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    }
    function fraction_sub(a, b) {
        a = Fraction(a);
        b = Fraction(b);
        return Fraction.toFraction(a.num * b.den - a.den * b.num, a.den * b.den);
    }
    function fraction_mul(a, b) {
        a = Fraction(a);
        b = Fraction(b);
        return Fraction.toFraction(a.num * b.num, a.den * b.den);
    }
    function fraction_div(a, b) {
        a = Fraction(a);
        b = Fraction(b);
        return Fraction.toFraction(a.num * b.den, a.den * b.num);
    }
    function fraction_mod(a, b) {
        var a1 = Fraction(a);
        var b1 = Fraction(b);
        return a - Integer.ediv(a1.num * b1.den, a1.den * b1.num) * b;
    }
    function fraction_eq(a, b) {
        a = Fraction(a);
        b = Fraction(b);
        /* we assume the fractions are normalized */
        return (a.num == b.num && a.den == b.den);
    }
    function fraction_lt(a, b) {
        a = Fraction(a);
        b = Fraction(b);
        return (a.num * b.den < b.num * a.den);
    }

    /* operators are needed for fractions */
    function float_add(a, b) {
        return Float(a) + Float(b);
    }
    function float_sub(a, b) {
        return Float(a) - Float(b);
    }
    function float_mul(a, b) {
        return Float(a) * Float(b);
    }
    function float_div(a, b) {
        return Float(a) / Float(b);
    }
    function float_mod(a, b) {
        return Float(a) % Float(b);
    }
    function float_pow(a, b) {
        return Float(a) ** Float(b);
    }
    function float_eq(a, b) {
        /* XXX: may be better to use infinite precision for the comparison */
        return Float(a) === Float(b);
    }
    function float_lt(a, b) {
        a = Float(a);
        b = Float(b);
        /* XXX: may be better to use infinite precision for the comparison */
        if (Float.isNaN(a) || Float.isNaN(b))
            return undefined;
        else
            return a < b;
    }
    
    operators_set(Fraction.prototype,
        {
            "+": fraction_add,
            "-": fraction_sub,
            "*": fraction_mul,
            "/": fraction_div,
            "%": fraction_mod,
            "**": generic_pow,
            "==": fraction_eq,
            "<": fraction_lt,
            "pos"(a) {
                return a;
            },
            "neg"(a) {
                return Fraction(-a.num, a.den);
            },
        },
        {
            left: [Number, BigInt],
            right: [Number, BigInt],
            "+": fraction_add,
            "-": fraction_sub,
            "*": fraction_mul,
            "/": fraction_div,
            "%": fraction_mod,
            "**": generic_pow,
            "==": fraction_eq,
            "<": fraction_lt,
        },
        {
            left: Float,
            right: Float,
            "+": float_add,
            "-": float_sub,
            "*": float_mul,
            "/": float_div,
            "%": float_mod,
            "**": float_pow,
            "==": float_eq,
            "<": float_lt,
        });
    
    add_props(Fraction, {
        /* (internal use) simplify 'a' to an integer when possible */
        toFraction(a, b) {
            var r = Fraction(a, b);
            if (algebraicMode && r.den == 1)
                return r.num;
            else
                return r;
        },
    });

    add_props(Fraction.prototype, {
        [Symbol.toPrimitive](hint) {