Electromagnetic phenomena are mathematically described by solutions of boundary value problems. For exploiting symmetries of these boundary value problems in a way that is offered by techniques of dimensional reduction, it needs to be justified that the derivative in symmetry direction is constant or even vanishing. A generalized notion of symmetry can be defined with different directions at every point in space, as long as it is possible to exhibit unidirectional symmetry in some coordinate representation. This can be achieved, for example, when the symmetry direction is given by the direct construction out of a unidirectional symmetry via a coordinate transformation which poses a demand on the boundary value problem. Coordinate independent formulations of boundary value problems do exist but turning that theory into practice demands a pedantic process of backtranslation to the computational notions. This becomes even more challenging when multiple chained transformations are necessary for propagating a symmetry. We try to fill this gap and present the more general, isolated problems of that translation. Within this contribution, the partial derivative and the corresponding chain rule for multivariate calculus are investigated with respect to their encodability in computational terms. We target the layer above univariate calculus, but below tensor calculus.

中文翻译：

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编码电磁变换定律以减少尺寸

电磁现象通过边值问题的解决方案在数学上进行描述。为了以降维技术提供的方式利用这些边值问题的对称性，需要证明对称方向上的导数是恒定的甚至消失的。只要可以在某些坐标表示中表现出单向对称性，就可以在空间的每个点用不同的方向定义广义的对称性概念。例如，这可以通过以下方式实现：当对称方向是通过单向对称性通过坐标变换直接构造而给出的，这对边界值问题提出了要求。确实存在坐标值问题的独立坐标表述，但要将其理论付诸实践，则需要将计算过程反向翻译的繁琐过程。当传播对称性需要多个链式转换时，这变得更具挑战性。我们试图填补这一空白，并提出该翻译的更一般，更孤立的问题。在此贡献范围内，针对多元演算的偏导数和相应的链规则，就其在计算方面的可编码性进行了研究。我们以单变量演算之上但张量演算之下的层为目标。我们试图填补这一空白，并提出该翻译的更一般，更孤立的问题。在此贡献范围内，针对多元演算的偏导数和相应的链规则，就其在计算方面的可编码性进行了研究。我们针对单变量演算之上但张量演算之下的层。我们试图填补这一空白，并提出该翻译的更一般，更孤立的问题。在此贡献范围内，针对多元演算的偏导数和相应的链规则，就其在计算方面的可编码性进行了研究。我们针对单变量演算之上但张量演算之下的层。