Janet Basis
extcyc7
Variables: w , x1 , x2 , x3 , x4 , x5 , x6, x7;
Ordering: DegreeReverseLexicographical;
Goal: Basis;
Polynomial set:
w^7 + 1,
w + x1 + x2 + x3 + x4 + x5 + x6 + x7,
w^2 + x1*x2 + x1*x7 + x2*x3 + x3*x4 + x4*x5 + x5*x6 + x6*x7,
w^3 + x1*x2*x3 + x1*x2*x7 + x1*x6*x7 + x2*x3*x4 + x3*x4*x5 + x4*x5*x6 + x5*
x6*x7,
w^4 + x1*x2*x3*x4 + x1*x2*x3*x7 + x1*x2*x6*x7 + x1*x5*x6*x7 + x2*x3*x4*x5 +
x3*x4*x5*x6 + x4*x5*x6*x7,
w^5 + x1*x2*x3*x4*x5 + x1*x2*x3*x4*x7 + x1*x2*x3*x6*x7 + x1*x2*x5*x6*x7 +
x1*x4*x5*x6*x7 + x2*x3*x4*x5*x6 + x3*x4*x5*x6*x7,
w^6 + x1*x2*x3*x4*x5*x6 + x1*x2*x3*x4*x5*x7 + x1*x2*x3*x4*x6*x7 + x1*x2*x3*
x5*x6*x7 + x1*x2*x4*x5*x6*x7 + x1*x3*x4*x5*x6*x7 + x2*x3*x4*x5*x6*x7,
x1*x2*x3*x4*x5*x6*x7 - 1
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