Tropical analysis
In the mathematical discipline of idempotent analysis, tropical analysis is the study of the tropical semiring.
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: (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.
gollark: Of course. It's much easier to produce gods in a central facility! It's very complicated.
gollark: Also, I have correct ideas, as opposed to other people's wrong ones.
gollark: As supreme world dictator, I would be uniquely placed to resolve all the coordination problems and stuff by dictating.
gollark: While you're all here, I'd like to propose the optimal political system, me (gollark) as supreme eternal world dictator.
gollark: It's based on the general principle that people want things, and will do things to attain things.
References
- 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
- 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. p. 224. ISBN 978-0-69111763-8.
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