# [WSS22] Extended Newton polytopes of tropical polynomials

Posted 8 months ago
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Posted 4 months ago
 It's two-dimensional but we can make more plots, we can visualize a two-dimensional tropical curve in a ContourPlot of the tropicalized polynomial. Manipulate[ Show[ ListPlot3D[ coord3D[Round[c] 2 + 8 x + 5 y, {x, y}], Mesh -> None, Axes -> True, PlotStyle -> {Yellow}, Filling -> Bottom, BoundaryStyle -> Thick, PlotLabels -> "Newton Polytope"], ListPointPlot3D[ coord3D[Round[c] 2 + 8 x + 5 y, {x, y}] ]], {c, 1, 10}] This precious article on the Newton Polytopes & those 3D coordinates, the co-efficients, the valuations, and most of all, an in-depth look at Tropical MinPlus algebra. Here, we have used the same polynomial p as above. Maybe some other kind of operations... like the one with regard to grouping, distribution, and order of operands. Or to the highest prime of numbers like 3 or 5, also, with regard to the CoefficientRules is this good? Hard-code variables like x and y? coord3D[poly_, variables_] := Flatten /@ Transpose[{First /@ CoefficientRules[poly, {x, y}], IntegerExponent[#, 2] & /@ Last /@ CoefficientRules[poly, {x, y}]}] 
Posted 8 months ago
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