import type { TwoDimensionalComponent, TwoDimensionalIndex } from '../dimensions.ts';
import type { Pipeable } from '../utils.ts';
import type { Vector2 } from '../vector/vector2.ts';
import type { Matrix2x2TypeId } from './matrix2x2.internal.ts';
/**
 * A type representing the coordinate of a 2D matrix.
 *
 * @since 1.0.0
 */
export type Matrix2x2Coordinate = TwoDimensionalIndex | TwoDimensionalComponent;
/**
 * A 2D matrix with 2 rows and 2 columns.
 *
 * All fields are readonly and immutable, and all operations create new instances.
 *
 * @since 1.0.0
 */
export interface Matrix2x2 extends Pipeable {
    readonly [Matrix2x2TypeId]: Matrix2x2TypeId;
    /**
     * The value in the first row and first column.
     */
    readonly m00: number;
    /**
     * The value in the first row and second column.
     */
    readonly m01: number;
    /**
     * The value in the second row and first column.
     */
    readonly m10: number;
    /**
     * The value in the second row and second column.
     */
    readonly m11: number;
}
/**
 * Checks if a value is a `Matrix2x2`.
 *
 * @param m - The value to check.
 * @returns `true` if the value is a `Matrix2x2`, `false` otherwise.
 * @since 1.0.0
 */
export declare const isMatrix2x2: (m: unknown) => m is Matrix2x2;
export declare const equals: {
    /**
     * Checks if two `Matrix2x2` instances are approximately equal within the
     * default absolute tolerance ({@link EPSILON}).
     *
     * @param a - The first matrix.
     * @param b - The second matrix.
     * @returns `true` when each pair of components is within tolerance.
     * @since 1.1.0
     */
    (a: Matrix2x2, b: Matrix2x2): boolean;
    /**
     * Checks if two `Matrix2x2` instances are approximately equal within the
     * default absolute tolerance ({@link EPSILON}).
     *
     * @param b - The second matrix.
     * @returns A function that takes the first matrix and returns the comparison result.
     * @since 1.1.0
     */
    (b: Matrix2x2): (a: Matrix2x2) => boolean;
};
/**
 * Creates a new `Matrix2x2` instance.
 *
 * @param m00 - The value in the first row and first column. Defaults to 0.
 * @param m01 - The value in the first row and second column. Defaults to 0.
 * @param m10 - The value in the second row and first column. Defaults to 0.
 * @param m11 - The value in the second row and second column. Defaults to 0.
 */
export declare const make: (m00?: number, m01?: number, m10?: number, m11?: number) => Matrix2x2;
/**
 * Creates a new `Matrix2x2` instance from two vectors representing rows.
 *
 * @param v0 - The first row vector.
 * @param v1 - The second row vector.
 * @returns A new `Matrix2x2` instance.
 * @since 1.0.0
 */
export declare const fromRows: (v0: Vector2, v1: Vector2) => Matrix2x2;
/**
 * Creates a new `Matrix2x2` instance from two vectors representing columns.
 *
 * @param v0 - The first column vector.
 * @param v1 - The second column vector.
 * @returns A new `Matrix2x2` instance.
 * @since 1.0.0
 */
export declare const fromColumns: (v0: Vector2, v1: Vector2) => Matrix2x2;
export declare const setRow: {
    /**
     * Sets the specified row of the matrix to the given vector.
     *
     * @param m - The matrix to modify.
     * @param row - The row index (0 or 1).
     * @param v - The vector to set the row to.
     * @returns A new `Matrix2x2` instance with the specified row set to the given vector.
     * @since 1.0.0
     */
    (m: Matrix2x2, row: Matrix2x2Coordinate, v: Vector2): Matrix2x2;
    /**
     * Sets the specified row of the matrix to the given vector.
     *
     * @param row - The row index (0 or 1).
     * @param v - The vector to set the row to.
     * @returns A function that takes a matrix and returns a new `Matrix2x2` instance with the specified row set to the given vector.
     * @since 1.0.0
     */
    (row: Matrix2x2Coordinate, v: Vector2): (m: Matrix2x2) => Matrix2x2;
};
export declare const setColumn: {
    /**
     * Sets the specified column of the matrix to the given vector.
