restart;
Solve({(6*(-8*L*alpha^2*a[1]^3+2*L*a[1]^3-2*a[1]^3))*d-24*L*alpha^2*a[0]*a[1]^2+6*L*a[0]*a[1]^2-6*a[0]*a[1]^2+12*alpha^2*k^2*lambda*v*a[1]-12*alpha^2*k^2*lambda*a[1]-3*k^2*lambda*v*a[1]+3*k^2*lambda*a[1]+(3*(8*alpha^2*k^2*v^2*a[1]-16*alpha^2*k^2*v*a[1]+8*alpha^2*k^2*a[1]-2*k^2*v^2*a[1]+4*k^2*v*a[1]-2*k^2*a[1]))*d = 0, (-8*L*alpha^2*a[1]^3+2*L*a[1]^3-2*a[1]^3)*d^6+(-24*L*alpha^2*a[0]*a[1]^2+6*L*a[0]*a[1]^2-6*a[0]*a[1]^2)*d^5+(-24*L*alpha^2*a[0]^2*a[1]-24*L*alpha^2*a[1]^2*a[2]-4*alpha^4*a[1]+6*L*a[0]^2*a[1]+6*L*a[1]^2*a[2]-4*alpha^2*beta*a[1]+alpha^2*a[1]-6*a[0]^2*a[1]-6*a[1]^2*a[2]+beta*a[1])*d^4+(4*alpha^2*k^2*lambda*mu*a[1]-8*L*alpha^2*a[0]^3-48*L*alpha^2*a[0]*a[1]*a[2]-4*alpha^4*a[0]-k^2*lambda*mu*a[1]+2*L*a[0]^3+12*L*a[0]*a[1]*a[2]-4*alpha^2*beta*a[0]+alpha^2*a[0]-2*a[0]^3-12*a[0]*a[1]*a[2]+beta*a[0])*d^3+(-24*L*alpha^2*a[0]^2*a[2]-24*L*alpha^2*a[1]*a[2]^2-4*alpha^4*a[2]+6*L*a[0]^2*a[2]+6*L*a[1]*a[2]^2-4*alpha^2*beta*a[2]+alpha^2*a[2]-6*a[0]^2*a[2]-6*a[1]*a[2]^2+beta*a[2])*d^2+(-4*alpha^2*k^2*lambda*mu*a[2]-24*L*alpha^2*a[0]*a[2]^2+k^2*lambda*mu*a[2]+6*L*a[0]*a[2]^2-6*a[0]*a[2]^2)*d+8*alpha^2*k^2*mu^2*a[2]-2*a[2]^3-2*k^2*mu^2*a[2]-8*L*alpha^2*a[2]^3+2*L*a[2]^3 = 0, (6*(-8*L*alpha^2*a[1]^3+2*L*a[1]^3-2*a[1]^3))*d^5+(5*(-24*L*alpha^2*a[0]*a[1]^2+6*L*a[0]*a[1]^2-6*a[0]*a[1]^2))*d^4+(4*(-24*L*alpha^2*a[0]^2*a[1]-24*L*alpha^2*a[1]^2*a[2]-4*alpha^4*a[1]+6*L*a[0]^2*a[1]+6*L*a[1]^2*a[2]-4*alpha^2*beta*a[1]+alpha^2*a[1]-6*a[0]^2*a[1]-6*a[1]^2*a[2]+beta*a[1]))*d^3+(3*(4*alpha^2*k^2*lambda*mu*a[1]-8*L*alpha^2*a[0]^3-48*L*alpha^2*a[0]*a[1]*a[2]-4*alpha^4*a[0]-k^2*lambda*mu*a[1]+2*L*a[0]^3+12*L*a[0]*a[1]*a[2]-4*alpha^2*beta*a[0]+alpha^2*a[0]-2*a[0]^3-12*a[0]*a[1]*a[2]+beta*a[0]))*d^2+(4*alpha^2*k^2*lambda^2*a[1]+8*alpha^2*k^2*mu*v*a[1]-8*alpha^2*k^2*mu*a[1]-k^2*lambda^2*a[1]-2*k^2*mu*v*a[1]+2*k^2*mu*a[1])*d^3+(2*(-24*L*alpha