import * as Auto from './Automorphism';
import * as Inf from './infix';
import * as IO from 'fp-ts/IO';
import * as M from './Matrix';
import * as Poly from './Polynomial';
import * as V from './Vector';
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const zero = 0;
/**
 * @since 1.0.0
 * @category Constructors
 */
export declare const one = 1;
/**
 * Uniform random variable in the interval: `[low, high)`
 *
 * @since 1.0.0
 * @category Constructors
 */
export declare const randNumber: (low: number, high: number) => IO.IO<number>;
/**
 * Exponential random variable with parameter `λ`
 *
 * @since 1.1.0
 * @category Constructors
 */
export declare const randExp: (λ: number) => IO.IO<number>;
/**
 * Normal random variable with mean `μ` and standard deviation `σ`. Uses the Box-Muller transform
 *
 * @since 1.1.0
 * @category Constructors
 */
export declare const randNorm: (μ?: number, σ?: number) => IO.IO<number>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const Eq: import("fp-ts/lib/Eq").Eq<number>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const Ord: import("fp-ts/lib/Ord").Ord<number>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const Bounded: import("fp-ts/lib/Bounded").Bounded<number>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const MagmaSub: import("fp-ts/lib/Magma").Magma<number>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const SemigroupSum: import("fp-ts/lib/Semigroup").Semigroup<number>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const SemigroupProduct: import("fp-ts/lib/Semigroup").Semigroup<number>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const MonoidSum: import("fp-ts/lib/Monoid").Monoid<number>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const MonoidProduct: import("fp-ts/lib/Monoid").Monoid<number>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const Field: import("fp-ts/lib/Field").Field<number>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const Show: import("fp-ts/lib/Show").Show<number>;
/**
 * @since 1.0.0
 * @category Infix
 */
export declare const _: (a: number, s: Inf.FieldSymbol, b: number) => number;
/**
 * @since 1.0.0
 * @category Infix
 */
export declare const $_: (s: Inf.FieldSymbol, x: number, y: number) => number;
/**
 * @since 1.0.0
 * @category Infix
 */
export declare const _$: (a: number, b: number, s: Inf.FieldSymbol) => number;
/**
 * @since 1.0.0
 * @category Model
 */
export declare type Vec<N> = V.Vec<N, number>;
/**
 * @since 1.1.0
 * @category Constructors
 */
export declare const onesN: <N extends number>(n: N) => Vec<N>;
/**
 * @since 1.1.0
 * @category Constructors
 */
export declare const zerosN: <N extends number>(n: N) => Vec<N>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const AdditiveAbGrpN: <N extends number>(n: N) => import("./typeclasses").AbelianGroup<V.Vec<N, number>>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const BiModN: <N extends number>(n: N) => import("./typeclasses").Bimodule<V.Vec<N, number>, number, number>;
/**
 * Add two vectors
 *
 * @since 1.1.0
 * @category Matrix Operations
 */
export declare const addV: <N>(x: V.Vec<N, number>, y: V.Vec<N, number>) => V.Vec<N, number>;
/**
 * Subtract two vectors
 *
 * @since 1.1.0
 * @category Matrix Operations
 */
export declare const subV: <N>(x: V.Vec<N, number>, y: V.Vec<N, number>) => V.Vec<N, number>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const get2dRotation: (theta: number) => Auto.Automorphism<V.Vec<2, number>>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const get3dXRotation: (theta: number) => Auto.Automorphism<V.Vec<3, number>>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const get3dYRotation: (theta: number) => Auto.Automorphism<V.Vec<3, number>>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const get3dZRotation: (theta: number) => Auto.Automorphism<V.Vec<3, number>>;
/**
 * @since 1.0.0
 * @category Vector Operations
 */
export declare const dot: <N>(x: V.Vec<N, number>, y: V.Vec<N, number>) => number;
/**
 * @since 1.0.0
 * @category Vector Operations
 */
export declare const cross: (x: V.Vec<3, number>, y: V.Vec<3, number>) => V.Vec<3, number>;
/**
 * @since 1.0.0
 * @category Vector Operations
 */
export declare const outerProduct: <M extends number, N extends number>(v1: V.Vec<M, number>, v2: V.Vec<N, number>) => M.Mat<M, N, number>;
/**
 * @since 1.0.0
 * @category Vector Operations
 */
export declare const l1Norm: <N>(x: V.Vec<N, number>) => number;
/**
 * @since 1.0.0
 * @category Vector Operations
 */
export declare const l2Norm: <N>(x: V.Vec<N, number>) => number;
/**
 * @since 1.0.0
 * @category Vector Operations
 */
export declare const lpNorm: (p: number) => <N>(v: V.Vec<N, number>) => number;
/**
 * @since 1.0.0
 * @category Vector Operations
 */
export declare const lInfNorm: <N>(x: V.Vec<N, number>) => number;
/**
 * @since 1.0.0
