/**
 * An integral data type without a decimal. Partially borrowed from Purescript.
 *
 * @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 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 Sh from 'fp-ts/Show';
import * as Inf from './infix';
import * as Iso from './Iso';
import * as TC from './typeclasses';
import * as V from './Vector';
import * as M from './Matrix';
import * as Poly from './Polynomial';
declare const IntegerSymbol: unique symbol;
declare type IntegerSymbol = typeof IntegerSymbol;
/**
 * @since 1.0.0
 * @category Model
 */
export declare type Int = number & {
    readonly _URI: IntegerSymbol;
};
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const fromNumber: (n: number) => Int;
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const zero: Int;
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const one: Int;
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const randInt: (min: number, max: number) => IO.IO<Int>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const Eq: Eq_.Eq<Int>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const Ord: Ord_.Ord<Int>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const Bounded: Bnd.Bounded<Int>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const MagmaSub: Mg.Magma<Int>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const SemigroupSum: Sg.Semigroup<Int>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const SemigroupProduct: Sg.Semigroup<Int>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const MonoidSum: Mn.Monoid<Int>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const MonoidProduct: Mn.Monoid<Int>;
/**
 * 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 EuclideanRing: TC.EuclidianRing<Int>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const Show: Sh.Show<Int>;
/**
 * @since 1.0.0
 * @category Infix
 */
export declare const _: (a: Int, s: Inf.EuclideanRingSymbol, b: Int) => Int;
/**
 * @since 1.0.0
 * @category Infix
 */
export declare const $_: (s: Inf.EuclideanRingSymbol, x: Int, y: Int) => Int;
/**
 * @since 1.0.0
 * @category Infix
 */
export declare const _$: (a: Int, b: Int, s: Inf.EuclideanRingSymbol) => Int;
/**
 * @since 1.0.0
 * @category Destructors
 */
export declare const toNumber: (x: Int) => number;
/**
 * @since 1.0.0
 * @category Isomorphisms
 */
export declare const isoNumber: Iso.Iso<Int, number>;
/**
 * @since 1.0.0
 * @category Integer Ops
 */
export declare const abs: (a: Int) => Int;
/**
 * @since 1.0.0
 * @category Model
 */
export declare type Vec<N> = V.Vec<N, Int>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const AdditiveAbGrpN: <N extends number>(n: N) => TC.AbelianGroup<V.Vec<N, Int>>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const BiModN: <N extends number>(n: N) => TC.Bimodule<V.Vec<N, Int>, Int, Int>;
/**
 * @since 1.0.0
 * @category Model
 */
export declare type Mat<M, N> = M.Mat<M, N, Int>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const AdditiveAbGrpMN: <M extends number, N extends number>(m: M, n: N) => TC.AbelianGroup<M.Mat<M, N, Int>>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const BiModMN: <M extends number, N extends number>(m: M, n: N) => TC.Bimodule<M.Mat<M, N, Int>, Int, Int>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const PolynomialAdditiveAbelianGroup: TC.AbelianGroup<Poly.Polynomial<Int>>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const PolynomialBimodule: TC.Bimodule<Poly.Polynomial<Int>, Int, Int>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const PolynomialRing: TC.CommutativeRing<Poly.Polynomial<Int>>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const PolynomialEuclidianRing: TC.EuclidianRing<Poly.Polynomial<Int>>;
/**
 * @since 1.0.0
 * @category Aliases
 */
export declare const add: (x: Int, y: Int) => Int;
/**
 * @since 1.0.0
 * @category Aliases
 */
export declare const sub: (x: Int, y: Int) => Int;
/**
 * @since 1.0.0
 * @category Aliases
 */
export declare const mul: (x: Int, y: Int) => Int;
/**
 * @since 1.0.0
 * @category Aliases
 */
export declare const div: (x: Int, y: Int) => Int;
/**
 * @since 1.0.0
 * @category Aliases
 */
export declare const mod: (x: Int, y: Int) => Int;
/**
 * @since 1.0.0
 * @category Aliases
 */
export declare const degree: (a: Int) => number;
export {};
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