^2*a[0]^2*a[2]-24*L*alpha^2*a[1]*a[2]^2-4*alpha^4*a[2]+6*L*a[0]^2*a[2]+6*L*a[1]*a[2]^2-4*alpha^2*beta*a[2]+alpha^2*a[2]-6*a[0]^2*a[2]-6*a[1]*a[2]^2+beta*a[2]))*d+12*alpha^2*k^2*lambda*mu*a[2]-24*L*alpha^2*a[0]*a[2]^2-3*k^2*lambda*mu*a[2]+6*L*a[0]*a[2]^2-6*a[0]*a[2]^2+(-4*alpha^2*k^2*lambda^2*a[2]-8*alpha^2*k^2*mu*v*a[2]+8*alpha^2*k^2*mu*a[2]+k^2*lambda^2*a[2]+2*k^2*mu*v*a[2]-2*k^2*mu*a[2])*d = 0, (15*(-8*L*alpha^2*a[1]^3+2*L*a[1]^3-2*a[1]^3))*d^2+(5*(-24*L*alpha^2*a[0]*a[1]^2+6*L*a[0]*a[1]^2-6*a[0]*a[1]^2))*d+(3*(12*alpha^2*k^2*lambda*v*a[1]-12*alpha^2*k^2*lambda*a[1]-3*k^2*lambda*v*a[1]+3*k^2*lambda*a[1]))*d+(3*(8*alpha^2*k^2*v^2*a[1]-16*alpha^2*k^2*v*a[1]+8*alpha^2*k^2*a[1]-2*k^2*v^2*a[1]+4*k^2*v*a[1]-2*k^2*a[1]))*d^2+8*alpha^2*k^2*mu*v*a[1]-6*a[0]^2*a[1]-6*a[1]^2*a[2]-4*alpha^4*a[1]+4*alpha^2*k^2*lambda^2*a[1]-8*alpha^2*k^2*mu*a[1]-2*k^2*mu*v*a[1]-24*L*alpha^2*a[0]^2*a[1]-24*L*alpha^2*a[1]^2*a[2]-k^2*lambda^2*a[1]+2*k^2*mu*a[1]+6*L*a[0]^2*a[1]+6*L*a[1]^2*a[2]-4*alpha^2*beta*a[1]+alpha^2*a[1]+beta*a[1] = 0, (15*(-8*L*alpha^2*a[1]^3+2*L*a[1]^3-2*a[1]^3))*d^4+(10*(-24*L*alpha^2*a[0]*a[1]^2+6*L*a[0]*a[1]^2-6*a[0]*a[1]^2))*d^3+(6*(-24*L*alpha^2*a[0]^2*a[1]-24*L*alpha^2*a[1]^2*a[2]-4*alpha^4*a[1]+6*L*a[0]^2*a[1]+6*L*a[1]^2*a[2]-4*alpha^2*beta*a[1]+alpha^2*a[1]-6*a[0]^2*a[1]-6*a[1]^2*a[2]+beta*a[1]))*d^2+(12*alpha^2*k^2*lambda*v*a[1]-12*alpha^2*k^2*lambda*a[1]-3*k^2*lambda*v*a[1]+3*k^2*lambda*a[1])*d^3+(3*(4*alpha^2*k^2*lambda*mu*a[1]-8*L*alpha^2*a[0]^3-48*L*alpha^2*a[0]*a[1]*a[2]-4*alpha^4*a[0]-k^2*lambda*mu*a[1]+2*L*a[0]^3+12*L*a[0]*a[1]*a[2]-4*alpha^2*beta*a[0]+alpha^2*a[0]-2*a[0]^3-12*a[0]*a[1]*a[2]+beta*a[0]))*d+(3*(4*alpha^2*k^2*lambda^2*a[1]+8*alpha^2*k^2*mu*v*a[1]-8*alpha^2*k^2*mu*a[1]-k^2*lambda^2*a[1]-2*k^2*mu*v*a[1]+2*k^2*mu*a[1]))*d^2+(-12*alpha^2*k^2*lambda*v*a[2]+12*alpha^2*k^2*lambda*a[2]+3*k^2*lambda*v*a[2]-3*k^