View source for Tropical analysis

{{Short description|Study of the tropical semiring}}
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: <math>-\infty</math> (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.

== References ==
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* {{cite arXiv |author-link= |eprint=math/0507014v1 |title= The Maslov dequantization, idempotent and tropical mathematics: A brief introduction|class= |last1= Litvinov|first1= G. L.|year= 2005}}
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== Further reading ==
* {{citation|title=Max-linear Systems: Theory and Algorithms|first=Peter|last=Butkovič|series=Springer Monographs in Mathematics|doi=10.1007/978-1-84996-299-5|publisher=Springer-Verlag|year=2010|isbn=978-1-84996-298-8|url=http://swbplus.bsz-bw.de/bsz329518011inh.htm }}
* {{cite book |title=Max Plus at Work: Modeling and Analysis of Synchronized Systems: A Course on Max-Plus Algebra and Its Applications |url=https://press.princeton.edu/titles/8120.html |author1=Bernd Heidergott |author2=Geert Jan Olsder |author3=Jacob van der Woude |year=2005 |isbn=978-0-69111763-8 |pages=224|publisher=Princeton University Press }}

==See also==
*[[Lunar arithmetic]]

== External links ==
* [http://maxplus.org/ MaxPlus algebra]
* [http://www.cmap.polytechnique.fr/~gaubert/maxplus.html Max Plus] working group, INRIA Rocquencourt


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[[Category:Tropical analysis| ]]
[[Category:Tropical geometry]]