     *
     * @param m - The matrix to modify.
     * @param column - The column index (0 or 1).
     * @param v - The vector to set the column to.
     * @returns A new `Matrix2x2` instance with the specified column set to the given vector.
     * @since 1.0.0
     */
    (m: Matrix2x2, column: Matrix2x2Coordinate, v: Vector2): Matrix2x2;
    /**
     * Sets the specified column of the matrix to the given vector.
     *
     * @param column - The column index (0 or 1).
     * @param v - The vector to set the column to.
     * @returns A function that takes a matrix and returns a new `Matrix2x2` instance with the specified column set to the given vector.
     * @since 1.0.0
     */
    (column: Matrix2x2Coordinate, v: Vector2): (m: Matrix2x2) => Matrix2x2;
};
/**
 * Calculates the determinant of a 2D matrix.
 *
 * @param m - The matrix to calculate the determinant for.
 * @returns The determinant of the matrix.
 * @since 1.0.0
 */
export declare const determinant: (m: Matrix2x2) => number;
export declare const vectorProductLeft: {
    /**
     * Calculates the left vector product of a matrix and a vector.
     *
     * @example
     * ```ts
     * import * as Matrix2x2 from 'curvy/matrix2x2'
     * import * as Vector2 from 'curvy/vector2'
     *
     * const matrix = Matrix2x2.make(1, 2, 3, 4)
     * const vector = Vector2.make(5, 6)
     *
     * // Performs:
     * // x = 1 * 5 + 2 * 6 = 17
     * // y = 3 * 5 + 4 * 6 = 39
     * const result = Matrix2x2.vectorProductLeft(matrix, vector)
     * ```
     * @param m - The matrix to multiply.
     * @param v - The vector to multiply.
     * @returns The resulting vector after the left vector product.
     * @since 1.0.0
     */
    (m: Matrix2x2, v: Vector2): Vector2;
    /**
     * Calculates the left vector product of a matrix and a vector.
     *
     * @example
     * ```ts
     * import * as Matrix2x2 from 'curvy/matrix2x2'
     * import * as Vector2 from 'curvy/vector2'
     *
     * const matrix = Matrix2x2.make(1, 2, 3, 4)
     * const vector = Vector2.make(5, 6)
     *
     * // Performs:
     * // x = 1 * 5 + 2 * 6 = 17
     * // y = 3 * 5 + 4 * 6 = 39
     * const result = Matrix2x2.vectorProductLeft(vector)(matrix)
     * ```
     * @param v - The vector to multiply.
     * @returns A function that takes a matrix and returns the resulting vector after the left vector product.
     * @since 1.0.0
     */
    (v: Vector2): (m: Matrix2x2) => Vector2;
};
export declare const vectorProductRight: {
    /**
     * Calculates the right vector product of a matrix and a vector.
     *
     * @example
     * ```ts
     * import * as Matrix2x2 from 'curvy/matrix2x2'
     * import * as Vector2 from 'curvy/vector2'
     *
     * const matrix = Matrix2x2.make(1, 2, 3, 4)
     * const vector = Vector2.make(5, 6)
     *
     * // Performs:
     * // x = 1 * 5 + 3 * 6 = 33
     * // y = 2 * 5 + 4 * 6 = 62
     * const result = Matrix2x2.vectorProductRight(matrix, vector)
     * ```
     * @param m - The matrix to multiply.
     * @param v - The vector to multiply.
     * @returns The resulting vector after the right vector product.
     * @since 1.0.0
     */
    (m: Matrix2x2, v: Vector2): Vector2;
    /**
     * Calculates the right vector product of a matrix and a vector.
     *
     * @example
     * ```ts
     * import * as Matrix2x2 from 'curvy/matrix2x2'
     * import * as Vector2 from 'curvy/vector2'
     *
     * const matrix = Matrix2x2.make(1, 2, 3, 4)
     * const vector = Vector2.make(5, 6)
     *
     * // Performs:
     * // x = 1 * 5 + 3 * 6 = 33
     * // y = 2 * 5 + 4 * 6 = 62
     * const result = Matrix2x2.vectorProductRight(vector)(matrix)
     * ```
     * @param v - The vector to multiply.