2*lambda*a[2])*d+8*alpha^2*k^2*mu*v*a[2]-6*a[0]^2*a[2]-6*a[1]*a[2]^2-4*alpha^4*a[2]+4*alpha^2*k^2*lambda^2*a[2]-8*alpha^2*k^2*mu*a[2]-2*k^2*mu*v*a[2]-24*L*alpha^2*a[0]^2*a[2]-24*L*alpha^2*a[1]*a[2]^2-k^2*lambda^2*a[2]+2*k^2*mu*a[2]+6*L*a[0]^2*a[2]+6*L*a[1]*a[2]^2-4*alpha^2*beta*a[2]+alpha^2*a[2]+beta*a[2] = 0, (20*(-8*L*alpha^2*a[1]^3+2*L*a[1]^3-2*a[1]^3))*d^3+(10*(-24*L*alpha^2*a[0]*a[1]^2+6*L*a[0]*a[1]^2-6*a[0]*a[1]^2))*d^2+(4*(-24*L*alpha^2*a[0]^2*a[1]-24*L*alpha^2*a[1]^2*a[2]-4*alpha^4*a[1]+6*L*a[0]^2*a[1]+6*L*a[1]^2*a[2]-4*alpha^2*beta*a[1]+alpha^2*a[1]-6*a[0]^2*a[1]-6*a[1]^2*a[2]+beta*a[1]))*d+(8*alpha^2*k^2*v^2*a[1]-16*alpha^2*k^2*v*a[1]+8*alpha^2*k^2*a[1]-2*k^2*v^2*a[1]+4*k^2*v*a[1]-2*k^2*a[1])*d^3+(3*(4*alpha^2*k^2*lambda^2*a[1]+8*alpha^2*k^2*mu*v*a[1]-8*alpha^2*k^2*mu*a[1]-k^2*lambda^2*a[1]-2*k^2*mu*v*a[1]+2*k^2*mu*a[1]))*d+(3*(12*alpha^2*k^2*lambda*v*a[1]-12*alpha^2*k^2*lambda*a[1]-3*k^2*lambda*v*a[1]+3*k^2*lambda*a[1]))*d^2+(-8*alpha^2*k^2*v^2*a[2]+16*alpha^2*k^2*v*a[2]-8*alpha^2*k^2*a[2]+2*k^2*v^2*a[2]-4*k^2*v*a[2]+2*k^2*a[2])*d+4*alpha^2*k^2*lambda*v*a[2]+2*L*a[0]^3-4*alpha^4*a[0]-48*L*alpha^2*a[0]*a[1]*a[2]+4*alpha^2*k^2*lambda*mu*a[1]-4*alpha^2*k^2*lambda*a[2]-k^2*lambda*v*a[2]-k^2*lambda*mu*a[1]+12*L*a[0]*a[1]*a[2]+k^2*lambda*a[2]-8*L*alpha^2*a[0]^3-12*a[0]*a[1]*a[2]-4*alpha^2*beta*a[0]+alpha^2*a[0]+beta*a[0]-2*a[0]^3 = 0, 8*alpha^2*k^2*v^2*a[1]-8*L*alpha^2*a[1]^3-16*alpha^2*k^2*v*a[1]+8*alpha^2*k^2*a[1]-2*k^2*v^2*a[1]+2*L*a[1]^3+4*k^2*v*a[1]-2*k^2*a[1]-2*a[1]^3 = 0}, {alpha, a[0], a[1], a[2]});
/ / / 2 3 3 3\
Solve|{ 6 \-8 L alpha a[1] + 2 L a[1] - 2 a[1] / d
\ \
2 2 2 2
- 24 L alpha a[0] a[1] + 6 L a[0] a[1] - 6 a[0] a[1]
2 2 2 2
+ 12 alpha k lambda v a[1] - 12 alpha k lambda a[1]
2 2 / 2 2 2
- 3 k lambda v a[1] + 3 k lambda a[1] + 3 \8 alpha k v a[
2 2 2 2 2 2
1] - 16 alpha k v a[1] + 8 alpha k a[1] - 2 k v a[1]
