2015/05/24 by Hoon Hong, Hong, Hoon, Yonggu Kim +5
Computer Science · Mathematics · #Commutative Algebra and Its Applications #FOS: Mathematics #Formal Methods in Verification #Polynomial and algebraic computation #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1505.06470
openalex publication_date 2015/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The resultant plays a crucial role in (computational) algebra and algebraic geometry. One of the most important and well known properties of the resultant is that it is equal to the determinant of the Sylvester matrix. In 2008, Odagiri proved that a similar property holds over the tropical semiring if one replaces subtraction with addition. The tropical semiring belongs to a large family of algebraic structures called commutative idempotent semiring. In this paper, we prove that the same property (with subtraction replaced with addition) holds over an arbitrary\/ commutative idempotent semiring.