ... e36*e163*e13*e313+2*e36*e152*e313*e122-6*e36*e152*e313* ... e132+6*e362*e162*e132*e332-2*e36*e33*e124*e312-4*e36* ... e342*e31*e134-2*e36*e132*e122*e313+6*e362*e162*e132* ... e312+6*e362*e152*e132*e312-4*e362*e152*e122*e312-2* ... e363*e33*e122*e132+2*e363*e12*e32*e133-12*e362*e312* ... e16*e133+6*e362*e132*e122*e312-4*e362*e142*e122*e332+ ... 2*e363*e13*e32*e123+4*e362*e33*e124*e31+3*e362*e342* ... e132*e122-2*e362*e322*e16*e133+2*e362*e162*e312*e122+ ... 2*e362*e162*e332*e122+2*e362*e162*e322*e132+2*e362* ... e142*e132*e332+2*e363*e142*e132*e31-2*e362*e16*e342* ... e133-4*e363*e16*e32*e123-2*e363*e34*e15*e123-2*e363* ... e142*e132*e33-2*e363*e35*e14*e123+2*e363*e34*e14*e133-2* ... e313*e142*e33*e132+2*e312*e142*e132*e332-12*e313* ... e162*e132*e33+4*e313*e16*e133*e33+2*e142*e352*e322* ... e132+2*e312*e142*e122*e332+2*e363*e152*e122*e31-2* ... e363*e152*e122*e33-2*e363*e152*e132*e31+2*e363*e152* ... e132*e33-2*e363*e35*e15*e133+2*e363*e142*e122*e33+4* ... e363*e31*e16*e133-6*e363*e132*e122*e31-4*e363*e16*e133* ... e33+2*e362*e142*e312*e122-2*e363*e142*e122*e31-4*e362* ... e142*e312*e132+4*e133*e322*e34*e31*e14+6*e362*e162* ... e322*e122-4*e132*e31*e343*e16*e14+e342*e132*e352*e122+ ... e362*e132*e352*e122+2*e313*e36*e142*e132+e312*e132* ... e352*e122+2*e31*e163*e323*e12+4*e31*e163*e13*e333+e312* ... e162*e322*e122-2*e13*e322*e342*e16*e142-2*e13*e342* ... e312*e16*e142+12*e313*e163*e33*e13+2*e313*e162*e33* ... e122-3*e312*e162*e352*e122-4*e312*e162*e352*e132-4* ... e312*e162*e332*e122+6*e312*e162*e132*e332-12*e312* ... e163*e13*e332+e312*e162*e342*e122+2*e313*e163*e32*e12+ ... 2*e313*e35*e15*e133-2*e313*e152*e132*e33-2*e313*e152* ... e122*e33+2*e312*e352*e16*e133-4*e14*e343*e33*e133+e142* ... e342*e332*e122+6*e142*e342*e332*e132-3*e142*e352* ... e312*e132+2*e142*e352*e312*e122-4*e143*e34*e13*e333+ ... e142*e362*e322*e122-3*e142*e362*e322*e132+2*e153*e35* ... e313*e13+e352*e152*e312*e132-2*e31*e132*e15*e12*e343-2* ... e132*e32*e14*e12*e343+2*e342*e162*e132*e332-2*e342* ... e352*e16*e133-2*e343*e36*e15*e123+2*e343*e36*e133*e14-2* ... e342*e33*e36*e124-2*e343*e12*e35*e133-2*e343*e13*e35* ... e123-2*e133*e32*e31*e12*e342+e342*e152*e312*e122+4*e32* ... e132*e15*e16*e343-4*e312*e13*e152*e16*e342+4*e13*e323* ... e15*e162*e34+2*e31*e132*e323*e12*e16-2*e132*e323*e34*e15* ... e16+4*e13*e322*e14*e152*e34*e31+e134*e344+2*e132*e152* ... e314+2*e134*e342*e312+6*e132*e162*e314-4*e133*e16* ... e314+e122*e132*e344-4*e314*e13*e163-2*e133*e16*e344+ ... e132*e324*e142-2*e13*e324*e163+e132*e324*e162-2*e132* ... e323*e34*e12*e14-2*e122*e16*e322*e13*e342-2*e13*e322*e16* ... e312*e142+2*e313*e13*e14*e152*e34-2*e132*e323*e14*e15* ... e31-2*e13*e32*e34*e312*e153+4*e312*e12*e15*e34*e132*e33-2* ... e312*e14*e33*e15*e32*e122+14*e312*e34*e33*e14*e16*e132+6* ... e312*e14*e32*e15*e132*e33+2*e312*e36*e12*e142*e32*e13+6* ... e312*e36*e12*e35*e14*e132+4*e362*e31*e13*e33*e16*e122+8* ... e362*e31*e13*e35*e15*e122+6*e362*e31*e14*e15*e32*e132+14* ... e362*e31*e132*e16*e32*e12-4*e362*e12*e14*e34*e32*e132+6* ... e362*e12*e33*e35*e14*e132+10*e362*e12*e33*e142*e32*e13-8* ... e362*e12*e15*e14*e13*e332-4*e362*e13*e14*e34*e122*e31+4* ... e362*e12*e15*e34*e132*e33-6*e362*e14*e33*e15*e32*e122-8* ... e363*e13*e14*e15*e12*e31+8*e363*e13*e14*e15*e12*e33+6*e362* ... e14*e32*e15*e132*e33+2*e362*e12*e142*e31*e32*e13-8*e362* ... e142*e31*e16*e13*e33-6*e362*e15*e31*e14*e32*e122-8*e362* ... e15*e312*e14*e16*e12-6*e362*e15*e35*e16*e122*e31+6*e362* ... e15*e35*e16*e122*e33-8*e362*e15*e14*e16*e12*e332-10*e362* ... e13*e152*e31*e32*e12+8*e36*e16*e14*e313*e15*e12+8*e36*e16* ... e342*e13*e31*e122+4*e36*e16*e14*e312*e34*e132-8*e36*e13* ... e14*e313*e15*e12-10*e36*e13*e35*e312*e15*e122+8*e36*e13* ... e152*e312*e32*e12-4*e36*e31*e13*e352*e16*e122+4*e36*e34* ... e32*e31*e15*e133+4*e36*e142*e31*e16*e13*e332+4*e36*e142* ... e33*e312*e16*e13+8*e36*e32*e35*e34*e16*e133-4*e36*e342*e13* ... e33*e16*e122-4*e36*e34*e33*e35*e16*e123+8*e36*e34*e33*e31* ... e14*e133+10*e36*e34*e332*e14*e16*e122+8*e36*e34*e332*e14* ... e16*e132-4*e36*e15*e14*e16*e323*e13-2*e36*e32*e12*e162*e13* ... e332+2*e36*e15*e32*e312*e14*e122+4*e36*e12*e35*e31*e34* ... e133+2*e36*e12*e15*e312*e34*e132-4*e36*e33*e142*e16*e322* ... e13+10*e36*e14*e34*e16*e322*e132+2*e36*e13*e14*e312*e34* ... e122+4*e36*e13*e35*e31*e34*e123+8*e36*e13*e31*e16*e322* ... e122-4*e36*e33*e35*e31*e14*e123-8*e36*e33*e31*e16*e32*e123- ... 8*e36*e122*e31*e16*e13*e332+8*e313*e13*e14*e35*e16*e12-8* ... e313*e15*e14*e16*e12*e33+2*e312*e15*e35*e16*e122*e33+16* ... e312*e15*e14*e16*e12*e332+4*e312*e13*e33*e162*e32*e12+6* ... e312*e12*e33*e35*e14*e132-8*e312*e12*e15*e14*e13*e332-2* ... e312*e12*e33*e142*e32*e13+6*e36*e162*e15*e312*e34*e12+6* ... e36*e162*e15*e35*e322*e13+6*e36*e162*e15*e34*e12*e332-8* ... e36*e162*e32*e35*e34*e122-8*e36*e162*e32*e35*e34*e132+14* ... e36*e162*e12*e32*e13*e312+6*e36*e162*e14*e35*e12*e332+2* ... e36*e162*e15*e35*e13*e332+8*e36*e163*e33*e31*e32*e12-2*e36* ... e162*e14*e312*e34*e13-2*e36*e162*e14*e34*e13*e332+2*e36* ... e162*e14*e35*e322*e12+2*e36*e162*e15*e35*e13*e312+6*e36* ... e162*e14*e35*e12*e312+2*e36*e162*e15*e34*e322*e12-6*e36* ... e162*e14*e34*e322*e13-2*e36*e16*e14*e312*e34*e122-4*e36* ... e16*e35*e31*e34*e123-16*e36*e16*e12*e32*e132*e312+4*e36* ... e16*e33*e13*e122*e312-16*e36*e16*e33*e152*e312*e13+8*e36* ... e16*e152*e31*e13*e332+8*e36*e16*e152*e31*e322*e13+10*e36* ... e16*e35*e312*e15*e122+6*e362*e34*e31*e14*e16*e122+14*e31* ... e162*e14*e34*e13*e332-2*e31*e162*e14*e35*e322*e12+8*e31* ... 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e142*e35*e15*e36*e13*e332-6*e14*e16*e342*e32*e35*e122-6* ... e14*e16*e342*e32*e35*e132-2*e14*e35*e342*e12*e31*e132-2* ... e14*e35*e13*e32*e362*e122+e134*e314-2*e14*e362*e13*e34* ... e122*e33+4*e14*e362*e13*e15*e322*e12+6*e14*e35*e32*e16* ... e132*e312-4*e14*e33*e122*e34*e16*e322-6*e14*e32*e15*e342* ... e33*e122+2*e14*e32*e15*e342*e132*e33+6*e14*e32*e13*e35* ... e342*e122+4*e14*e32*e33*e36*e34*e123-4*e14*e13*e36*e34* ... e322*e122+2*e14*e342*e33*e12*e35*e132+4*e14*e352*e13*e36* ... e34*e122-4*e14*e31*e13*e352*e34*e122-2*e14*e13*e312*e34* ... e122*e33-2*e14*e15*e35*e312*e34*e122-4*e14*e15*e34*e35* ... e132*e312+2*e14*e13*e35*e312*e32*e122+8*e14*e31*e35*e32* ... e36*e133+2*e142*e35*e15*e36*e13*e312-4*e142*e16*e32*e31* ... e12*e332-2*e142*e16*e32*e36*e12*e332-6*e142*e36*e15*e34* ... e322*e12-8*e143*e36*e31*e34*e13*e33-2*e142*e36*e15*e312* ... e34*e12-6*e142*e36*e15*e332*e34*e12+4*e142*e36*e34*e35*e32* ... e132+6*e142*e16*e34*e35*e322*e12+8*e142*e16*e31*e342*e13* ... 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e34*e16*e322*e12+8*e36*e15*e31*e14*e16*e322*e12-12*e36*e31* ... e13*e33*e162*e32*e12-8*e36*e31*e15*e14*e16*e12*e332-4*e36* ... e32*e15*e14*e16*e13*e332+16*e36*e12*e15*e31*e14*e13*e332-12* ... e36*e12*e33*e35*e31*e14*e132+4*e36*e12*e14*e31*e34*e32*e132- ... 12*e36*e14*e32*e31*e15*e132*e33-8*e36*e16*e15*e13*e312*e34* ... e12-4*e36*e34*e33*e12*e35*e16*e132-8*e36*e16*e15*e31*e34*e32* ... e132+4*e36*e162*e14*e31*e34*e13*e33-4*e36*e162*e33*e15*e35* ... e13*e31-12*e36*e162*e33*e14*e35*e12*e31-12*e36*e16*e14*e31* ... e34*e132*e33-12*e36*e162*e15*e31*e34*e12*e33-4*e36*e16*e12* ... e35*e31*e34*e132-4*e36*e15*e312*e14*e16*e32*e13-8*e36*e16* ... e33*e14*e312*e15*e12-12*e36*e13*e14*e35*e16*e12*e312-4*e14* ... e35*e13*e15*e36*e34*e32*e12-4*e14*e35*e13*e15*e31*e34*e32*e12- ... 8*e14*e36*e13*e33*e34*e16*e32*e12+8*e36*e31*e15*e33*e14*e16* ... e32*e13+16*e31*e36*e13*e14*e35*e16*e12*e33+8*e36*e16*e15*e13* ... e31*e34*e12*e33+4*e32*e15*e31*e14*e16*e352*e13+4*e32*e14*e33* ... e152*e31*e35*e13+4*e13*e12*e322*e34*e15*e16*e33-4*e32*e15* ... e36*e14*e16*e352*e13-4*e16*e15*e13*e312*e34*e12*e33+4*e14* ... e31*e13*e36*e34*e122*e33+4*e14*e31*e15*e34*e35*e122*e33+4* ... e14*e31*e15*e34*e35*e132*e33-4*e14*e31*e13*e36*e15*e322*e12+ ... 4*e14*e32*e12*e34*e16*e13*e332-4*e14*e32*e33*e12*e31*e34* ... e132+4*e14*e32*e33*e12*e36*e34*e132-12*e14*e35*e33*e12*e16* ... e13*e312+4*e14*e35*e15*e36*e34*e132*e31-4*e14*e35*e15*e36* ... e34*e132*e33-4*e14*e16*e15*e34*e35*e13*e332+4*e14*e162*e33* ... e31*e34*e32*e12-4*e15*e31*e35*e33*e16*e36*e132-4*e36*e32*e15* ... e34*e16*e132*e33+8*e36*e14*e33*e31*e15*e32*e122-4*e36*e14* ... e12*e35*e16*e13*e332-4*e362*e13*e15*e35*e16*e32*e12-8*e362* ... e31*e13*e14*e15*e12*e33-4*e362*e13*e14*e35*e16*e12*e33+4* ... e362*e16*e15*e13*e34*e12*e31+4*e362*e13*e14*e35*e16*e12*e31+ ... 4*e362*e16*e12*e14*e34*e32*e13+16*e362*e15*e31*e14*e16*e12* ... e33-4*e362*e16*e15*e13*e34*e12*e33+4*e31*e14*e12*e35*e16*e13* ... e332+4*e31*e32*e15*e33*e34*e16*e122-4*e31*e32*e13*e35*e34* ... e16*e122+4*e31*e32*e15*e14*e16*e13*e332+4*e35*e162*e15*e33* ... e31*e32*e12+4*e31*e34*e33*e12*e35*e16*e132+4*e31*e32*e15*e34* ... e16*e132*e33+8*e16*e35*e15*e33*e13*e36*e32*e12-8*e31*e36*e34* ... e33*e14*e16*e122-8*e16*e35*e15*e33*e13*e31*e32*e12-12*e31* ... e36*e14*e35*e16*e32*e132+4*e312*e13*e15*e35*e16*e32*e12-8* ... e312*e13*e14*e36*e15*e12*e33-8*e312*e15*e33*e14*e16*e32*e13+ ... 8*e14*e15*e33*e12*e34*e35*e32*e13+8*e35*e36*e152*e14*e31*e12* ... e33+4*e31*e12*e15*e14*e36*e16*e342+4*e31*e16*e14*e33*e152* ... e36*e34+4*e122*e32*e14*e33*e35*e31*e16-4*e33*e12*e15*e14*e36* ... e16*e342-4*e32*e35*e34*e12*e33*e15*e14*e16-4*e122*e32*e14* ... e33*e35*e36*e16-12*e34*e35*e33*e12*e162*e13*e31-8*e34*e162* ... e33*e15*e32*e13*e31+8*e342*e36*e13*e14*e15*e12*e33-8*e342* ... e36*e13*e14*e15*e12*e31-4*e16*e33*e122*e34*e35*e32*e13+4*e33* ... e12*e14*e36*e15*e16*e352+4*e16*e132*e31*e33*e36*e32*e12+ ... e344*e152*e132+e162*e354*e132+e142*e354*e132+e162* ... e344*e132-4*e162*e35*e14*e32*e31*e13*e33+e322*e362*e144+ ... 