/**
 * A fractional number type with typeclass instances. **Note:** this data type shouldn't
 * be used for computations involving large numbers, because the lawfulness of these
 * particular instances breaks down due to floating point error quicker than the others by
 * the nature of reducing fractional values
 *
 * @since 1.0.0
 */
import * as Bnd from 'fp-ts/Bounded';
import * as Eq_ from 'fp-ts/Eq';
import * as IO from 'fp-ts/IO';
import * as Fld from 'fp-ts/Field';
import * as Mg from 'fp-ts/Magma';
import * as Mn from 'fp-ts/Monoid';
import * as Sg from 'fp-ts/Semigroup';
import * as Ord_ from 'fp-ts/Ord';
import * as O from 'fp-ts/Option';
import * as Sh from 'fp-ts/Show';
import * as Inf from './infix';
import * as Int from './integer';
import * as M from './Matrix';
import * as V from './Vector';
declare const RationalSymbol: unique symbol;
declare type RationalSymbol = typeof RationalSymbol;
/**
 * @since 1.0.0
 * @category Model
 */
export interface Rational {
    readonly _URI: RationalSymbol;
    readonly top: Int.Int;
    readonly bottom: Int.Int;
}
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const of: (top: Int.Int, bottom: Int.Int) => O.Option<Rational>;
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const zero: Rational;
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const one: Rational;
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const fromInt: (top: Int.Int) => Rational;
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const randRational: (low: number, high: number) => IO.IO<Rational>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const Eq: Eq_.Eq<Rational>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const Ord: Ord_.Ord<Rational>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const Bounded: Bnd.Bounded<Rational>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const MagmaSub: Mg.Magma<Rational>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const SemigroupSum: Sg.Semigroup<Rational>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const SemigroupProduct: Sg.Semigroup<Rational>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const MonoidSum: Mn.Monoid<Rational>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const MonoidProduct: Mn.Monoid<Rational>;
/**
 * Adapted from Purescript:
 * https://github.com/purescript/purescript-prelude/blob/v6.0.0/src/Data/EuclideanRing.js
 *
 * @since 1.0.0
 * @category Instances
 */
export declare const Field: Fld.Field<Rational>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const Show: Sh.Show<Rational>;
/**
 * @since 1.0.0
 * @category Infix
 */
export declare const _: (a: Rational, s: Inf.FieldSymbol, b: Rational) => Rational;
/**
 * @since 1.0.0
 * @category Infix
 */
export declare const $_: (s: Inf.FieldSymbol, x: Rational, y: Rational) => Rational;
/**
 * @since 1.0.0
 * @category Infix
 */
export declare const _$: (a: Rational, b: Rational, s: Inf.FieldSymbol) => Rational;
/**
 * @since 1.0.0
 * @category Destructors
 */
export declare const toNumber: (r: Rational) => number;
/**
 * @since 1.0.0
 * @category Rational Ops
 */
export declare const abs: (a: Rational) => Rational;
/**
 * @since 1.0.0
 * @category Model
 */
export declare type Vec<N> = V.Vec<N, Rational>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const AdditiveAbGrpN: <N extends number>(n: N) => import("./typeclasses").AbelianGroup<V.Vec<N, Rational>>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const BiModN: <N extends number>(n: N) => import("./typeclasses").Bimodule<V.Vec<N, Rational>, Rational, Rational>;
/**
 * @since 1.0.0
 * @category Model
 */
export declare type Mat<M, N> = M.Mat<M, N, Rational>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const AdditiveAbGrpMN: <M extends number, N extends number>(m: M, n: N) => import("./typeclasses").AbelianGroup<M.Mat<M, N, Rational>>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const BiModMN: <M extends number, N extends number>(m: M, n: N) => import("./typeclasses").Bimodule<M.Mat<M, N, Rational>, Rational, Rational>;
/**
 * @since 1.0.0
 * @category Aliases
 */
export declare const add: (x: Rational, y: Rational) => Rational;
/**
 * @since 1.0.0
 * @category Aliases
 */
export declare const sub: (x: Rational, y: Rational) => Rational;
/**
 * @since 1.0.0
 * @category Aliases
 */
export declare const mul: (x: Rational, y: Rational) => Rational;
/**
 * @since 1.0.0
 * @category Aliases
 */
export declare const div: (x: Rational, y: Rational) => Rational;
export {};
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