//! Auto-generated module
//!
//! 🤖 Generated with [SplitRS](https://github.com/cool-japan/splitrs)

use scirs2_core::ndarray::Array1;
use scirs2_core::Complex64;
use scirs2_special::*;
use std::collections::{HashMap, VecDeque};
use std::f64::consts::PI;
use std::time::{Duration, Instant};

use super::types::{AdaptiveLearningSession, AssessmentQuestion, AssessmentResult, ConceptNode, LearningProfile, LearningStyle, QuestionType};

#[allow(dead_code)]
fn main() -> Result<(), Box<dyn std::error::Error>> {
    println!("🎓 Advanced Interactive Learning Module for Special Functions");
    println!("============================================================\n");
    let profile = create_or_loadprofile()?;
    let mut session = AdaptiveLearningSession::new(profile.clone());
    println!("Welcome back, {}! 👋", profile.user_id);
    display_learning_dashboard(&profile);
    loop {
        println!("\n🎯 What would you like to do today?");
        println!("1. 📚 Continue adaptive learning path");
        println!("2. 🔍 Explore specific topics");
        println!("3. 📊 Take comprehensive assessment");
        println!("4. 📈 View learning analytics");
        println!("5. 🎨 Interactive visualizations");
        println!("6. 🧠 Proof exploration mode");
        println!("7. ⚙️ Adjust learning preferences");
        println!("8. 💾 Save progress and exit");
        let choice = get_user_input("Enter your choice (1-8): ")?;
        match choice.parse::<u32>() {
            Ok(1) => run_adaptive_learning(&mut session)?,
            Ok(2) => explore_topics(&mut session)?,
            Ok(3) => run_comprehensive_assessment(&mut session)?,
            Ok(4) => display_learning_analytics(&session.profile)?,
            Ok(5) => run_interactive_visualizations()?,
            Ok(6) => run_proof_exploration()?,
            Ok(7) => adjust_learning_preferences(&mut session.profile)?,
            Ok(8) => {
                saveprofile(&session.profile)?;
                println!("👋 Progress saved! See you next time!");
                break;
            }
            _ => println!("❌ Invalid choice. Please try again."),
        }
    }
    Ok(())
}
#[allow(dead_code)]
fn create_or_loadprofile() -> Result<LearningProfile, Box<dyn std::error::Error>> {
    let user_id = get_user_input("Enter your name or user ID: ")?;
    let mut skill_levels = HashMap::new();
    skill_levels.insert("calculus_integration".to_string(), 0.8);
    skill_levels.insert("factorial_concept".to_string(), 0.9);
    skill_levels.insert("differential_equations".to_string(), 0.7);
    skill_levels.insert("complex_analysis".to_string(), 0.6);
    skill_levels.insert("gamma_basics".to_string(), 0.3);
    Ok(LearningProfile {
        user_id,
        skill_levels,
        learning_speed: 200.0,
        preferred_learning_style: LearningStyle::Analytical,
        completed_modules: Vec::new(),
        time_spent: HashMap::new(),
        assessment_scores: Vec::new(),
        mistake_patterns: HashMap::new(),
        mastery_goals: vec!["gamma_advanced".to_string(), "bessel_basics".to_string()],
        last_session: None,
    })
}
#[allow(dead_code)]
fn display_learning_dashboard(profile: &LearningProfile) {
    println!("\n📊 Your Learning Dashboard");
    println!("==========================");
    let total_modules = profile.skill_levels.len();
    let mastered_modules = profile
        .skill_levels
        .values()
        .filter(|&&level| level >= 0.8)
        .count();
    let in_progress = profile
        .skill_levels
        .values()
        .filter(|&&level| (0.3..0.8).contains(&level))
        .count();
    println!("📚 Modules mastered: {}/{}", mastered_modules, total_modules);
    println!("📖 Modules in progress: {}", in_progress);
    println!("🎯 Learning style: {:?}", profile.preferred_learning_style);
    if !profile.mastery_goals.is_empty() {
        println!("🎯 Current goals: {}", profile.mastery_goals.join(", "));
    }
    println!("\n📈 Skill Levels:");
    let mut skills: Vec<_> = profile.skill_levels.iter().collect();
    skills.sort_by(|a, b| b.1.partial_cmp(a.1).expect("Operation failed"));
    for (skill, level) in skills.iter().take(5) {
        let bar_length = 20;
        let filled = (*level * bar_length as f64) as usize;
        let bar: String = (0..bar_length)
            .map(|i| if i < filled { '█' } else { '░' })
            .collect();
        println!("  {:<25} [{}] {:.1}%", skill, bar, * level * 100.0);
    }
}
#[allow(dead_code)]
fn run_adaptive_learning(
    session: &mut AdaptiveLearningSession,
) -> Result<(), Box<dyn std::error::Error>> {
    println!("\n🧠 Adaptive Learning Mode");
    println!("=========================\n");
    if let Some(next_topic) = session.recommend_next_topic() {
        println!("📚 Recommended topic: {}", next_topic);
        if let Some(node) = session.knowledge_graph.get(&next_topic).cloned() {
            println!("📝 Description: {}", node.description);
            println!(
                "⏱️ Estimated time: {:.0} minutes", node.estimated_time.as_secs_f64()
                / 60.0
            );
            println!("🎯 Difficulty: {}/5", node.difficulty);
