函数
ExpressionResult	arc_length_checked_impl (std::shared_ptr< SymbolicExpr > f, std::shared_ptr< SymbolicExpr > a, std::shared_ptr< SymbolicExpr > b, const std::string &variable, ComputationContext &context, const std::string &operation)
ExpressionResult	definite_integral_geometry_checked (const std::shared_ptr< SymbolicExpr > &integrand, const std::string &variable, const std::shared_ptr< SymbolicExpr > &lower_bound, const std::shared_ptr< SymbolicExpr > &upper_bound, const std::string &operation, ComputationContext &context)
ExpressionResult	differentiate_geometry_checked (const std::shared_ptr< SymbolicExpr > &expr, const std::string &variable, const std::string &operation, ComputationContext &context)
ExpressionResult	simplify_geometry_checked (std::shared_ptr< SymbolicExpr > expr, const std::string &operation, const std::string &message, ComputationContext &context)
std::shared_ptr< SymbolicExpr >	squared_profile (const std::shared_ptr< SymbolicExpr > &f, ComputationContext &context)
Result< void >	validate_geometry_inputs (const std::shared_ptr< SymbolicExpr > &function, const std::shared_ptr< SymbolicExpr > &lower, const std::shared_ptr< SymbolicExpr > &upper, ComputationContext &context, const std::string &operation)
ExpressionResult	volume_of_revolution_checked_impl (std::shared_ptr< SymbolicExpr > f, std::shared_ptr< SymbolicExpr > a, std::shared_ptr< SymbolicExpr > b, const std::string &variable, ComputationContext &context, const std::string &operation)

函数说明

◆ arc_length_checked_impl()

ExpressionResult LMCAS::anonymous_namespace{symbolic_geometry.cpp}::arc_length_checked_impl	(	std::shared_ptr< SymbolicExpr >	f,
		std::shared_ptr< SymbolicExpr >	a,
		std::shared_ptr< SymbolicExpr >	b,
		const std::string &	variable,
		ComputationContext &	context,
		const std::string &	operation )

在文件 symbolic_geometry.cpp 第 197 行定义.

{
    auto valid = validate_geometry_inputs(f, a, b, context, operation);
    if (!valid) return ExpressionResult::failure(valid.error());
 
    auto step = context.consume_steps(10, operation);
    if (!step) return ExpressionResult::failure(step.error());
 
    try {
        auto derivative_result = differentiate_geometry_checked(f, variable, operation, context);
        if (!derivative_result) return derivative_result;
        auto integrand = SymbolicExpr::sqrt(SymbolicExpr::add(
            SymbolicExpr::number(1),
            SymbolicExpr::power(derivative_result.value(), SymbolicExpr::number(2))));
        return definite_integral_geometry_checked(
            integrand, variable, a, b, operation, context);
    } catch (const std::bad_alloc&) {
        return ExpressionResult::failure(CasErrc::ResourceLimit,
                                           "symbolic geometry allocation failed",
                                           operation);
    } catch (const std::exception& e) {
        return ExpressionResult::failure(CasErrc::InternalInvariant,
                                           e.what(), operation);
    }
}

引用了 LMCAS::a, arc_length_checked_impl(), LMCAS::b, LMCAS::context, definite_integral_geometry_checked(), differentiate_geometry_checked(), LMCAS::e(), LMCAS::Result< std::shared_ptr< SymbolicExpr > >::failure(), LMCAS::InternalInvariant, LMCAS::ResourceLimit, validate_geometry_inputs() , 以及 LMCAS::variable.

被这些函数引用 arc_length_checked_impl().

函数调用图:

这是这个函数的调用关系图:

◆ definite_integral_geometry_checked()

ExpressionResult LMCAS::anonymous_namespace{symbolic_geometry.cpp}::definite_integral_geometry_checked	(	const std::shared_ptr< SymbolicExpr > &	integrand,
		const std::string &	variable,
		const std::shared_ptr< SymbolicExpr > &	lower_bound,
		const std::shared_ptr< SymbolicExpr > &	upper_bound,
		const std::string &	operation,
		ComputationContext &	context )

在文件 symbolic_geometry.cpp 第 95 行定义.

