In the mathematical discipline of idempotent analysis, tropical analysis is the study of the tropical semiring.
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Applications
The max tropical semiring can be used appropriately to determine marking times within a given Petri net and a vector filled with marking state at the beginning: − ∞ {\displaystyle -\infty } (unit for max, tropical addition) means "never before", while 0 (unit for addition, tropical multiplication) is "no additional time".
Tropical cryptography is cryptography based on the tropical semiring.
Tropical geometry is an analog to algebraic geometry, using the tropical semiring.
- Litvinov, G. L. (2005). "The Maslov dequantization, idempotent and tropical mathematics: A brief introduction". arXiv:math/0507014v1.
Further reading
- Butkovič, Peter (2010), Max-linear Systems: Theory and Algorithms, Springer Monographs in Mathematics, Springer-Verlag, doi:10.1007/978-1-84996-299-5, ISBN 978-1-84996-298-8
- Bernd Heidergott; Geert Jan Olsder; Jacob van der Woude (2005). Max Plus at Work: Modeling and Analysis of Synchronized Systems: A Course on Max-Plus Algebra and Its Applications. Princeton University Press. p. 224. ISBN 978-0-69111763-8.
See also
External links
- MaxPlus algebra
- Max Plus working group, INRIA Rocquencourt