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Usually, this goes like that

sage: x,y,z = polygens(QQ, 'x,y,z')
sage: P = x**3+y**3+z**3
sage: R = x.parent()
sage: I = R.ideal([P] + [P.derivative(var) for var in R.gens()])
sage: I.dimension()
0
sage: I.vector_space_dimension()
8