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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 significantly more powerful than `nlinarith` and `positivity` -- i.e., they can prove inequalities they cannot. 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. Theorems proving the existence of such decompositions were one of the landmark achievements of real algebraic geometry in the 20th century, and its connection to semidefinite programming in the 21st century made it a practical computational tool, and is what this software does in the background.
Show HN: Sostactic – polynomial inequalities using sums-of-squares in Lean
A significantly more powerful tool for proving nonlinear polynomial inequalities within the Lean theorem prover, surpassing the capabilities of existing tactics like `nlinarith` and `positivity`.
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A significantly more powerful tool for proving nonlinear polynomial inequalities within the Lean theorem prover, surpassing the capabilities of existing tactics like `nlinarith` and `positivity`.
Sostactic targets a specialized yet critical gap within the Lean theorem prover ecosystem: the limited support for nonlinear inequalities. By leveraging sum-of-squares decompositions and semidefinite programming, this package substantially enhances the capabilities for formal verification in domains such as control theory, optimization, and safety-critical systems. This tool directly improves the rigor and scope of mathematical proofs and software verification within the Lean environment. While its market is niche, primarily comprising researchers, academics, and developers engaged in formal methods, the impact on proof automation and reliability for complex systems is considerable. The integration of a Python backend for computational heavy lifting demonstrates a pragmatic approach to operationalizing advanced mathematical theory into a practical software tool.
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What is Sostactic – polynomial inequalities using sums-of-squares in Lean?
Sostactic – polynomial inequalities using sums-of-squares in Lean is analyzed by our AI as: A significantly more powerful tool for proving nonlinear polynomial inequalities within the Lean theorem prover, surpassing the capabilities of existing tactics like `nlinarith` and `positivity`.. It focuses on Sostactic targets a specialized yet critical gap within the Lean theorem prover ecosystem: the limited support for nonlinear inequalities. By lever...
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Data for Sostactic – polynomial inequalities using sums-of-squares in Lean was aggregated directly from the Hacker News community ecosystem, representing raw developer and early-adopter sentiment.
When was Sostactic – polynomial inequalities using sums-of-squares in Lean publicly launched?
The initial public indexing or launch date for Sostactic – polynomial inequalities using sums-of-squares in Lean within our tracked developer communities was recorded on April 19, 2026.
How popular is Sostactic – polynomial inequalities using sums-of-squares in Lean?
Sostactic – polynomial inequalities using sums-of-squares in Lean has achieved measurable traction, logging over 10 traction score and facilitating 1 recorded discussions or engagements.
Which technical categories define Sostactic – polynomial inequalities using sums-of-squares in Lean?
Based on metadata extraction, Sostactic – polynomial inequalities using sums-of-squares in Lean is categorized under topics such as: nonlinear inequalities, Lean, Lean4 tactics, polynomial inequalities.
What are some commercial alternatives to Sostactic – polynomial inequalities using sums-of-squares in Lean?
Our semantic intelligence engine identifies potential commercial alternatives in the SaaS space, such as Memori, which offers overlapping value propositions.
How does the creator describe Sostactic – polynomial inequalities using sums-of-squares in Lean?
The original author or development team describes the product as follows: "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-sq..."
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