6 papers
On Minimum CADs for Algebraic Sets in Dimension Three
Lucas Michel
Cylindrical Algebraic Decomposition (CAD) algorithms typically produce a decomposition adapted to a finite family of semi-algebraic sets (i.e. every member of $\mathc…
On some Exotic Cylindrical Algebraic Decompositions and Cells
Lucas Michel
Cylindrical Algebraic Decompositions (CADs) endowed with additional topological properties have found applications beyond their original logical setting, including algorithmic opti…
Further results on Minimal and Minimum Cylindrical Algebraic Decompositions
Lucas Michel, Pierre Mathonet, Naïm Zénaïdi
We consider cylindrical algebraic decompositions (CADs) as a tool for representing semi-algebraic subsets of . In this framework, a CAD is adapted to a…
Projective Delineability for Single Cell Construction
Jasper Nalbach, Lucas Michel, Erika Ãbrahám +5
The cylindrical algebraic decomposition (CAD) is the only complete method used in practice for solving problems like quantifier elimination or SMT solving related to real algebra,…
On Projective Delineability
Lucas Michel, Jasper Nalbach, Pierre Mathonet +5
We consider cylindrical algebraic decomposition (CAD) and the key concept of delineability which underpins CAD theory. We introduce the novel concept of projective delineability wh…
On Minimal and Minimum Cylindrical Algebraic Decompositions
Lucas Michel, Pierre Mathonet, Naïm Zénaïdi
We consider cylindrical algebraic decompositions (CADs) as a tool for representing semi-algebraic subsets of . In this framework, a CAD is adapted to a…