Tropical geometry: Difference between revisions

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The adjective ''[[tropical]]'' in the name of the area was coined by French mathematicians in honor of the [[Hungary|Hungarian]]-born [[Brazil]]ian computer scientist [[Imre Simon]], who wrote on the field. [[Jean-Éric Pin]] attributes the coinage to [[Dominique Perrin]],<ref name="Pin1998">{{cite book |last=Pin |first=Jean-Eric |chapter=Tropical semirings |editor-last=Gunawardena |editor-first=J. |title=Idempotency |chapter-url= |publisher=[[Cambridge University Press]] |series=Publications of the Newton Institute |volume=11 |year=1998 |pages=50–69 |doi=10.1017/CBO9780511662508.004 |isbn=9780511662508}}</ref> whereas Simon himself attributes the word to Christian Choffrut.<ref name="Simon1988">{{Cite book |doi = 10.1007/BFb0017135 |chapter = Recognizable sets with multiplicities in the tropical semiring |title = Mathematical Foundations of Computer Science 1988 |volume = 324 |pages = 107–120 |series = [[Lecture Notes in Computer Science]] |year = 1988 |last1 = Simon |first1 = Imre |isbn = 978-3-540-50110-7}}</ref>
Quite independently of the use of the term ``tropical<nowiki>''</nowiki> by the Brazilian school concerning the new mathematics,V.P. Maslov, in connection with the situation that occurred in the USSR during the 1980<nowiki>'s (the ``perestroika''</nowiki> years) and the opening of the ``iron curtain<nowiki>''</nowiki> between the communist and capitalist countries, used this term repeatedly beginning from the mid 1980<nowiki>'s. In numerous oral presentations (e.g. at the General Meetings of the USSR Academy of Sciences) and articles in the Soviet press, he warned that the opening of the curtain between the two groups of countries would inevitably lead to a situation similar to the one that arose in the 17th century when the ocean ceased to be boundary between Europe and the Americas, on the one hand, and Africa on the other. At that time cheap European and American goods were exchanged for expensive Africa ressourses  and the slave trade began. This unequal exchange could be described by the rules of the new arithmetic, which Maslov and his followers first called ``idempotent (tropical) analysis''</nowiki> or ``Min; + algebra<nowiki>''</nowiki>. The term ``idempotent<nowiki>''</nowiki> did not survive in the literature, while the term ``tropical<nowiki>''</nowiki>, being more expressive  and pleasant to the ear, became more popular, although different schools gave it somewhat different meanings<ref></ref><ref></ref>.  
== Algebra background ==