如何在例假期间做爱
How to Integrate a Polynomial over a Simplex
摘要：
本文解决了在有理单形上求多项式函数f的积分问题的计算复杂性。通过推广Motzkin和Straus的一个定理，证明了该问题对于任意多项式是NP-困难的.另一方面，如果多项式只依赖于一个固定数量的变量，而它的程度和尺寸的单形是允许的变化，我们证明，集成可以在多项式时间。因此，对于固定全次数的多项式，也存在多项式时间算法。最后，我们的文章与其他多面体的扩展，讨论其他可用的方法和实验结果。
英文摘要：
This paper settles the computational complexity of the problem of integrating a polynomial function f over a rational simplex. We prove that the problem is NP-hard for arbitrary polynomials via a generalization of a theorem of Motzkin and Straus. On the other hand, if the polynomial depends only on a fixed number of variables, while its degree and the dimension of the simplex are allowed to vary, we prove that integration can be done in polynomial time. As a consequence, for polynomials of fixed total degree, there is a polynomial time algorithm as well. We conclude the article with extensions to other polytopes, discussion of other available methods and experimental results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
