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For applying Buchberger algorithm on simple ideals, you can have a look at https://doc.sagemath.org/html/en/reference/polynomial_rings/sage/rings/polynomial/toy_buchberger.html

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For applying Buchberger algorithm on simple uncomplicated ideals, you can have a look at https://doc.sagemath.org/html/en/reference/polynomial_rings/sage/rings/polynomial/toy_buchberger.html