            let start_learning = get_user_input("Start this learning module? (y/n): ")?;
            if start_learning.to_lowercase() == "y" {
                let start_time = Instant::now();
                let score = run_learning_module(&next_topic, &node, &session.profile)?;
                let time_taken = start_time.elapsed();
                session
                    .performance_history
                    .push_back((next_topic.clone(), score, time_taken));
                if session.performance_history.len() > 10 {
                    session.performance_history.pop_front();
                }
                session.profile.skill_levels.insert(next_topic.clone(), score);
                if score >= 0.8 {
                    session.profile.completed_modules.push(next_topic.clone());
                }
                session.profile.time_spent.insert(next_topic.clone(), time_taken);
                session.provide_personalized_feedback(&next_topic, score, time_taken);
                session.adapt_difficulty_based_on_performance();
            }
        }
    } else {
        println!(
            "🎉 Congratulations! You've mastered all available topics in your current path."
        );
        println!(
            "Consider setting new learning goals or exploring advanced research topics."
        );
    }
    Ok(())
}
#[allow(dead_code)]
fn run_learning_module(
    topic: &str,
    node: &ConceptNode,
    profile: &LearningProfile,
) -> Result<f64, Box<dyn std::error::Error>> {
    println!("\n📖 Learning Module: {}", node.name);
    println!("======================================\n");
    println!("🎯 Learning Objectives:");
    for (i, objective) in node.learning_objectives.iter().enumerate() {
        println!("  {}. {}", i + 1, objective);
    }
    match profile.preferred_learning_style {
        LearningStyle::Visual => present_visual_content(topic, node)?,
        LearningStyle::Analytical => present_analytical_content(topic, node)?,
        LearningStyle::Practical => present_practical_content(topic, node)?,
        LearningStyle::Intuitive => present_intuitive_content(topic, node)?,
        LearningStyle::Historical => present_historical_content(topic, node)?,
    }
    println!("\n📝 Let's assess your understanding...");
    let mut total_score = 0.0;
    let mut total_questions = 0;
    for question in &node.assessment_questions {
        total_questions += 1;
        let score = run_assessment_question(question)?;
        total_score += score;
    }
    let final_score = total_score / total_questions as f64;
    println!("\n✅ Module completed!");
    println!(
        "Final score: {:.1}% ({}/{})", final_score * 100.0, (total_score as u32),
        total_questions
    );
    Ok(final_score)
}
#[allow(dead_code)]
fn present_visual_content(
    topic: &str,
    node: &ConceptNode,
) -> Result<(), Box<dyn std::error::Error>> {
    println!("🎨 Visual Learning Mode");
    println!("========================\n");
    match topic {
        "gamma_basics" => {
            println!("📊 Visualizing the Gamma Function:");
            println!("The gamma function extends the factorial to real numbers.");
            println!("Let's see how Γ(x) behaves for different values of x:\n");
            println!("Γ(x) for x ∈ [0.1, 5.0]:");
            println!("    y");
            println!("    ↑");
            println!("10  |     ●");
            println!(" 8  |   ● ●");
            println!(" 6  |  ●   ●");
            println!(" 4  | ●     ●");
            println!(" 2  |●       ●");
            println!(" 0  +―――――――――→ x");
            println!("    0 1 2 3 4 5");
            println!();
            let x_values = Array1::linspace(0.1, 5.0, 20);
            println!("Computed values:");
            for (i, &x) in x_values.iter().enumerate() {
                if i % 4 == 0 {
                    let gamma_val = gamma(x);
                    println!("  Γ({:.1}) = {:.3}", x, gamma_val);
                }
            }
        }
        "bessel_basics" => {
            println!("🌊 Visualizing Bessel Functions:");
            println!("Bessel functions are oscillatory with decreasing amplitude.");
            println!();
            println!("J₀(x) oscillation pattern:");
            for i in 0..15 {
                let x = i as f64 * 0.5;
                let j0_val = j0(x);
                let normalized = ((j0_val + 1.0) * 10.0) as usize;
                let display = if normalized > 20 { 20 } else { normalized };
                print!("x={:4.1}: ", x);
                for j in 0..20 {
                    if j == 10 {
                        print!("|");
                    } else if j == display {
                        print!("●");
                    } else {
                        print!(" ");
                    }
                }
                println!(" ({:6.3})", j0_val);
            }
        }
        _ => {
            println!("📈 Conceptual visualization for {}:", node.name);
            println!("{}", node.description);
        }
    }
    println!(
        "\n💡 Visual insight: Notice the patterns and symmetries in the functions!"
