Sostactic – polynomial inequalities using sums-of-squares in Lean

In plain words

Sostatic is a Lean4 package for proving polynomial inequalities using sum-of-squares decompositions, backed by a Python solver. It provides tactics that work in both Python and Lean to handle nonlinear inequalities, including proving polynomials are nonnegative globally or over specific regions, and determining when systems of polynomial inequalities have no solutions. The tactics are more capable than existing Lean alternatives like `nlinarith` and `positivity`.

written from the facts on this page · September 2026

From the sources

Proving polynomial inequalities with sum-of-squares certificates - mmaaz-git/sostactic

In the maker’s words, at launch

Current support for nonlinear inequalities in Lean is quite limited. This package attempts to solve this. It contains a collection of Lean4 tactics for proving polynomial inequalities via sum-of-squares (SOS) decompositions, powered by a Python backend. You can use it via Python or Lean. These tactics are…

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