desformules

Desformules is a theoretical framework used in mathematics and related fields to describe the decomposition of formulas under transformations into more elementary components called desformules. The approach treats a given expression as a composition of units, each carrying specific structural or transformational information. The desformulation process then maps the original formula to a structured set of desformules along with rules for recomposition, allowing researchers to study invariants, equivalence, and canonical representations across different representations.

Etymology and scope: The term desformules is formed from des- (a prefix suggesting separation or removal) and formules (formulas). It is used primarily in theoretical discussions rather than as a widely adopted standard. The concept is typically presented as a methodological idea rather than a fixed formalism, with room for variation in how desformules are defined and used.

Formal concept: A desformule is intended as a modular piece of a formula with metadata about its role (for example, operand, operator, or transformation-tolerance). A desformulation associates to each expression a structure that records how the expression changes under a given set of transformations, such as scaling, translations, substitutions, or coordinate changes. The goal is to enable comparison between expressions that are semantically equivalent but syntactically different, and to facilitate simplification, normalization, or feature extraction in symbolic computation.

Applications and limitations: The approach is most relevant in symbolic computation, computer algebra, and the study of transformation groups. It is not a standardized or universally adopted formalism, and different authors may define desformules and desformulation rules in varying ways. It remains primarily a conceptual tool and a topic for theoretical exploration.

See also: invariant theory, canonical form, symbolic computation, normalization, transformation group.