    );
    wait_for_user_input()?;
    Ok(())
}
#[allow(dead_code)]
fn present_analytical_content(
    topic: &str,
    node: &ConceptNode,
) -> Result<(), Box<dyn std::error::Error>> {
    println!("🔬 Analytical Learning Mode");
    println!("============================\n");
    match topic {
        "gamma_basics" => {
            println!("📐 Mathematical Definition and Properties:");
            println!();
            println!("Definition: Γ(z) = ∫₀^∞ t^(z-1) e^(-t) dt  for Re(z) > 0");
            println!();
            println!("Key Properties:");
            println!("1. Recurrence relation: Γ(z+1) = z·Γ(z)");
            println!("2. For positive integers: Γ(n) = (n-1)!");
            println!("3. Special value: Γ(1/2) = √π");
            println!();
            println!("Derivation of Γ(1/2) = √π:");
            println!("Step 1: Γ(1/2) = ∫₀^∞ t^(-1/2) e^(-t) dt");
            println!("Step 2: Substitute t = u², dt = 2u du");
            println!("Step 3: Γ(1/2) = 2∫₀^∞ e^(-u²) du");
            println!("Step 4: Use Gaussian integral ∫₋∞^∞ e^(-u²) du = √π");
            println!("Step 5: Therefore Γ(1/2) = 2 · (√π/2) = √π ✓");
            let gamma_half = gamma(0.5);
            let sqrt_pi = PI.sqrt();
            println!("\nNumerical verification:");
            println!("  Γ(1/2) = {:.10}", gamma_half);
            println!("  √π     = {:.10}", sqrt_pi);
            println!("  Error  = {:.2e}", (gamma_half - sqrt_pi).abs());
        }
        "bessel_basics" => {
            println!("📐 Bessel's Differential Equation:");
            println!();
            println!("x²y'' + xy' + (x² - ν²)y = 0");
            println!();
            println!("Series Solution (Frobenius method):");
            println!("Assume y = x^r ∑_{{n=0}}^∞ aₙx^n");
            println!();
            println!("Indicial equation: r² - ν² = 0 → r = ±ν");
            println!();
            println!("For r = ν, the solution is:");
            println!(
                "Jᵥ(x) = (x/2)^ν ∑_{{k=0}}^∞ (-1)^k / (k!Γ(ν+k+1)) (x/2)^(2k)"
            );
            println!();
            println!("First few terms for J₀(x):");
            println!("J₀(x) = 1 - x²/4 + x⁴/64 - x⁶/2304 + ...");
            let x = 2.0;
            let mut sum = 1.0;
            let mut term = 1.0;
            println!("\nConvergence demonstration for J₀(2.0):");
            println!("  Term 0: {:.6}", sum);
            for k in 1..=5 {
                term *= -(x * x) / (4.0 * k as f64 * k as f64);
                sum += term;
                println!("  Term {}: {:.6} (sum = {:.6})", k, term, sum);
            }
            let exact = j0(x);
            println!("  Exact J₀(2.0) = {:.6}", exact);
            println!("  Error = {:.2e}", (sum - exact).abs());
        }
        _ => {
            println!("📊 Analytical approach to {}:", node.name);
            println!("{}", node.description);
        }
    }
    wait_for_user_input()?;
    Ok(())
}
#[allow(dead_code)]
fn present_practical_content(
    topic: &str,
    node: &ConceptNode,
) -> Result<(), Box<dyn std::error::Error>> {
    println!("🔧 Practical Application Mode");
    println!("==============================\n");
    println!("🎯 Real-world applications of {}:", node.name);
    for (i, application) in node.applications.iter().enumerate() {
        println!("  {}. {}", i + 1, application);
    }
    println!();
    match topic {
        "gamma_basics" => {
            println!("📊 Application: Probability Distributions");
