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rr = QQ['x0, x1, x2, x3, x4, x5, x6, x7']
rr.inject_variables()
I = rr.ideal (x1*x2*x7, x6*x7, x1*x4*x7, x0*x2*x4*x6, x0*x3*x5, x2*x3, x0*x1, x3*x5*x6, x4*x5)
frobby.hilbert(I)
Defining x0, x1, x2, x3, x4, x5, x6, x7 x0*x1*x2*x3*x4*x5*x6*x7 + x0*x1*x2*x3*x4*x5*x6 + x0*x1*x2*x3*x4*x5*x7 + x0*x1*x2*x3*x4*x6*x7 + x0*x1*x2*x3*x5*x6*x7 + x0*x1*x2*x4*x5*x6*x7 + x0*x1*x3*x4*x5*x6*x7 + x0*x2*x3*x4*x5*x6*x7 + x1*x2*x3*x4*x5*x6*x7 + x0*x1*x2*x3*x4*x6 + x0*x1*x2*x4*x5*x6 + x1*x2*x3*x4*x5*x7 + x0*x2*x3*x4*x6*x7 + x0*x1*x3*x5*x6*x7 + x0*x2*x4*x5*x6*x7 + x0*x1*x2*x3*x5 + x0*x1*x3*x4*x5 + x0*x2*x3*x4*x5 + x0*x1*x2*x4*x6 + x0*x2*x3*x4*x6 + x0*x2*x3*x5*x6 + x0*x2*x4*x5*x6 + x0*x3*x4*x5*x6 + x2*x3*x4*x5*x6 + x0*x1*x2*x3*x7 + x0*x1*x2*x4*x7 + x0*x1*x4*x5*x7 + x0*x1*x2*x6*x7 + x1*x2*x3*x6*x7 + x0*x1*x4*x6*x7 + x0*x2*x4*x6*x7 + x1*x2*x4*x6*x7 + x2*x3*x5*x6*x7 + x1*x4*x5*x6*x7 + x3*x4*x5*x6*x7 + x0*x1*x2*x3 + x0*x1*x3*x5 + x0*x2*x3*x5 + x0*x1*x4*x5 + x0*x3*x4*x5 + x2*x3*x4*x5 + x0*x2*x4*x6 + x0*x3*x5*x6 + x2*x3*x5*x6 + x3*x4*x5*x6 + x0*x1*x2*x7 + x1*x2*x3*x7 + x0*x1*x4*x7 + x1*x2*x4*x7 + x1*x4*x5*x7 + x0*x1*x6*x7 + x1*x2*x6*x7 + x2*x3*x6*x7 + x1*x4*x6*x7 + x3*x5*x6*x7 + x4*x5*x6*x7 + x0*x3*x5 + x3*x5*x6 + x1*x2*x7 + x1*x4*x7 + x0*x1 + x2*x3 + x4*x5 + x6*x7 + 1