4*e32*e35*e12*e15*e36*e162*e31+e332*e124*e342+e122*e162* ... e344-4*e32*e34*e36*e14*e12*e162*e31+e342*e362*e124+e124* ... e332*e362+e122*e344*e152+e322*e342*e154-4*e36*e15*e13* ... e33*e14*e322*e12+e332*e342*e154+e312*e342*e154+4*e33* ... e16*e31*e142*e15*e36*e35+e324*e162*e152+e324*e142*e152+ ... e332*e312*e154+e322*e312*e154-2*e33*e313*e154+e312* ... e362*e154+e332*e362*e154+e322*e362*e154+e312*e362* ... e144+e332*e362*e144+e324*e142*e162-2*e313*e36*e154+4* ... e36*e35*e13*e33*e14*e32*e122+4*e36*e152*e33*e13*e31*e32*e12+ ... e312*e124*e352+e124*e362*e352+e312*e144*e352+e122* ... e142*e354+e322*e144*e352-4*e313*e164*e33+e124*e342* ... e352+e332*e144*e352+8*e36*e15*e33*e14*e16*e322*e12+8*e14* ... e342*e15*e13*e31*e12*e33-8*e31*e15*e33*e14*e16*e322*e12+4* ... e31*e15*e13*e33*e14*e322*e12-4*e31*e35*e13*e33*e14*e32*e122- ... 2*e333*e36*e144+e322*e332*e144-2*e333*e31*e144+e312* ... e332*e144+2*e334*e142*e162+2*e332*e322*e164-4*e333* ... e31*e164+6*e312*e332*e164+e122*e162*e354+2*e312*e322* ... e164+2*e314*e152*e162-4*e36*e134*e313-2*e332*e34*e12* ... e32*e14*e152+4*e31*e35*e34*e33*e14*e153-2*e122*e34*e36* ... e352*e16*e14-2*e12*e32*e15*e35*e162*e342-2*e33*e12*e14*e35* ... e162*e342+2*e31*e12*e14*e35*e162*e342+4*e32*e142*e12*e36* ... e16*e342-4*e12*e32*e31*e152*e16*e352-4*e32*e31*e142*e12* ... e16*e352+2*e33*e34*e12*e15*e162*e352-2*e31*e34*e12*e15* ... e162*e352-2*e32*e34*e14*e12*e162*e352-6*e122*e32*e14*e15* ... e31*e352+6*e33*e12*e34*e15*e142*e352+6*e122*e32*e14*e15* ... e36*e352-6*e31*e12*e34*e15*e142*e352+4*e332*e32*e14*e36* ... e162*e15+4*e312*e32*e14*e36*e162*e15-4*e32*e31*e33*e36* ... e143*e15+4*e31*e36*e33*e35*e16*e153-2*e332*e36*e32*e12*e16* ... e152+2*e332*e31*e32*e12*e16*e152+4*e32*e34*e33*e31*e16* ... e153-4*e33*e12*e34*e31*e36*e153-4*e32*e14*e33*e31*e36*e153- ... 2*e32*e34*e14*e12*e362*e152+6*e31*e12*e14*e152*e342*e35+4* ... e12*e32*e34*e152*e14*e352+4*e12*e32*e16*e33*e142*e352+4* ... e12*e32*e36*e152*e16*e352+4*e32*e142*e12*e15*e342*e35-6* ... e33*e12*e14*e152*e342*e35+8*e16*e14*e33*e34*e15*e36*e35*e13- ... 8*e16*e14*e31*e34*e15*e36*e35*e13+2*e364*e132*e122+2*e362* ... e342*e134-2*e363*e33*e124+e362*e124*e312-2*e363*e124* ... e31+6*e362*e134*e312-4*e363*e134*e31+e324*e164+e334* ... e164+e314*e164+e314*e154+e334*e144; g2 = 2*e11*e354*e132+24*e11*e36*e31*e16*e13*e332-8*e11*e36*e33* ... e152*e312*e13-12*e132*e162*e322*e312+4*e11*e36*e15*e35* ... e13*e332-8*e11*e36*e332*e16*e122*e31+6*e133*e16*e322* ... e312+4*e11*e133*e344+12*e133*e16*e342*e312-28*e11*e36* ... e332*e16*e32*e12+6*e11*e324*e162+8*e11*e36*e14*e35*e12* ... e332-3*e122*e132*e342*e312+6*e133*e11*e342*e312+16* ... e11*e35*e15*e33*e13*e36*e32*e12+16*e11*e36*e33*e16*e122* ... e312+12*e11*e334*e162-16*e11*e31*e36*e13*e14*e35*e12*e33+ ... 24*e11*e36*e33*e16*e132*e312+24*e11*e36*e33*e16*e13*e312+8* ... e11*e36*e14*e34*e322*e13+2*e11*e122*e354-4*e11*e344*e132+ ... 8*e13*e152*e16*e314-48*e11*e36*e31*e16*e132*e332-6*e133* ... e34*e14*e313+8*e11*e36*e152*e31*e322*e13+4*e11*e36*e15* ... e312*e34*e12+8*e11*e36*e15*e35*e322*e13-32*e11*e36*e33*e14* ... e31*e15*e32*e13+16*e11*e36*e152*e31*e13*e332+12*e11*e36*e15* ... e34*e12*e332+4*e11*e36*e312*e16*e32*e12+12*e11*e36*e15*e35* ... e13*e312-4*e11*e36*e14*e312*e34*e132+4*e11*e36*e14*e35* ... e322*e12+2*e132*e323*e34*e15+12*e11*e36*e14*e34*e13*e332+ ... 4*e11*e36*e14*e312*e34*e13-16*e11*e36*e15*e13*e31*e34*e12* ... e33-4*e11*e312*e33*e162*e32*e12-32*e11*e36*e33*e13*e31*e16* ... e32*e12-16*e11*e313*e15*e35*e16*e13+32*e11*e31*e322*e162* ... e13*e33+16*e11*e31*e33*e352*e16*e132+8*e11*e31*e33*e352* ... e16*e122-8*e112*e36*e12*e35*e31*e34*e13+8*e11*e33*e35*e12* ... e34*e32*e15*e14+16*e112*e36*e34*e12*e35*e13*e33-8*e112*e14* ... e31*e15*e33*e35*e34+24*e112*e32*e14*e33*e15*e31*e36-8*e112* ... e32*e35*e12*e15*e31*e36-16*e11*e12*e32*e35*e34*e15*e31*e14-8* ... e112*e32*e35*e14*e33*e31*e16-8*e112*e35*e12*e33*e34*e31*e16- ... 8*e112*e33*e15*e36*e32*e12*e35-32*e112*e34*e35*e32*e16*e31* ... e13+16*e112*e16*e35*e32*e33*e34*e13+24*e112*e32*e34*e33*e15* ... e36*e13+8*e112*e32*e35*e14*e33*e36*e13-8*e112*e32*e35*e14* ... e36*e31*e13-8*e11*e31*e332*e162*e32*e12-16*e11*e34*e33*e15* ... e32*e16*e13*e31-8*e112*e36*e14*e31*e34*e13*e33-32*e11*e34* ... e33*e12*e35*e16*e13*e31+16*e11*e14*e33*e31*e34*e16*e32*e12-8* ... e11*e31*e342*e33*e16*e132-8*e11*e142*e31*e342*e13*e33+16* ... e112*e36*e33*e14*e35*e12*e31-8*e112*e36*e33*e31*e16*e32*e12+ ... 24*e112*e36*e33*e15*e35*e13*e31+24*e112*e36*e15*e31*e34*e12* ... e33-8*e11*e32*e34*e33*e15*e31*e142+16*e11*e332*e14*e15*e32* ... e16*e31-8*e11*e32*e34*e31*e14*e12*e36-16*e11*e142*e32*e36* ... e12*e332+8*e11*e33*e14*e152*e32*e31*e35+8*e11*e31*e14*e35* ... e16*e12*e332-8*e11*e15*e312*e34*e16*e12*e33-8*e11*e14*e15* ... e34*e35*e322*e13+24*e11*e35*e14*e32*e16*e13*e312-8*e11* ... e342*e13*e14*e35*e12*e31+8*e11*e342*e13*e14*e35*e12*e33-8* ... e11*e36*e12*e35*e31*e34*e13-8*e11*e36*e34*e12*e35*e13*e33-8* ... e11*e36*e14*e13*e35*e322*e12-8*e11*e32*e16*e14*e312*e15*e33- ... 16*e11*e14*e34*e16*e13*e333-8*e11*e14*e33*e352*e34*e122+16* ... e11*e32*e36*e12*e152*e31*e33-8*e11*e32*e14*e33*e15*e31*e36+8* ... e11*e32*e35*e12*e15*e31*e36+8*e11*e32*e34*e33*e15*e31*e16-20* ... e11*e14*e31*e352*e34*e132+16*e11*e32*e35*e14*e33*e31*e16+4* ... e11*e14*e31*e352*e34*e122-8*e11*e14*e15*e332*e342*e12+24* ... e11*e35*e12*e33*e34*e31*e16+8*e11*e32*e35*e34*e31*e142*e13+8* ... e11*e32*e34*e33*e152*e35*e13-16*e11*e32*e34*e31*e152*e35* ... e13+12*e11*e14*e342*e32*e35*e132-8*e11*e35*e15*e312*e16* ... e32*e12+8*e11*e342*e132*e36*e32*e12+4*e11*e342*e15*e35* ... e132*e31+16*e11*e34*e35*e32*e16*e31*e13-3*e312*e132*e322* ... e152+4*e13*e324*e16*e142+12*e11*e342*e15*e35*e132*e33-8* ... e11*e32*e34*e36*e15*e31*e13+16*e11*e16*e35*e32*e33*e34*e13-3* ... e132*e322*e312*e142-16*e11*e32*e34*e33*e15*e36*e13+2*e13* ... e322*e312*e142+8*e11*e342*e33*e152*e13*e31+8*e11*e343* ... e15*e13*e12*e33-8*e11*e32*e35*e14*e33*e36*e13-16*e11*e32*e35* ... e14*e36*e31*e13-16*e11*e32*e35*e34*e33*e142*e13+2*e122* ... e322*e13*e342-3*e132*e322*e122*e342+8*e11*e36*e33*e15* ... e14*e322*e12-8*e11*e342*e35*e32*e14*e13-8*e11*e16*e33*e342* ... e31*e13-8*e11*e33*e15*e35*e16*e322*e13-8*e11*e36*e33*e15*e35* ... e132*e31-8*e11*e352*e15*e12*e34*e13*e33+8*e11*e352*e15*e12* ... e34*e13*e31-16*e11*e352*e14*e31*e15*e12*e33+8*e11*e35*e33* ... e122*e34*e16*e32+16*e11*e36*e12*e14*e31*e34*e32*e13-8*e11* ... e352*e13*e33*e16*e32*e12+16*e11*e352*e13*e31*e16*e32*e12-4* ... e11*e322*e35*e15*e36*e132+16*e11*e35*e14*e32*e16*e13*e332+ ... 8*e11*e33*e35*e15*e342*e13+16*e11*e342*e13*e33*e16*e32*e12- ... 32*e11*e34*e32*e35*e16*e132*e33-16*e11*e34*e13*e35*e16*e322* ... e12+24*e11*e34*e12*e35*e16*e13*e332+24*e11*e34*e35*e12*e16* ... e13*e312-4*e11*e15*e35*e31*e342*e13+24*e11*e34*e15*e32*e16* ... e13*e332-8*e11*e142*e33*e32*e36*e12*e31+8*e11*e14*e15*e31* ... e342*e12*e33+16*e11*e14*e33*e15*e34*e35*e13*e31+8*e11*e34* ... e352*e31*e14*e13-8*e11*e14*e332*e34*e16*e32*e12-8*e11*e14* ... e15*e34*e35*e13*e332-8*e11*e14*e33*e34*e16*e322*e13-8*e11* ... e14*e15*e34*e35*e13*e312+24*e11*e31*e14*e34*e16*e13*e332-8* ... e11*e31*e14*e35*e16*e322*e12+8*e11*e31*e32*e35*e34*e16*e122+ ... 16*e11*e31*e32*e35*e34*e16*e132-8*e11*e31*e14*e36*e34*e122* ... e33-8*e11*e31*e15*e35*e16*e13*e332-8*e11*e31*e15*e35*e16* ... e322*e13+24*e11*e31*e15*e34*e16*e12*e332-4*e11*e34*e352* ... e33*e14*e13+24*e11*e31*e36*e14*e35*e32*e132+8*e11*e36*e14* ... e31*e15*e322*e12+24*e11*e36*e14*e31*e34*e132*e33-16*e11*e36* ... e14*e31*e34*e13*e33-8*e11*e36*e14*e312*e15*e32*e13-8*e11*e36* ... e12*e32*e16*e13*e312+16*e11*e36*e12*e35*e31*e34*e132-8*e11* ... e36*e15*e31*e34*e32*e122+16*e11*e36*e14*e31*e15*e12*e332-8* ... e11*e36*e33*e14*e35*e12*e31+24*e11*e36*e33*e31*e16*e32*e12-32* ... e11*e36*e33*e14*e312*e15*e12-8*e11*e36*e33*e35*e31*e15*e122+ ... 8*e11*e323*e14*e35*e16*e13-16*e11*e36*e33*e15*e35*e13*e31+4* ... e11*e13*e322*e152*e342+4*e11*e132*e31*e343*e14-12*e11* ... e132*e16*e312*e342-4*e11*e12*e32*e33*e362*e132-16*e11* ... e36*e15*e31*e34*e12*e33+8*e11*e36*e15*e31*e34*e32*e132-8*e11* ... e36*e15*e13*e312*e34*e12+8*e11*e13*e323*e16*e15*e34-8*e11* ... e312*e14*e34*e16*e13*e33+24*e11*e312*e33*e15*e35*e16*e13-8* ... e11*e36*e32*e15*e14*e13*e332-8*e11*e36*e32*e12*e16*e13*e332- ... 8*e11*e36*e13*e15*e34*e322*e12-8*e11*e36*e34*e33*e12*e35* ... e132-8*e11*e36*e32*e15*e34*e132*e33+16*e11*e36*e32*e13*e35* ... e34*e122-8*e11*e36*e14*e12*e35*e13*e332+16*e11*e312*e13* ... e16*e32*e15*e34-8*e11*e12*e32*e16*e31*e13*e342-8*e11*e13* ... e322*e16*e34*e14*e31-8*e11*e36*e322*e16*e13*e31+16*e11*e36* ... 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e34*e12*e312*e152-4*e11*e332*e36*e32*e12*e152+12*e11*e12* ... e322*e34*e152*e35-8*e11*e12*e323*e15*e16*e35+4*e11*e332* ... e12*e34*e152*e35-2*e114*e354+8*e11*e122*e322*e36*e15*e35+ ... 2*e113*e354-2*e112*e122*e354-12*e11*e32*e12*e152*e342* ... e33+8*e11*e122*e35*e15*e342*e33-8*e11*e322*e15*e35*e142* ... e33+12*e11*e34*e312*e152*e14*e33-8*e11*e323*e14*e15*e16* ... e33-16*e11*e322*e31*e152*e16*e33-20*e11*e31*e34*e152*e332* ... e14-4*e11*e32*e132*e15*e343+8*e11*e32*e34*e33*e31*e153+4* ... e11*e332*e31*e15*e35*e142+4*e11*e12*e32*e152*e31*e342-4* ... e132*e16*e34*e15*e32*e312+12*e11*e32*e312*e12*e152*e36+8* ... e11*e322*e14*e152*e34*e33-4*e11*e122*e15*e36*e35*e332+16* ... e11*e333*e12*e15*e36*e14-8*e13*e32*e16*e14*e15*e313-4*e11* ... e12*e32*e16*e33*e342-4*e11*e32*e12*e15*e35*e342+8*e11*e322* ... e34*e33*e16*e14+4*e11*e31*e12*e342*e35*e14-12*e11*e312*e16* ... e32*e35*e14-4*e11*e132*e16*e322*e342-4*e11*e33*e35*e12* ... e342*e14+4*e11*e16*e34*e312*e33*e14-16*e11*e322*e16*e35* ... e15*e33+4*e11*e312*e13*e152*e342-8*e11*e333*e12*e35*e14* ... e16-16*e11*e333*e12*e34*e15*e16-8*e11*e333*e14*e15*e32*e16- ... 