Discriminant

A scalar invariant associated to a polynomial, algebraic equation, or algebraic object (e.g., number field, bilinear form) that vanishes exactly when roots collide (multiple roots) and encodes arithmetic and ramification information; often computed as a determinant or as a product of squared differences of roots.

A discriminant is a scalar invariant associated to a polynomial, algebraic form, or algebraic object that vanishes precisely when the object has singularities such as repeated roots, multiple factors, or non-transverse intersections.