Janet Basis
rbpl
Variables: a , b , c , u , v , w , t , d;
Ordering: DegreeReverseLexicographical;
Polynomial set:
u^2 + v^2 + w^2 - 1,

2*a^2*u + 2*a^2*v + a^2 + 8*a*b*v + 4*a*b + 8*a*c*u + 8*a*c*w + 4*a*c - 8*
a*d*v - 4*a*d - 6*b^2*u + 2*b^2*v + 5*b^2 + 8*b*c*v + 4*b*c + 8*b*d*u - 8*
b*d*w - 12*b*d - 6*c^2*u + 2*c^2*v + 8*c^2*w + 13*c^2 + 8*c*d*v + 4*c*d + 2*
d^2*u + 2*d^2*v + 8*d^2*w + 9*d^2,

- 150*a^2*u - 50*a^2*v + 143*a^2 + 200*a*b*u - 300*a*b + 200*a*c*u - 300*
a*c - 200*a*d*v + 200*a*d*w + 100*a*d - 150*b^2*u + 150*b^2*v + 243*b^2 + 200
*b*c*v + 200*b*c*w + 300*b*c + 200*b*d*u - 300*b*d - 150*c^2*u - 50*c^2*v +
200*c^2*w + 343*c^2 - 200*c*d*u + 300*c*d - 150*d^2*u + 150*d^2*v + 200*
d^2*w + 443*d^2,

- 10*a^2*u - 2*a^2*v + 7*a^2 - 8*a*b*v + 4*a*b + 8*a*c*u - 8*a*c*w - 20*
a*c - 8*a*d*v + 4*a*d - 2*b^2*u - 2*b^2*v - 5*b^2 + 8*b*c*v - 4*b*c + 8*b*
d*u + 8*b*d*w - 4*b*d - 2*c^2*u - 2*c^2*v + 8*c^2*w + 3*c^2 - 8*c*d*v + 4*
c*d - 10*d^2*u - 2*d^2*v + 8*d^2*w + 15*d^2,

- 24*a^2*u + 36*a^2*v + 72*a^2*w - 59*a^2 - 144*a*b*u + 48*a*b - 144*a*
d*w - 144*a*d - 24*b^2*u - 108*b^2*v + 72*b^2*w + 13*b^2 - 144*b*c*w - 144*
b*c - 24*c^2*u + 36*c^2*v + 72*c^2*w - 59*c^2 + 144*c*d*u - 48*c*d - 24*
d^2*u - 108*d^2*v + 72*d^2*w + 13*d^2,

2*( - a^2*u - a^2*v - a^2*w + 2*a*b*u + 2*a*b*v - 4*a*b + 2*a*c*u + 2*a*c*
w - 4*a*c - 2*a*d*v + 2*a*d*w - 3*b^2*u + b^2*v - b^2*w + 4*b^2 + 2*b*c*
v + 2*b*c*w + 2*b*d*u - 2*b*d*w - 4*b*d - 3*c^2*u - c^2*v + c^2*w + 4*c^2 -
2*c*d*u + 2*c*d*v + 4*c*d - d^2*u + d^2*v + d^2*w);
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