    {
 
    if (!integrand || !LMCAS::detail::node(integrand)) {
        return ExpressionResult::failure(
            CasErrc::Inconclusive,
            "geometry integrand is outside the supported domain",
            operation);
    }
    Integrator integrator;
    auto integrated = integrator.integrate_def_checked(
        *integrand, variable, *lower_bound, *upper_bound, context);
    if (!integrated) { return ExpressionResult::failure(integrated.error()); }
    auto result = detail::make_expression_ptr(std::move(integrated.value()));
    if (contains_unevaluated_integral(detail::node(result))) {
        return ExpressionResult::failure(
            CasErrc::Inconclusive,
            "geometry integral is outside the supported domain",
            operation);
    }
    return simplify_geometry_checked(
        result, operation,
        "geometry definite integral result is outside the supported domain", context);
} catch (const CasError& error) {
    return ExpressionResult::failure(error);
} catch (const std::bad_alloc&) {
    return ExpressionResult::failure(CasErrc::ResourceLimit, "allocation failed", operation);
} catch (const std::length_error& error) {
    return ExpressionResult::failure(CasErrc::ResourceLimit, error.what(), operation);
} catch (const std::exception& error) {
    return ExpressionResult::failure(CasErrc::InternalInvariant, error.what(), operation);
}

引用了 LMCAS::contains_unevaluated_integral(), LMCAS::context, definite_integral_geometry_checked(), LMCAS::Result< std::shared_ptr< SymbolicExpr > >::failure(), LMCAS::Inconclusive, LMCAS::integrator, LMCAS::detail::make_expression_ptr(), LMCAS::detail::node(), simplify_geometry_checked() , 以及 LMCAS::variable.

被这些函数引用 arc_length_checked_impl(), definite_integral_geometry_checked() , 以及 volume_of_revolution_checked_impl().

函数调用图:

这是这个函数的调用关系图:

◆ differentiate_geometry_checked()

ExpressionResult LMCAS::anonymous_namespace{symbolic_geometry.cpp}::differentiate_geometry_checked	(	const std::shared_ptr< SymbolicExpr > &	expr,
		const std::string &	variable,
		const std::string &	operation,
		ComputationContext &	context )

在文件 symbolic_geometry.cpp 第 68 行定义.

    {
 
    detail::RewriteBudget transform_budget(context, (context).limits().max_recursion_depth,
                                            (context).limits().max_ast_nodes, "transform");
    auto derivative = detail::make_expression_ptr(
        detail::differentiate_node(detail::node(expr), variable, transform_budget));
    return simplify_geometry_checked(
        derivative, operation,
        "geometry derivative is outside the supported domain", context);
} catch (const CasError& error) {
    if (error.code == CasErrc::UnsupportedExpression) {
        return ExpressionResult::failure(CasErrc::Inconclusive,
            "geometry derivative is outside the supported domain", operation);
    }
    return ExpressionResult::failure(error);
} catch (const std::bad_alloc&) {
    return ExpressionResult::failure(CasErrc::ResourceLimit, "allocation failed", operation);
} catch (const std::length_error& error) {
    return ExpressionResult::failure(CasErrc::ResourceLimit, error.what(), operation);
} catch (const std::exception& error) {
    return ExpressionResult::failure(CasErrc::InternalInvariant, error.what(), operation);
}

引用了 LMCAS::context, differentiate_geometry_checked(), LMCAS::detail::differentiate_node(), LMCAS::detail::make_expression_ptr(), LMCAS::detail::node(), simplify_geometry_checked() , 以及 LMCAS::variable.

被这些函数引用 arc_length_checked_impl() , 以及 differentiate_geometry_checked().

函数调用图:

这是这个函数的调用关系图:

◆ simplify_geometry_checked()

ExpressionResult LMCAS::anonymous_namespace{symbolic_geometry.cpp}::simplify_geometry_checked	(	std::shared_ptr< SymbolicExpr >	expr,
		const std::string &	operation,
		const std::string &	message,
		ComputationContext &	context )

在文件 symbolic_geometry.cpp 第 36 行定义.

