Number - Scala Mathematical Library

= Number: A Scala Mathematical Library =

Number is a comprehensive Scala 3 library providing exact and fuzzy arithmetic with sophisticated type hierarchies, lazy evaluation, and units and dimensions.

== Modules ==

The library is organized into six modules:

• `core`: Core type hierarchy including Number, Eager, Structure, and basic arithmetic operations
• `algebra`: Algebraic types including WholeNumber, RationalNumber, Real, Angle, Complex
• `expression`: Expression types for lazy evaluation and symbolic computation
• `parse`: LaTeX expression parsing using Scala Parser Combinators
• `dimensions`: Quantities with units and dimensions
• `top`: Top-level convenience APIs and string interpolators

== Key Concepts ==

=== Exact vs Fuzzy Arithmetic === The library supports both exact computations (for rational and algebraic numbers) and probabilistic fuzzy numbers with uncertainty propagation.

=== Normalization vs Materialization ===

• normalize: Symbolic simplification to canonical form, may change type to most appropriate representation
• materialize: Numeric evaluation to approximate values

=== Equality ===

• ===: Exact equality (using Cats Eq typeclass)
• ~=: Fuzzy equality based on probabilistic overlap of uncertainty distributions

== Getting Started ==

import com.phasmidsoftware.number._

// Using string interpolators for LaTeX expressions
val expr = math"2 + 3 * x"

// Exact arithmetic with rationals
val rational = Rational(22, 7)

// Fuzzy arithmetic with uncertainty
val fuzzy = Number.create(3.14159, 0.00001)

== Integration ==

The library integrates with the Cats ecosystem for typeclass-based abstractions and uses FastParse for parsing LaTeX mathematical expressions with KaTeX rendering support.