Proves Frost and Storey's conjecture for multivariate polynomial matrices: equivalence to Smith normal form holds iff reduced minors of each order generate the unit ideal, with extension via ring automorphisms.
On the equivalence problem of smith forms for multivariate polynomial matrices
2 Pith papers cite this work. Polarity classification is still indexing.
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math.AC 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Criteria for Smith form equivalence of several classes of multivariate polynomial matrices are derived via algebra isomorphisms and extended to non-square and rank-deficient cases using the Quillen-Suslin and Lin-Bose theorems, with algorithmic verification via Gröbner bases.
citing papers explorer
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Matrix equivalence to Smith normal form: new theoretical results for multivariate polynomial matrices
Proves Frost and Storey's conjecture for multivariate polynomial matrices: equivalence to Smith normal form holds iff reduced minors of each order generate the unit ideal, with extension via ring automorphisms.
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Smith Form Equivalence for Several Classes of Multivariate Polynomial Matrices
Criteria for Smith form equivalence of several classes of multivariate polynomial matrices are derived via algebra isomorphisms and extended to non-square and rank-deficient cases using the Quillen-Suslin and Lin-Bose theorems, with algorithmic verification via Gröbner bases.