什么是Mathematica的CylindricalDecomposition的计算复杂性

问题描述

数学CylindricalDecomposition实现被称为圆柱代数分解算法。沃尔弗拉姆MathWorld对圆柱代数分解文章说，这种算法成为计算不可行复杂的不平等。

可这种说法变得更为precise？具体而言，如何在时间和空间上涉及到的多元多项式变量的程度和数量？难道时间和空间依赖于其它参数？

解决方案

参考：MIT 6.972代数技术和semide无限优化的，由Pablo A. Parrilo 的

修改：一个漂亮的MMA的CAD算法 此处

Mathematica' CylindricalDecomposition implements an algorithm known as Cylindrical Algebraic Decomposition. Wolfram MathWorld's article on Cylindrical Algebraic Decomposition says that this algorithm "becomes computationally infeasible for complicated inequalities."

Can this statement be made more precise? Specifically, how does the time and space relate to the degree and number of variables of the multivariate polynomials? Does the time and space depend on other parameters?

解决方案

Reference: MIT 6.972 Algebraic techniques and semidefinite optimization by Pablo A. Parrilo

Edit: A nice article on Mma CAD algorithms here

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