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cylindric cell - traduction vers arabe
![Staining of a ''[[Caenorhabditis elegans]]'' highlights the nuclei of its cells.](https://commons.wikimedia.org/wiki/Special:FilePath/C elegans stained.jpg?width=200 "Staining of a ''[[Caenorhabditis elegans]]'' highlights the nuclei of its cells.")
![An outline of the [[catabolism]] of [[protein]]s, [[carbohydrate]]s and [[fat]]s](https://commons.wikimedia.org/wiki/Special:FilePath/Catabolism schematic.svg?width=200 "An outline of the [[catabolism]] of [[protein]]s, [[carbohydrate]]s and [[fat]]s")
![A fluorescent image of an endothelial cell. Nuclei are stained blue, [[mitochondria]] are stained red, and microfilaments are stained green.](https://commons.wikimedia.org/wiki/Special:FilePath/DAPIMitoTrackerRedAlexaFluor488BPAE.jpg?width=200 "A fluorescent image of an endothelial cell. Nuclei are stained blue, [[mitochondria]] are stained red, and microfilaments are stained green."){kind=tracking}
![Deoxyribonucleic acid]] (DNA)](https://commons.wikimedia.org/wiki/Special:FilePath/DNA orbit animated.gif?width=200 "Deoxyribonucleic acid]] (DNA)")
![Diagram of the [[endomembrane system]]](https://commons.wikimedia.org/wiki/Special:FilePath/Endomembrane system diagram en.svg?width=200 "Diagram of the [[endomembrane system]]")
![Human cancer cells, specifically [[HeLa cells]], with DNA stained blue. The central and rightmost cell are in [[interphase]], so their DNA is diffuse and the entire nuclei are labelled. The cell on the left is going through [[mitosis]] and its chromosomes have condensed.](https://commons.wikimedia.org/wiki/Special:FilePath/HeLa cells stained with Hoechst 33258.jpg?width=200 "Human cancer cells, specifically [[HeLa cells]], with DNA stained blue. The central and rightmost cell are in [[interphase]], so their DNA is diffuse and the entire nuclei are labelled. The cell on the left is going through [[mitosis]] and its chromosomes have condensed.")
![Structure of a typical [[plant cell]]](https://commons.wikimedia.org/wiki/Special:FilePath/Plant cell structure-en.svg?width=200 "Structure of a typical [[plant cell]]")
![Structure of a typical [[prokaryotic]] cell](https://commons.wikimedia.org/wiki/Special:FilePath/Prokaryote cell.svg?width=200 "Structure of a typical [[prokaryotic]] cell")
![tRNA]]. Newly synthesized proteins (''black'') are often further modified, such as by binding to an effector molecule (''orange''), to become fully active.](https://commons.wikimedia.org/wiki/Special:FilePath/Proteinsynthesis.png?width=200 "tRNA]]. Newly synthesized proteins (''black'') are often further modified, such as by binding to an effector molecule (''orange''), to become fully active.")
![cork]], 1665](https://commons.wikimedia.org/wiki/Special:FilePath/RobertHookeMicrographia1665.jpg?width=200 "cork]], 1665")
![Glacier National Park]] in the United States.](https://commons.wikimedia.org/wiki/Special:FilePath/Stromatolites.jpg?width=200 "Glacier National Park]] in the United States.")
![[[Prokaryotes]] divide by [[binary fission]], while [[eukaryotes]] divide by [[mitosis]] or [[meiosis]].](https://commons.wikimedia.org/wiki/Special:FilePath/Three cell growth types.svg?width=200 "[[Prokaryotes]] divide by [[binary fission]], while [[eukaryotes]] divide by [[mitosis]] or [[meiosis]].")
Définition
Wikipédia
In mathematics, cylindrical algebraic decomposition (CAD) is a notion, and an algorithm to compute it, that are fundamental for computer algebra and real algebraic geometry. Given a set S of polynomials in Rn, a cylindrical algebraic decomposition is a decomposition of Rn into connected semialgebraic sets called cells, on which each polynomial has constant sign, either +, − or 0. To be cylindrical, this decomposition must satisfy the following condition: If 1 ≤ k < n and π is the projection from Rn onto Rn−k consisting in removing the last k coordinates, then for every pair of cells c and d, one has either π(c) = π(d) or π(c) ∩ π(d) = ∅. This implies that the images by π of the cells define a cylindrical decomposition of Rn−k.
The notion was introduced by George E. Collins in 1975, together with an algorithm for computing it.
Collins' algorithm has a computational complexity that is double exponential in n. This is an upper bound, which is reached on most entries. There are also examples for which the minimal number of cells is doubly exponential, showing that every general algorithm for cylindrical algebraic decomposition has a double exponential complexity.
CAD provides an effective version of quantifier elimination over the reals that has a much better computational complexity than that resulting from the original proof of Tarski–Seidenberg theorem. It is efficient enough to be implemented on a computer. It is one of the most important algorithms of computational real algebraic geometry. Searching to improve Collins' algorithm, or to provide algorithms that have a better complexity for subproblems of general interest, is an active field of research.
