In the mathematical discipline of
idempotent analysis
In mathematical analysis, idempotent analysis is the study of idempotent semirings, such as the tropical semiring. The lack of an additive inverse in the semiring is compensated somewhat by the idempotent rule A \oplus A = A.
References
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, tropical analysis is the study of the
tropical semiring
In idempotent analysis, the tropical semiring is a semiring of extended real numbers with the operations of minimum (or maximum) and addition replacing the usual ("classical") operations of addition and multiplication, respectively.
The tropical s ...
.
Applications
The max tropical semiring can be used appropriately to determine marking times within a given
Petri net
A Petri net, also known as a place/transition net (PT net), is one of several mathematical modeling languages for the description of distributed systems. It is a class of discrete event dynamic system. A Petri net is a directed bipartite graph t ...
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
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...
, using the tropical semiring.
References
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Further reading
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See also
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Lunar arithmetic
Lunar most commonly means "of or relating to the Moon
The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). Th ...
External links
MaxPlus algebraworking group, INRIA Rocquencourt
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Tropical geometry