            println!("The gamma function appears in many probability distributions:");
            println!();
            println!("Gamma Distribution: f(x) = (β^α/Γ(α)) x^(α-1) e^(-βx)");
            println!();
            let alpha = 2.0;
            let beta: f64 = 1.5;
            println!("Example: α = {}, β = {}", alpha, beta);
            println!(
                "Normalization constant: β^α/Γ(α) = {:.4}", beta.powf(alpha) /
                gamma(alpha)
            );
            println!("\nChi-square Distribution (special case of Gamma):");
            let dof = vec![1, 2, 5, 10];
            for &k in &dof {
                let chi_sq_norm = 1.0
                    / (2.0_f64.powf(k as f64 / 2.0) * gamma(k as f64 / 2.0));
                println!("  χ²({} dof): normalization = {:.6}", k, chi_sq_norm);
            }
        }
        "bessel_basics" => {
            println!("🎵 Application: Vibrating Circular Membrane");
            println!(
                "Natural frequencies of a circular drum involve Bessel function zeros:"
            );
            println!();
            let radius = 0.3;
            let wave_speed = 343.0;
            println!("Drum radius: {} m", radius);
            println!("Wave speed: {} m/s", wave_speed);
            println!();
            let j0_zeros = [2.4048, 5.5201, 8.6537];
            println!("Fundamental frequencies (J₀ zeros):");
            for (mode, &zero) in j0_zeros.iter().enumerate() {
                let frequency = zero * wave_speed / (2.0 * PI * radius);
                println!(
                    "  Mode {}: {:.1} Hz (wavelength: {:.3} m)", mode + 1, frequency,
                    wave_speed / frequency
                );
            }
            let j1_zeros = [3.8317, 7.0156, 10.1735];
            println!("\nNext mode family (J₁ zeros):");
            for (mode, &zero) in j1_zeros.iter().enumerate() {
                let frequency = zero * wave_speed / (2.0 * PI * radius);
                println!("  Mode {}: {:.1} Hz", mode + 1, frequency);
            }
        }
        _ => {
            println!("🔧 Practical examples for {}:", node.name);
            println!("This topic has applications in:");
            for app in &node.applications {
                println!("  • {}", app);
            }
        }
    }
    wait_for_user_input()?;
    Ok(())
}
#[allow(dead_code)]
fn present_intuitive_content(
    topic: &str,
    node: &ConceptNode,
) -> Result<(), Box<dyn std::error::Error>> {
    println!("💡 Intuitive Understanding Mode");
    println!("================================\n");
    match topic {
        "gamma_basics" => {
            println!("🤔 What is the Gamma Function Really?");
            println!();
            println!("Think of the gamma function as a 'smooth factorial':");
            println!("• Factorials work for positive integers: 5! = 5×4×3×2×1");
            println!("• But what about 2.5! or π! ?");
            println!(
                "• The gamma function extends this idea to ALL positive real numbers!"
            );
            println!();
            println!("🎯 Key Insight: Γ(n) = (n-1)! for positive integers");
            println!("So Γ(5) = 4! = 24, Γ(3) = 2! = 2, etc.");
            println!();
            println!("🌟 The Magic: Γ(1/2) = √π");
            println!("This connects factorials to the famous number π!");
            println!(
                "It's like asking 'What is (-1/2)!' and getting √π as the answer."
