LMCAS::anonymous_namespace{univariate_factor_bridge.cpp} 命名空间参考

函数
Result< void >	bridge_append_repeated (MathResult< std::vector< Polynomial< Rational > > > &factors, const TfSquareFreeResult &square_free, ComputationContext &context)
UnivariateFactorResult	bridge_factor (const Polynomial< Rational > &poly, ComputationContext &context)
UnivariateFactorResult	bridge_inconclusive (const Polynomial< Rational > &poly, const char *reason)
bool	bridge_inconclusive_error (const CasError &error)
UnivariateFactorResult	bridge_lift_and_combine (const Polynomial< Rational > &original, const Polynomial< Rational > &work, BerlekampResult &reduction, ComputationContext &context, bool &whole_input)
Result< int >	bridge_lift_bound (const Polynomial< BigInt > &poly, int64_t prime, BigInt &modulus, ComputationContext &context)
Result< BerlekampResult >	bridge_reduction (const Polynomial< Rational > &poly, ComputationContext &context)

变量
constexpr const char *	bridge_operation = "factor_univariate"

函数说明

bridge_append_repeated()

Result< void > LMCAS::anonymous_namespace{univariate_factor_bridge.cpp}::bridge_append_repeated	(	MathResult< std::vector< Polynomial< Rational > > > &	factors,
		const TfSquareFreeResult &	square_free,
		ComputationContext &	context )

在文件 univariate_factor_bridge.cpp 第 114 行定义.

                                                                        {
    if (!square_free.had_repeated_factors || square_free.repeated_factor.degree() < 1) {
        return Result<void>::success();
    }
    auto repeated = factor_univariate_bridge_checked(square_free.repeated_factor, context);
    if (!repeated) return Result<void>::failure(repeated.error());
    if (repeated.value().completeness == Completeness::Inconclusive) {
        factors.completeness = Completeness::Inconclusive;
        if (factors.reason.empty()) factors.reason = repeated.value().reason;
    }
    auto& values = repeated.value().value;
    factors.value.insert(factors.value.end(), std::make_move_iterator(values.begin()),
                         std::make_move_iterator(values.end()));
    return Result<void>::success();
}

引用了 bridge_append_repeated(), LMCAS::context, LMCAS::Polynomial< CoeffType >::degree(), LMCAS::factor_univariate_bridge_checked(), LMCAS::Result< T >::failure(), LMCAS::TfSquareFreeResult::had_repeated_factors, LMCAS::Inconclusive, LMCAS::TfSquareFreeResult::repeated_factor , 以及 LMCAS::Result< T >::success().

被这些函数引用 bridge_append_repeated() , 以及 bridge_factor().

函数调用图:

这是这个函数的调用关系图:

bridge_factor()

UnivariateFactorResult LMCAS::anonymous_namespace{univariate_factor_bridge.cpp}::bridge_factor	(	const Polynomial< Rational > &	poly,
		ComputationContext &	context )

在文件 univariate_factor_bridge.cpp 第 132 行定义.

                                                                   {
    auto square_free = tf_square_free(poly);
    auto work = square_free.square_free.make_monic();
    auto reduction = bridge_reduction(work, context);
    if (!reduction) return UnivariateFactorResult::failure(reduction.error());
    if (reduction.value().factors.empty()) {
        return bridge_inconclusive(poly, "未找到保持次数且无平方的有效模素数");
    }
    MathResult<std::vector<Polynomial<Rational>>> factors{
        {}, Completeness::Complete, {}};
    if (reduction.value().factors.size() <= 1) {
        factors.value.push_back(work.make_monic());
    } else {
        bool whole_input = false;
        auto combined = bridge_lift_and_combine(
            poly, work, reduction.value(), context, whole_input);
        if (!combined) return combined;
        if (whole_input) return combined;
        factors = std::move(combined.value());
    }
    auto appended = bridge_append_repeated(factors, square_free, context);
    if (!appended) return UnivariateFactorResult::failure(appended.error());
    Polynomial<Rational> product({Rational(1)}, poly.variable_name);
    for (const auto& factor : factors.value) product = product * factor;
    if (!(product == poly.make_monic())) {
        return UnivariateFactorResult::failure(CasErrc::InternalInvariant,
            "一元因子未能精确重构输入多项式", bridge_operation);
    }
    return UnivariateFactorResult::success(std::move(factors));
}

