MATH.13:2 - Problem

A suggestive symmetry can omit the feature that decides the problem. Equal-looking components can have different costs. A law can be unchanged while its boundary or initial data change. A function can require its output to rotate with its input rather than stay numerically identical.

A second error begins after a real symmetry is established: the solver assumes more than it implies. A symmetric problem can have several asymmetric solutions. A rotation-respecting numerical scheme can fail to conserve the physical angular momentum. To obtain a usable conclusion, follow the transformation through the actual solution condition.