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Integration of polynomials over n-dimensional simplices

Rouigueb Abdenebi, Maiza Mohamed, Tkourt Abderahmane, Cherchour Imed

Annals of Computer Science and Information Systems

2019

Vol. 18

157--163

Integrating an arbitrary polynomial function f of degree D over a general simplex in dimension n is well-known in the state of the art to be NP-hard when D and n are allowed to vary, but it is time-polynomial when D or n are fixed. This paper presents an efficient algorithm to compute the exact value of this integral. The proposed algorithm has a time-polynomial complexity when D or n are fixed, and it requires a reasonable time when the values of D and n are less than 10 using widely available standard calculators such as desktops.