    {
 
    detail::RewriteBudget transform_budget(context, (context).limits().max_recursion_depth,
                                            (context).limits().max_ast_nodes, "transform");
    if (!expr || !LMCAS::detail::node(expr)) {
        return ExpressionResult::failure(CasErrc::Inconclusive,
                                           message, operation);
    }
    auto simplified = detail::make_expression_ptr(detail::normalize_node(detail::node(expr), transform_budget));
    if (!simplified || !LMCAS::detail::node(simplified)) {
        return ExpressionResult::failure(CasErrc::Inconclusive,
                                           message, operation);
    }
    if (contains_unevaluated_integral(LMCAS::detail::node(simplified))) {
        return ExpressionResult::failure(CasErrc::Inconclusive,
                                           "geometry integral is outside the supported domain",
                                           operation);
    }
    return ExpressionResult::success(std::move(simplified));
} catch (const CasError& error) {
    return ExpressionResult::failure(error);
} catch (const std::bad_alloc&) {
    return ExpressionResult::failure(CasErrc::ResourceLimit, "allocation failed", operation);
} catch (const std::length_error& error) {
    return ExpressionResult::failure(CasErrc::ResourceLimit, error.what(), operation);
} catch (const std::exception& error) {
    return ExpressionResult::failure(CasErrc::InternalInvariant, error.what(), operation);
}

引用了 LMCAS::contains_unevaluated_integral(), LMCAS::context, LMCAS::Result< std::shared_ptr< SymbolicExpr > >::failure(), LMCAS::Inconclusive, LMCAS::detail::make_expression_ptr(), LMCAS::detail::node(), LMCAS::detail::normalize_node(), simplify_geometry_checked() , 以及 LMCAS::Result< std::shared_ptr< SymbolicExpr > >::success().

被这些函数引用 definite_integral_geometry_checked(), differentiate_geometry_checked() , 以及 simplify_geometry_checked().

函数调用图:

这是这个函数的调用关系图:

◆ squared_profile()

std::shared_ptr< SymbolicExpr > LMCAS::anonymous_namespace{symbolic_geometry.cpp}::squared_profile	(	const std::shared_ptr< SymbolicExpr > &	f,
		ComputationContext &	context )

在文件 symbolic_geometry.cpp 第 133 行定义.

                                                                                                               {
 
    detail::RewriteBudget transform_budget(context, (context).limits().max_recursion_depth,
                                            (context).limits().max_ast_nodes, "transform");
    if (f) {
        if (auto func = std::dynamic_pointer_cast<const FunctionNode>(LMCAS::detail::node(f))) {
            if (func->type() == FunctionNode::FuncType::Sqrt && func->arguments().size() == 1) {
                return detail::make_expression_ptr(detail::normalize_node(func->arguments()[0], transform_budget));
            }
        }
        if (auto power = std::dynamic_pointer_cast<const PowerNode>(LMCAS::detail::node(f))) {
            auto exponent = std::dynamic_pointer_cast<const NumberNode>(power->exponent());
            if (exponent && std::holds_alternative<Rational>(exponent->value())) {
                const auto& rational = std::get<Rational>(exponent->value());
                if (rational.get_numerator() == BigInt(1) &&
                    rational.get_denominator() == BigInt(2)) {
                    return detail::make_expression_ptr(detail::normalize_node(power->base(), transform_budget));
                }
            }
        }
    }
    return detail::make_expression_ptr(detail::normalize_node(detail::node(SymbolicExpr::power(f, SymbolicExpr::number(2))), transform_budget));
}

引用了 LMCAS::context, LMCAS::exponent, LMCAS::detail::make_expression_ptr(), LMCAS::detail::node(), LMCAS::detail::normalize_node(), LMCAS::rational(), LMCAS::FunctionNode::Sqrt , 以及 squared_profile().

被这些函数引用 squared_profile() , 以及 volume_of_revolution_checked_impl().

函数调用图:

这是这个函数的调用关系图:

◆ validate_geometry_inputs()

Result< void > LMCAS::anonymous_namespace{symbolic_geometry.cpp}::validate_geometry_inputs	(	const std::shared_ptr< SymbolicExpr > &	function,
		const std::shared_ptr< SymbolicExpr > &	lower,
		const std::shared_ptr< SymbolicExpr > &	upper,
		ComputationContext &	context,
		const std::string &	operation )

在文件 symbolic_geometry.cpp 第 14 行定义.

