Janet Basis
cyclic8
Variables: x1,x2,x3,x4,x5,x6,x7,x8;
Ordering: DegreeReverseLexicographical;
Goal: Basis;
Polynomial set:
x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8,
x1*x2 + x1*x8 + x2*x3 + x3*x4 + x4*x5 + x5*x6 + x6*x7 + x7*x8,
x1*x2*x3 + x1*x2*x8 + x1*x7*x8 + x2*x3*x4 + x3*x4*x5 + x4*x5*x6 + x5*x6*x7 + x6*x7*x8,
x1*x2*x3*x4 + x1*x2*x3*x8 + x1*x2*x7*x8 + x1*x6*x7*x8 + x2*x3*x4*x5 + x3*x4* x5*x6 + x4*x5*x6*x7 + x5*x6*x7*x8,
x1*x2*x3*x4*x5 + x1*x2*x3*x4*x8 + x1*x2*x3*x7*x8 + x1*x2*x6*x7*x8 + x1*x5*x6* x7*x8 + x2*x3*x4*x5*x6 + x3*x4*x5*x6*x7 + x4*x5*x6*x7*x8,
x1*x2*x3*x4*x5*x6 + x1*x2*x3*x4*x5*x8 + x1*x2*x3*x4*x7*x8 + x1*x2*x3*x6*x7* x8 + x1*x2*x5*x6*x7*x8 + x1*x4*x5*x6*x7*x8 + x2*x3*x4*x5*x6*x7 + x3*x4*x5*x6* x7*x8,
x1*x2*x3*x4*x5*x6*x7 + x1*x2*x3*x4*x5*x6*x8 + x1*x2*x3*x4*x5*x7*x8 + x1*x2*x3*x4*x6*x7*x8 + x1*x2*x3*x5*x6*x7*x8 + x1*x2*x4*x5*x6*x7*x8 + x1*x3*x4*x5*x6*x7*x8 + x2*x3*x4*x5*x6*x7*x8,
x1*x2*x3*x4*x5*x6*x7*x8 - 1;

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