2 2 \ / 2 3
+ 4 k v a[1] - 2 k a[1]/ d = 0, \-8 L alpha a[1]
3 3\ 6
+ 2 L a[1] - 2 a[1] / d
/ 2 2 2 2\ 5
+ \-24 L alpha a[0] a[1] + 6 L a[0] a[1] - 6 a[0] a[1] / d +
/ 2 2 2 2
\-24 L alpha a[0] a[1] - 24 L alpha a[1] a[2]
4 2 2
- 4 alpha a[1] + 6 L a[0] a[1] + 6 L a[1] a[2]
2 2 2
- 4 alpha beta a[1] + alpha a[1] - 6 a[0] a[1]
2 \ 4 / 2 2
- 6 a[1] a[2] + beta a[1]/ d + \4 alpha k lambda mu a[1]
2 3 2
- 8 L alpha a[0] - 48 L alpha a[0] a[1] a[2]
4 2 3
- 4 alpha a[0] - k lambda mu a[1] + 2 L a[0]
2 2
+ 12 L a[0] a[1] a[2] - 4 alpha beta a[0] + alpha a[0]
3 \ 3 /
- 2 a[0] - 12 a[0] a[1] a[2] + beta a[0]/ d + \
2 2 2 2 4
-24 L alpha a[0] a[2] - 24 L alpha a[1] a[2] - 4 alpha a[2]
2 2 2
+ 6 L a[0] a[2] + 6 L a[1] a[2] - 4 alpha beta a[2]
2 2 2 \ 2
+ alpha a[2] - 6 a[0] a[2] - 6 a[1] a[2] + beta a[2]/ d +
/ 2 2 2 2
\-4 alpha k lambda mu a[2] - 24 L alpha a[0] a[2]
2 2 2\
+ k lambda mu a[2] + 6 L a[0] a[2] - 6 a[0] a[2] / d
2 2 2 3 2 2
+ 8 alpha k mu a[2] - 2 a[2] - 2 k mu a[2]
2 3 3 / 2 3
- 8 L alpha a[2] + 2 L a[2] = 0, 6 \-8 L alpha a[1]
3 3\ 5
+ 2 L a[1] - 2 a[1] / d
/ 2 2 2 2\
+ 5 \-24 L alpha a[0] a[1] + 6 L a[0] a[1] - 6 a[0] a[1] /
4 / 2 2 2 2
d + 4 \-24 L alpha a[0] a[1] - 24 L alpha a[1] a[2]
4 2 2
- 4 alpha a[1] + 6 L a[0] a[1] + 6 L a[1] a[2]
2 2 2
- 4 alpha beta a[1] + alpha a[1] - 6 a[0] a[1]
2 \ 3 / 2 2
- 6 a[1] a[2] + beta a[1]/ d + 3 \4 alpha k lambda mu a[1]
2 3 2
- 8 L alpha a[0] - 48 L alpha a[0] a[1] a[2]
4 2 3
- 4 alpha a[0] - k lambda mu a[1] + 2 L a[0]
2 2
+ 12 L a[0] a[1] a[2] - 4 alpha beta a[0] + alpha a[0]
3 \ 2 / 2 2
- 2 a[0] - 12 a[0] a[1] a[2] + beta a[0]/ d + \4 alpha k
2 2 2 2 2
lambda a[1] + 8 alpha k mu v a[1] - 8 alpha k mu a[1]
2 2 2 2 \ 3 /
- k lambda a[1] - 2 k mu v a[1] + 2 k mu a[1]/ d + 2 \
2 2 2 2 4
-24 L alpha a[0] a[2] - 24 L alpha a[1] a[2] - 4 alpha a[2]
2 2 2