12*e132*e32*e34*e15*e11*e312+4*e11*e332*e14*e15*e32*e36-8* ... e11*e332*e16*e34*e31*e14+4*e11*e322*e34*e14*e16*e31+4*e11* ... e322*e16*e35*e15*e31+32*e11*e332*e16*e35*e15*e31-12*e11*e34* ... e312*e35*e12*e16+20*e11*e12*e32*e33*e352*e16-12*e11*e312* ... e13*e162*e322-20*e11*e31*e32*e12*e352*e16-4*e11*e332*e32* ... e14*e35*e16+12*e11*e12*e322*e16*e35*e34+8*e11*e32*e34*e13* ... e15*e312-12*e11*e332*e16*e12*e35*e34+4*e11*e32*e31*e12*e16* ... e342+4*e11*e36*e14*e312*e34*e16*e13+12*e11*e36*e14*e34*e16* ... e13*e332-8*e11*e34*e32*e15*e352*e13+4*e11*e36*e14*e35*e16* ... e322*e12+12*e11*e36*e15*e35*e16*e13*e312+8*e11*e36*e14*e34* ... e16*e322*e13-8*e11*e152*e352*e33*e13*e31-8*e11*e36*e32*e35* ... e34*e16*e122+8*e11*e36*e32*e35*e34*e16*e132-4*e11*e15*e352* ... e32*e34*e132+8*e11*e36*e14*e35*e16*e12*e332+4*e11*e36*e15* ... e35*e16*e13*e332+12*e11*e36*e33*e31*e162*e32*e12-8*e11*e16* ... e352*e33*e31*e13-4*e11*e36*e32*e12*e352*e132+4*e11*e36*e15* ... e312*e34*e16*e12+8*e11*e36*e15*e35*e16*e322*e13+8*e11*e31* ... e33*e352*e142*e13-28*e11*e15*e35*e36*e312*e132-28*e11* ... e312*e16*e35*e15*e33+12*e11*e36*e15*e34*e16*e12*e332-8*e11* ... e32*e16*e34*e312*e15-4*e11*e362*e12*e14*e34*e32*e13+4*e11* ... e32*e14*e36*e15*e312+12*e11*e362*e12*e32*e16*e13*e31+8*e11* ... e362*e33*e14*e15*e12*e31+12*e11*e362*e33*e13*e16*e32*e12+4* ... e11*e362*e15*e13*e34*e12*e33+8*e11*e362*e15*e13*e34*e12*e31- ... 4*e11*e362*e13*e15*e35*e32*e12+4*e11*e32*e35*e34*e36*e142* ... e13-8*e11*e35*e32*e342*e16*e14*e13-4*e11*e31*e16*e15*e35* ... e342*e13+8*e11*e33*e16*e15*e35*e342*e13+8*e11*e34*e35*e32* ... e162*e31*e13-4*e11*e332*e35*e14*e15*e34-4*e11*e32*e14*e15* ... e342*e33+4*e11*e32*e15*e31*e14*e352-8*e11*e32*e34*e31*e152* ... e35+4*e11*e32*e34*e33*e152*e35+16*e11*e332*e36*e142*e31-4* ... e11*e36*e32*e12*e352*e13+4*e11*e362*e13*e14*e35*e12*e31+8* ... e11*e362*e13*e14*e35*e12*e33-4*e11*e342*e13*e36*e32*e12-20* ... e112*e33*e35*e15*e342*e13-8*e12*e34*e13*e15*e16*e313+12* ... e112*e34*e352*e31*e14*e13+4*e112*e34*e352*e33*e14*e13+8* ... e11*e32*e34*e31*e15*e36*e16-8*e11*e31*e34*e152*e32*e16*e35+4* ... e11*e33*e34*e152*e32*e16*e35+4*e11*e32*e15*e31*e14*e16*e352- ... 4*e11*e32*e14*e33*e152*e36*e35+8*e11*e32*e35*e34*e16*e142* ... e33+8*e11*e33*e14*e34*e36*e31*e152-4*e11*e33*e12*e16*e14*e35* ... e342+4*e11*e33*e12*e14*e15*e36*e342-4*e11*e31*e12*e14*e15* ... e36*e342-4*e11*e32*e16*e12*e15*e35*e342+4*e11*e31*e12*e16* ... e14*e35*e342-4*e11*e31*e36*e15*e33*e35*e142-4*e11*e33*e12* ... e34*e36*e35*e152-4*e11*e32*e35*e34*e16*e142*e31-4*e11*e16* ... e14*e35*e332*e15*e34+8*e11*e353*e13*e14*e12*e31-4*e11*e32* ... e15*e14*e16*e342*e33+4*e11*e34*e312*e15*e35*e14-4*e11*e12* ... e32*e36*e16*e352*e13-4*e11*e342*e16*e13*e36*e32*e12+12*e11* ... 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e16*e14*e31*e34*e352*e13+6*e132*e34*e14*e313+2*e122*e13* ... e342*e312+8*e11*e33*e162*e32*e35*e34*e13+32*e112*e36* ... e332*e16*e32*e12-4*e112*e36*e14*e35*e12*e332-4*e112*e36* ... e15*e35*e322*e13-12*e112*e36*e15*e34*e12*e332+16*e112*e36* ... e15*e35*e13*e312-28*e112*e36*e14*e34*e13*e332+8*e112*e36* ... e32*e35*e34*e16*e13+4*e112*e32*e35*e14*e36*e31*e16+8*e112* ... e14*e35*e33*e32*e36*e16+4*e112*e35*e12*e33*e34*e36*e16+4* ... e112*e34*e31*e35*e12*e36*e16+12*e112*e32*e34*e33*e15*e36* ... e16+12*e112*e33*e16*e35*e15*e31*e36-12*e132*e16*e322*e312- ... 4*e112*e33*e34*e36*e15*e35*e14+4*e112*e31*e34*e36*e15*e35* ... e14+4*e112*e16*e14*e31*e33*e34*e36-4*e112*e342*e35*e32*e14* ... e13+16*e112*e16*e33*e342*e31*e13-4*e112*e31*e34*e12*e15* ... e352-8*e112*e362*e33*e13*e32*e12-12*e11*e12*e323*e16*e13* ... e31-4*e112*e362*e12*e32*e13*e31-8*e13*e323*e16*e14*e15*e31+ ... 6*e132*e322*e34*e11*e14*e31-32*e112*e36*e32*e35*e34*e132+ ... 20*e132*e322*e16*e34*e14*e31-8*e112*e36*e322*e16*e13*e33+ ... 16*e112*e36*e322*e16*e13*e31-48*e112*e36*e33*e16*e13*e312- ... 4*e112*e36*e14*e34*e322*e13+4*e112*e36*e15*e34*e322*e12+ ... 24*e112*e36*e31*e16*e13*e332-4*e112*e36*e15*e35*e13*e332- ... 16*e13*e322*e16*e34*e14*e31-8*e112*e16*e352*e33*e31*e13-12* ... e132*e16*e312*e342+16*e112*e312*e16*e35*e15*e33-4*e112* ... e332*e16*e34*e31*e14-28*e112*e332*e16*e35*e15*e31-16*e112* ... e12*e32*e33*e352*e16+12*e112*e31*e32*e12*e352*e16-4*e112* ... e332*e32*e14*e35*e16+4*e132*e31*e343*e14-12*e112*e332* ... e16*e32*e15*e34-4*e112*e12*e322*e16*e35*e34-4*e133*e31* ... e343*e14-4*e112*e12*e32*e16*e33*e342-2*e132*e322*e342* ... e142+4*e112*e32*e12*e15*e35*e342-4*e112*e322*e34*e33*e16* ... e14-2*e132*e342*e312*e142-12*e112*e334*e162+20*e112* ... e322*e16*e35*e15*e33+4*e112*e33*e34*e12*e15*e352-8*e13* ... e322*e34*e14*e162*e31+4*e112*e14*e36*e33*e34*e31+16*e112* ... e34*e35*e32*e16*e31+4*e112*e32*e35*e14*e36*e31+8*e112*e36* ... e32*e35*e34*e13+4*e112*e35*e12*e33*e34*e36-4*e32*e132*e15* ... 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e32*e34*e33*e15*e36-4*e11*e32*e31*e12*e13*e342+10*e12*e32* ... e31*e13*e162*e342-4*e12*e34*e13*e15*e313+20*e12*e32*e16* ... e31*e13*e342-2*e132*e32*e34*e15*e312-16*e132*e32*e16*e12* ... e31*e342+4*e12*e32*e152*e13*e31*e342-4*e31*e12*e13*e15*e16* ... e343+12*e13*e16*e32*e12*e313-4*e13*e32*e14*e12*e16*e343+4* ... e11*e33*e31*e342*e142+12*e12*e32*e162*e13*e313+6*e132* ... e32*e15*e14*e313-4*e312*e13*e16*e32*e15*e34-2*e312*e13*e32* ... e15*e162*e34-4*e13*e32*e15*e14*e313-24*e11*e33*e162*e322* ... e31+2*e113*e352*e342+4*e113*e354*e13-18*e12*e32*e16* ... e132*e313+12*e132*e16*e34*e14*e313-8*e11*e31*e33*e352* ... e142+6*e12*e32*e31*e132*e342*e11+6*e12*e32*e152*e13*e313+ ... 8*e13*e322*e152*e16*e312-6*e13*e322*e152*e11*e312+6* ... e133*e15*e32*e34*e312+4*e122*e16*e13*e342*e312-12*e11* ... e16*e322*e13*e312+4*e11*e322*e31*e152*e36+6*e132*e34*e15* ... e12*e313+6*e122*e322*e16*e13*e312-4*e13*e323*e14*e15*e31+ ... 10*e132*e322*e34*e14*e31+12*e113*e362*e332+2*e113*e322* ... 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... e142+6*e333*e31*e122*e142+4*e333*e35*e12*e143+4*e333* ... e15*e32*e143+2*e333*e36*e152*e142-4*e333*e31*e152*e142+ ... 8*e312*e332*e152*e142-2*e333*e34*e16*e143-4*e332*e31* ... e36*e144-2*e333*e12*e32*e163-4*e333*e31*e122*e162+2* ... e333*e36*e122*e162+3*e122*e332*e342*e162+2*e33*e31* ... e144*e352-e122*e152*e342*e352-e122*e142*e342*e352+2* ... e33*e12*e143*e353-2*e31*e12*e143*e353-4*e123*e14*e31* ... e353-2*e122*e322*e142*e352-6*e312*e152*e332*e162+2* ... e333*e31*e152*e162+6*e333*e31*e142*e162-6*e312*e332* ... e142*e162-3*e322*e142*e332*e162-2*e123*e34*e16*e353-2* ... e322*e312*e152*e142+2*e313*e36*e152*e142-e322*e312* ... e162*e142-3*e322*e312*e152*e162+18*e11*e322*e332* ... e162-2*e16*e312*e352*e142+2*e313*e34*e152*e14-2*e312* ... e152*e16*e352-2*e122*e322*e16*e352-2*e122*e15*e31*e353+ ... 2*e123*e32*e36*e352-2*e123*e32*e31*e352+2*e122*e15*e36* ... e353+2*e312*e153*e36*e35+4*e33*e312*e153*e35+2*e332*e34* ... e32*e153-2*e323*e31*e12*e152+2*e323*e36*e12*e152+2*e32* ... 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... e152*e312-8*e11*e333*e142*e31-2*e11*e332*e122*e342-4* ... e11*e33*e152*e313-4*e11*e333*e31*e152+2*e11*e122*e322* ... e352+2*e11*e332*e322*e152+4*e11*e332*e342*e132+12*e11* ... e36*e132*e313-12*e11*e36*e133*e313+6*e11*e312*e352* ... e133-4*e11*e312*e352*e122-2*e11*e312*e352*e132+4*e11* ... e352*e322*e132-4*e11*e122*e333*e36+4*e11*e322*e332* ... e142+4*e11*e332*e142*e312+2*e11*e332*e122*e352+8*e11* ... e332*e152*e312-8*e11*e13*e324*e16+6*e11*e133*e322*e342+ ... 6*e113*e322*e332*e16-6*e113*e333*e34*e14-6*e113*e333* ... e35*e15+6*e113*e332*e342*e13-12*e113*e36*e13*e333-4* ... e113*e352*e33*e31-4*e113*e33*e322*e36+12*e113*e332*e31* ... e36+6*e113*e332*e352*e13+6*e113*e322*e352*e13-12*e113* ... e333*e16*e31-12*e112*e322*e332*e16+6*e112*e333*e142* ... e31-3*e112*e332*e122*e342+2*e112*e333*e34*e14+6*e112* ... e333*e31*e152+6*e112*e333*e35*e15-3*e112*e122*e322* ... e352-3*e112*e332*e322*e152-2*e112*e332*e342*e13-6* ... e112*e332*e342*e132-4*e11*e123*e32*e36*e352+4*e11*e122* ... 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... e32*e13-2*e11*e362*e322*e16*e132+4*e36*e32*e15*e34*e16* ... e132*e33-16*e36*e14*e33*e31*e15*e32*e122+4*e36*e14*e12*e35* ... e16*e13*e332-4*e11*e362*e142*e312*e13-12*e11*e36*e162* ... e13*e333-6*e11*e36*e162*e323*e12+24*e36*e33*e14*e35*e16* ... e12*e31-8*e36*e14*e31*e34*e16*e13*e33+8*e11*e362*e142*e13* ... e332-12*e11*e36*e162*e13*e313+8*e362*e31*e13*e14*e15*e12* ... e33-8*e11*e363*e33*e13*e122+12*e11*e362*e16*e132*e332-8* ... e35*e15*e33*e31*e16*e32*e12-8*e31*e14*e12*e35*e16*e13*e332-8* ... e31*e32*e15*e33*e34*e16*e122+8*e31*e32*e13*e35*e34*e16*e122+ ... 8*e11*e362*e332*e16*e122-8*e31*e32*e15*e14*e16*e13*e332- ... 16*e31*e36*e13*e14*e35*e12*e33-4*e35*e162*e15*e33*e31*e32* ... e12-8*e31*e34*e33*e12*e35*e16*e132-8*e31*e32*e15*e34*e16* ... e132*e33-2*e11*e362*e152*e322*e13-8*e16*e35*e15*e33*e13* ... e36*e32*e12+8*e31*e36*e34*e33*e14*e16*e122-8*e11*e363*e31* ... e13*e122-24*e11*e362*e312*e16*e132-4*e11*e362*e312*e16* ... e122+16*e16*e35*e15*e33*e13*e31*e32*e12+12*e31*e36*e14*e35* ... e16*e32*e132+4*e11*e362*e342*e13*e122+8*e11*e362*e152* ... e13*e312-4*e11*e362*e152*e13*e332-8*e312*e13*e15*e35*e16* ... e32*e12+16*e312*e13*e14*e36*e15*e12*e33+16*e312*e15*e33*e14* ... e16*e32*e13-36*e11*e312*e162*e33*e36+36*e11*e332*e162*e31* ... e36+8*e11*e33*e152*e362*e31+4*e11*e33*e342*e36*e142-4*e11* ... e33*e343*e16*e14-12*e11*e352*e33*e162*e31+12*e11*e33*e342* ... e162*e31-8*e11*e33*e142*e362*e31+12*e11*e31*e322*e36* ... e162-12*e11*e33*e322*e36*e162-16*e14*e15*e33*e12*e34*e35* ... e32*e13+4*e11*e15*e31*e16*e353-4*e11*e33*e15*e16*e353+4*e11* ... e32*e14*e16*e353-8*e35*e36*e152*e14*e31*e12*e33-4*e11*e31* ... e36*e152*e352+4*e11*e33*e36*e152*e352-4*e11*e15*e36*e353* ... e13+8*e11*e362*e322*e16*e13-8*e11*e363*e12*e32*e13+24*e11* ... e362*e16*e13*e332+24*e11*e362*e16*e13*e312-4*e11*e14*e36* ... e343*e13+4*e11*e31*e343*e16*e14-4*e11*e32*e15*e16*e343+8* ... e11*e16*e352*e342*e13+2*e11*e31*e343*e14*e152-4*e11*e31* ... e342*e36*e142+2*e11*e31*e15*e142*e353-2*e11*e33*e343*e14* ... e152-2*e11*e33*e15*e142*e353+2*e11*e31*e34*e143*e352-2* ... e11*e322*e352*e162*e13+2*e11*e31*e153*e342*e35-2*e11*e33* ... e153*e342*e35-2*e11*e33*e34*e143*e352-2*e11*e332*e162* ... e342*e13-2*e11*e322*e342*e162*e13+6*e11*e352*e332*e162* ... e13-2*e11*e15*e36*e353*e132+6*e11*e312*e342*e162*e13-2* ... e11*e352*e312*e162*e13-2*e11*e16*e352*e342*e132+4*e11* ... e14*e36*e343*e132-2*e16*e344*e132+2*e11*e152*e342*e352* ... e13+2*e11*e142*e342*e352*e13+2*e112*e34*e36*e352*e14-8* ... e112*e16*e352*e31*e36-6*e112*e32*e35*e14*e362-2*e112*e15* ... e35*e362*e33-6*e112*e15*e32*e34*e362-8*e112*e33*e342*e16* ... e36+2*e112*e15*e35*e36*e342+24*e112*e31*e16*e33*e362+2* ... e112*e14*e33*e34*e362-4*e112*e35*e12*e34*e362+2*e112*e15* ... e31*e35*e362+8*e112*e16*e352*e33*e36-2*e112*e33*e343*e16* ... e14+12*e112*e312*e162*e33*e36-24*e112*e332*e162*e31*e36+ ... 