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  "body": "\n## Summary\n\nA tropical variety is a polyhedral complex in $\\R^n$ attached to an algebraic subvariety of a torus over a field with a [[valuation|B85T5VKR3M]].\nIt is the set where tropical polynomials are \"zero\", meaning that the minimum of their linear terms is attained at least twice.\nOver an algebraically closed field with a nontrivial valuation, it equals the closure of the image of the variety under the coordinatewise valuation.\nThis is the fundamental theorem of [[tropical geometry|7YTC3BHK60]].\nTropical varieties keep dimension, degree and intersection data of the original variety in combinatorial form.\n\n## Explanations\n\n### L1 human\n\nTake the line $x + y + 1 = 0$, with $x$ and $y$ in a field of power series in a small parameter $t$.\nRecord for each solution the orders of vanishing of $x$ and $y$ in $t$.\nTwo of the three terms $x$, $y$, $1$ must have the same lowest order, or they could not cancel.\nSo the orders lie on three rays from the origin: one where $x$ and $y$ tie below $0$, and two where one of them ties with $1$.\nThis tripod is the tropical line, a skeleton of the original line.\n",
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