Algebraic invariants

Algebraic invariants are properties of mathematical objects that remain unchanged under certain transformations or operations. For example, in algebra, the degree of a polynomial stays the same even if the polynomial is rewritten or factored differently. These invariants help mathematicians classify and understand objects like equations, shapes, or structures by identifying what fundamentally stays the same even when they are viewed or manipulated differently. Essentially, invariants act as "fingerprints," capturing the core features of mathematical entities that do not change under specific changes or transformations.