2009/02/09 by Jiayuan Lin, Lin, Jiayuan, Janice Wethington +1 · 1 citation
Computer Science · Mathematics · #32S10 #58K20 #58K40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #Commutative Algebra (math.AC) #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.AG #msc:32S10 #msc:58K20 #msc:58K40
paper · pdf · doi:10.48550/arxiv.0902.1518
First draft, comments are welcome
arxiv created 2009/02/09 · openalex publication_date 2009/02/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Thom-Boardman symbol was first introduced by Thom in 1956 to classify singularities of differentiable maps. It was later generalized by Boardman to a more general setting. Although the Thom-Boardman symbol is realized by a sequence of non-increasing, nonnegative integers, to compute those numbers is, in general, extremely difficult. In the case of polynomial multiplication maps, Robert Varley conjectured that computing the Thom-Boardman symbol for polynomial multiplication reduces to computing the successive quotients and remainders for the Euclidean algorithm applied to the degrees of the two polynomials. In this paper, we confirm this conjecture.