引用了 bridge_append_repeated(), bridge_factor(), bridge_inconclusive(), bridge_lift_and_combine(), bridge_operation, bridge_reduction(), LMCAS::Complete, LMCAS::context, LMCAS::Result< MathResult< std::vector< Polynomial< Rational > > > >::failure(), LMCAS::InternalInvariant, LMCAS::Polynomial< CoeffType >::make_monic(), LMCAS::Result< MathResult< std::vector< Polynomial< Rational > > > >::success(), LMCAS::tf_square_free(), LMCAS::MathResult< T >::value , 以及 LMCAS::Polynomial< CoeffType >::variable_name.

被这些函数引用 bridge_factor().

函数调用图:

这是这个函数的调用关系图:

bridge_inconclusive()

UnivariateFactorResult LMCAS::anonymous_namespace{univariate_factor_bridge.cpp}::bridge_inconclusive	(	const Polynomial< Rational > &	poly,
		const char *	reason )

在文件 univariate_factor_bridge.cpp 第 27 行定义.

                                                          {
    return UnivariateFactorResult::success(
        MathResult<std::vector<Polynomial<Rational>>>{
            {poly.make_monic()}, Completeness::Inconclusive, reason});
}

引用了 bridge_inconclusive(), LMCAS::Inconclusive, LMCAS::Polynomial< CoeffType >::make_monic() , 以及 LMCAS::Result< MathResult< std::vector< Polynomial< Rational > > > >::success().

被这些函数引用 bridge_factor(), bridge_inconclusive() , 以及 bridge_lift_and_combine().

函数调用图:

这是这个函数的调用关系图:

bridge_inconclusive_error()

bool LMCAS::anonymous_namespace{univariate_factor_bridge.cpp}::bridge_inconclusive_error

(

const CasError &

error

)

在文件 univariate_factor_bridge.cpp 第 74 行定义.

                                                      {
    return error.code == CasErrc::InvalidArgument || error.code == CasErrc::Inconclusive;
}

引用了 bridge_inconclusive_error(), LMCAS::CasError::code, LMCAS::Inconclusive , 以及 LMCAS::InvalidArgument.

被这些函数引用 bridge_inconclusive_error() , 以及 bridge_lift_and_combine().

函数调用图:

这是这个函数的调用关系图:

bridge_lift_and_combine()

UnivariateFactorResult LMCAS::anonymous_namespace{univariate_factor_bridge.cpp}::bridge_lift_and_combine	(	const Polynomial< Rational > &	original,
		const Polynomial< Rational > &	work,
		BerlekampResult &	reduction,
		ComputationContext &	context,
		bool &	whole_input )

在文件 univariate_factor_bridge.cpp 第 78 行定义.

                                                                                {
    auto integer_poly = factor_integer_polynomial(work);
    BigInt modulus;
    auto bound = bridge_lift_bound(integer_poly, reduction.prime, modulus, context);
    if (!bound) {
        if (bound.error().code == CasErrc::Inconclusive) {
            whole_input = true;
            return bridge_inconclusive(original, bound.error().message.c_str());
        }
        return UnivariateFactorResult::failure(bound.error());
    }
    const ModInt unit(
        (integer_poly.coeffs.back() % BigInt(reduction.prime)).to_int(),
        reduction.prime);
    for (auto& coefficient : reduction.factors.front().coeffs) {
        coefficient = coefficient * unit;
    }
    auto lifted = hensel_lift_checked(
        integer_poly, reduction.factors, reduction.prime, bound.value());
    if (!lifted) {
        if (bridge_inconclusive_error(lifted.error())) {
            whole_input = true;
            return bridge_inconclusive(original, "当前模素数的提升前置条件不成立");
        }
        return UnivariateFactorResult::failure(lifted.error());
    }
    auto combined = zassenhaus_combine_checked(work, lifted.value(), modulus, context);
    if (!combined && bridge_inconclusive_error(combined.error())) {
        whole_input = true;
        return bridge_inconclusive(original, "提升因子无法完成精确有理重构");
    }
    return combined;
}

引用了 bridge_inconclusive(), bridge_inconclusive_error(), bridge_lift_and_combine(), bridge_lift_bound(), LMCAS::context, LMCAS::factor_integer_polynomial(), LMCAS::BerlekampResult::factors, LMCAS::Result< MathResult< std::vector< Polynomial< Rational > > > >::failure(), LMCAS::hensel_lift_checked(), LMCAS::Inconclusive, LMCAS::BerlekampResult::prime, LMCAS::unit , 以及 LMCAS::zassenhaus_combine_checked().