8*e112*e33*e322*e36*e162+6*e112*e33*e142*e362*e31+8* ... e112*e36*e342*e16*e31-4*e112*e33*e342*e162*e31+8*e112* ... e352*e33*e162*e31-2*e112*e33*e152*e362*e31+2*e112*e33* ... e342*e36*e142-4*e112*e31*e322*e36*e162-6*e112*e15*e31* ... e16*e353+4*e112*e33*e15*e16*e353-4*e112*e32*e14*e16*e353- ... 2*e112*e14*e34*e362*e31-2*e112*e36*e31*e352*e142+4*e112* ... e36*e33*e352*e142-4*e112*e33*e36*e152*e352+6*e112*e31* ... e36*e152*e352-2*e112*e34*e12*e16*e353+2*e112*e14*e36*e12* ... e353-2*e112*e12*e16*e343*e35+2*e112*e14*e15*e343*e35+2* ... e112*e34*e15*e14*e353+2*e112*e15*e12*e36*e343-2*e112*e33* ... e152*e36*e342+4*e112*e31*e152*e36*e342-8*e12*e32*e34*e36* ... e15*e35*e14-8*e12*e32*e35*e15*e31*e36*e16-8*e34*e36*e12*e33* ... e32*e14*e16-8*e122*e32*e14*e33*e35*e31*e16+4*e32*e35*e34*e12* ... e33*e15*e14*e16+8*e32*e34*e31*e14*e12*e36*e16+4*e122*e32*e14* ... e33*e35*e36*e16+12*e34*e35*e33*e12*e162*e13*e31-8*e35*e15* ... e33*e13*e36*e32*e12+8*e35*e15*e33*e13*e31*e32*e12+8*e35*e14* ... e32*e31*e16*e13*e33+8*e34*e162*e33*e15*e32*e13*e31-8*e342* ... e36*e13*e14*e15*e12*e33+8*e342*e36*e13*e14*e15*e12*e31+8*e16* ... e33*e122*e34*e35*e32*e13-8*e16*e132*e31*e33*e36*e32*e12- ... e344*e152*e132-e142*e354*e132+4*e162*e35*e14*e32*e31* ... e13*e33-2*e16*e354*e132+2*e342*e352*e133-3*e332*e124* ... e342-e342*e362*e124-2*e124*e332*e362-e122*e344*e152- ... e322*e342*e154+8*e36*e15*e13*e33*e14*e322*e12-e332*e342* ... e154-e312*e342*e154-e324*e162*e152-2*e324*e142*e152- ... 2*e332*e312*e154-2*e322*e312*e154+4*e33*e313*e154- ... e324*e142*e162+2*e313*e36*e154-8*e36*e35*e13*e33*e14*e32* ... e122-8*e36*e152*e33*e13*e31*e32*e12-3*e312*e124*e352- ... e124*e362*e352-e312*e144*e352-e122*e142*e354-e322* ... e144*e352-2*e124*e342*e352-e332*e144*e352-8*e36*e15* ... e33*e14*e16*e322*e12-16*e14*e342*e15*e13*e31*e12*e33+16*e31* ... e15*e33*e14*e16*e322*e12-12*e31*e15*e13*e33*e14*e322*e12+12* ... e31*e35*e13*e33*e14*e32*e122+2*e333*e36*e144-2*e322*e332* ... e144+4*e333*e31*e144-2*e312*e332*e144-2*e334*e142* ... e162-2*e314*e152*e162-2*e312*e352*e133+6*e112*e324* ... e13*e16+6*e132*e11*e324*e16-12*e36*e133*e313+12*e36*e134* ... e313+4*e363*e33*e133-4*e112*e352*e33*e31*e13+8*e112*e15* ... e312*e35*e33+12*e112*e14*e34*e13*e333-12*e113*e322*e35* ... e15*e33+6*e113*e332*e35*e12*e34+12*e113*e332*e32*e15*e34+ ... 6*e113*e12*e32*e33*e352+6*e113*e332*e32*e14*e35+12*e113* ... e332*e35*e15*e31-18*e113*e36*e332*e32*e12-36*e113*e36*e31* ... e13*e332+12*e113*e322*e36*e13*e33+8*e113*e33*e35*e32*e34+ ... 12*e113*e352*e33*e31*e13-8*e11*e14*e34*e13*e333-2*e112* ... e14*e332*e34*e31+12*e112*e322*e31*e152*e33+6*e112*e323* ... e14*e15*e33+10*e112*e322*e35*e15*e33+6*e112*e333*e14*e15* ... e32+6*e112*e333*e14*e12*e35+12*e112*e34*e15*e12*e333-18* ... e112*e333*e12*e32*e16-2*e112*e322*e34*e33*e14-6*e112* ... e332*e32*e15*e34-8*e112*e12*e32*e33*e352+6*e112*e31*e32* ... e12*e352-2*e112*e332*e32*e14*e35-6*e112*e12*e323*e33*e16+ ... 8*e112*e33*e16*e322*e31-14*e112*e332*e35*e15*e31+6*e112* ... e12*e323*e15*e35+16*e112*e36*e332*e32*e12+36*e112*e36*e31* ... e132*e332-24*e112*e36*e33*e13*e312+36*e112*e36*e33*e132* ... e312+12*e112*e36*e31*e13*e332+18*e112*e36*e332*e122*e31- ... 6*e112*e13*e36*e323*e12-12*e112*e322*e36*e132*e31-12* ... e112*e322*e36*e132*e33-12*e112*e31*e342*e132*e33+6* ... e112*e33*e36*e322*e122-2*e112*e33*e342*e32*e12+8*e112* ... e31*e342*e13*e33-4*e112*e322*e36*e13*e33+8*e112*e322*e36* ... e13*e31-2*e112*e34*e35*e322*e12-6*e112*e35*e14*e323*e13+ ... 18*e112*e322*e16*e13*e332-12*e112*e31*e33*e352*e132-6* ... e112*e31*e33*e352*e122-36*e112*e31*e16*e13*e333+36*e112* ... e312*e16*e13*e332+12*e11*e36*e322*e133*e31-24*e11*e36*e31* ... e132*e332+8*e11*e36*e33*e122*e312+12*e11*e36*e33*e132* ... e312-4*e11*e36*e332*e122*e31-36*e11*e36*e33*e133*e312-4* ... e11*e36*e31*e322*e122+8*e11*e13*e36*e323*e12-4*e11*e322* ... e36*e132*e31+8*e11*e322*e36*e132*e33-4*e11*e31*e342*e132* ... e33-8*e11*e33*e36*e322*e122+4*e363*e32*e123-12*e11*e312* ... e142*e13*e332+24*e11*e33*e16*e13*e313-36*e11*e33*e16*e132* ... e313+4*e11*e35*e14*e323*e13-6*e11*e12*e36*e323*e132-12* ... e11*e322*e16*e13*e332+8*e11*e31*e33*e352*e132+4*e11*e31* ... e33*e352*e122+24*e11*e31*e16*e13*e333+12*e11*e313*e15*e35* ... e132+12*e11*e31*e142*e13*e333+12*e11*e31*e342*e33*e133+ ... 12*e11*e312*e13*e352*e122+12*e11*e313*e33*e152*e13+36* ... e11*e312*e16*e132*e332-48*e11*e312*e16*e13*e332-12*e11* ... e312*e152*e13*e332-12*e11*e312*e332*e16*e122-8*e11* ... e313*e15*e35*e13+12*e11*e342*e122*e13*e332+18*e11*e132* ... e16*e322*e312+6*e11*e12*e32*e333*e142+12*e11*e333*e122* ... e16*e31-8*e11*e322*e31*e152*e33-4*e11*e323*e14*e15*e33-4* ... e11*e333*e14*e15*e32+6*e11*e332*e35*e34*e123-6*e11*e123* ... e32*e36*e332-12*e11*e34*e122*e14*e333+6*e11*e322*e122* ... e332*e16-4*e11*e333*e14*e12*e35-8*e11*e34*e15*e12*e333+12* ... e11*e333*e12*e32*e16+8*e11*e12*e323*e33*e16+6*e11*e123*e32* ... e31*e352-4*e11*e12*e323*e15*e35-6*e11*e142*e332*e322*e13- ... 4*e363*e31*e133+12*e362*e133*e312+2*e362*e342*e133-4* ... e11*e32*e35*e12*e15*e312+8*e11*e332*e14*e15*e32*e31-4*e11* ... e32*e14*e33*e15*e312+6*e11*e15*e35*e33*e312*e132-4*e11*e33* ... e15*e35*e322*e13+4*e11*e31*e14*e35*e12*e332+12*e11*e35*e32* ... e312*e14*e13-4*e11*e15*e312*e34*e12*e33-18*e11*e12*e35* ... e312*e34*e132-18*e112*e31*e32*e12*e352*e13+6*e112*e12* ... e32*e33*e352*e13-12*e112*e332*e32*e14*e35*e13-18*e112*e34* ... e15*e32*e13*e332+6*e112*e14*e33*e34*e322*e13+6*e112*e31* ... e332*e16*e32*e12+6*e112*e31*e15*e35*e13*e332-18*e112*e31* ... e15*e34*e12*e332-24*e112*e31*e322*e16*e13*e33-24*e112* ... e312*e33*e15*e35*e13-4*e112*e36*e33*e31*e32*e12-18*e112* ... e12*e34*e35*e13*e332+24*e112*e32*e34*e35*e132*e33+24*e112* ... e32*e34*e35*e132*e31+6*e112*e13*e34*e35*e322*e12+6*e112* ... e13*e33*e342*e32*e12+6*e112*e332*e13*e36*e32*e12+6*e112* ... e14*e31*e34*e13*e332-16*e112*e32*e34*e35*e13*e31+8*e112* ... e32*e34*e35*e13*e33-6*e112*e12*e322*e34*e33*e15-4*e112*e32* ... e35*e14*e33*e31-4*e112*e33*e35*e12*e34*e31-18*e112*e332* ... e14*e15*e32*e31+6*e112*e33*e15*e35*e322*e13-12*e112*e31* ... e14*e35*e12*e332-24*e113*e32*e34*e35*e13*e33+6*e11*e142* ... e32*e31*e12*e332-4*e11*e31*e14*e35*e322*e12-8*e11*e31*e332* ... e16*e32*e12-4*e11*e31*e15*e35*e13*e332+12*e11*e31*e15*e34* ... e12*e332-4*e11*e31*e15*e35*e322*e13+4*e11*e31*e32*e35*e34* ... e122+32*e11*e31*e322*e16*e13*e33-24*e11*e31*e34*e332*e14* ... e132+6*e11*e31*e34*e332*e14*e122-24*e11*e31*e322*e16* ... e132*e33-24*e11*e31*e32*e35*e34*e133+12*e11*e31*e33*e16* ... e322*e122+6*e11*e312*e14*e34*e132*e33-4*e11*e312*e33*e16* ... e32*e12+24*e11*e312*e14*e15*e12*e332+12*e11*e312*e33*e15* ... e35*e13-12*e11*e36*e33*e31*e32*e123+12*e11*e36*e13*e31*e322* ... e122-24*e11*e36*e122*e31*e13*e332-4*e11*e36*e12*e32*e13* ... e312+6*e11*e36*e12*e32*e132*e312-24*e11*e36*e33*e13*e122* ... e312+12*e11*e12*e34*e35*e13*e332-4*e11*e33*e14*e312*e34* ... e13-16*e11*e32*e34*e35*e132*e33+8*e11*e32*e34*e35*e132*e31- ... 8*e11*e13*e34*e35*e322*e12+8*e11*e13*e33*e342*e32*e12-4*e11* ... e332*e13*e36*e32*e12-4*e11*e32*e14*e34*e12*e332+12*e11*e14* ... e31*e34*e13*e332-12*e11*e122*e322*e31*e15*e35+6*e11*e12* ... e32*e332*e31*e152-18*e11*e32*e312*e12*e152*e33-6*e11* ... e122*e34*e332*e15*e32-24*e11*e333*e12*e14*e15*e31+6*e11* ... e332*e122*e35*e15*e31+4*e11*e122*e32*e35*e33*e34+12*e11* ... e122*e322*e36*e33*e13-12*e11*e12*e323*e33*e16*e13+6*e11* ... e322*e35*e15*e31*e132+6*e11*e31*e32*e12*e352*e132+6*e11* ... e12*e322*e35*e34*e132+8*e11*e31*e32*e12*e352*e13-4*e11*e12* ... e32*e33*e352*e13+8*e11*e332*e32*e14*e35*e13+12*e11*e34*e15* ... e32*e13*e332+12*e11*e34*e35*e12*e13*e312-18*e11*e342*e12* ... e33*e32*e132-4*e11*e14*e33*e34*e322*e13-18*e11*e14*e35*e32* ... e132*e312+4*e332*e34*e12*e32*e14*e152-4*e31*e35*e34*e33* ... e14*e153+4*e12*e32*e31*e152*e16*e352+4*e32*e31*e142*e12* ... e16*e352+12*e122*e32*e14*e15*e31*e352-6*e33*e12*e34*e15* ... e142*e352-6*e122*e32*e14*e15*e36*e352+6*e31*e12*e34*e15* ... e142*e352-4*e33*e12*e34*e36*e35*e142+4*e31*e12*e34*e36*e35* ... e142+4*e32*e31*e33*e36*e143*e15+2*e332*e36*e32*e12*e16* ... e152-4*e332*e31*e32*e12*e16*e152-4*e32*e34*e33*e31*e16* ... e153+4*e33*e12*e34*e31*e36*e153+4*e32*e14*e33*e31*e36*e153- ... 6*e31*e12*e14*e152*e342*e35-4*e12*e32*e34*e152*e14*e352+4* ... e31*e34*e15*e12*e16*e352-4*e12*e32*e16*e33*e142*e352+4*e32* ... e34*e14*e12*e16*e352-4*e33*e34*e15*e12*e16*e352-6*e114* ... e332*e352+4*e33*e12*e34*e36*e35*e152-4*e32*e142*e12*e15* ... e342*e35+6*e33*e12*e14*e152*e342*e35-6*e112*e334*e142- ... 12*e112*e334*e16-4*e31*e36*e15*e33*e35*e142-4*e31*e12*e16* ... e14*e35*e342-2*e113*e322*e352+4*e32*e16*e12*e15*e35*e342- ... 2*e113*e332*e342-4*e31*e12*e14*e15*e36*e342+4*e33*e12*e14* ... e15*e36*e342-12*e113*e36*e333+4*e33*e12*e16*e14*e35*e342+ ... 6*e113*e332*e352+12*e113*e334*e16-4*e33*e14*e34*e36*e31* ... e152+12*e114*e36*e333+4*e11*e334*e142-4*e332*e14*e15* ... e32*e16*e31-24*e11*e35*e15*e33*e13*e31*e32*e12-24*e11*e12*e33* ... e14*e31*e34*e32*e13-16*e11*e33*e12*e34*e35*e13*e31-2*e362* ... e342*e134+2*e362*e322*e133+2*e363*e33*e124-2*e362* ... e124*e312+2*e363*e124*e31-2*e362*e352*e133-12*e362* ... e134*e312+4*e363*e134*e31-2*e153*e313*e35-2*e324*e16* ... e152+2*e323*e34*e153-2*e122*e16*e354-2*e123*e34*e353-2* ... e314*e154-4*e334*e163-2*e334*e144-4*e334*e142*e16-4* ... e324*e163-8*e322*e332*e163-8*e312*e322*e163-2*e324* ... e16*e142+2*e323*e35*e143+16*e313*e33*e163-24*e332*e312* ... e163-4*e314*e152*e16-2*e333*e34*e143+16*e333*e163*e31- ... 2*e122*e16*e344-2*e123*e35*e343-4*e314*e163; g3 = -2*e11*e354*e132-2*e11*e344*e13-24*e11*e36*e31*e16*e13* ... e332+4*e11*e36*e33*e152*e312*e13+6*e132*e162*e322*e312- ... 