/**
 * A quaternion is a 4-component analog to complex numbers. Useful in a handful of cases
 * like the effecient and safe rotation of a 3-dimensional vector
 *
 * @since 1.0.0
 */
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 Sh from 'fp-ts/Show';
import * as Auto from './Automorphism';
import * as Iso from './Iso';
import * as TC from './typeclasses';
import * as V from './Vector';
import * as Inf from './infix';
/**
 * @since 1.0.0
 * @category Model
 */
export interface Quaternion {
    a: number;
    b: number;
    c: number;
    d: number;
}
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const zero: Quaternion;
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const one: Quaternion;
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const scalar: (a: number) => Quaternion;
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const i: Quaternion;
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const j: Quaternion;
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const k: Quaternion;
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const of: (a: number, b: number, c: number, d: number) => Quaternion;
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const fromVector4: (v: V.Vec<4, number>) => Quaternion;
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const fromVector3: (v: V.Vec<3, number>) => Quaternion;
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const randQuaternion: (min: number, max: number) => IO.IO<Quaternion>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const Eq: Eq_.Eq<Quaternion>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const MagmaSub: Mg.Magma<Quaternion>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const SemigroupSum: Sg.Semigroup<Quaternion>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const SemigroupProduct: Sg.Semigroup<Quaternion>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const MonoidSum: Mn.Monoid<Quaternion>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const MonoidProduct: Mn.Monoid<Quaternion>;
/**
 * @since 1.0.0
 * @category Instance Operations
 */
export declare const recip: (q: Quaternion) => Quaternion;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const DivisionRing: TC.DivisionRing<Quaternion>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const Show: Sh.Show<Quaternion>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const AdditiveAbelianGroup: TC.AbelianGroup<Quaternion>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const Bimodule: TC.Bimodule<Quaternion, number>;
/**
 * @since 1.0.0
 * @category Instance Operations
 */
export declare const rotateVector: (axis: V.Vec<3, number>, theta: number) => (v: V.Vec<3, number>) => V.Vec<3, number>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const getRotationAutomorphism: (axis: V.Vec<3, number>, theta: number) => Auto.Automorphism<V.Vec<3, number>>;
/**
 * @since 1.0.0
 * @category Infix
 */
export declare const _: (a: Quaternion, s: Inf.DivisionRingSymbol, b: Quaternion) => Quaternion;
/**
 * @since 1.0.0
 * @category Infix
 */
export declare const $_: (s: Inf.DivisionRingSymbol, x: Quaternion, y: Quaternion) => Quaternion;
/**
 * @since 1.0.0
 * @category Infix
 */
export declare const _$: (a: Quaternion, b: Quaternion, s: Inf.DivisionRingSymbol) => Quaternion;
/**
 * @since 1.0.0
 * @category Destructors
 */
export declare const toVector4: (q: Quaternion) => V.Vec<4, number>;
/**
 * **Note:** Disregards the real part of a quaternion
 *
 * @since 1.0.0
 * @category Destructors
 */
export declare const toVector3: (q: Quaternion) => V.Vec<3, number>;
/**
 * @since 1.0.0
 * @category Destructors
 */
export declare const norm: (q: Quaternion) => number;
/**
 * @since 1.0.0
 * @category Destructors
 */
export declare const IsoVector4: Iso.Iso<Quaternion, V.Vec<4, number>>;
/**
 * @since 1.0.0
 * @category Quaternion Ops
 */
export declare const asUnit: (q: Quaternion) => Quaternion;
/**
 * @since 1.0.0
 * @category Quaternion Ops
 */
export declare const getRotationQuaternion: (axis: V.Vec<3, number>) => (theta: number) => Quaternion;
/**
 * @since 1.0.0
 * @category Quaternion Ops
 */
export declare const conj: (q: Quaternion) => Quaternion;
/**
 * @since 1.0.0
 * @category Aliases
 */
export declare const add: (x: Quaternion, y: Quaternion) => Quaternion;
/**
 * @since 1.0.0
 * @category Aliases
 */
export declare const sub: (x: Quaternion, y: Quaternion) => Quaternion;
/**
 * @since 1.0.0
 * @category Aliases
 */
export declare const mul: (x: Quaternion, y: Quaternion) => Quaternion;
/**
 * @since 1.0.0
 * @category Aliases
 */
export declare const div: (x: Quaternion, y: Quaternion) => Quaternion;
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