Izhakian, Zur and Knebusch, Manfred and Rowen, Louis (2014) Layered tropical mathematics. JOURNAL OF ALGEBRA, 416. pp. 200-273. ISSN 0021-8693, 1090-266X
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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. (C) 2014 Elsevier Inc. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SUPERTROPICAL MATRIX ALGEBRA; Tropical algebra; Layered supertropic.1 domains; Polynomial semiring; Resultant; Sylvester matrix; Discriminant; Layered derivatives |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Professoren und akademische Räte im Ruhestand > Prof. Dr. Manfred Knebusch |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 12 Aug 2019 07:40 |
| Last Modified: | 12 Aug 2019 07:40 |
| URI: | https://pred.uni-regensburg.de/id/eprint/9355 |
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