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

类
struct	QuadRadical

函数
bool	trigsub_half_exponent (const NumberNode &number, Rational &exponent)
bool	trigsub_match_radical (const std::shared_ptr< const SymbolicNode > &node, const std::string &var, ComputationContext &context, QuadRadical &out)
bool	trigsub_quadratic_coefficients (const detail::SymbolicNodePtr &radicand, const std::string &var, ComputationContext &context, Rational &c0, Rational &c2)

---

类说明

LMCAS::anonymous_namespace{integration_trig_substitution.cpp}::QuadRadical

struct LMCAS::anonymous_namespace{integration_trig_substitution.cpp}::QuadRadical

在文件 integration_trig_substitution.cpp 第 10 行定义.

LMCAS::anonymous_namespace{integration_trig_substitution.cpp}::QuadRadical 的协作图:

类成员
Rational	a_sq {0}
Rational	exponent {0}
int	pattern = 0

函数说明

trigsub_half_exponent()

bool LMCAS::anonymous_namespace{integration_trig_substitution.cpp}::trigsub_half_exponent	(	const NumberNode &	number,
		Rational &	exponent )

在文件 integration_trig_substitution.cpp 第 16 行定义.

                                                                         {
    const auto exact = detail::exact_rational_value(number);
    if (!exact || (*exact != Rational(1, 2) && *exact != Rational(-1, 2))) {
        return false;
    }
    exponent = *exact;
    return true;
}

引用了 LMCAS::detail::exact_rational_value(), LMCAS::exponent , 以及 trigsub_half_exponent().

被这些函数引用 trigsub_half_exponent() , 以及 trigsub_match_radical().

函数调用图:

这是这个函数的调用关系图:

trigsub_match_radical()

bool LMCAS::anonymous_namespace{integration_trig_substitution.cpp}::trigsub_match_radical	(	const std::shared_ptr< const SymbolicNode > &	node,
		const std::string &	var,
		ComputationContext &	context,
		QuadRadical &	out )

在文件 integration_trig_substitution.cpp 第 41 行定义.

                                             {
    auto pw = std::dynamic_pointer_cast<const PowerNode>(node);
    if (!pw) { return false; }
    auto en = std::dynamic_pointer_cast<const NumberNode>(pw->exponent());
    if (!en) { return false; }
    Rational exponent;
    auto radicand = pw->base();
    const auto outer = detail::exact_rational_value(*en);
    if (outer && *outer == Rational(-1)) {
        if (const auto* root = dynamic_cast<const PowerNode*>(radicand.get())) {
            const auto inner = detail::exact_rational_value(root->exponent());
            if (!inner || *inner != Rational(1, 2)) { return false; }
            radicand = root->base();
        } else if (const auto* root = dynamic_cast<const FunctionNode*>(radicand.get());
                   root && root->type() == FunctionNode::FuncType::Sqrt &&
                   root->arguments().size() == 1) {
            radicand = root->arguments()[0];
        } else {
            return false;
        }
        exponent = Rational(-1, 2);
    } else if (!trigsub_half_exponent(*en, exponent)) {
        return false;
    }
    Rational c0, c2;
    if (!trigsub_quadratic_coefficients(radicand, var, context, c0, c2)) { return false; }
    out.exponent = exponent;
    if (c2 < Rational(0) && c0 > Rational(0)) { out.pattern = 1; out.a_sq = c0; }
    else if (c2 > Rational(0) && c0 > Rational(0)) { out.pattern = 2; out.a_sq = c0; }
    else if (c2 > Rational(0) && c0 < Rational(0)) { out.pattern = 3; out.a_sq = Rational(0) - c0; }
    else return false;
    return true;
}

引用了 LMCAS::anonymous_namespace{integration_trig_substitution.cpp}::QuadRadical::a_sq, LMCAS::context, LMCAS::detail::exact_rational_value(), LMCAS::anonymous_namespace{integration_trig_substitution.cpp}::QuadRadical::exponent, LMCAS::exponent, LMCAS::anonymous_namespace{integration_trig_substitution.cpp}::QuadRadical::pattern, LMCAS::FunctionNode::Sqrt, trigsub_half_exponent(), trigsub_match_radical(), trigsub_quadratic_coefficients() , 以及 LMCAS::FunctionNode::type().

被这些函数引用 trigsub_match_radical().

函数调用图:

这是这个函数的调用关系图:

trigsub_quadratic_coefficients()

bool LMCAS::anonymous_namespace{integration_trig_substitution.cpp}::trigsub_quadratic_coefficients	(	const detail::SymbolicNodePtr &	radicand,
		const std::string &	var,
		ComputationContext &	context,
		Rational &	c0,
		Rational &	c2 )

在文件 integration_trig_substitution.cpp 第 25 行定义.

                                                                                   {
    auto polynomial = recognize_rational_polynomial(
        detail::expression_from_node(radicand), var, context);
    if (!polynomial) { throw polynomial.error(); }
    if (!polynomial.value() || polynomial.value()->degree() != 2) { return false; }
    const auto& coefficients = polynomial.value()->coeffs;
    if (coefficients[1] != Rational(0) ||
        (coefficients[2] != Rational(1) && coefficients[2] != Rational(-1))) {
        return false;
    }
    c0 = coefficients[0];
    c2 = coefficients[2];
    return true;
}

引用了 LMCAS::context, LMCAS::detail::expression_from_node(), LMCAS::recognize_rational_polynomial() , 以及 trigsub_quadratic_coefficients().

被这些函数引用 trigsub_match_radical() , 以及 trigsub_quadratic_coefficients().

函数调用图:

这是这个函数的调用关系图: