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A Constructive Formalisation of Semi-algebraic Sets and Functions
Abstract
International audienceSemi-algebraic sets and semi-algebraic functions are essential to specify and certify cylindrical algebraic decomposition algorithms. We formally define in Coq the base operations on semi-algebraic sets and functions using embedded first-order formulae over the language of real closed fields, and we prove the correctness of their geometrical interpretation. In doing so, we exploit a previous formalisation of quantifier elimination on such embedded formulae to guarantee the decidability of several first-order properties and keep our development constructive. We also exploit it to formalise formulae substitution without having to handle bound variables- info:eu-repo/semantics/conferenceObject
- Conference papers
- Semi-Algebraic Functions
- Real Algebraic Geometry
- Substitution
- Coq
- Quantifier Elimination
- Semi-Algebraic Sets
- Formalisation of Mathematics
- [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG]
- [MATH.MATH-LO]Mathematics [math]/Logic [math.LO]