Machine-checked formalization in Lean 4 of the Wu-Ritt method with proofs that characteristic sets and zero decompositions correctly capture the solution sets of polynomial systems.
Formalizing Gr\"obner Basis Theory in Lean
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We present a formalization of Gr\"obner basis theory in Lean 4, built on top of Mathlib's infrastructure for multivariate polynomials and monomial orders. Our development covers the core foundations of Gr\"obner basis theory, including polynomial division with remainder, Buchberger's criterion, and the existence and uniqueness of reduced Gr\"obner bases. We develop the theory uniformly for polynomial rings indexed by arbitrary types, enabling the treatment of Gr\"obner bases in rings with infinitely many variables. Furthermore, we connect the finite and infinite settings by showing that infinite-variable reduced Gr\"obner bases can be characterized via reduced Gr\"obner bases on finite-variable subrings through monomial-order embeddings and filter-based limit constructions.
years
2026 2representative citing papers
Develops certificate-based tactics in Lean 4 that import and formally verify Gröbner basis results from external computer algebra systems for polynomial ideal problems.
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Formalizing Wu-Ritt Method in Lean 4
Machine-checked formalization in Lean 4 of the Wu-Ritt method with proofs that characteristic sets and zero decompositions correctly capture the solution sets of polynomial systems.
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Automated Tactics for Polynomial Reasoning in Lean 4
Develops certificate-based tactics in Lean 4 that import and formally verify Gröbner basis results from external computer algebra systems for polynomial ideal problems.