            );
            println!();
            println!("💭 Intuitive Properties:");
            println!("• Γ(x+1) = x·Γ(x) - like factorial recurrence but smooth");
            println!(
                "• Γ(x) → ∞ as x → 0⁺ - dividing by smaller and smaller numbers"
            );
            println!("• Γ(x) grows very fast for large x - faster than exponential!");
            println!("\n🔗 Recurrence Relation Demo:");
            for n in 1..5 {
                let x = n as f64 + 0.5;
                let gamma_x = gamma(x);
                let gamma_x_plus_1 = gamma(x + 1.0);
                let ratio = gamma_x_plus_1 / gamma_x;
                println!(
                    "  Γ({}) / Γ({}) = {:.6} (should equal {})", x + 1.0, x, ratio, x
                );
            }
        }
        "bessel_basics" => {
            println!("🌊 Understanding Bessel Functions Intuitively");
            println!();
            println!("🎯 Think of Bessel functions as 'circular waves':");
            println!("• Sine waves oscillate in straight lines");
            println!("• Bessel functions oscillate in circles!");
            println!();
            println!("🥁 Drum Analogy:");
            println!(
                "When you hit a circular drum, the vibration patterns are described by Bessel functions."
            );
            println!(
                "• J₀ describes the fundamental mode - like a piston moving up and down"
            );
            println!("• J₁ describes the next mode - like a saddle shape");
            println!("• Higher orders give more complex patterns");
            println!();
            println!("📉 Key Intuitions:");
            println!(
                "• They oscillate like sine/cosine but with decreasing amplitude"
            );
            println!("• They have zeros (like sine) but the spacing changes");
            println!(
                "• Near x=0, they behave like powers: J₀(x) ≈ 1, J₁(x) ≈ x/2"
            );
            println!("• For large x, they look like shifted and scaled sine waves");
            println!();
            println!("🌀 Why do they appear everywhere?");
            println!("Whenever you have circular or cylindrical symmetry in physics:");
            println!("• Heat flow in circular pipes");
            println!("• Electromagnetic fields around antennas");
            println!("• Quantum mechanics in circular potentials");
            println!("• Sound waves in cylindrical spaces");
        }
        _ => {
            println!("💡 Intuitive understanding of {}:", node.name);
            println!("{}", node.description);
            println!();
            println!(
                "💭 Think of this concept as connecting to everyday experience through:"
            );
            for app in &node.applications {
                println!("  • {}", app);
            }
        }
    }
    wait_for_user_input()?;
    Ok(())
}
#[allow(dead_code)]
fn present_historical_content(
    topic: &str,
    node: &ConceptNode,
) -> Result<(), Box<dyn std::error::Error>> {
    println!("📜 Historical Context Mode");
    println!("===========================\n");
    match topic {
        "gamma_basics" => {
            println!("🏛️ The Historical Journey of the Gamma Function");
            println!();
            println!("📅 Timeline:");
            println!(
                "• 1728: Leonhard Euler first studied the factorial interpolation problem"
            );
            println!(
                "• 1729: Euler derived the integral representation Γ(n) = ∫₀^∞ t^(n-1) e^(-t) dt"
            );
            println!("• 1812: Adrien-Marie Legendre introduced the notation Γ(z)");
            println!(
                "• 1856: Karl Weierstrass proved the infinite product representation"
            );
            println!();
            println!("🎯 Euler's Original Question:");
            println!("'How can we extend n! to non-integer values?'");
            println!("This led to one of the most important functions in mathematics!");
            println!();
            println!("🌟 Key Historical Insights:");
            println!(
                "• Euler discovered Γ(1/2) = √π by connecting it to the Gaussian integral"
            );
            println!(
                "• The reflection formula Γ(z)Γ(1-z) = π/sin(πz) unified many identities"
            );
            println!(
                "• Stirling's approximation provided asymptotic behavior for large arguments"
            );
            println!();
            println!(
                "🎓 Fun Fact: Euler calculated Γ(1/2) without knowing about normal distributions!"
            );
            println!(
                "He derived √π purely from mathematical curiosity about factorials."
            );
        }
        "bessel_basics" => {
            println!("🔭 The Historical Development of Bessel Functions");
            println!();
            println!("📅 Timeline:");
            println!(
                "• 1732: Daniel Bernoulli studied vibrating chains (early Bessel-like functions)"
            );
            println!(
                "• 1824: Friedrich Bessel systematically studied these functions for astronomy"
            );
            println!(
                "• 1826: Bessel applied them to planetary motion and Kepler's equation"
            );
            println!(
                "• 1838: Used Bessel functions to measure stellar parallax (first stellar distance!)"
