numeriko

Numeriko is a hypothetical formal framework for representing, transforming, and reasoning about numbers and numeric expressions. It is used in mathematical pedagogy and theoretical computer science to explore how numbers can be modeled, computed, and manipulated across different numeric regimes.

The framework defines a core set of numeric types, including integers, rationals, real numbers, complex numbers, and algebraic numbers, together with primitive operations such as addition, subtraction, multiplication, division, and exponentiation. It specifies semantics for evaluation, precision, and rounding, enabling both exact symbolic computation and approximate numerical computation within a single formalism.

Numeriko includes features such as exact arithmetic on symbolic literals, interval arithmetic for error bounds, support for algebraic numbers and continued fractions, and constructs for representing uncertainty and measurement error. Expressions in Numeriko are typically modeled as abstract syntax trees with type annotations and evaluation rules.

Applications and usage: In education, Numeriko serves as a didactic device to illustrate numerical methods and the trade-offs between exactness and efficiency. In research, it provides a reference model for reasoning about the complexity and stability of arithmetic algorithms, and for comparing different numeric representations in programming languages and libraries.

See also: numerical analysis, computer arithmetic, symbolic computation, arbitrary-precision arithmetic, type systems.

Notes: As a conceptual framework, Numeriko exists primarily in theoretical discussions and pedagogical materials rather than as an implemented standard.