4*e11*e36*e15*e35*e13*e332+4*e11*e36*e332*e16*e122*e31-6* ... e133*e16*e322*e312-2*e11*e133*e344-6*e133*e16*e342* ... e312+28*e11*e36*e332*e16*e32*e12-6*e11*e324*e162-8*e11* ... e36*e14*e35*e12*e332+3*e122*e132*e342*e312-6*e133*e11* ... e342*e312-8*e11*e35*e15*e33*e13*e36*e32*e12-8*e11*e36*e33* ... e16*e122*e312-12*e11*e334*e162+8*e11*e31*e36*e13*e14*e35* ... e12*e33-12*e11*e36*e33*e16*e132*e312-24*e11*e36*e33*e16*e13* ... e312-8*e11*e36*e14*e34*e322*e13-2*e11*e122*e354-2*e11* ... e354*e13+4*e11*e344*e132-4*e13*e152*e16*e314+24*e11*e36* ... e31*e16*e132*e332+6*e133*e34*e14*e313-10*e12*e32*e342* ... e31*e13-4*e11*e36*e152*e31*e322*e13-4*e11*e36*e15*e312*e34* ... e12-8*e11*e36*e15*e35*e322*e13+16*e11*e36*e33*e14*e31*e15* ... e32*e13-8*e11*e36*e152*e31*e13*e332-12*e11*e36*e15*e34*e12* ... e332-4*e11*e36*e312*e16*e32*e12-12*e11*e36*e15*e35*e13* ... e312+2*e11*e36*e14*e312*e34*e132-4*e11*e36*e14*e35*e322* ... e12-4*e132*e323*e34*e15-12*e11*e36*e14*e34*e13*e332-4*e11* ... e36*e14*e312*e34*e13+8*e11*e36*e15*e13*e31*e34*e12*e33+2*e11* ... e312*e33*e162*e32*e12+16*e11*e36*e33*e13*e31*e16*e32*e12+8* ... e11*e313*e15*e35*e16*e13-16*e11*e31*e322*e162*e13*e33-8* ... e11*e31*e33*e352*e16*e132-4*e11*e31*e33*e352*e16*e122+4* ... e112*e36*e12*e35*e31*e34*e13-4*e11*e33*e35*e12*e34*e32*e15* ... e14-8*e112*e36*e34*e12*e35*e13*e33+4*e112*e14*e31*e15*e33* ... e35*e34-12*e112*e32*e14*e33*e15*e31*e36+4*e112*e32*e35*e12* ... e15*e31*e36+8*e11*e12*e32*e35*e34*e15*e31*e14+4*e112*e32*e35* ... e14*e33*e31*e16+4*e112*e35*e12*e33*e34*e31*e16+4*e112*e33* ... e15*e36*e32*e12*e35+16*e112*e34*e35*e32*e16*e31*e13-8*e112* ... e16*e35*e32*e33*e34*e13-12*e112*e32*e34*e33*e15*e36*e13-4* ... e112*e32*e35*e14*e33*e36*e13+4*e112*e32*e35*e14*e36*e31*e13+ ... 4*e11*e31*e332*e162*e32*e12+8*e11*e34*e33*e15*e32*e16*e13* ... e31+4*e112*e36*e14*e31*e34*e13*e33+16*e11*e34*e33*e12*e35* ... e16*e13*e31-6*e11*e342*e312*e13-8*e11*e14*e33*e31*e34*e16* ... e32*e12+4*e11*e31*e342*e33*e16*e132+4*e11*e142*e31*e342* ... e13*e33-8*e112*e36*e33*e14*e35*e12*e31+4*e112*e36*e33*e31* ... e16*e32*e12-12*e112*e36*e33*e15*e35*e13*e31-12*e112*e36*e15* ... e31*e34*e12*e33+4*e11*e32*e34*e33*e15*e31*e142-8*e11*e332* ... e14*e15*e32*e16*e31+8*e11*e32*e34*e31*e14*e12*e36+8*e11*e142* ... e32*e36*e12*e332-4*e11*e33*e14*e152*e32*e31*e35-4*e11*e31* ... e14*e35*e16*e12*e332+4*e11*e15*e312*e34*e16*e12*e33+4*e11* ... e14*e15*e34*e35*e322*e13-12*e11*e35*e14*e32*e16*e13*e312+4* ... e11*e342*e13*e14*e35*e12*e31-4*e11*e342*e13*e14*e35*e12*e33+ ... 8*e11*e36*e12*e35*e31*e34*e13+8*e11*e36*e34*e12*e35*e13*e33+4* ... e11*e36*e14*e13*e35*e322*e12+4*e11*e32*e16*e14*e312*e15*e33+ ... 8*e11*e14*e34*e16*e13*e333+4*e11*e14*e33*e352*e34*e122-8* ... e11*e32*e36*e12*e152*e31*e33+8*e11*e32*e14*e33*e15*e31*e36-8* ... e11*e32*e35*e12*e15*e31*e36-8*e11*e32*e34*e33*e15*e31*e16+10* ... e11*e14*e31*e352*e34*e132-16*e11*e32*e35*e14*e33*e31*e16-2* ... e11*e14*e31*e352*e34*e122+4*e11*e14*e15*e332*e342*e12-24* ... e11*e35*e12*e33*e34*e31*e16-4*e11*e32*e35*e34*e31*e142*e13-4* ... e11*e32*e34*e33*e152*e35*e13+8*e11*e32*e34*e31*e152*e35*e13- ... 6*e11*e14*e342*e32*e35*e132+4*e11*e35*e15*e312*e16*e32*e12- ... 4*e11*e342*e132*e36*e32*e12-2*e11*e342*e15*e35*e132*e31- ... 16*e11*e34*e35*e32*e16*e31*e13+3*e312*e132*e322*e152-2* ... e13*e324*e16*e142-6*e11*e342*e15*e35*e132*e33+8*e11*e32* ... e34*e36*e15*e31*e13-16*e11*e16*e35*e32*e33*e34*e13+3*e132* ... e322*e312*e142+16*e11*e32*e34*e33*e15*e36*e13-4*e13*e322* ... e312*e142-4*e11*e342*e33*e152*e13*e31-4*e11*e343*e15*e13* ... e12*e33+8*e11*e32*e35*e14*e33*e36*e13+16*e11*e32*e35*e14*e36* ... e31*e13+8*e11*e32*e35*e34*e33*e142*e13-4*e122*e322*e13* ... e342+3*e132*e322*e122*e342-4*e11*e36*e33*e15*e14*e322* ... e12+8*e11*e342*e35*e32*e14*e13+8*e11*e16*e33*e342*e31*e13+4* ... e11*e33*e15*e35*e16*e322*e13+4*e11*e36*e33*e15*e35*e132*e31+ ... 4*e11*e352*e15*e12*e34*e13*e33-4*e11*e352*e15*e12*e34*e13* ... e31+8*e11*e352*e14*e31*e15*e12*e33-4*e11*e35*e33*e122*e34* ... e16*e32-8*e11*e36*e12*e14*e31*e34*e32*e13+4*e11*e352*e13*e33* ... e16*e32*e12-8*e11*e352*e13*e31*e16*e32*e12+2*e11*e322*e35* ... e15*e36*e132-8*e11*e35*e14*e32*e16*e13*e332-8*e11*e33*e35* ... e15*e342*e13-8*e11*e342*e13*e33*e16*e32*e12+16*e11*e34*e32* ... e35*e16*e132*e33+8*e11*e34*e13*e35*e16*e322*e12-12*e11*e34* ... e12*e35*e16*e13*e332-12*e11*e34*e35*e12*e16*e13*e312+4*e11* ... e15*e35*e31*e342*e13-12*e11*e34*e15*e32*e16*e13*e332+4*e11* ... e142*e33*e32*e36*e12*e31-4*e11*e14*e15*e31*e342*e12*e33-8* ... e11*e14*e33*e15*e34*e35*e13*e31-8*e11*e34*e352*e31*e14*e13+4* ... e11*e14*e332*e34*e16*e32*e12+4*e11*e14*e15*e34*e35*e13*e332+ ... 4*e11*e14*e33*e34*e16*e322*e13+4*e11*e14*e15*e34*e35*e13* ... e312-12*e11*e31*e14*e34*e16*e13*e332+4*e11*e31*e14*e35*e16* ... e322*e12-4*e11*e31*e32*e35*e34*e16*e122-8*e11*e31*e32*e35* ... e34*e16*e132+4*e11*e31*e14*e36*e34*e122*e33+4*e11*e31*e15* ... e35*e16*e13*e332+4*e11*e31*e15*e35*e16*e322*e13-12*e11*e31* ... e15*e34*e16*e12*e332+4*e11*e34*e352*e33*e14*e13-12*e11*e31* ... e36*e14*e35*e32*e132-4*e11*e36*e14*e31*e15*e322*e12-12*e11* ... e36*e14*e31*e34*e132*e33+16*e11*e36*e14*e31*e34*e13*e33+4* ... e11*e36*e14*e312*e15*e32*e13+4*e11*e36*e12*e32*e16*e13*e312- ... 8*e11*e36*e12*e35*e31*e34*e132+4*e11*e36*e15*e31*e34*e32* ... e122-8*e11*e36*e14*e31*e15*e12*e332+8*e11*e36*e33*e14*e35* ... e12*e31-24*e11*e36*e33*e31*e16*e32*e12+16*e11*e36*e33*e14* ... e312*e15*e12+4*e11*e36*e33*e35*e31*e15*e122-4*e11*e323*e14* ... e35*e16*e13+16*e11*e36*e33*e15*e35*e13*e31-2*e11*e13*e322* ... e152*e342-2*e11*e132*e31*e343*e14+6*e11*e132*e16*e312* ... e342+2*e11*e12*e32*e33*e362*e132+16*e11*e36*e15*e31*e34* ... e12*e33-4*e11*e36*e15*e31*e34*e32*e132+4*e11*e36*e15*e13* ... e312*e34*e12-4*e11*e13*e323*e16*e15*e34+4*e11*e312*e14*e34* ... e16*e13*e33-12*e11*e312*e33*e15*e35*e16*e13+4*e11*e36*e32* ... e15*e14*e13*e332+4*e11*e36*e32*e12*e16*e13*e332+4*e11*e36* ... e13*e15*e34*e322*e12+4*e11*e36*e34*e33*e12*e35*e132+4*e11* ... e36*e32*e15*e34*e132*e33-8*e11*e36*e32*e13*e35*e34*e122+4* ... e11*e36*e14*e12*e35*e13*e332-8*e11*e312*e13*e16*e32*e15*e34+ ... 4*e11*e12*e32*e16*e31*e13*e342+4*e11*e13*e322*e16*e34*e14* ... e31+8*e11*e36*e322*e16*e13*e31-8*e11*e36*e142*e33*e312*e13+ ... 4*e11*e36*e142*e31*e13*e332-8*e11*e36*e322*e16*e132*e33+2* ... e11*e36*e14*e34*e322*e132-10*e11*e36*e34*e332*e14*e122-8* ... e11*e36*e13*e16*e323*e12-4*e11*e36*e33*e142*e322*e13+8*e11* ... e36*e33*e16*e322*e122-8*e11*e36*e32*e35*e34*e133+8*e11*e36* ... e32*e35*e34*e122-8*e11*e36*e32*e35*e34*e132+4*e11*e36*e31* ... e16*e322*e122+8*e11*e36*e31*e13*e352*e122+4*e11*e36*e322* ... e16*e132*e31+8*e11*e36*e322*e16*e13*e33-8*e11*e36*e34*e332* ... e14*e132+4*e11*e36*e34*e33*e35*e123+8*e11*e35*e14*e32*e31* ... e16*e13*e33+8*e11*e36*e342*e13*e33*e122-12*e11*e362*e33* ... e13*e32*e12-16*e11*e362*e33*e13*e122*e31-12*e11*e362*e12* ... e32*e13*e31+4*e11*e362*e12*e32*e132*e31+6*e112*e362*e312+ ... 4*e112*e354*e13+e112*e324*e162-2*e112*e344*e13+e112* ... e354*e132+e112*e344*e132-2*e11*e12*e32*e33*e142*e352+4* ... e11*e32*e31*e12*e152*e352+e112*e344+e112*e354-2*e11*e32* ... e31*e142*e12*e352+6*e11*e32*e34*e122*e15*e352-8*e11*e14* ... e312*e15*e12*e352-2*e11*e322*e14*e152*e34*e31+2*e11*e35* ... e34*e12*e312*e152+2*e11*e332*e36*e32*e12*e152-6*e11*e12* ... e322*e34*e152*e35+4*e11*e12*e323*e15*e16*e35-2*e11*e332* ... e12*e34*e152*e35+e114*e354-4*e11*e122*e322*e36*e15*e35-2* ... e113*e354+e112*e122*e354+6*e112*e362*e332+2*e112* ... e322*e362+2*e112*e352*e342+6*e11*e32*e12*e152*e342*e33- ... 4*e11*e122*e35*e15*e342*e33+4*e11*e322*e15*e35*e142*e33-6* ... e11*e34*e312*e152*e14*e33+4*e11*e323*e14*e15*e16*e33+8*e11* ... e322*e31*e152*e16*e33+10*e11*e31*e34*e152*e332*e14+2*e11* ... e32*e132*e15*e343-4*e11*e32*e34*e33*e31*e153-12*e33*e12* ... e34*e35*e13*e31-2*e11*e332*e31*e15*e35*e142-2*e11*e12*e32* ... e152*e31*e342+2*e132*e16*e34*e15*e32*e312-6*e11*e32*e312* ... e12*e152*e36-4*e11*e322*e14*e152*e34*e33+2*e11*e122*e15* ... e36*e35*e332-8*e11*e333*e12*e15*e36*e14+4*e13*e32*e16*e14* ... e15*e313+4*e11*e12*e32*e16*e33*e342+4*e11*e32*e12*e15*e35* ... e342-8*e11*e322*e34*e33*e16*e14-4*e11*e31*e12*e342*e35*e14+ ... 12*e11*e312*e16*e32*e35*e14+2*e11*e132*e16*e322*e342+4* ... e11*e33*e35*e12*e342*e14-4*e11*e16*e34*e312*e33*e14+16*e11* ... e322*e16*e35*e15*e33-2*e11*e312*e13*e152*e342+4*e11*e333* ... e12*e35*e14*e16+8*e11*e333*e12*e34*e15*e16+4*e11*e333*e14* ... e15*e32*e16+12*e132*e32*e34*e15*e11*e312-4*e11*e332*e14* ... e15*e32*e36+8*e11*e332*e16*e34*e31*e14-4*e11*e322*e34*e14* ... e16*e31-4*e11*e322*e16*e35*e15*e31-32*e11*e332*e16*e35*e15* ... e31+12*e11*e34*e312*e35*e12*e16-20*e11*e12*e32*e33*e352*e16+ ... 6*e11*e312*e13*e162*e322+20*e11*e31*e32*e12*e352*e16+4* ... e11*e332*e32*e14*e35*e16-12*e11*e12*e322*e16*e35*e34-16*e11* ... e32*e34*e13*e15*e312+12*e11*e332*e16*e12*e35*e34-4*e11*e32* ... e31*e12*e16*e342+8*e11*e34*e32*e15*e352*e13+4*e11*e152* ... e352*e33*e13*e31+2*e11*e15*e352*e32*e34*e132+8*e11*e16* ... e352*e33*e31*e13+2*e11*e36*e32*e12*e352*e132-4*e11*e31*e33* ... e352*e142*e13+14*e11*e15*e35*e36*e312*e132+28*e11*e312* ... e16*e35*e15*e33+8*e11*e32*e16*e34*e312*e15-4*e11*e32*e14*e36* ... e15*e312+4*e11*e32*e35*e14*e33*e36+4*e11*e32*e34*e33*e15*e36+ ... 4*e11*e332*e35*e14*e15*e34+4*e11*e32*e14*e15*e342*e33-4*e11* ... e32*e15*e31*e14*e352+8*e11*e32*e34*e31*e152*e35-4*e11*e32* ... e34*e33*e152*e35-16*e11*e332*e36*e142*e31+4*e11*e36*e32* ... e12*e352*e13+4*e11*e342*e13*e36*e32*e12+10*e112*e33*e35* ... e15*e342*e13+4*e12*e34*e13*e15*e16*e313-6*e112*e34*e352* ... e31*e14*e13-2*e112*e34*e352*e33*e14*e13-4*e11*e353*e13*e14* ... e12*e31-4*e11*e34*e312*e15*e35*e14-8*e11*e32*e35*e34*e33* ... e142-4*e11*e32*e34*e36*e15*e31-2*e11*e332*e34*e15*e32*e142- ... 4*e11*e322*e152*e312-8*e13*e322*e152*e312+4*e11*e32*e35* ... e34*e31*e142+2*e11*e32*e312*e14*e35*e152-4*e11*e14*e36*e33* ... e34*e31+24*e11*e34*e35*e32*e16*e31+12*e132*e11*e342*e312-4* ... e11*e32*e35*e14*e36*e31+16*e11*e36*e32*e35*e34*e13-12*e132* ... e34*e14*e313-4*e122*e13*e342*e312-24*e11*e16*e35*e32*e33* ... e34+4*e11*e15*e31*e35*e33*e36-16*e112*e36*e332*e16*e32*e12+ ... 