            );
            println!();
            println!("🌟 Why 'Bessel' Functions?");
            println!(
                "Friedrich Bessel was an astronomer who needed to solve Kepler's equation:"
            );
            println!(
                "M = E - e sin(E)  (Mean anomaly = Eccentric anomaly - eccentricity × sin(E))"
            );
            println!();
            println!(
                "This led him to study functions that are now central to physics and engineering!"
            );
            println!();
            println!("🎯 Historical Applications:");
            println!(
                "• Stellar parallax measurement (1838) - first distance to a star"
            );
            println!("• Telegraph cable theory (Lord Kelvin, 1850s)");
            println!("• Radio wave propagation (Marconi era, 1900s)");
            println!("• Quantum mechanics foundations (1920s)");
            println!();
            println!(
                "🎓 Amazing Fact: Bessel measured the distance to 61 Cygni (11 light-years)"
            );
            println!("using mathematical techniques he developed for these functions!");
        }
        _ => {
            println!("📚 Historical perspective on {}:", node.name);
            println!("{}", node.description);
            println!();
            println!("This topic developed through the work of many mathematicians");
            println!("who were solving practical problems in their time.");
        }
    }
    wait_for_user_input()?;
    Ok(())
}
#[allow(dead_code)]
fn run_assessment_question(
    question: &AssessmentQuestion,
) -> Result<f64, Box<dyn std::error::Error>> {
    println!("\n❓ Assessment Question (Difficulty: {}/5)", question.difficulty);
    println!(
        "⏱️ Suggested time: {:.1} minutes", question.expected_time.as_secs_f64() /
        60.0
    );
    println!();
    println!("{}", question.content);
    match &question.question_type {
        QuestionType::MultipleChoice { options, correct } => {
            println!();
            for (i, option) in options.iter().enumerate() {
                println!("  {}. {}", (b'A' + i as u8) as char, option);
            }
            let answer = get_user_input("\nYour answer (A, B, C, etc.): ")?;
            let answer_index = answer
                .to_uppercase()
                .chars()
                .next()
                .and_then(|c: char| {
                    if c.is_ascii_uppercase() {
                        Some((c as u8 - b'A') as usize)
                    } else {
                        None
                    }
                });
            if let Some(idx) = answer_index {
                if idx == *correct {
                    println!("✅ Correct!");
                    Ok(1.0)
                } else {
                    println!(
                        "❌ Incorrect. The correct answer is {}.", (b'A' + * correct as
                        u8) as char
                    );
                    offer_hints_and_retry(question)
                }
            } else {
                println!("❌ Invalid answer format.");
                Ok(0.0)
            }
        }
        QuestionType::NumericalAnswer { expected, tolerance } => {
            let answer = get_user_input("\nEnter your numerical answer: ")?;
            match answer.parse::<f64>() {
                Ok(value) => {
                    let error = (value - expected).abs();
                    if error <= *tolerance {
                        println!(
                            "✅ Correct! (Answer: {:.6}, Your answer: {:.6})", expected,
                            value
                        );
                        Ok(1.0)
                    } else {
                        println!(
                            "❌ Close, but not quite. Expected: {:.6}, Your answer: {:.6}",
                            expected, value
                        );
                        println!("Error: {:.6} (tolerance: {:.6})", error, tolerance);
                        offer_hints_and_retry(question)
                    }
                }
                Err(_) => {
                    println!("❌ Invalid numerical format.");
                    Ok(0.0)
                }
            }
        }
        _ => {
            println!("This question type is not yet implemented in the demo.");
            Ok(0.5)
        }
    }
}
#[allow(dead_code)]
fn offer_hints_and_retry(
    question: &AssessmentQuestion,
) -> Result<f64, Box<dyn std::error::Error>> {
    if !question.hints.is_empty() {
        let want_hint = get_user_input("Would you like a hint? (y/n): ")?;
        if want_hint.to_lowercase() == "y" {
            println!("\n💡 Hint: {}", question.hints[0]);
