Sostactic: Lean4 Tactics for Proving Polynomial Inequalities with Sum-of-Squares Certificates
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mmaaz
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Summary
Sostactic is a Lean4 mathematical proof assistant tool that provides tactics for proving polynomial inequalities using sum-of-squares (SOS) decompositions. The tool features a Python backend and offers more powerful capabilities than existing tools like nlinarith and positivity, enabling proofs of polynomial inequalities that those tools cannot handle. The article serves as documentation and introduction to the tool, including quick examples and implementation details for mathematical proof automation.
Key quotes
· 5 pulledThese tactics are significantly more powerful than nlinarith and positivity -- i.e., they can prove inequalities they cannot.
This is a collection of Lean4 tactics for proving polynomial inequalities via sum-of-squares (SOS) decompositions, powered by a Python backend.
In theory, they can be used to prove any of the following types of statements
Full documentation is provided towards the end of this README; feel free to point your coding agent at it.
Look at Sostactic/Examples.lean for more
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