/**
 * @file      Math.Types.ts
 * @author    Gage Sorrell <gage@sorrell.sh>
 * @copyright (c) 2026 Gage Sorrell
 * @license   MIT
 */
import type * as InternalTypes from "./Math.Internal.Types.mjs";
import type { TBuildTuple, TInclusiveRangeFromTuple, TIsLessThanOrEqual } from "./Math.Internal.Types.mjs";
/**
 * Determines whether a given {@link NumberType} is a nonnegative integer.
 *
 * @template NumberType - The number type to check.  This is expected,
 * but not required, to be a single number literal.
 *
 * @returns `true` iff the given {@link NumberType} is a numeric type,
 * and `false` otherwise.
 */
export type TIsNonNegativeInteger<NumberType extends number> = `${NumberType}` extends `-${string}` ? false : `${NumberType}` extends `${bigint}` ? true : false;
export declare namespace Symmetry {
    /**
     * The symmetric group of the five given type parameters.
     *
     * @template OneType - The first specified type.
     * @template TwoType - The second specified type.
     * @template ThreeType - The third specified type.
     * @template FourType - The fourth specified type.
     * @template FiveType - The fifth specified type.
     */
    type Five<OneType, TwoType, ThreeType, FourType, FiveType> = InternalTypes.Five<OneType, TwoType, ThreeType, FourType, FiveType>;
    /**
     * The symmetric group of the four given type parameters.
     *
     * @template OneType - The first specified type.
     * @template TwoType - The second specified type.
     * @template ThreeType - The third specified type.
     * @template FourType - The fourth specified type.
     */
    type Four<OneType, TwoType, ThreeType, FourType> = InternalTypes.Four<OneType, TwoType, ThreeType, FourType>;
    /**
     * The symmetric group of the three given type parameters.
     *
     * @template OneType - The first specified type.
     * @template TwoType - The second specified type.
     * @template ThreeType - The third specified type.
     */
    type Three<OneType, TwoType, ThreeType> = InternalTypes.Three<OneType, TwoType, ThreeType>;
    /**
     * The symmetric group of the two given type parameters.
     *
     * @template OneType - The first specified type.
     * @template TwoType - The second specified type.
     */
    type Two<OneType, TwoType> = InternalTypes.Two<OneType, TwoType>;
}
export declare namespace Permutations {
    /**
     * The symmetric group of the five given type parameters.
     *
     * @template OneType - The first specified type.
     * @template TwoType - The second specified type.
     * @template ThreeType - The third specified type.
     * @template FourType - The fourth specified type.
     * @template FiveType - The fifth specified type.
     */
    type Five<OneType, TwoType, ThreeType, FourType, FiveType> = InternalTypes.Five<OneType, TwoType, ThreeType, FourType, FiveType>;
    /**
     * The symmetric group of the four given type parameters.
     *
     * @template OneType - The first specified type.
     * @template TwoType - The second specified type.
     * @template ThreeType - The third specified type.
     * @template FourType - The fourth specified type.
     */
    type Four<OneType, TwoType, ThreeType, FourType> = InternalTypes.Four<OneType, TwoType, ThreeType, FourType>;
    /**
     * The symmetric group of the three given type parameters.
     *
     * @template OneType - The first specified type.
     * @template TwoType - The second specified type.
     * @template ThreeType - The third specified type.
     */
    type Three<OneType, TwoType, ThreeType> = InternalTypes.Three<OneType, TwoType, ThreeType>;
    /**
     * The symmetric group of the two given type parameters.
     *
     * @template OneType - The first specified type.
     * @template TwoType - The second specified type.
     */
    type Two<OneType, TwoType> = InternalTypes.Two<OneType, TwoType>;
}
/**
 * The union of integers from {@link StartValue} to {@link EndValue}, inclusive.
 *
 * @template StartValue - The least value in the range.
 * @template EndValue - The greatest value in the range.
 */
export type TIntegralRange<StartValue extends number, EndValue extends number> = number extends StartValue ? never : number extends EndValue ? never : TIsNonNegativeInteger<StartValue> extends true ? TIsNonNegativeInteger<EndValue> extends true ? TIsLessThanOrEqual<StartValue, EndValue> extends true ? TInclusiveRangeFromTuple<TBuildTuple<StartValue>, EndValue> : never : never : never;
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