            let retry = get_user_input("Try again? (y/n): ")?;
            if retry.to_lowercase() == "y" {
                return run_assessment_question(question);
            }
        }
    }
    Ok(0.3)
}
#[allow(dead_code)]
fn explore_topics(
    session: &mut AdaptiveLearningSession,
) -> Result<(), Box<dyn std::error::Error>> {
    println!("\n🔍 Topic Explorer");
    println!("=================\n");
    println!("📚 Available topics:");
    let mut topics: Vec<_> = session.knowledge_graph.keys().collect();
    topics.sort();
    for (i, topic) in topics.iter().enumerate() {
        if let Some(node) = session.knowledge_graph.get(topic.as_str()) {
            let skill_level = session
                .profile
                .skill_levels
                .get(topic.as_str())
                .unwrap_or(&0.0);
            let status = if *skill_level >= 0.8 {
                "✅"
            } else if *skill_level >= 0.3 {
                "📖"
            } else {
                "🔒"
            };
            println!(
                "  {}. {} {} (Level: {:.1}%) - {}", i + 1, status, node.name, skill_level
                * 100.0, node.description
            );
        }
    }
    let choice = get_user_input("\nEnter topic number to explore: ")?;
    if let Ok(index) = choice.parse::<usize>() {
        if index > 0 && index <= topics.len() {
            let topic = topics[index - 1];
            if let Some(node) = session.knowledge_graph.get(topic).cloned() {
                println!("\n📖 Topic: {}", node.name);
                println!("Description: {}", node.description);
                println!("Difficulty: {}/5", node.difficulty);
                println!("Prerequisites: {}", node.prerequisites.join(", "));
                println!("Applications: {}", node.applications.join(", "));
                let explore = get_user_input("\nStart learning this topic? (y/n): ")?;
                if explore.to_lowercase() == "y" {
                    let start_time = Instant::now();
                    let score = run_learning_module(topic, &node, &session.profile)?;
                    let time_taken = start_time.elapsed();
                    session.profile.skill_levels.insert(topic.to_string(), score);
                    session.profile.time_spent.insert(topic.to_string(), time_taken);
                }
            }
        }
    }
    Ok(())
}
#[allow(dead_code)]
fn run_comprehensive_assessment(
    session: &mut AdaptiveLearningSession,
) -> Result<(), Box<dyn std::error::Error>> {
    println!("\n📊 Comprehensive Assessment");
    println!("============================\n");
    println!("This assessment will evaluate your understanding across multiple topics.");
    println!("It will help identify your strengths and areas for improvement.\n");
    let proceed = get_user_input("Start comprehensive assessment? (y/n): ")?;
    if proceed.to_lowercase() != "y" {
        return Ok(());
    }
    let start_time = Instant::now();
    let mut total_score = 0.0;
    let mut topic_scores = HashMap::new();
    let mut questions_answered = 0;
    for (topic, node) in &session.knowledge_graph {
        if session.profile.skill_levels.get(topic).unwrap_or(&0.0) >= &0.3 {
            println!("\n--- {} Section ---", node.name);
            let mut topic_score = 0.0;
            let mut topic_questions = 0;
            for question in node.assessment_questions.iter().take(3) {
                topic_questions += 1;
                questions_answered += 1;
                let score = run_assessment_question(question)?;
                topic_score += score;
                total_score += score;
            }
            if topic_questions > 0 {
                topic_scores.insert(topic.clone(), topic_score / topic_questions as f64);
            }
        }
    }
    let time_taken = start_time.elapsed();
    let average_score = if questions_answered > 0 {
        total_score / questions_answered as f64
    } else {
        0.0
    };
    println!("\n🎉 Assessment Complete!");
    println!("========================");
    println!("⏱️ Time taken: {:.1} minutes", time_taken.as_secs_f64() / 60.0);
    println!(
        "📊 Overall score: {:.1}% ({}/{})", average_score * 100.0, total_score as u32,
        questions_answered
    );
    println!();
    println!("📈 Topic Performance:");
    let mut sorted_topics: Vec<_> = topic_scores.iter().collect();
    sorted_topics.sort_by(|a, b| b.1.partial_cmp(a.1).expect("Operation failed"));
    for (topic, &score) in sorted_topics {
        let node = session.knowledge_graph.get(topic).expect("Operation failed");
        println!("  {:<30} {:.1}%", node.name, score * 100.0);
        session.profile.skill_levels.insert(topic.clone(), score);
