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: $-\infty$ (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.

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, 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

• Lunar arithmetic

External links

• MaxPlus algebra
• Max Plus working group, INRIA Rocquencourt