MATH.13:9 - Consequences

Symmetry can reduce calculation, generate useful related solutions or expose an impossible selection requirement before implementing a solver. The preservation argument also locates what new information would make a choice possible.

The main cost is identifying the relevant structure and following the transformation through the whole problem. Large or continuous symmetry groups may require substantial mathematical methods. The direct consequence obtained here can make that further work worthwhile or show that the simpler calculation already suffices.