+ 6 L a[0] a[2] + 6 L a[1] a[2] - 4 alpha beta a[2]
2 2 2 \
+ alpha a[2] - 6 a[0] a[2] - 6 a[1] a[2] + beta a[2]/ d
2 2 2 2
+ 12 alpha k lambda mu a[2] - 24 L alpha a[0] a[2]
2 2 2 /
- 3 k lambda mu a[2] + 6 L a[0] a[2] - 6 a[0] a[2] + \
2 2 2 2 2
-4 alpha k lambda a[2] - 8 alpha k mu v a[2]
2 2 2 2 2
+ 8 alpha k mu a[2] + k lambda a[2] + 2 k mu v a[2]
2 \ / 2 3 3
- 2 k mu a[2]/ d = 0, 15 \-8 L alpha a[1] + 2 L a[1]
3\ 2
- 2 a[1] / d
/ 2 2 2 2\
+ 5 \-24 L alpha a[0] a[1] + 6 L a[0] a[1] - 6 a[0] a[1] / d + 3
/ 2 2 2 2
\12 alpha k lambda v a[1] - 12 alpha k lambda a[1]
2 2 \ / 2 2 2
- 3 k lambda v a[1] + 3 k lambda a[1]/ d + 3 \8 alpha k v
2 2 2 2 2 2
a[1] - 16 alpha k v a[1] + 8 alpha k a[1] - 2 k v a[1]
2 2 \ 2 2 2
+ 4 k v a[1] - 2 k a[1]/ d + 8 alpha k mu v a[1]
2 2 4
- 6 a[0] a[1] - 6 a[1] a[2] - 4 alpha a[1]
2 2 2 2 2
+ 4 alpha k lambda a[1] - 8 alpha k mu a[1]
2 2 2
- 2 k mu v a[1] - 24 L alpha a[0] a[1]
2 2 2 2 2
- 24 L alpha a[1] a[2] - k lambda a[1] + 2 k mu a[1]
2 2 2
+ 6 L a[0] a[1] + 6 L a[1] a[2] - 4 alpha beta a[1]
2 / 2 3
+ alpha a[1] + beta a[1] = 0, 20 \-8 L alpha a[1]
3 3\ 3
+ 2 L a[1] - 2 a[1] / d
/ 2 2 2 2\
+ 10 \-24 L alpha a[0] a[1] + 6 L a[0] a[1] - 6 a[0] a[1] /
2 / 2 2 2 2
d + 4 \-24 L alpha a[0] a[1] - 24 L alpha a[1] a[2]
4 2 2
- 4 alpha a[1] + 6 L a[0] a[1] + 6 L a[1] a[2]
2 2 2
- 4 alpha beta a[1] + alpha a[1] - 6 a[0] a[1]
2 \ / 2 2 2
- 6 a[1] a[2] + beta a[1]/ d + \8 alpha k v a[1]
2 2 2 2 2 2
- 16 alpha k v a[1] + 8 alpha k a[1] - 2 k v a[1]
2 2 \ 3 / 2 2 2
+ 4 k v a[1] - 2 k a[1]/ d + 3 \4 alpha k lambda a[1]
2 2 2 2
+ 8 alpha k mu v a[1] - 8 alpha k mu a[1]
2 2 2 2 \ /
- k lambda a[1] - 2 k mu v a[1] + 2 k mu a[1]/ d + 3 \12
2 2 2 2
alpha k lambda v a[1] - 12 alpha k lambda a[1]
2 2 \ 2 /
- 3 k lambda v a[1] + 3 k lambda a[1]/ d + \
2 2 2 2 2 2 2
-8 alpha k v a[2] + 16 alpha k v a[2] - 8 alpha k a[2]
2 2 2 2 \
