import * as Eq from 'fp-ts/Eq';
import * as Fld from 'fp-ts/Field';
import * as Fun from 'fp-ts/Functor';
import * as FunI from 'fp-ts/FunctorWithIndex';
import * as IO from 'fp-ts/IO';
import { Monoid } from 'fp-ts/Monoid';
import * as Ord from 'fp-ts/Ord';
import * as Rng from 'fp-ts/Ring';
import { Semigroup } from 'fp-ts/Semigroup';
import { Show } from 'fp-ts/Show';
import * as TC from './typeclasses';
import { Complex } from './complex';
declare const PolynomialSymbol: unique symbol;
declare type PolynomialSymbol = typeof PolynomialSymbol;
/**
 * @since 1.0.0
 * @category Model
 */
export interface Polynomial<R> extends ReadonlyArray<R> {
    _URI: PolynomialSymbol;
}
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const fromCoefficientArray: <R>(Eq: Eq.Eq<R>, R: Rng.Ring<R>) => (rs: readonly R[]) => Polynomial<R>;
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const one: <R>(R: Rng.Ring<R>) => Polynomial<R>;
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const zero: <R>() => Polynomial<R>;
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const randPolynomial: <R>(terms: number, make: IO.IO<R>) => IO.IO<Polynomial<R>>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const URI = "Polynomial";
/**
 * @since 1.0.0
 * @category Instances
 */
export declare type URI = typeof URI;
declare module 'fp-ts/HKT' {
    interface URItoKind<A> {
        readonly [URI]: Polynomial<A>;
    }
}
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const getPolynomialEq: <R>(Eq: Eq.Eq<R>) => Eq.Eq<Polynomial<R>>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const getPolynomialOrd: <R>(Eq: Ord.Ord<R>) => Ord.Ord<Polynomial<R>>;
/**
 * @since 1.0.0
 * @category Instance Operations
 */
export declare const add: <R>(Eq: Eq.Eq<R>, R: Rng.Ring<R>) => (x: Polynomial<R>, y: Polynomial<R>) => Polynomial<R>;
/**
 * @since 1.0.0
 * @category Instance Operations
 */
export declare const sub: <R>(Eq: Eq.Eq<R>, R: Rng.Ring<R>) => (x: Polynomial<R>, y: Polynomial<R>) => Polynomial<R>;
/**
 * @since 1.0.0
 * @category Instance Operations
 */
export declare const mul: <R>(Eq: Eq.Eq<R>, R: Rng.Ring<R>) => (xs: Polynomial<R>, ys: Polynomial<R>) => Polynomial<R>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const getAdditiveAbelianGroup: <R>(Eq: Eq.Eq<R>, R: Rng.Ring<R>) => TC.AbelianGroup<Polynomial<R>>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const getCommutativeRing: <R>(E: Eq.Eq<R>, R: Rng.Ring<R>) => TC.CommutativeRing<Polynomial<R>>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const getBimodule: <R>(E: Eq.Eq<R>, R: Rng.Ring<R>) => TC.Bimodule<Polynomial<R>, R>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const getEuclidianRing: <F>(E: Eq.Eq<F>, F: Fld.Field<F>) => TC.EuclidianRing<Polynomial<F>>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const getCompositionSemigroup: <R>(Eq_: Eq.Eq<R>, R: Rng.Ring<R>) => Semigroup<Polynomial<R>>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const getCompositionMonoid: <R>(Eq_: Eq.Eq<R>, R: Rng.Ring<R>) => Monoid<Polynomial<R>>;
/**
 * @since 1.0.0
 * @category Instance Operations
 */
export declare const map: <A, B>(f: (a: A) => B) => (fa: Polynomial<A>) => Polynomial<B>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const Functor: Fun.Functor1<URI>;
/**
 * @since 1.0.0
 * @category Instance Operations
 */
export declare const mapWithIndex: <A, B>(f: (i: number, a: A) => B) => (fa: Polynomial<A>) => Polynomial<B>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const FunctorWithIndex: FunI.FunctorWithIndex1<URI, number>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const getShow: (variable: string) => <A>(S: Show<A>, isZero: (a: A) => boolean, isOne: (a: A) => boolean) => Show<Polynomial<A>>;
/**
 * @since 1.0.0
 * @category Destructors
 */
export declare const coefficients: <R>(p: Polynomial<R>) => ReadonlyArray<R>;
/**
 * @since 1.0.0
 * @category Polynomial Operations
 */
export declare const identity: <R>(R: Rng.Ring<R>) => Polynomial<R>;
/**
 * @since 1.0.0
 * @category Polynomial Operations
 */
export declare const constant: <R>(Eq: Eq.Eq<R>, R: Rng.Ring<R>) => (a: R) => Polynomial<R>;
/**
 * @since 1.0.0
 * @category Polynomial Operations
 */
export declare const evaluate: <R>(R: Rng.Ring<R>) => (p: Polynomial<R>) => (x: R) => R;
/**
 * @since 1.0.0
 * @category Polynomial Operations
 */
export declare const polynomialCompose: <R>(Eq: Eq.Eq<R>, R: Rng.Ring<R>) => (x: Polynomial<R>) => (y: Polynomial<R>) => Polynomial<R>;
/**
 * @since 1.0.0
 * @category Polynomial Operations
 */
export declare const polynomialDegree: <R>(p: Polynomial<R>) => number;
/**
 * @since 1.0.0
 * @category Polynomial Operations
 */
export declare const derivative: <R>(scaleLeft: (n: number, r: R) => R) => (coeffs: Polynomial<R>) => Polynomial<R>;
/**
 * @since 1.0.0
 * @category Polynomial Operations
 */
export declare const integrate: <R>(R: Rng.Ring<R>, scaleLeft: (n: number, r: R) => R) => (lower: R, upper: R) => (p: Polynomial<R>) => R;
/**
 * @since 1.0.0
 * @category Polynomial Operations
 */
export declare const antiderivative: <R>(constantTerm: R, scaleLeft: (n: number, r: R) => R) => (p: Polynomial<R>) => Polynomial<R>;
/**
 * @since 1.0.0
 * @category Polynomial Operations
 */
export declare const l2InnerProduct: <R extends number | Complex>(Eq_: Eq.Eq<R>, R: Rng.Ring<R>, scaleLeft: (n: number, r: R) => R, conj: (r: R) => R) => (p: Polynomial<R>, q: Polynomial<R>) => R;
/**
 * @since 1.0.0
 * @category Polynomial Operations
 */
export declare const norm: <R extends number | Complex>(Eq_: Eq.Eq<R>, R: Rng.Ring<R>, scaleLeft: (n: number, r: R) => R, sqrt: (r: R) => R, conj: (r: R) => R) => (p: Polynomial<R>) => R;
/**
 * @since 1.0.0
 * @category Polynomial Operations
 */
export declare const projection: <R extends number | Complex>(Eq_: Eq.Eq<R>, F: Fld.Field<R>, scaleLeft: (n: number, r: R) => R, conj: (r: R) => R) => (p: Polynomial<R>, q: Polynomial<R>) => Polynomial<R>;
/**
 * @since 1.0.0
 * @category Utilities
 */
export declare const preservingZipWith: <R, S>(f: (x: R, y: R) => S, def: R) => (xs: readonly R[], ys: readonly R[]) => readonly S[];
/**
 * @since 1.0.0
 * @category Internal
 */
export declare const shiftBy: <R>(n: number, r: R) => (p: ReadonlyArray<R>) => ReadonlyArray<R>;
export {};
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