We discuss a numerical package, named ORTHOCUB, for the computation of linear functionals of both integral and differential type on multivariate polynomial spaces. The weighted sums corresponding to such integral and differential cubatures are implemented via orthogonal polynomial moments and auxiliary near-minimal algebraic cubature in a bounding box, with no conditioning issue since no matrix inversion or factorization is needed. The whole computational process indeed reduces to moment computation and dense matrix-vector products of relatively small size. The Matlab and Python codes are freely available, to be used as building blocks for integral and differential problems.

翻译：本文介绍了一个名为ORTHOCUB的数值计算包，用于计算多元多项式空间上积分型和微分型线性泛函。对应的加权求和（即积分与微分求积）通过正交多项式矩及边界框内的辅助近极小代数求积实现，无需矩阵求逆或分解，因此不存在条件数问题。整个计算过程实际上简化为矩的计算以及规模相对较小的稠密矩阵-向量乘积。Matlab和Python代码已开源，可作为积分与微分问题的构建模块使用。