MATH.13:4.1 - Name what must stay the same and what may transform

Recover the problem: admitted candidates, supplied data, conditions, criterion if there is one, and the required kind of answer.

Choose a transformation g and say how it acts on those participants. A permutation can exchange components; a rotation can change coordinates or rotate a physical configuration. Explain which operation is intended. For a symmetry claim, the transformation must be invertible on the relevant domain and retain the stated structure.

Several transformations may form a group: they include doing nothing, composing transformations and undoing each transformation. Name the action on the objects used by the problem. A familiar group name alone leaves that action unspecified.

Keep supplied data in the comparison. If swapping two components also swaps their different costs, the result can be an equivalent problem with transformed data. It is a symmetry of the fixed original problem only if the data required to remain fixed are preserved.