In the mathematical discipline of
idempotent analysis In mathematical analysis, idempotent analysis is the study of idempotent semirings, such as the tropical semiring
In idempotent analysis, the tropical semiring is a semiring of extended real numbers with the operations of minimum (or maximum) and ...
, 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 ...
.
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 (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 that ...
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
In mathematics, tropical geometry is the study of polynomials and their geometric properties when addition is replaced with minimization and multiplication is replaced with ordinary addition:
: x \oplus y = \min\,
: x \otimes y = x + y.
So f ...
is an analog to
algebraic geometry, using the tropical semiring.
References
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Further reading
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See also
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Lunar arithmetic
External links
MaxPlus algebraworking group, INRIA Rocquencourt
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Tropical geometry