被这些函数引用 bridge_factor() , 以及 bridge_lift_and_combine().

函数调用图:

这是这个函数的调用关系图:

bridge_lift_bound()

Result< int > LMCAS::anonymous_namespace{univariate_factor_bridge.cpp}::bridge_lift_bound	(	const Polynomial< BigInt > &	poly,
		int64_t	prime,
		BigInt &	modulus,
		ComputationContext &	context )

在文件 univariate_factor_bridge.cpp 第 51 行定义.

                                                                            {
    BigInt coefficient_sum(0);
    for (const auto& coefficient : poly.coeffs) {
        coefficient_sum = coefficient_sum + coefficient.abs();
    }
    BigInt target = coefficient_sum * BigInt(2);
    for (int i = 0; i < poly.degree(); ++i) target = target * BigInt(2);
    int bound = 1;
    modulus = BigInt(static_cast<std::int64_t>(prime));
    while (modulus <= target && bound < 100) {
        auto step = context.consume_steps(1, bridge_operation);
        if (!step) return Result<int>::failure(step.error());
        modulus = modulus * BigInt(static_cast<std::int64_t>(prime));
        ++bound;
    }
    if (modulus <= target) {
        return Result<int>::failure(CasErrc::Inconclusive,
            "提升次数上限不足以保证重构", bridge_operation);
    }
    return Result<int>::success(bound);
}

引用了 bridge_lift_bound(), bridge_operation, LMCAS::Polynomial< CoeffType >::coeffs, LMCAS::context, LMCAS::Polynomial< CoeffType >::degree(), LMCAS::Result< T >::failure(), LMCAS::Inconclusive, LMCAS::prime, LMCAS::Result< T >::success() , 以及 LMCAS::target.

被这些函数引用 bridge_lift_and_combine() , 以及 bridge_lift_bound().

函数调用图:

这是这个函数的调用关系图:

bridge_reduction()

Result< BerlekampResult > LMCAS::anonymous_namespace{univariate_factor_bridge.cpp}::bridge_reduction	(	const Polynomial< Rational > &	poly,
		ComputationContext &	context )

在文件 univariate_factor_bridge.cpp 第 34 行定义.

                                                                   {
    static const int64_t primes[] = {3, 5, 7, 11, 13, 17, 19, 23, 29, 31};
    for (int64_t prime : primes) {
        auto step = context.consume_steps(1, bridge_operation);
        if (!step) return Result<BerlekampResult>::failure(step.error());
        auto reduction = berlekamp_factor(poly, prime);
        if (reduction.prime > 0 && !reduction.factors.empty() &&
            (poly.degree() == 1 ||
             static_cast<int>(reduction.factors.size()) == reduction.null_space_dim)) {
            return Result<BerlekampResult>::success(std::move(reduction));
        }
    }
    return Result<BerlekampResult>::success(BerlekampResult{});
}

引用了 LMCAS::berlekamp_factor(), bridge_operation, bridge_reduction(), LMCAS::context, LMCAS::Polynomial< CoeffType >::degree(), LMCAS::Result< T >::failure(), LMCAS::prime , 以及 LMCAS::Result< T >::success().

被这些函数引用 bridge_factor() , 以及 bridge_reduction().

函数调用图:

这是这个函数的调用关系图:

变量说明

bridge_operation

const char* LMCAS::anonymous_namespace{univariate_factor_bridge.cpp}::bridge_operation = "factor_univariate"

constexpr

在文件 univariate_factor_bridge.cpp 第 25 行定义.

被这些函数引用 bridge_factor(), bridge_lift_bound() , 以及 bridge_reduction().