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//! Types that form a field (commutative division ring with Euclidean structure).
//!
//! ### Examples
//!
//! ```
//! use fp_library::classes::{
//! DivisionRing,
//! EuclideanRing,
//! Semiring,
//! };
//!
//! let a = 6.0f64;
//! let b = 2.0f64;
//! assert_eq!(f64::divide(a, b), 3.0);
//! assert_eq!(f64::reciprocate(b), 0.5);
//! ```
#[fp_macros::document_module]
mod inner {
use {
crate::classes::*,
fp_macros::*,
};
/// A marker trait for types that form a field.
///
/// A field is both an [`EuclideanRing`] and a [`DivisionRing`],
/// combining commutative ring structure with multiplicative inverses.
///
/// ### Laws
///
/// All [`EuclideanRing`] and [`DivisionRing`] laws apply.
#[document_examples]
///
/// ```
/// use fp_library::classes::{
/// DivisionRing,
/// Semiring,
/// };
///
/// // For fields, multiply(a, reciprocate(a)) = one
/// let a = 3.0f64;
/// assert_eq!(f64::multiply(a, f64::reciprocate(a)), f64::one());
/// ```
pub trait Field: EuclideanRing + DivisionRing {}
impl Field for f32 {}
impl Field for f64 {}
}
pub use inner::*;