Layered tropical mathematics

Zur Izhakian, Manfred Knebusch, Louis Rowen

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Generalizing supertropical algebras, we present a “layered” structure, “sorted” by a semiring which permits varying ghost layers, and indicate how it is more amenable than the “standard” supertropical construction in factorizations of polynomials, description of varieties, and for mathematical analysis and calculus, in particular with respect to multiple roots of polynomials. This gives rise to a significantly better understanding of the tropical resultant and discriminant. Explicit examples and comparisons are given for various sorting semirings such as the natural numbers and the positive rational numbers, and we see how this theory relates to some recent developments in the tropical literature.
Original languageEnglish
Pages (from-to)200-273
Number of pages74
JournalJournal of Algebra
Volume416
Early online date11 Jul 2014
DOIs
Publication statusPublished - 15 Oct 2014

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Semiring
Multiple Roots
Polynomial
Mathematical Analysis
Discriminant
Natural number
Sorting
Factorization
Calculus
Algebra
Standards

Keywords

  • Tropical algebra
  • Layered supertropical domains
  • Polynomial semiring
  • Resultant
  • Sylvester matrix
  • Discriminant
  • Layered derivatives

Cite this

Layered tropical mathematics. / Izhakian, Zur; Knebusch, Manfred; Rowen, Louis.

In: Journal of Algebra, Vol. 416, 15.10.2014, p. 200-273.

Research output: Contribution to journalArticle

Izhakian, Zur ; Knebusch, Manfred ; Rowen, Louis. / Layered tropical mathematics. In: Journal of Algebra. 2014 ; Vol. 416. pp. 200-273.
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