+ 2 k v a[2] - 4 k v a[2] + 2 k a[2]/ d
2 2 3 4
+ 4 alpha k lambda v a[2] + 2 L a[0] - 4 alpha a[0]
2 2 2
- 48 L alpha a[0] a[1] a[2] + 4 alpha k lambda mu a[1]
2 2 2
- 4 alpha k lambda a[2] - k lambda v a[2]
2 2
- k lambda mu a[1] + 12 L a[0] a[1] a[2] + k lambda a[2]
2 3 2
- 8 L alpha a[0] - 12 a[0] a[1] a[2] - 4 alpha beta a[0]
2 3 / 2 3
+ alpha a[0] + beta a[0] - 2 a[0] = 0, 15 \-8 L alpha a[1]
3 3\ 4
+ 2 L a[1] - 2 a[1] / d
/ 2 2 2 2\
+ 10 \-24 L alpha a[0] a[1] + 6 L a[0] a[1] - 6 a[0] a[1] /
3 / 2 2 2 2
d + 6 \-24 L alpha a[0] a[1] - 24 L alpha a[1] a[2]
4 2 2
- 4 alpha a[1] + 6 L a[0] a[1] + 6 L a[1] a[2]
2 2 2
- 4 alpha beta a[1] + alpha a[1] - 6 a[0] a[1]
2 \ 2 / 2 2
- 6 a[1] a[2] + beta a[1]/ d + \12 alpha k lambda v a[1]
2 2 2
- 12 alpha k lambda a[1] - 3 k lambda v a[1]
2 \ 3 / 2 2
+ 3 k lambda a[1]/ d + 3 \4 alpha k lambda mu a[1]
2 3 2
- 8 L alpha a[0] - 48 L alpha a[0] a[1] a[2]
4 2 3
- 4 alpha a[0] - k lambda mu a[1] + 2 L a[0]
2 2
+ 12 L a[0] a[1] a[2] - 4 alpha beta a[0] + alpha a[0]
3 \ / 2 2
- 2 a[0] - 12 a[0] a[1] a[2] + beta a[0]/ d + 3 \4 alpha k
2 2 2 2 2
lambda a[1] + 8 alpha k mu v a[1] - 8 alpha k mu a[1]
2 2 2 2 \ 2 /
- k lambda a[1] - 2 k mu v a[1] + 2 k mu a[1]/ d + \
2 2 2 2
-12 alpha k lambda v a[2] + 12 alpha k lambda a[2]
2 2 \
+ 3 k lambda v a[2] - 3 k lambda a[2]/ d
2 2 2 2
+ 8 alpha k mu v a[2] - 6 a[0] a[2] - 6 a[1] a[2]
4 2 2 2
- 4 alpha a[2] + 4 alpha k lambda a[2]
2 2 2
- 8 alpha k mu a[2] - 2 k mu v a[2]
2 2 2 2
- 24 L alpha a[0] a[2] - 24 L alpha a[1] a[2]
2 2 2 2
- k lambda a[2] + 2 k mu a[2] + 6 L a[0] a[2]
2 2 2
+ 6 L a[1] a[2] - 4 alpha beta a[2] + alpha a[2]
2 2 2 2 3
+ beta a[2] = 0, 8 alpha k v a[1] - 8 L alpha a[1]
2 2 2 2 2 2
- 16 alpha k v a[1] + 8 alpha k a[1] - 2 k v a[1]
3 2 2 3 \
+ 2 L a[1] + 4 k v a[1] - 2 k a[1] - 2 a[1] = 0 },
/
\
{alpha, a[0], a[1], a[2]}|
/
