##  [Cylindrical Algebraic Decomposition](/cylindrical-algebraic-decomposition) 

  ##  [Cylindrical Algebraic Decomposition](https://algebra.quantumdictionary.io/cylindrical-algebraic-decomposition-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A recursive projection–lifting algorithm that partitions real n‑space into finitely many cylindrically arranged cells (cells whose projections onto lower dimensions are cells in the decomposition) on which a given finite set of real polynomials has invariant sign, enabling decision procedures for real quantifier and sign queries.