import type { array, matrix } from "../types";
/**
 * Left array division X .\ Y.
 *
 * Performs element-wise left division of arrays or matrices. For scalar inputs, performs standard division.
 *
 * @param x The divisor, can be a number, array, or matrix
 * @param y The dividend, can be a number, array, or matrix
 * @returns The result of element-wise left division y ./ x
 * @throws If the input dimensions do not agree or if no arguments are provided
 *
 * @example Divide two numbers
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide(2, 6), 3);
 *
 * ```
 *
 * @example Element-wise division of arrays
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide([2, 4, 8], [6, 8, 16]), [3, 2, 2]);
 *
 * ```
 *
 * @example Divide array by scalar
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide(2, [6, 8, 10]), [3, 4, 5]);
 *
 * ```
 *
 * @example Element-wise division of matrices
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide([[2, 4], [6, 8]], [[6, 8], [12, 16]]), [[3, 2], [2, 2]]);
 * ```
 */
export default function ldivide(x: number, y: number): number;
/**
 * Left array division X .\ Y.
 *
 * Performs element-wise left division of arrays or matrices. For scalar inputs, performs standard division.
 *
 * @param x The divisor, can be a number, array, or matrix
 * @param y The dividend, can be a number, array, or matrix
 * @returns The result of element-wise left division y ./ x
 * @throws If the input dimensions do not agree or if no arguments are provided
 *
 * @example Divide two numbers
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide(2, 6), 3);
 *
 * ```
 *
 * @example Element-wise division of arrays
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide([2, 4, 8], [6, 8, 16]), [3, 2, 2]);
 *
 * ```
 *
 * @example Divide array by scalar
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide(2, [6, 8, 10]), [3, 4, 5]);
 *
 * ```
 *
 * @example Element-wise division of matrices
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide([[2, 4], [6, 8]], [[6, 8], [12, 16]]), [[3, 2], [2, 2]]);
 * ```
 */
export default function ldivide(x: number, y: array): array;
/**
 * Left array division X .\ Y.
 *
 * Performs element-wise left division of arrays or matrices. For scalar inputs, performs standard division.
 *
 * @param x The divisor, can be a number, array, or matrix
 * @param y The dividend, can be a number, array, or matrix
 * @returns The result of element-wise left division y ./ x
 * @throws If the input dimensions do not agree or if no arguments are provided
 *
 * @example Divide two numbers
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide(2, 6), 3);
 *
 * ```
 *
 * @example Element-wise division of arrays
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide([2, 4, 8], [6, 8, 16]), [3, 2, 2]);
 *
 * ```
 *
 * @example Divide array by scalar
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide(2, [6, 8, 10]), [3, 4, 5]);
 *
 * ```
 *
 * @example Element-wise division of matrices
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide([[2, 4], [6, 8]], [[6, 8], [12, 16]]), [[3, 2], [2, 2]]);
 * ```
 */
export default function ldivide(x: array, y: number): array;
/**
 * Left array division X .\ Y.
 *
 * Performs element-wise left division of arrays or matrices. For scalar inputs, performs standard division.
 *
 * @param x The divisor, can be a number, array, or matrix
 * @param y The dividend, can be a number, array, or matrix
 * @returns The result of element-wise left division y ./ x
 * @throws If the input dimensions do not agree or if no arguments are provided
 *
 * @example Divide two numbers
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide(2, 6), 3);
 *
 * ```
 *
 * @example Element-wise division of arrays
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide([2, 4, 8], [6, 8, 16]), [3, 2, 2]);
 *
 * ```
 *
 * @example Divide array by scalar
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide(2, [6, 8, 10]), [3, 4, 5]);
 *
 * ```
 *
 * @example Element-wise division of matrices
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide([[2, 4], [6, 8]], [[6, 8], [12, 16]]), [[3, 2], [2, 2]]);
 * ```
 */
export default function ldivide(x: array, y: array): array;
/**
 * Left array division X .\ Y.
 *
 * Performs element-wise left division of arrays or matrices. For scalar inputs, performs standard division.
 *
 * @param x The divisor, can be a number, array, or matrix
 * @param y The dividend, can be a number, array, or matrix
 * @returns The result of element-wise left division y ./ x
 * @throws If the input dimensions do not agree or if no arguments are provided
 *
 * @example Divide two numbers
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide(2, 6), 3);
 *
 * ```
 *
 * @example Element-wise division of arrays
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide([2, 4, 8], [6, 8, 16]), [3, 2, 2]);
 *
 * ```
 *
 * @example Divide array by scalar
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide(2, [6, 8, 10]), [3, 4, 5]);
 *
 * ```
 *
 * @example Element-wise division of matrices
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide([[2, 4], [6, 8]], [[6, 8], [12, 16]]), [[3, 2], [2, 2]]);
 * ```
 */
export default function ldivide(x: number, y: matrix): matrix;
/**
 * Left array division X .\ Y.
 *
 * Performs element-wise left division of arrays or matrices. For scalar inputs, performs standard division.
 *
 * @param x The divisor, can be a number, array, or matrix
 * @param y The dividend, can be a number, array, or matrix
 * @returns The result of element-wise left division y ./ x
 * @throws If the input dimensions do not agree or if no arguments are provided
 *
 * @example Divide two numbers
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide(2, 6), 3);
 *
 * ```
 *
 * @example Element-wise division of arrays
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide([2, 4, 8], [6, 8, 16]), [3, 2, 2]);
 *
 * ```
 *
 * @example Divide array by scalar
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide(2, [6, 8, 10]), [3, 4, 5]);
 *
 * ```
 *
 * @example Element-wise division of matrices
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide([[2, 4], [6, 8]], [[6, 8], [12, 16]]), [[3, 2], [2, 2]]);
 * ```
 */
export default function ldivide(x: matrix, y: number): matrix;
/**
 * Left array division X .\ Y.
 *
 * Performs element-wise left division of arrays or matrices. For scalar inputs, performs standard division.
 *
 * @param x The divisor, can be a number, array, or matrix
 * @param y The dividend, can be a number, array, or matrix
 * @returns The result of element-wise left division y ./ x
 * @throws If the input dimensions do not agree or if no arguments are provided
 *
 * @example Divide two numbers
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide(2, 6), 3);
 *
 * ```
 *
 * @example Element-wise division of arrays
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide([2, 4, 8], [6, 8, 16]), [3, 2, 2]);
 *
 * ```
 *
 * @example Divide array by scalar
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide(2, [6, 8, 10]), [3, 4, 5]);
 *
 * ```
 *
 * @example Element-wise division of matrices
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(ldivide([[2, 4], [6, 8]], [[6, 8], [12, 16]]), [[3, 2], [2, 2]]);
 * ```
 */
export default function ldivide(x: matrix, y: matrix): matrix;
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