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Apr 13, 2022 at 14:11 comment added David Loeffler The specific Sage command you're after is "elimination_ideal", see doc.sagemath.org/html/en/reference/polynomial_rings/sage/rings/…
Apr 12, 2022 at 22:43 comment added Max Alekseyev In your case, yes. You can view your polynomials as linear combinations of $1, y, z$ with coefficients being polynomials in $x$, then you'd need to form a $3\times 3$ matrix with those coefficients and compute its determinant.
Apr 12, 2022 at 22:39 comment added Turbo Actually it seemed I can use 'linear algebra' to eliminate monomial $x^2y$ and then $x^2z$ since $y$ and $z$ depends only on these monomials. Is that correct way to do?
Apr 12, 2022 at 22:35 comment added Max Alekseyev Not sure what python package you mean, but SageMath is python-based and it can be used as a python module.
Apr 12, 2022 at 22:33 comment added Turbo Would there be any python package?
Apr 12, 2022 at 22:28 history answered Max Alekseyev CC BY-SA 4.0