 * @category Vector Operations
 */
export declare const projection: <N extends number>(u: V.Vec<N, number>, v: V.Vec<N, number>) => V.Vec<N, number>;
/**
 * @since 1.0.0
 * @category Model
 */
export declare type Mat<M, N> = M.Mat<M, N, number>;
/**
 * @since 1.1.0
 * @category Instances
 */
export declare const MonoidProductMM: <M extends number>(m: M) => import("fp-ts/lib/Monoid").Monoid<M.Mat<M, M, number>>;
/**
 * @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, number>>;
/**
 * @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, number>, number, number>;
/**
 * @since 1.0.0
 * @category Matrix Operations
 */
export declare const idMat: <M extends number>(m: M) => M.Mat<M, M, number>;
/**
 * Multiply two matricies with matching inner dimensions
 *
 * ```math
 * (A ∈ R_mn) (B ∈ R_np) = C ∈ R_mp
 * ```
 *
 * Efficiency: `2mpn` flops
 *
 * @since 1.0.0
 * @category Matrix Operations
 */
export declare const mulM: <M extends number, N1 extends number, N2 extends N1, P extends number>(x: M.Mat<M, N1, number>, y: M.Mat<N2, P, number>) => M.Mat<M, P, number>;
/**
 * Add two matricies
 *
 * @since 1.1.0
 * @category Matrix Operations
 */
export declare const addM: <M, N>(x: M.Mat<M, N, number>, y: M.Mat<M, N, number>) => M.Mat<M, N, number>;
/**
 * Subtract two matricies
 *
 * @since 1.1.0
 * @category Matrix Operations
 */
export declare const subM: <M, N>(x: M.Mat<M, N, number>, y: M.Mat<M, N, number>) => M.Mat<M, N, number>;
/**
 * Transform a column vector `x` into vector `b` by matrix `A`
 *
 * ```math
 * Ax = b
 * ```
 *
 * Efficiency: `2mn` flops
 *
 * @since 1.0.0
 * @category Matrix Operations
 */
export declare const linMap: <M, N1, N2 extends N1>(A: M.Mat<M, N1, number>, x: V.Vec<N2, number>) => V.Vec<M, number>;
/**
 * Transform a row-vector `x` into vector `b` by matrix `A`
 *
 * ```math
 * xA = b
 * ```
 *
 * Efficiency: `2mn` flops
 *
 * @since 1.1.0
 * @category Matrix Operations
 */
export declare const linMapR: <M extends number, N1 extends number, N2 extends N1>(x: V.Vec<N1, number>, A: M.Mat<N2, M, number>) => V.Vec<M, number>;
/**
 * The sum of the diagonal elements
 *
 * Efficiency: `m` flops (for numeric Ring)
 *
 * @since 1.0.0
 * @category Matrix Operations
 */
export declare const trace: <M extends number>(fa: M.Mat<M, M, number>) => number;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const PolynomialAdditiveAbelianGroup: import("./typeclasses").AbelianGroup<Poly.Polynomial<number>>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const PolynomialBimodule: import("./typeclasses").Bimodule<Poly.Polynomial<number>, number, number>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const PolynomialRing: import("./typeclasses").CommutativeRing<Poly.Polynomial<number>>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const PolynomialEuclidianRing: import("./typeclasses").EuclidianRing<Poly.Polynomial<number>>;
/**
 * @since 1.0.0
 * @category Instances
 */
export declare const getDifferentialAutomorphism: (constantTerm: number) => Auto.Automorphism<Poly.Polynomial<number>>;
/**
 * @since 1.0.0
 * @category Polynomial Operations
 */
export declare const evaluatePolynomial: (p: Poly.Polynomial<number>) => (x: number) => number;
/**
 * @since 1.0.0
 * @category Polynomial Operations
 */
export declare const derivative: (coeffs: Poly.Polynomial<number>) => Poly.Polynomial<number>;
/**
 * @since 1.0.0
 * @category Polynomial Operations
 */
export declare const integrate: (lower: number, upper: number) => (p: Poly.Polynomial<number>) => number;
/**
 * @since 1.0.0
 * @category Polynomial Operations
 */
export declare const getAntiderivative: (constantTerm: number) => (p: Poly.Polynomial<number>) => Poly.Polynomial<number>;
/**
 * @since 1.0.0
 * @category Polynomial Operations
 */
export declare const polynomialInnerProduct: (p: Poly.Polynomial<number>, q: Poly.Polynomial<number>) => number;
/**
 * @since 1.0.0
 * @category Polynomial Operations
 */
export declare const polynomialNorm: (p: Poly.Polynomial<number>) => number;
/**
 * @since 1.0.0
 * @category Polynomial Operations
 */
export declare const polynomialProjection: (p: Poly.Polynomial<number>, q: Poly.Polynomial<number>) => Poly.Polynomial<number>;
/**
 * @since 1.0.0
 * @category Aliases
 */
export declare const add: (x: number, y: number) => number;
/**
 * @since 1.0.0
 * @category Aliases
 */
export declare const sub: (x: number, y: number) => number;
/**
 * @since 1.0.0
 * @category Aliases
 */
export declare const mul: (x: number, y: number) => number;
/**
 * @since 1.0.0
 * @category Aliases
 */
export declare const div: (x: number, y: number) => number;
/**
 * @since 1.0.0
 * @category Aliases
 */
export declare const mod: (x: number, y: number) => number;
/**
 * @since 1.0.0
 * @category Aliases
 */
export declare const degree: (a: number) => number;
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