reducedfunction

Reducedfunction is a term encountered in mathematics and computer algebra to describe a function whose expression has been transformed into a reduced or canonical form under a specified set of rules. Because there is no universal standard, the precise meaning depends on context, but common themes include simplification, removal of redundancy, and representation by a unique, minimal form that preserves the function’s values over its domain.

In symbolic computation and algebra, reduction or normalization aims to produce a consistent, minimal expression. A reducedfunction is typically one that cannot be simplified further using the chosen rules. Many systems designate the reduced form as the simplest expression that yields the same output for all inputs within the domain.

In multivariable settings, reduction often involves using constraints or symmetries to express the function in terms of a smaller or independent set of variables. For example, given a relation y = g(x), the reduced function could be written as f(x) = F(x, g(x)), thereby reducing the dependence to a single variable.

In algebraic geometry and commutative algebra, reduction can also refer to passing to a quotient by an ideal; the resulting function is defined on the reduced space and reflects the original function modulo the chosen relations. In this sense, reducedforms enable comparison and computation on a simplified or canonical representative.

The term is informal and its exact interpretation varies by field and source; when encountered, consult the specific definitions of reduction rules or normal form used in that context.

See also: normal form, canonical form, reduction (mathematics), symbolic computation, simplification.