Questions tagged [tropical-arithmetic]

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choosing between the two ways to tropicalize

When tropicalizing a subtraction-free expression (see Do all subtraction-free identities tropicalize?), is it more common to replace addition by max or by min? Related issues: Is there a name for ...
James Propp's user avatar
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40 votes
5 answers
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How should one approach tropical mathematics?

Let me preface this by saying that my background is pretty meagre (i.e. solid undergrad). However, a few months ago I came across Litvinov - The Maslov dequantization, idempotent and tropical ...
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Do all subtraction-free identities tropicalize?

If you take a subtraction-free rational identity like $(xxx+yyy)/(x+y)+xy=xx+yy$ and replace $\times$,$/$,$+$,$1$ by $+$,$-$,min,$0$, do you always get a valid min,plus,minus identity like min(min($x+...
James Propp's user avatar
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9 votes
1 answer
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Generalizing detropicalization

Given an identity in max,plus arithmetic, are there ways to turn it into an ordinary algebraic identity it other than by replacing addition by multiplication and replacing max by series-plus or by ...
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5 votes
2 answers
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Name and notation for a binary operation

Is there a standard name or standard symbol for the binary operation that combines $x$ and $y$ to give $xy/(x+y)$, or equivalently $1/(1/x+1/y)$? (At least the expressions are equivalent if we ignore ...
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4 votes
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Is there any "fundamental" distinction between min-plus, max-plus, min-product, and max-product algebras?

In the paper Faster Algorithms for Max-Product Message Passing by McAuley and Caetano (see e.g. here or here), several statements are made which seem mathematically questionable to me. For ...
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2 votes
1 answer
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Can we have "tropical polynomials" with arbitrary real powers?

I am referring to the definition of a tropical polynomial given on page 8 (top of section 3) here in this review, https://arxiv.org/pdf/math/0306366.pdf. I understand that here the notion of a ...
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