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... e313*e142*e33*e13-6*e313*e142*e33*e132-16*e312*e142* ... e13*e332+6*e312*e142*e132*e332-12*e313*e162*e132*e33+ ... 12*e313*e16*e133*e33+2*e142*e352*e322*e132+6*e312* ... e142*e122*e332+36*e33*e16*e13*e313+36*e33*e162*e13*e313- ... 48*e33*e16*e132*e313+2*e11*e352*e342*e132+2*e35*e14* ... e323*e13-4*e12*e36*e323*e132-6*e162*e322*e13*e332+4* ... e352*e322*e16*e132-4*e36*e33*e352*e132-4*e36*e33*e352* ... e122-12*e36*e16*e13*e333-12*e36*e16*e323*e12+12*e36*e16* ... e13*e313-4*e36*e16*e122*e313-24*e36*e16*e132*e313-6* ... e322*e16*e13*e332+4*e36*e31*e352*e132+4*e36*e31*e352* ... e122-4*e36*e342*e31*e132+8*e36*e152*e313*e13+8*e36*e342* ... e31*e133+8*e36*e13*e122*e313-4*e36*e342*e31*e122+4*e36* ... e342*e33*e122+4*e36*e342*e33*e132+8*e12*e34*e323*e13*e14+ ... 12*e133*e322*e34*e31*e14+2*e312*e342*e16*e122-12*e11* ... e362*e13*e332-4*e11*e362*e322*e13+e342*e132*e352*e122- ... 4*e11*e352*e342*e13-4*e362*e33*e31*e122-12*e362*e33*e31* ... e132+12*e362*e33*e133*e31-8*e362*e13*e312*e122+4*e31* 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... e362*e32*e123*e31+6*e334*e112-12*e334*e113+6*e334* ... e114-6*e112*e33*e31*e152*e352-2*e112*e12*e32*e15*e353- ... 12*e11*e12*e323*e132*e31-12*e11*e332*e31*e32*e123-12*e33* ... e13*e323*e12*e112-2*e112*e33*e12*e14*e353+4*e112*e31*e12* ... e14*e353-12*e33*e13*e312*e32*e123+2*e31*e122*e333+6* ... e332*e124*e312-4*e112*e36*e33*e352*e132+12*e11*e132* ... e312*e33*e32*e12+24*e11*e33*e13*e31*e322*e122-4*e11*e362* ... e13*e312*e122-12*e11*e362*e33*e133*e31-12*e11*e362*e33* ... e31*e132+4*e11*e362*e33*e31*e122+4*e11*e36*e342*e33*e132- ... 4*e11*e36*e342*e33*e122+8*e11*e36*e342*e31*e133+4*e11*e36* ... e152*e313*e13-16*e11*e36*e342*e31*e132-4*e11*e36*e31* ... e352*e122+12*e322*e332*e162+4*e11*e36*e31*e352*e132-12* ... e11*e36*e16*e132*e313+24*e11*e36*e16*e13*e313+12*e11*e36* ... e16*e323*e12+24*e11*e36*e16*e13*e333+8*e11*e36*e33*e352* ... e122+8*e11*e36*e33*e352*e132-4*e11*e352*e322*e16*e132+6* ... e11*e162*e322*e13*e332+e344*e132+e354*e132-12*e11*e33* ... 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e14*e31*e34*e13*e332-8*e11*e32*e34*e35*e13*e31-8*e11*e32*e34* ... e35*e13*e33+12*e11*e122*e322*e31*e15*e35-6*e11*e12*e32* ... e332*e31*e152+18*e11*e32*e312*e12*e152*e33+6*e11*e122* ... e34*e332*e15*e32+24*e11*e333*e12*e14*e15*e31-6*e11*e332* ... e122*e35*e15*e31-8*e11*e122*e32*e35*e33*e34-12*e11*e122* ... e322*e36*e33*e13+12*e11*e12*e323*e33*e16*e13-6*e11*e322* ... e35*e15*e31*e132-6*e11*e31*e32*e12*e352*e132-6*e11*e12* ... e322*e35*e34*e132-16*e11*e31*e32*e12*e352*e13+8*e11*e12* ... e32*e33*e352*e13-16*e11*e332*e32*e14*e35*e13-24*e11*e34*e15* ... e32*e13*e332-24*e11*e34*e35*e12*e13*e312+18*e11*e342*e12* ... e33*e32*e132+8*e11*e14*e33*e34*e322*e13+18*e11*e14*e35*e32* ... e132*e312-2*e332*e34*e12*e32*e14*e152-6*e122*e32*e14*e15* ... e31*e352+2*e332*e31*e32*e12*e16*e152+6*e114*e332*e352- ... 12*e112*e36*e333+6*e112*e332*e352+6*e112*e334*e142+24* ... e112*e334*e16+4*e113*e322*e352+4*e113*e332*e342+24* ... e113*e36*e333-12*e113*e332*e352-12*e113*e334*e16-12* ... e114*e36*e333-4*e32*e34*e31*e14*e12*e36-8*e11*e334*e142- ... 12*e11*e334*e16+4*e332*e14*e15*e32*e16*e31+2*e112*e352* ... e312-4*e112*e322*e352-4*e112*e332*e342+e322*e352* ... e142+24*e11*e35*e15*e33*e13*e31*e32*e12+24*e11*e12*e33*e14* ... e31*e34*e32*e13+32*e11*e33*e12*e34*e35*e13*e31-2*e362*e322* ... e133+e362*e124*e312+6*e362*e134*e312+2*e332*e342* ... e132+e332*e352*e152+e332*e322*e152+2*e153*e313*e35+2* ... e324*e16*e152-2*e323*e34*e153+e322*e352*e152+e312* ... e152*e352+2*e123*e34*e353+e122*e322*e352+e332*e352* ... e142+e314*e154+e334*e144+4*e334*e142*e16+e122*e354+ ... e324*e152+2*e333*e36*e152-2*e333*e31*e152+2*e324*e16* ... e142-2*e323*e35*e143+e322*e122*e342+e322*e312*e142+4* ... e314*e152*e16+2*e333*e34*e143+2*e122*e352*e342+e332* ... e152*e342+e322*e152*e342+2*e123*e35*e343-6*e33*e152* ... e313+e324*e142+e342*e312*e142+6*e334*e162+2*e334* ... e142+e332*e342*e142+e312*e352*e142+e322*e342*e142+ ... e312*e152*e342-3*e332*e122*e342+12*e312*e162*e322+6* ... e314*e162+e122*e344-6*e333*e142*e31+3*e322*e152*e312- ... 2*e33*e142*e313-2*e313*e152*e36-2*e333*e142*e36; g4 = 2*e133*e16*e322*e312-e122*e132*e342*e312+2*e133*e11* ... e342*e312-2*e133*e34*e14*e313+10*e12*e32*e342*e31*e13+2* ... e132*e323*e34*e15+6*e11*e342*e312*e13-e312*e132*e322* ... e152-e132*e322*e312*e142+2*e13*e322*e312*e142+2*e122* ... e322*e13*e342-e132*e322*e122*e342+12*e33*e12*e34*e35* ... e13*e31-4*e132*e32*e34*e15*e11*e312+8*e11*e32*e34*e13*e15* ... e312+2*e11*e322*e152*e312+4*e13*e322*e152*e312-6*e132* ... e11*e342*e312+6*e132*e34*e14*e313+2*e122*e13*e342*e312- ... 12*e132*e16*e322*e312-4*e11*e12*e323*e16*e13*e31+2*e132* ... e322*e34*e11*e14*e31-6*e13*e34*e313*e14-4*e13*e323*e15*e34- ... 2*e11*e323*e15*e34-2*e132*e112*e322*e342-2*e132*e11* ... e322*e342-2*e13*e11*e322*e342+18*e312*e13*e16*e322+6* ... e312*e11*e16*e322-4*e31*e11*e322*e13*e34*e14+2*e323*e14* ... e15*e31-4*e11*e32*e31*e12*e13*e342-4*e12*e34*e13*e15*e313-2* ... e132*e32*e34*e15*e312+12*e13*e16*e32*e12*e313+2*e132*e32* ... e15*e14*e313-4*e13*e32*e15*e14*e313-6*e12*e32*e16*e132* ... e313+2*e12*e32*e31*e132*e342*e11+2*e12*e32*e152*e13*e313- ... 2*e13*e322*e152*e11*e312+2*e133*e15*e32*e34*e312-12*e11* ... e16*e322*e13*e312+2*e132*e34*e15*e12*e313+2*e122*e322* ... e16*e13*e312-4*e13*e323*e14*e15*e31+10*e132*e322*e34*e14* ... e31+8*e12*e323*e16*e13*e31+4*e11*e12*e323*e16*e31-2*e322* ... e35*e15*e31+6*e14*e332*e34*e31+2*e322*e34*e14*e31-2*e12* ... e323*e33*e142-2*e12*e32*e333*e142-2*e12*e32*e313*e152-4* ... e333*e122*e16*e31-2*e123*e32*e33*e342+4*e322*e31*e152* ... e33+2*e323*e14*e15*e33+2*e322*e35*e15*e33+2*e333*e14*e15* ... e32-2*e332*e35*e34*e123+2*e123*e32*e36*e332+4*e34*e122* ... e14*e333-2*e322*e122*e332*e16+2*e333*e14*e12*e35+4*e34* ... e15*e12*e333-6*e333*e12*e32*e16+2*e312*e35*e32*e14-2*e322* ... e34*e33*e14+4*e332*e35*e12*e34+2*e332*e32*e15*e34-4*e12*e32* ... e33*e352+4*e31*e32*e12*e352+2*e332*e32*e14*e35-6*e12*e323* ... e33*e16-6*e33*e14*e312*e34+16*e33*e16*e322*e31-6*e332*e35* ... e15*e31-2*e332*e122*e312*e152-e122*e322*e312*e152+2* ... e333*e31*e122*e142-2*e123*e32*e31*e352+2*e12*e323*e15* ... e35-2*e323*e31*e12*e152+2*e142*e332*e322*e13+2*e11*e322* ... e34*e14*e31-8*e13*e322*e34*e14*e31+2*e31*e124*e332*e36- ... e322*e332*e122*e142+2*e36*e33*e124*e312-4*e36*e322* ... e133*e31+2*e36*e132*e122*e313+4*e36*e332*e32*e12+12*e36* ... e31*e132*e332-2*e36*e33*e122*e312+12*e36*e33*e13*e312-24* ... e36*e33*e132*e312-12*e36*e31*e13*e332-2*e36*e332*e122* ... e31+12*e36*e33*e133*e312+6*e36*e31*e322*e122+2*e36*e32* ... e123*e312-6*e13*e36*e323*e12+8*e322*e36*e132*e31-4*e322* ... e36*e132*e33+8*e31*e342*e132*e33+6*e33*e36*e322*e122+4* ... e33*e342*e32*e12-4*e31*e342*e13*e33-4*e31*e342*e32*e12+4* ... e322*e36*e13*e33-4*e322*e36*e13*e31-4*e34*e35*e322*e12-4* ... e313*e142*e33*e13+2*e313*e142*e33*e132+8*e312*e142*e13* ... e332-2*e312*e142*e132*e332-4*e313*e16*e133*e33-2*e312* ... e142*e122*e332-36*e33*e16*e13*e313+24*e33*e16*e132*e313- ... 2*e35*e14*e323*e13+2*e12*e36*e323*e132+6*e322*e16*e13* ... e332-4*e36*e13*e122*e313-4*e12*e34*e323*e13*e14-4*e133* ... e322*e34*e31*e14+4*e36*e312*e32*e12-4*e31*e33*e352*e132-2* ... e31*e33*e352*e122-12*e31*e16*e13*e333-e312*e132*e352* ... e122+2*e313*e15*e35*e132-6*e31*e16*e323*e12-2*e31*e342* ... e33*e122-4*e31*e142*e13*e333-4*e31*e342*e33*e133-2*e313* ... e35*e15*e133+2*e313*e152*e132*e33+2*e313*e152*e122*e33- ... 2*e312*e13*e352*e122-8*e12*e32*e31*e132*e342+2*e14*e323* ... e34*e12-2*e312*e35*e34*e123-2*e312*e16*e322*e122-4*e313* ... e33*e16*e122-8*e313*e33*e152*e13-12*e312*e16*e132*e332+ ... 36*e312*e16*e13*e332+4*e312*e152*e13*e332+8*e312*e332* ... e16*e122+2*e313*e15*e34*e12+4*e313*e14*e35*e12-6*e313*e16* ... e32*e12+4*e313*e35*e15*e122+2*e313*e15*e35*e13-4*e11*e15* ... e312*e32*e34-2*e13*e15*e312*e32*e34-4*e342*e122*e13*e332+ ... 2*e133*e32*e31*e12*e342+4*e13*e11*e323*e15*e34+2*e11*e32* ... e31*e12*e342-2*e31*e132*e323*e12*e16-2*e132*e323*e34*e15* ... e11-4*e332*e13*e31*e32*e12-2*e132*e152*e314-2*e134*e342* ... e312-12*e132*e16*e314+4*e13*e152*e314+6*e133*e342* ... e312+4*e133*e16*e314-2*e133*e322*e342+12*e314*e13*e16- ... 2*e112*e324*e16-2*e132*e324*e16+4*e132*e322*e342-2* ... e112*e322*e342+6*e13*e324*e16+6*e11*e324*e16-e132*e324* ... e142+2*e13*e324*e142+2*e11*e324*e152-e112*e324*e152+2* ... e132*e323*e34*e12*e14+2*e132*e323*e14*e15*e31+2*e11*e323* ... e31*e12*e152-4*e312*e12*e15*e34*e132*e33+2*e312*e14*e33* ... e15*e32*e122-6*e312*e14*e32*e15*e132*e33+4*e312*e15*e13* ... e34*e12*e33-8*e312*e33*e13*e16*e32*e12+8*e312*e33*e14*e15* ... e32*e13-4*e312*e13*e15*e35*e32*e12-6*e312*e12*e33*e35*e14* ... e132+8*e312*e12*e15*e14*e13*e332+2*e312*e12*e33*e142*e32* ... e13-4*e31*e34*e33*e12*e35*e132-4*e31*e32*e15*e33*e34*e122-4* ... e31*e32*e15*e34*e132*e33+4*e31*e32*e13*e35*e34*e122-4*e31* ... e32*e15*e14*e13*e332-4*e31*e32*e12*e16*e13*e332-4*e31*e14* ... e12*e35*e13*e332+12*e14*e35*e33*e12*e13*e312-4*e134*e314- ... 4*e14*e32*e12*e34*e13*e332+2*e14*e13*e312*e34*e122*e33-2* ... e14*e13*e35*e312*e32*e122-6*e142*e332*e13*e31*e32*e12+12* ... e133*e314+8*e34*e32*e31*e15*e13*e33+4*e13*e314-12*e132* ... e314-4*e36*e33*e13*e31*e32*e123-8*e313*e13*e14*e15*e12*e33+ ... 2*e16*e132*e312*e33*e32*e12+4*e16*e33*e13*e31*e322*e122-4* ... e35*e32*e31*e14*e122*e33+4*e33*e122*e34*e35*e32*e13-4*e15* ... e13*e33*e34*e322*e12+4*e35*e32*e31*e14*e13*e33-4*e132*e31* ... e33*e36*e32*e12-4*e35*e32*e31*e15*e12*e33+2*e35*e312*e15*e13* ... e33*e122-4*e14*e13*e33*e34*e322*e122+2*e312*e152*e33*e13* ... e32*e12+8*e31*e33*e15*e14*e322*e12-2*e31*e12*e14*e35*e322* ... e132+2*e31*e32*e14*e15*e122*e332-8*e322*e31*e13*e33-8* ... e322*e31*e33*e11+8*e13*e31*e323*e12-12*e13*e322*e11*e312+ ... 8*e322*e31*e132*e33-8*e33*e31*e322*e122+36*e312*e132* ... e332*e11+36*e13*e312*e332*e112-12*e332*e11*e122*e312+ ... 