{
    auto step = context.consume_steps(1, operation);
    if (!step) return step;
    if (!function || !LMCAS::detail::node(function)) {
        return Result<void>::failure(CasErrc::InvalidArgument,
                                     "profile expression cannot be null",
                                     operation);
    }
    if (!lower || !LMCAS::detail::node(lower) || !upper || !LMCAS::detail::node(upper)) {
        return Result<void>::failure(CasErrc::InvalidArgument,
                                     "integration bounds cannot be null",
                                     operation);
    }
    return Result<void>::success();
}

引用了 LMCAS::context, LMCAS::Result< T >::failure(), LMCAS::function(), LMCAS::InvalidArgument, LMCAS::lower, LMCAS::detail::node(), LMCAS::Result< T >::success(), LMCAS::upper , 以及 validate_geometry_inputs().

被这些函数引用 arc_length_checked_impl(), validate_geometry_inputs() , 以及 volume_of_revolution_checked_impl().

函数调用图:

这是这个函数的调用关系图:

◆ volume_of_revolution_checked_impl()

ExpressionResult LMCAS::anonymous_namespace{symbolic_geometry.cpp}::volume_of_revolution_checked_impl	(	std::shared_ptr< SymbolicExpr >	f,
		std::shared_ptr< SymbolicExpr >	a,
		std::shared_ptr< SymbolicExpr >	b,
		const std::string &	variable,
		ComputationContext &	context,
		const std::string &	operation )

在文件 symbolic_geometry.cpp 第 157 行定义.

    {
    detail::RewriteBudget transform_budget(context, (context).limits().max_recursion_depth,
                                            (context).limits().max_ast_nodes, "transform");
    auto valid = validate_geometry_inputs(f, a, b, context, operation);
    if (!valid) return ExpressionResult::failure(valid.error());
 
    auto step = context.consume_steps(8, operation);
    if (!step) return ExpressionResult::failure(step.error());
 
    try {
        auto pi = LMCAS::detail::make_expression_ptr(
            LMCAS::detail::make_node<VariableNode>("pi", true));
        auto integrand = detail::make_expression_ptr(detail::normalize_node(detail::node(SymbolicExpr::multiply(pi, squared_profile(f, context))), transform_budget));
        return definite_integral_geometry_checked(
            integrand, variable, a, b, operation, context);
    } catch (const std::bad_alloc&) {
        return ExpressionResult::failure(CasErrc::ResourceLimit,
                                           "symbolic geometry allocation failed",
                                           operation);
    } catch (const std::length_error& error) { return ExpressionResult::failure(CasErrc::ResourceLimit, error.what(), operation); } catch (const std::exception& e) {
        return ExpressionResult::failure(CasErrc::InternalInvariant,
                                           e.what(), operation);
    }
} catch (const CasError& error) {
    return ExpressionResult::failure(error);
} catch (const std::bad_alloc&) {
    return ExpressionResult::failure(CasErrc::ResourceLimit, "allocation failed", operation);
} catch (const std::length_error& error) {
    return ExpressionResult::failure(CasErrc::ResourceLimit, error.what(), operation);
} catch (const std::exception& error) {
    return ExpressionResult::failure(CasErrc::InternalInvariant, error.what(), operation);
}

引用了 LMCAS::a, LMCAS::b, LMCAS::context, definite_integral_geometry_checked(), LMCAS::e(), LMCAS::Result< std::shared_ptr< SymbolicExpr > >::failure(), LMCAS::InternalInvariant, LMCAS::detail::make_expression_ptr(), LMCAS::detail::make_node(), LMCAS::detail::node(), LMCAS::detail::normalize_node(), LMCAS::pi(), LMCAS::ResourceLimit, squared_profile(), validate_geometry_inputs(), LMCAS::variable , 以及 volume_of_revolution_checked_impl().

被这些函数引用 volume_of_revolution_checked_impl().

函数调用图:

这是这个函数的调用关系图: