Section: New Results

Formalization of semi-algebraic sets

Participants : Yves Bertot, Cyril Cohen, Boris Djalal.

We developed the necessary results about first-order logical formulae to be able to define semi-algebraic sets and semi-algebraic functions in Coq. This required that we provide elements of language to describe quantification over blocks of variables. We show that the equality of semi-algebraic sets is decidable, thanks to the already formalized decision procedure based on quantifier elimination. We then show that our formalized semi-algebraic sets do satisfy general abstract interfaces for sets, as seen in section 5.8

In the long run this work will be instrumental to describe the output of cylindrical algebraic decomposition algorithms. Indeed, this output is usually made of semi-algebraic sets.