24*e33*e11*e13*e313+2*e33*e312*e32*e12-36*e33*e11*e132* ... e313+12*e33*e13*e122*e313-48*e312*e13*e332*e11+18*e322* ... e11*e132*e312-18*e12*e32*e132*e313+12*e12*e32*e13*e313+4* ... e31*e323*e12*e11-36*e31*e13*e333*e112+24*e31*e13*e333*e11+ ... 2*e31*e332*e32*e12+8*e12*e32*e133*e313-8*e322*e11*e133* ... e312-12*e122*e312*e13*e332+6*e13*e312*e322*e122-8*e33* ... e122*e132*e313-6*e33*e312*e32*e123+16*e313*e133*e33* ... e11-24*e312*e132*e332*e112+16*e31*e13*e333*e113+8*e31* ... e322*e33*e112-4*e122*e322*e36*e33*e13+4*e12*e323*e33*e16* ... e13-2*e322*e35*e15*e31*e132-2*e31*e32*e12*e352*e132-2*e12* ... e322*e35*e34*e132-2*e31*e32*e12*e352*e13+2*e12*e32*e33* ... e352*e13-4*e332*e32*e14*e35*e13-6*e34*e15*e32*e13*e332-6* ... e34*e35*e12*e13*e312-2*e342*e33*e122*e31*e132+6*e342*e12* ... e33*e32*e132+2*e14*e33*e34*e322*e13-6*e14*e35*e32*e132* ... e312-2*e14*e33*e312*e34*e122+4*e14*e33*e122*e34*e322+4* ... e14*e35*e32*e133*e312+4*e14*e35*e12*e132*e313+4*e142* ... e322*e31*e132*e33+4*e142*e32*e31*e12*e332-2*e142*e33*e32* ... e312*e12+2*e31*e14*e35*e322*e12+6*e31*e332*e16*e32*e12+2* ... e31*e15*e35*e13*e332-6*e31*e15*e34*e12*e332+4*e31*e15*e35* ... e322*e13-4*e31*e32*e35*e34*e122-24*e31*e322*e16*e13*e33-8* ... e31*e33*e142*e322*e13+4*e31*e342*e13*e33*e122+8*e31*e34* ... e332*e14*e132-2*e31*e34*e332*e14*e122+8*e31*e322*e16* ... e132*e33+8*e31*e32*e35*e34*e133-8*e31*e33*e16*e322*e122-4* ... e312*e122*e16*e13*e332+4*e312*e34*e33*e14*e133+2*e312* ... e12*e35*e34*e133+2*e312*e13*e35*e34*e123-2*e312*e33*e16* ... e32*e123+4*e313*e13*e33*e16*e122-8*e313*e13*e14*e35*e12- ... 14*e312*e14*e34*e132*e33-4*e313*e13*e35*e15*e122-2*e312* ... e33*e35*e15*e122+8*e313*e33*e14*e15*e12+6*e312*e33*e16*e32* ... e12-6*e312*e33*e14*e35*e12-16*e312*e14*e15*e12*e332-4* ... e312*e33*e15*e35*e13+8*e36*e33*e31*e32*e123+6*e36*e33*e122* ... e132*e312-8*e36*e13*e31*e322*e122-2*e36*e13*e32*e123* ... e312+8*e36*e122*e31*e13*e332-6*e36*e12*e32*e133*e312-14* ... e36*e12*e32*e13*e312+16*e36*e12*e32*e132*e312-8*e36*e33* ... e31*e32*e12-4*e36*e33*e13*e122*e312-6*e12*e34*e35*e13*e332+ ... 16*e33*e14*e312*e34*e13+8*e32*e34*e35*e132*e33-16*e32*e34* ... e35*e132*e31+6*e13*e34*e35*e322*e12-10*e13*e33*e342*e32* ... e12+2*e332*e13*e36*e32*e12+4*e32*e14*e34*e12*e332-14*e14* ... e31*e34*e13*e332+8*e32*e34*e35*e13*e31-8*e32*e34*e35*e13*e33+ ... 2*e312*e123*e32*e15*e35-2*e123*e34*e312*e15*e33+2*e123* ... e14*e32*e332*e34+4*e122*e322*e31*e15*e35-2*e12*e32*e332* ... e31*e152-2*e123*e32*e31*e332*e16-2*e123*e14*e31*e35*e332+ ... 4*e32*e312*e12*e152*e33+2*e312*e122*e32*e35*e14+2*e122* ... e34*e332*e15*e32+8*e333*e12*e14*e15*e31-2*e332*e122*e35* ... e15*e31-4*e122*e32*e35*e33*e34+2*e12*e322*e34*e33*e15-4*e32* ... e35*e14*e33*e31-4*e32*e34*e33*e15*e31-8*e33*e35*e12*e34*e31+4* ... e32*e35*e12*e15*e312-2*e332*e14*e15*e32*e31-2*e32*e14*e33* ... e15*e312-2*e15*e35*e33*e312*e132+2*e36*e132*e31*e322* ... e122-12*e322*e13*e332*e11+12*e333*e32*e12*e11+6*e332* ... e322*e122*e11-6*e33*e323*e12*e112+4*e33*e13*e323*e12+2* ... e142*e13*e33*e323*e12-6*e12*e323*e132*e31-6*e332*e31*e32* ... e123+18*e332*e112*e322*e13-18*e333*e112*e32*e12+2*e342* ... e13*e33*e32*e123+8*e33*e323*e12*e11+2*e33*e15*e35*e322*e13+ ... 8*e333*e113*e32*e12-8*e332*e113*e322*e13-4*e332*e322* ... e122*e112-8*e31*e333*e112*e122+12*e31*e122*e11*e333-4* ... e132*e312*e322*e122+12*e33*e13*e312*e32*e12*e11+12*e31* ... e32*e12*e13*e332*e11-8*e31*e32*e12*e13*e332*e112+4*e352* ... e33*e31*e13+2*e112*e36*e323*e12+12*e112*e36*e13*e333+8* ... e112*e352*e33*e31+8*e112*e33*e322*e36-24*e112*e332*e31* ... e36+12*e112*e312*e33*e36-4*e112*e31*e322*e36-2*e112* ... e312*e352*e132-2*e112*e352*e322*e132+4*e112*e352* ... e312*e13-6*e112*e332*e352*e13+4*e112*e322*e342*e13-2* ... e112*e322*e352*e13+2*e112*e122*e333*e36+2*e112*e323* ... e14*e35-e112*e322*e332*e142-e112*e332*e122*e352+24* ... e112*e333*e16*e31-12*e112*e332*e16*e312-2*e112*e332* ... e152*e312-4*e112*e33*e342*e31+18*e11*e322*e332*e16-8* ... e11*e333*e142*e31-2*e11*e332*e122*e342+2*e11*e333*e34* ... e14-4*e11*e33*e152*e313-4*e11*e333*e31*e152-6*e11*e333* ... e35*e15+2*e11*e122*e322*e352+2*e11*e332*e322*e152-2*e11* ... e332*e342*e13+4*e11*e332*e342*e132-6*e11*e36*e323*e12- ... 12*e11*e36*e13*e313+12*e11*e36*e132*e313-4*e11*e36*e133* ... e313-12*e11*e36*e13*e333-4*e11*e352*e33*e31-4*e11*e33* ... e322*e36+12*e11*e332*e31*e36-12*e11*e312*e33*e36+4*e11*e31* ... e322*e36+2*e11*e312*e352*e133-4*e11*e312*e352*e122-2* ... e11*e312*e352*e132+4*e11*e352*e322*e132-2*e11*e352* ... e312*e13+6*e11*e332*e352*e13-2*e11*e322*e352*e13-4*e11* ... e122*e333*e36-4*e11*e323*e14*e35+4*e11*e322*e332*e142+4* ... e11*e332*e142*e312+2*e11*e332*e122*e352-36*e11*e333* ... e16*e31-12*e11*e313*e16*e33+36*e11*e332*e16*e312+4*e11*e15* ... e313*e35+8*e11*e332*e152*e312+4*e11*e33*e342*e31-8*e11* ... e13*e324*e16+2*e11*e133*e322*e342+2*e113*e322*e332*e16- ... 2*e113*e333*e34*e14-2*e113*e333*e35*e15+2*e113*e332* ... e342*e13-4*e113*e36*e13*e333-4*e113*e352*e33*e31-4*e113* ... e33*e322*e36+12*e113*e332*e31*e36+2*e113*e332*e352*e13+ ... 2*e113*e322*e352*e13-4*e113*e333*e16*e31-12*e112*e322* ... e332*e16+2*e112*e333*e142*e31-e112*e332*e122*e342+2* ... e112*e333*e34*e14+2*e112*e333*e31*e152+6*e112*e333*e35* ... e15-e112*e122*e322*e352-e112*e332*e322*e152-2*e112* ... e332*e342*e13-2*e112*e332*e342*e132-2*e324*e132+2* ... e324*e11+2*e324*e13-2*e324*e112+4*e112*e33*e12*e32*e36* ... e13*e31+4*e112*e35*e32*e31*e15*e12*e33+4*e112*e35*e32*e31* ... e14*e13*e33+4*e112*e33*e12*e34*e35*e13*e31+4*e11*e31*e14*e13* ... e35*e322*e12-16*e11*e33*e12*e32*e36*e13*e31+8*e11*e33*e32* ... e14*e34*e12*e31-4*e11*e31*e33*e15*e14*e322*e12+4*e11*e132* ... e31*e33*e36*e32*e12-8*e11*e35*e32*e31*e14*e13*e33+4*e11*e15* ... e13*e33*e34*e322*e12-4*e11*e33*e122*e34*e35*e32*e13-8*e11* ... e34*e32*e31*e15*e13*e33+4*e11*e14*e32*e12*e34*e13*e332+4*e11* ... e31*e14*e12*e35*e13*e332+4*e11*e31*e32*e12*e16*e13*e332+4* ... e11*e31*e32*e15*e14*e13*e332-4*e11*e31*e32*e13*e35*e34*e122+ ... 4*e11*e31*e32*e15*e34*e132*e33+4*e11*e31*e32*e15*e33*e34* ... e122+4*e11*e31*e34*e33*e12*e35*e132+4*e11*e312*e13*e15*e35* ... e32*e12+4*e11*e312*e33*e14*e15*e32*e13+4*e11*e312*e33*e13* ... e16*e32*e12+4*e11*e312*e15*e13*e34*e12*e33-12*e334*e112+12* ... e334*e113+4*e334*e11-4*e334*e114+8*e11*e12*e323*e132* ... e31+8*e11*e332*e31*e32*e123+8*e33*e13*e323*e12*e112+8*e33* ... e13*e312*e32*e123-4*e31*e122*e333-4*e332*e124*e312-8* ... e11*e132*e312*e33*e32*e12-16*e11*e33*e13*e31*e322*e122-8* ... e33*e12*e32*e13*e312-4*e33*e12*e32*e11*e312-8*e332*e31*e32* ... e12*e11+32*e13*e322*e31*e33*e11-4*e33*e32*e14*e34*e12*e31-2* ... e152*e314-6*e332*e152*e312-2*e15*e313*e35-24*e332*e16* ... e312+2*e34*e313*e14+16*e313*e16*e33+16*e333*e16*e31+6* ... e322*e13*e312+2*e322*e11*e312-2*e31*e323*e12+2*e322*e13* ... e332-12*e322*e332*e112+6*e322*e332*e11-8*e324*e11*e13- ... 2*e33*e323*e12-2*e333*e32*e12+6*e132*e312*e33*e32*e12+6* ... e332*e113*e322-2*e332*e322*e122+6*e13*e324*e112+6* ... e324*e11*e132+12*e33*e13*e31*e322*e122-12*e33*e13*e323* ... e12*e11-4*e324*e112*e132+16*e122*e312*e13*e332*e11+12* ... e31*e33*e322*e122*e11-24*e31*e322*e132*e33*e11+16*e31* ... e322*e132*e33*e112-12*e31*e13*e323*e12*e11-24*e31*e322* ... e13*e33*e112+6*e31*e332*e32*e12*e112-e332*e122*e352+6* ... e15*e312*e35*e33+4*e14*e34*e13*e333+2*e32*e34*e312*e15+2* ... e32*e15*e313*e14+4*e34*e312*e35*e12-6*e332*e142*e312-3* ... e322*e332*e142+4*e322*e142*e33*e31-12*e322*e132*e312- ... 4*e31*e13*e333-12*e312*e332*e112+8*e332*e122*e312-12* ... e312*e132*e332-4*e33*e122*e313-12*e33*e13*e313+24*e33* ... e132*e313-12*e31*e333*e113-12*e31*e333*e11+24*e31*e333* ... e112-2*e312*e322*e122-4*e33*e11*e313-12*e33*e133*e313+ ... 12*e312*e13*e332+12*e312*e332*e11-2*e313*e32*e12+6*e322* ... e133*e312+2*e323*e14*e35+4*e14*e32*e33*e12*e31*e34*e132+ ... 12*e33*e12*e32*e36*e13*e31+2*e122*e333*e36+2*e322*e352* ... e13-2*e322*e342*e13-2*e332*e352*e13-2*e352*e312*e13-6* ... e132*e342*e312+8*e35*e15*e33*e13*e31*e32*e12-2*e352*e322* ... e132-e332*e124*e342-e312*e124*e352-4*e31*e15*e13*e33* ... e14*e322*e12+4*e31*e35*e13*e33*e14*e32*e122+4*e312*e352* ... e132+3*e312*e352*e122-e312*e342*e122-2*e312*e352* ... e133+2*e112*e324*e13*e16+2*e132*e11*e324*e16+4*e36*e13* ... e333-12*e36*e133*e313+4*e36*e134*e313+12*e36*e132*e313- ... 16*e112*e33*e35*e32*e34-4*e112*e352*e33*e31*e13+8*e112* ... e34*e35*e32*e31+8*e112*e15*e312*e35*e33+4*e112*e14*e34*e13* ... e333-4*e113*e322*e35*e15*e33+2*e113*e332*e35*e12*e34+4* ... e113*e332*e32*e15*e34+2*e113*e12*e32*e33*e352+2*e113* ... e332*e32*e14*e35+4*e113*e332*e35*e15*e31-6*e113*e36*e332* ... e32*e12-12*e113*e36*e31*e13*e332+4*e113*e322*e36*e13*e33+ ... 8*e113*e33*e35*e32*e34+4*e113*e352*e33*e31*e13+8*e11*e33* ... e35*e32*e34-4*e11*e352*e33*e31*e13-8*e11*e34*e35*e32*e31-14* ... e11*e15*e312*e35*e33-8*e11*e14*e34*e13*e333-6*e11*e34*e312* ... e35*e12-2*e112*e14*e332*e34*e31+4*e112*e322*e31*e152*e33+ ... 2*e112*e323*e14*e15*e33+10*e112*e322*e35*e15*e33+2*e112* ... e333*e14*e15*e32+2*e112*e333*e14*e12*e35+4*e112*e34*e15* ... e12*e333-6*e112*e333*e12*e32*e16-2*e112*e322*e34*e33*e14- ... 6*e112*e332*e32*e15*e34-8*e112*e12*e32*e33*e352+6*e112* ... e31*e32*e12*e352-2*e112*e332*e32*e14*e35-2*e112*e12*e323* ... e33*e16+8*e112*e33*e16*e322*e31-14*e112*e332*e35*e15*e31+ ... 2*e112*e12*e323*e15*e35+16*e112*e36*e332*e32*e12+12*e112* ... e36*e31*e132*e332-24*e112*e36*e33*e13*e312+12*e112*e36* ... e33*e132*e312+12*e112*e36*e31*e13*e332+6*e112*e36*e332* ... e122*e31-2*e112*e13*e36*e323*e12-4*e112*e322*e36*e132* ... e31-4*e112*e322*e36*e132*e33-4*e112*e31*e342*e132*e33+2* ... e112*e33*e36*e322*e122-2*e112*e33*e342*e32*e12+8*e112* ... e31*e342*e13*e33-4*e112*e322*e36*e13*e33+8*e112*e322*e36* ... e13*e31-2*e112*e34*e35*e322*e12-2*e112*e35*e14*e323*e13+6* ... e112*e322*e16*e13*e332-4*e112*e31*e33*e352*e132-2*e112* ... e31*e33*e352*e122-12*e112*e31*e16*e13*e333+12*e112*e312* ... e16*e13*e332+4*e11*e36*e322*e133*e31-14*e11*e36*e332*e32* ... e12-24*e11*e36*e31*e132*e332+8*e11*e36*e33*e122*e312+12* ... e11*e36*e33*e13*e312+12*e11*e36*e33*e132*e312+12*e11*e36* ... e31*e13*e332-4*e11*e36*e332*e122*e31-12*e11*e36*e33*e133* ... e312-4*e11*e36*e31*e322*e122+8*e11*e13*e36*e323*e12-4*e11* ... e322*e36*e132*e31+8*e11*e322*e36*e132*e33-4*e11*e31*e342* ... e132*e33-8*e11*e33*e36*e322*e122-2*e11*e33*e342*e32*e12-4* ... e11*e31*e342*e13*e33-4*e11*e322*e36*e13*e33-4*e11*e322*e36* ... e13*e31+6*e11*e34*e35*e322*e12-4*e11*e312*e142*e13*e332+ ... 