I want to know what is the difference between Tropical algebra and min-plus algebra and the difference between Tropical semiring and semiring . I need Reference explains these differences and tropical algebra please.

  • $\begingroup$ Tropical algebra is commonly encountered as either $(\min, +)$ or $(\max, +)$ algebra (the two are isomorphic). The $(\min, +)$ semiring is a specific semiring where $\min$ is acting as binary "addition" and $+$ is acting as "multiplication". For a reference you can check Butkovic's book or this expository article by Speyer and Sturmfels. $\endgroup$ – VHarisop Jan 25 at 16:20

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