Here I have some basic questions about max-plus algebra. How this is useful? Why we need to define a different algebra? What aspects are highlighted in this which were untouched in conventional algebra?
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1In a sense, your tag provides an answer to the question - the max-plus algebra gives us a neat way to tropicalize a variety, and then there are various theorems relating properties of the original variety to properties of the tropical variety, which are potentially easier to compute because of the combinatorial nature of the object. I believe there are other applications of max-plus not directly to do with tropical geometry, but I don't know what they are. – mdp Jul 11 '14 at 09:25
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There are many applications of max-plus like railway network modeling. Actually I am not yet familiar with tropical. So I was expecting some answer independent to tropical geometry. What was the need of introducing this algebra(History of this)? Is there anything you know about it? – Sourabh Jul 11 '14 at 12:09