Interpolation is a prime tool in algebraic computation while symmetry is a qualitative feature that can be more relevant to a mathematical model than the numerical accuracy of the parameters. The article shows how to exactly preserve symmetry in multivariate interpolation while exploiting it to alleviate the computational cost. We revisit minimal degree and least interpolation with symmetry adapted bases, rather than monomial bases. For a space of linear forms invariant under a group action, we construct bases of invariant interpolation spaces in blocks, capturing the inherent redundancy in the computations. With the so constructed symmetry adapted interpolation bases, the uniquely defined interpolant automatically preserves any equivariance the interpolation problem might have. Even with no equivariance, the computational cost to obtain the interpolant is alleviated thanks to the smaller size of the matrices to be inverted.

插值是代数计算的主要工具，而对称性是定性特征，与参数的数值精度相比，它与数学模型更相关。本文介绍了如何在利用多元插值来减轻计算成本的同时，精确地保留对称性。我们使用对称适应的基数而不是单项式基数重新研究最小度和最小插值。对于在群作用下线性形式不变的空间，我们在块中构造不变插值空间的基础，以捕获计算中固有的冗余。利用如此构造的对称适应插值基，唯一定义的插值将自动保留插值问题可能具有的任何等方差。即使没有等方差，