24*e11*e33*e16*e13*e313-12*e11*e33*e16*e132*e313+2*e36* ... e122*e313+4*e11*e35*e14*e323*e13-2*e11*e12*e36*e323*e132- ... 12*e11*e322*e16*e13*e332-4*e36*e13*e313+2*e11*e36*e312* ... e32*e12+8*e11*e31*e33*e352*e132+4*e11*e31*e33*e352*e122+ ... 24*e11*e31*e16*e13*e333+4*e11*e313*e15*e35*e132+4*e11*e31* ... e142*e13*e333+4*e11*e31*e342*e33*e133+4*e11*e312*e13* ... e352*e122+4*e11*e313*e33*e152*e13+12*e11*e312*e16*e132* ... e332-48*e11*e312*e16*e13*e332-4*e11*e312*e152*e13*e332- ... 4*e11*e312*e332*e16*e122-8*e11*e313*e15*e35*e13+4*e11* ... e342*e122*e13*e332+6*e11*e132*e16*e322*e312+2*e11*e322* ... e35*e15*e31-4*e11*e14*e332*e34*e31+2*e11*e12*e32*e333*e142+ ... 4*e11*e333*e122*e16*e31-8*e11*e322*e31*e152*e33-4*e11* ... e323*e14*e15*e33-8*e11*e322*e35*e15*e33-4*e11*e333*e14*e15* ... e32+2*e11*e332*e35*e34*e123-2*e11*e123*e32*e36*e332-4*e11* ... e34*e122*e14*e333+2*e11*e322*e122*e332*e16-4*e11*e333* ... e14*e12*e35-8*e11*e34*e15*e12*e333+12*e11*e333*e12*e32*e16- ... 6*e11*e312*e35*e32*e14+4*e11*e322*e34*e33*e14-6*e11*e332* ... e35*e12*e34+10*e11*e12*e32*e33*e352-10*e11*e31*e32*e12*e352- ... 2*e11*e332*e32*e14*e35+8*e11*e12*e323*e33*e16+2*e11*e33*e14* ... e312*e34-24*e11*e33*e16*e322*e31+16*e11*e332*e35*e15*e31+2* ... e11*e123*e32*e31*e352-4*e11*e12*e323*e15*e35-2*e11*e142* ... e332*e322*e13+8*e11*e32*e35*e14*e33*e31+4*e11*e32*e34*e33* ... e15*e31+12*e11*e33*e35*e12*e34*e31-4*e11*e32*e35*e12*e15* ... e312+8*e11*e332*e14*e15*e32*e31-4*e11*e32*e14*e33*e15*e312+ ... 2*e11*e15*e35*e33*e312*e132-4*e11*e33*e15*e35*e322*e13+4* ... e11*e31*e14*e35*e12*e332+12*e11*e35*e32*e312*e14*e13-4*e11* ... e15*e312*e34*e12*e33-6*e11*e12*e35*e312*e34*e132-6*e112* ... e31*e32*e12*e352*e13+2*e112*e12*e32*e33*e352*e13-4*e112* ... e332*e32*e14*e35*e13-6*e112*e34*e15*e32*e13*e332+2*e112* ... e14*e33*e34*e322*e13+2*e112*e31*e332*e16*e32*e12+2*e112* ... e31*e15*e35*e13*e332-6*e112*e31*e15*e34*e12*e332-8*e112* ... e31*e322*e16*e13*e33-8*e112*e312*e33*e15*e35*e13-4*e112* ... e36*e33*e31*e32*e12-6*e112*e12*e34*e35*e13*e332+8*e112*e32* ... e34*e35*e132*e33+8*e112*e32*e34*e35*e132*e31+2*e112*e13* ... e34*e35*e322*e12+2*e112*e13*e33*e342*e32*e12+2*e112*e332* ... e13*e36*e32*e12+2*e112*e14*e31*e34*e13*e332-16*e112*e32* ... e34*e35*e13*e31+8*e112*e32*e34*e35*e13*e33-2*e112*e12*e322* ... e34*e33*e15-4*e112*e32*e35*e14*e33*e31-4*e112*e33*e35*e12* ... e34*e31-6*e112*e332*e14*e15*e32*e31+2*e112*e33*e15*e35* ... e322*e13-4*e112*e31*e14*e35*e12*e332-8*e113*e32*e34*e35* ... e13*e33+2*e11*e142*e32*e31*e12*e332-4*e11*e31*e14*e35*e322* ... e12-8*e11*e31*e332*e16*e32*e12-4*e11*e31*e15*e35*e13*e332+ ... 12*e11*e31*e15*e34*e12*e332-4*e11*e31*e15*e35*e322*e13+4* ... e11*e31*e32*e35*e34*e122+32*e11*e31*e322*e16*e13*e33-8*e11* ... e31*e34*e332*e14*e132+2*e11*e31*e34*e332*e14*e122-8*e11* ... e31*e322*e16*e132*e33-8*e11*e31*e32*e35*e34*e133+4*e11*e31* ... e33*e16*e322*e122+2*e11*e312*e14*e34*e132*e33-4*e11*e312* ... e33*e16*e32*e12+8*e11*e312*e14*e15*e12*e332+12*e11*e312* ... e33*e15*e35*e13-4*e11*e36*e33*e31*e32*e123+4*e11*e36*e13*e31* ... e322*e122-8*e11*e36*e122*e31*e13*e332-4*e11*e36*e12*e32* ... e13*e312+2*e11*e36*e12*e32*e132*e312+12*e11*e36*e33*e31* ... e32*e12-8*e11*e36*e33*e13*e122*e312+12*e11*e12*e34*e35*e13* ... e332-4*e11*e33*e14*e312*e34*e13-16*e11*e32*e34*e35*e132* ... e33+8*e11*e32*e34*e35*e132*e31-8*e11*e13*e34*e35*e322*e12+8* ... e11*e13*e33*e342*e32*e12-4*e11*e332*e13*e36*e32*e12-4*e11* ... e32*e14*e34*e12*e332+12*e11*e14*e31*e34*e13*e332+8*e11*e32* ... e34*e35*e13*e31+8*e11*e32*e34*e35*e13*e33-4*e11*e122*e322* ... e31*e15*e35+2*e11*e12*e32*e332*e31*e152-6*e11*e32*e312*e12* ... e152*e33-2*e11*e122*e34*e332*e15*e32-8*e11*e333*e12*e14* ... e15*e31+2*e11*e332*e122*e35*e15*e31+4*e11*e122*e32*e35*e33* ... e34+4*e11*e122*e322*e36*e33*e13-4*e11*e12*e323*e33*e16*e13+ ... 2*e11*e322*e35*e15*e31*e132+2*e11*e31*e32*e12*e352*e132+2* ... e11*e12*e322*e35*e34*e132+8*e11*e31*e32*e12*e352*e13-4*e11* ... e12*e32*e33*e352*e13+8*e11*e332*e32*e14*e35*e13+12*e11*e34* ... e15*e32*e13*e332+12*e11*e34*e35*e12*e13*e312-6*e11*e342* ... e12*e33*e32*e132-4*e11*e14*e33*e34*e322*e13-6*e11*e14*e35* ... e32*e132*e312-2*e114*e332*e352+12*e112*e36*e333-6* ... e112*e332*e352-2*e112*e334*e142-12*e112*e334*e16-2* ... e113*e322*e352-2*e113*e332*e342-12*e113*e36*e333+6* ... e113*e332*e352+4*e113*e334*e16+4*e114*e36*e333+2*e11* ... e352*e312-2*e11*e322*e352-2*e11*e332*e342-4*e11*e36* ... e333+2*e11*e332*e352+4*e11*e334*e142+12*e11*e334*e16-2* ... e112*e352*e312+4*e112*e322*e352+4*e112*e332*e342-2* ... e11*e312*e342+4*e11*e313*e36+2*e11*e322*e342-8*e11*e35* ... e15*e33*e13*e31*e32*e12-8*e11*e12*e33*e14*e31*e34*e32*e13-16* ... e11*e33*e12*e34*e35*e13*e31+4*e36*e323*e12-2*e332*e342* ... e132+2*e332*e342*e13+2*e312*e342*e13-e332*e322*e152- ... e122*e322*e352-e324*e152+2*e333*e35*e15+2*e333*e31* ... e152-e322*e122*e342-e322*e312*e142+6*e33*e152*e313- ... e324*e142-2*e334*e142-4*e334*e16-2*e333*e34*e14-8*e312* ... e16*e322+2*e323*e15*e34+3*e332*e122*e342-4*e314*e16+6* ... e333*e142*e31-3*e322*e152*e312+2*e33*e142*e313-4*e324* ... e16-8*e322*e332*e16; g5 = 2*e332*e13*e31*e32*e12-4*e313*e33+6*e332*e312+2*e312* ... e322-4*e333*e31-4*e33*e322*e31+2*e332*e322+e134*e314-4* ... e133*e314-4*e13*e314+6*e132*e314+8*e322*e31*e13*e33+8* ... e322*e31*e33*e11-4*e13*e31*e323*e12+6*e13*e322*e11*e312-4* ... e322*e31*e132*e33+4*e33*e31*e322*e122-12*e312*e132* ... e332*e11-12*e13*e312*e332*e112+4*e332*e11*e122*e312-12* ... e33*e11*e13*e313-2*e33*e312*e32*e12+12*e33*e11*e132*e313- ... 4*e33*e13*e122*e313+24*e312*e13*e332*e11-6*e322*e11* ... e132*e312+6*e12*e32*e132*e313-6*e12*e32*e13*e313-2*e31* ... e323*e12*e11+12*e31*e13*e333*e112-12*e31*e13*e333*e11-2* ... e31*e332*e32*e12-2*e12*e32*e133*e313+2*e322*e11*e133* ... e312+4*e122*e312*e13*e332-2*e13*e312*e322*e122+2*e33* ... e122*e132*e313+2*e33*e312*e32*e123-4*e313*e133*e33*e11+ ... 6*e312*e132*e332*e112-4*e31*e13*e333*e113-4*e31*e322* ... e33*e112+6*e322*e13*e332*e11-6*e333*e32*e12*e11-2*e332* ... e322*e122*e11+2*e33*e323*e12*e112-2*e33*e13*e323*e12+2* ... e12*e323*e132*e31+2*e332*e31*e32*e123-6*e332*e112*e322* ... e13+6*e333*e112*e32*e12-4*e33*e323*e12*e11-2*e333*e113* ... e32*e12+2*e332*e113*e322*e13+e332*e322*e122*e112+2*e31* ... e333*e112*e122-4*e31*e122*e11*e333+e132*e312*e322* ... e122-4*e33*e13*e312*e32*e12*e11-4*e31*e32*e12*e13*e332*e11+ ... 2*e31*e32*e12*e13*e332*e112+e324*e132-2*e324*e11-2*e324* ... e13+e324*e112+6*e334*e112-4*e334*e113-4*e334*e11+e334* ... e114-2*e11*e12*e323*e132*e31-2*e11*e332*e31*e32*e123-2* ... e33*e13*e323*e12*e112-2*e33*e13*e312*e32*e123+2*e31*e122* ... e333+e332*e124*e312+2*e11*e132*e312*e33*e32*e12+4*e11* ... e33*e13*e31*e322*e122+4*e33*e12*e32*e13*e312+2*e33*e12*e32* ... e11*e312+4*e332*e31*e32*e12*e11-16*e13*e322*e31*e33*e11-6* ... e322*e13*e312-2*e322*e11*e312+2*e31*e323*e12-2*e322*e13* ... e332+6*e322*e332*e112-6*e322*e332*e11+4*e324*e11*e13+2* ... e33*e323*e12+2*e333*e32*e12-2*e132*e312*e33*e32*e12-2* ... e332*e113*e322+e332*e322*e122-2*e13*e324*e112-2*e324* ... e11*e132-4*e33*e13*e31*e322*e122+4*e33*e13*e323*e12*e11+ ... e324*e112*e132+e324+e314-4*e122*e312*e13*e332*e11-4* ... e31*e33*e322*e122*e11+8*e31*e322*e132*e33*e11-4*e31*e322* ... e132*e33*e112+4*e31*e13*e323*e12*e11+8*e31*e322*e13*e33* ... e112-2*e31*e332*e32*e12*e112+6*e322*e132*e312+4*e31*e13* ... e333+6*e312*e332*e112-4*e332*e122*e312+6*e312*e132* ... e332+2*e33*e122*e313+12*e33*e13*e313-12*e33*e132*e313+4* ... e31*e333*e113+12*e31*e333*e11-12*e31*e333*e112+e312* ... e322*e122+4*e33*e11*e313+4*e33*e133*e313-12*e312*e13* ... e332-12*e312*e332*e11+2*e313*e32*e12-2*e322*e133*e312+e334; % g1*r33^8+g2*r33^6+g3*r33^4+g4*r33^2+g5 r33s = roots([g1,g2,g3,g4,g5]); r33s = sqrt(r33s); nr_sols = 0; P = []; for i = 1:length(r33s) r33 = r33s(i); if isreal(r33) h1 = e122+e132-2*e11*e13+e112; h2 = 2*e15*r33*e12-2*e14*r33*e13+2*e11*e14*r33; h3 = 2*e13-2*e11*e13*r33^2-2*e16*r33^2*e13-e122-2*e132+2*e11* ... e13+r33^2*e122-2*e11+e142*r33^2+2*e132*r33^2+e152* ... r33^2+2*e11*e16*r33^2; h4 = 2*e16*r33^3*e14-2*e15*r33*e12+2*r33^3*e15*e12+2*e14*r33* ... e13-2*e14*r33^3*e13-2*e14*r33; h5 = 1+e132-2*e132*r33^2-2*e16*r33^4*e13+e132*r33^4-e152* ... r33^2+e162*r33^4+r33^4*e152-2*e13+2*e16*r33^2*e13+2*e13* ... r33^2-2*e16*r33^2; % h1*r13^4+h2*r13^3+h3*r13^2+h4*r13+h5 r13s = roots([h1,h2,h3,h4,h5]); for j = 1:length(r13s) r13 = r13s(j); if isreal(r13) p1 = e33; p2 = e35*r33+e32*r13; p3 = e31*r13^2+e36*r33^2+e34*r33*r13; % p1*r23^2+p2*r23+p3 r23s = roots([p1,p2,p3]); for k = 1:length(r23s) r23 = r23s(k); z = r13^2+r23^2+r33^2-1; if abs(z) < 10^-3 r12 = ((c52*c63-c53*c62)*(-c44*r13-c45*r23-c46*r33) ... -(c42*c63-c43*c62)*(-c54*r13-c55*r23-c56*r33) ... +(c42*c53- c43*c52)*(-c64*r13-c65*r23-c66*r33))/d2; r22 = (-(-c61*c53+c51*c63)*(-c44*r13-c45*r23-c46*r33) ... +(-c61*c43+c41* c63)*(-c54*r13- c55*r23- c56*r33) ... -(-c51*c43+c41* c53)*(-c64*r13- c65*r23- c66*r33))/d2; r32 = ((-c61*c52+c51*c62)*(-c44*r13-c45*r23-c46*r33) ... -(-c61*c42+c41* c62)*(-c54*r13- c55*r23- c56*r33) ... +(-c51*c42+c41* c52)*(-c64*r13- c65*r23- c66*r33))/d2; t1 = b11*r12+b12*r22+b13*r32+b14*r13+b15*r23+ b16*r33; t2 = b21*r12+b22*r22+b23*r32+b24*r13+b25*r23+ b26*r33; t3 = b31*r12+b32*r22+b33*r32+b34*r13+b35*r23+ b36*r33; R = [cross([r12,r22,r32],[r13,r23,r33]);... [r12,r22,r32]; ... [r13,r23,r33]]'; T = [t1,t2,t3]'; if det(R) < 0 R = -R; T = -T; end; nr_sols = nr_sols+1; P = [P;[R,T]]; end; end end; end; end; end;