/**
 * Exact rational arithmetic over bigint. No floating point is ever used in
 * correctness checks — rule property tests compare equation truth values
 * computed with this type.
 *
 * Always normalized: den > 0, gcd(|num|, den) === 1, and 0 is 0/1.
 */
export declare class Rational {
    readonly num: bigint;
    readonly den: bigint;
    constructor(num: bigint, den?: bigint);
    static of(n: bigint | number): Rational;
    /** Parse "3", "-3", or "3/4" (whitespace tolerated). Undefined on anything else. */
    static parse(s: string): Rational | undefined;
    static readonly zero: Rational;
    static readonly one: Rational;
    add(o: Rational): Rational;
    sub(o: Rational): Rational;
    mul(o: Rational): Rational;
    div(o: Rational): Rational;
    neg(): Rational;
    /** Integer exponent only; negative exponents of zero throw. */
    powInt(e: bigint): Rational;
    isZero(): boolean;
    isInteger(): boolean;
    equals(o: Rational): boolean;
    /** Exact ordering: -1, 0, or 1. */
    compare(o: Rational): -1 | 0 | 1;
    toString(): string;
}
export declare class DivisionByZero extends Error {
    constructor();
}
/** Greatest common divisor; expects non-negative inputs. */
export declare function gcd(a: bigint, b: bigint): bigint;
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