/**
 * Exact rational arithmetic (lowest-terms, positive denominator).
 * Shared by the Layer 1–3 rational-function integrators so those modules
 * can import each other without a cycle.
 */
/** Exact rational number with a bigint numerator `num` and denominator `den`. */
export interface Rat {
    num: bigint;
    den: bigint;
}
/**
 * Return the rational `num / den` in lowest terms, with a positive denominator.
 *
 * A zero numerator gives `0 / 1`.
 *
 * @throws Error if `den` is 0.
 */
export declare function ratNormalize(num: bigint, den: bigint): Rat;
/** Return the sum `a + b` in lowest terms. */
export declare function ratAdd(a: Rat, b: Rat): Rat;
/** Return the difference `a - b` in lowest terms. */
export declare function ratSub(a: Rat, b: Rat): Rat;
/** Return the product `a * b` in lowest terms. */
export declare function ratMul(a: Rat, b: Rat): Rat;
/**
 * Return the quotient `a / b` in lowest terms.
 *
 * @throws Error if `b` is 0.
 */
export declare function ratDiv(a: Rat, b: Rat): Rat;
/** Return the integer `n` as the rational `n / 1`. */
export declare function ratFromBigint(n: bigint): Rat;
export declare const RAT_ZERO: Rat;
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