     * @returns A function that takes a matrix and returns the resulting vector after the right vector product.
     * @since 1.0.0
     */
    (v: Vector2): (m: Matrix2x2) => Vector2;
};
export declare const solveSystem: {
    /**
     * Solves a system of linear equations represented by a matrix and a vector.
     *
     * @example
     * ```ts
     * import * as Matrix2x2 from 'curvy/matrix2x2'
     * import * as Vector2 from 'curvy/vector2'
     *
     * const matrix = Matrix2x2.make(1, 2, 3, 4)
     * const vector = Vector2.make(5, 6)
     *
     * // Solves the system of equations:
     * // 1x + 2y = 5
     * // 3x + 4y = 6
     * const result = Matrix2x2.solveSystem(matrix, vector)
     * ```
     * @param m - The matrix representing the coefficients of the system.
     * @param v - The vector representing the constants of the system.
     * @returns The solution vector.
     * @since 1.0.0
     */
    (m: Matrix2x2, v: Vector2): Vector2;
    /**
     * Solves a system of linear equations represented by a matrix and a vector.
     *
     * @example
     * ```ts
     * import * as Matrix2x2 from 'curvy/matrix2x2'
     * import * as Vector2 from 'curvy/vector2'
     *
     * const matrix = Matrix2x2.make(1, 2, 3, 4)
     * const vector = Vector2.make(5, 6)
     *
     * // Solves the system of equations:
     * // 1x + 2y = 5
     * // 3x + 4y = 6
     * const result = Matrix2x2.solveSystem(vector)(matrix)
     * ```
     * @param v - The vector representing the constants of the system.
     * @returns A function that takes a matrix and returns the solution vector.
     * @since 1.0.0
     */
    (v: Vector2): (m: Matrix2x2) => Vector2;
};
/**
 * Returns the rows of a matrix as an array of vectors.
 *
 * @param m - The matrix to convert.
 * @returns An array of vectors representing the rows of the matrix.
 * @since 1.0.0
 */
export declare const toRows: (m: Matrix2x2) => [Vector2, Vector2];
/**
 * Returns the columns of a matrix as an array of vectors.
 *
 * @param m - The matrix to convert.
 * @returns An array of vectors representing the columns of the matrix.
 * @since 1.0.0
 */
export declare const toColumns: (m: Matrix2x2) => [Vector2, Vector2];
/**
 * Returns the specified row of a matrix as a vector.
 *
 * @param m - The matrix to get the row from.
 * @param row - The row index (0 or 1).
 * @returns A vector representing the specified row of the matrix.
 * @since 1.0.0
 */
export declare const rowVector: (m: Matrix2x2, row: Matrix2x2Coordinate) => Vector2;
/**
 * Returns the specified column of a matrix as a vector.
 *
 * @param m - The matrix to get the column from.
 * @param column - The column index (0 or 1).
 * @returns A vector representing the specified column of the matrix.
 * @since 1.0.0
 */
export declare const columnVector: (m: Matrix2x2, column: Matrix2x2Coordinate) => Vector2;
/**
 * Transposes a matrix.
 *
 * @param m - The matrix to transpose.
 * @returns A new `Matrix2x2` instance representing the transposed matrix.
 * @since 1.0.0
 */
export declare const transpose: (m: Matrix2x2) => Matrix2x2;
/**
 * Reverses the rows of a matrix.
 *
 * @param m - The matrix to reverse the rows of.
 * @returns A new `Matrix2x2` instance with the rows reversed.
 * @since 1.0.0
 */
export declare const reverseRows: (m: Matrix2x2) => Matrix2x2;
/**
 * Reverses the columns of a matrix.
 *
 * @param m - The matrix to reverse the columns of.
 * @returns A new `Matrix2x2` instance with the columns reversed.
 * @since 1.0.0
 */
export declare const reverseColumns: (m: Matrix2x2) => Matrix2x2;