Miforms

Miforms are a term encountered in mathematical literature that refers to objects related to differential forms. Unlike standard differential forms, there is no single canonical definition of a “miform,” and the term is used variably by authors. In several sources, miforms are described as inhomogeneous differential forms—sums of differential forms of different degrees on a manifold. For example, a miform might be written as ω = ω0 + ω1 + … + ωk with ωi a i-form. Under this interpretation, the exterior derivative acts componentwise, dω = dω0 + dω1 + … + dωk, and the exterior product extends via graded algebra, though care must be taken to track degrees.

In other contexts, “miform” has been used as shorthand for multiform or multistructured objects, such as a family of forms indexed by a set, or as a generalization intended to handle mixed-degree data in computational frameworks. In physics, similar constructs appear when combining forms of different degrees to describe mixed-degree fields, for instance in formulations of theories with differential forms of various ranks.

Related concepts include the exterior algebra, graded algebras, and multivectors. See also differential form, inhomogeneous form, exterior derivative, wedge product, and graded algebra.

Because the term is not standardized, readers should consult the specific source for a precise definition in that context. The general idea is to extend the notion of a differential form to a collection or sum of forms of potentially different degrees, while preserving some algebraic structure.