  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, e.g., 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.
