Dequacions

Dequacions is a term used in this article to refer to a family of algebraic transformations applied to equations with the aim of highlighting structure and dependencies among variables. A dequacion takes a given equation or system and produces an equivalent expression that rearranges terms, isolates a chosen variable, or otherwise reexpresses the same solution set in a form that makes certain relationships more explicit.

In practice, dequacions are equivalence-preserving operations. For a single linear equation such as x + y = 3, dequacions include solving for a variable to obtain x = 3 − y or y = 3 − x. For a system, a sequence of admissible substitutions and rearrangements constitutes a chain of dequacions that maintains the same solutions while reducing the system to simpler or more interpretable relations, such as expressing each variable in terms of a subset of others.

Key properties include non-uniqueness and context dependence: many different dequacions can correspond to the same original equation, depending on which variables or terms are targeted. They are invertible in the sense that one can typically recover the original form from an appropriate dequacion, though practical reconstruction may vary in complexity.

History and usage: the term dequacion is used in contemporary mathematical pedagogy and symbolic computation to discuss problem reformulation and the explicit exposure of variable interdependencies. It has not achieved universal standardization in published literature, and its exact definition can vary by author or discipline.

See also: equations, solving linear equations, symbolic computation, elimination theory, reformulation of problems.