Show HN: Sostactic – polynomial inequalities using sums-of-squares in Lean

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Current support for nonlinear inequalities in Lean is quite limited.

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It contains a collection of Lean4 tactics for proving polynomial inequalities via sum-of-squares (SOS) decompositions, powered by a Python backend.

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You can use it via Python or Lean.These tactics are significantly more powerful than `nlinarith` and `positivity` -- i.e., they can prove inequalities they cannot.

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In theory, they can be used to prove any of the following types of statements- prove that a polynomial is nonnegative globally - prove that a polynomial is nonnegative over a semialgebraic set (i.e., defined by a set of polynomial inequalities) - prove that a semialgebraic set is empty, i.e., that a system of polynomial inequalities is infeasibleThe underlying theory is based on the following observation: if a polynomial can be written as a sum of squares of other polynomials, then it is nonnegative everywhere.

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Theorems proving the existence of such decompositions were one...

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