    }
    println!("\n💡 Recommendations:");
    for (topic, &score) in &topic_scores {
        if score < 0.7 {
            let node = session.knowledge_graph.get(topic).expect("Operation failed");
            println!("  📚 Review: {} (current: {:.1}%)", node.name, score * 100.0);
        }
    }
    let assessment = AssessmentResult {
        topic: "comprehensive".to_string(),
        score: average_score,
        time_taken,
        difficulty_level: 3,
        mistakes: Vec::new(),
        timestamp: Instant::now(),
    };
    session.profile.assessment_scores.push(assessment);
    Ok(())
}
#[allow(dead_code)]
fn display_learning_analytics(
    profile: &LearningProfile,
) -> Result<(), Box<dyn std::error::Error>> {
    println!("\n📈 Learning Analytics Dashboard");
    println!("===============================\n");
    let total_skills = profile.skill_levels.len();
    let mastered = profile.skill_levels.values().filter(|&&level| level >= 0.8).count();
    let learning = profile
        .skill_levels
        .values()
        .filter(|&&level| (0.3..0.8).contains(&level))
        .count();
    let not_started = total_skills - mastered - learning;
    println!("📊 Overall Progress:");
    println!(
        "  Mastered: {} topics ({:.1}%)", mastered, mastered as f64 / total_skills as f64
        * 100.0
    );
    println!(
        "  Learning: {} topics ({:.1}%)", learning, learning as f64 / total_skills as f64
        * 100.0
    );
    println!(
        "  Not started: {} topics ({:.1}%)", not_started, not_started as f64 /
        total_skills as f64 * 100.0
    );
    let total_time: Duration = profile.time_spent.values().sum();
    println!("\n⏱️ Time Investment:");
    println!("  Total study time: {:.1} hours", total_time.as_secs_f64() / 3600.0);
    if !profile.time_spent.is_empty() {
        let avg_time = total_time.as_secs_f64() / profile.time_spent.len() as f64;
        println!("  Average per topic: {:.1} minutes", avg_time / 60.0);
    }
    if !profile.assessment_scores.is_empty() {
        println!("\n📝 Assessment History:");
        let recent_scores: Vec<_> = profile
            .assessment_scores
            .iter()
            .rev()
            .take(5)
            .collect();
        for assessment in recent_scores {
            println!(
                "  {}: {:.1}% (Level {})", assessment.topic, assessment.score * 100.0,
                assessment.difficulty_level
            );
        }
    }
    println!("\n🧠 Learning Patterns:");
    println!("  Preferred style: {:?}", profile.preferred_learning_style);
    println!("  Reading speed: {:.0} WPM", profile.learning_speed);
    if !profile.mistake_patterns.is_empty() {
        println!("\n❌ Common Mistake Patterns:");
        let mut mistakes: Vec<_> = profile.mistake_patterns.iter().collect();
        mistakes.sort_by(|a, b| b.1.cmp(a.1));
        for (mistake_type, &count) in mistakes.iter().take(3) {
            println!("  {}: {} occurrences", mistake_type, count);
        }
    }
    wait_for_user_input()?;
    Ok(())
}
#[allow(dead_code)]
fn run_interactive_visualizations() -> Result<(), Box<dyn std::error::Error>> {
    println!("\n🎨 Interactive Visualizations");
    println!("=============================\n");
    println!("📊 Available visualizations:");
    println!("1. 📈 Function plots with parameter adjustment");
    println!("2. 🌀 Complex plane visualization");
    println!("3. 🎵 Bessel function animations");
    println!("4. 🌊 3D surface plots");
    println!("5. 📐 Geometric interpretations");
    let choice = get_user_input("Choose visualization (1-5): ")?;
    match choice.as_str() {
        "1" => {
            println!("\n📈 Interactive Function Plots");
            println!("=============================");
            println!("Choose a function to visualize:");
            println!("a) Gamma function");
            println!("b) Bessel functions");
            println!("c) Error function");
            let func_choice = get_user_input("Your choice (a-c): ")?;
            match func_choice.to_lowercase().as_str() {
                "a" => visualize_gamma_function()?,
                "b" => visualize_bessel_functions()?,
                "c" => visualize_error_function()?,
                _ => println!("Invalid choice"),
            }
        }
        "2" => visualize_complex_plane()?,
        "3" => animate_bessel_functions()?,
        "4" => visualize_3d_surfaces()?,
        "5" => show_geometric_interpretations()?,
        _ => println!("Invalid choice"),
    }
    Ok(())
}
#[allow(dead_code)]
fn visualize_gamma_function() -> Result<(), Box<dyn std::error::Error>> {
    println!("\n🎲 Gamma Function Visualization");
    println!("===============================\n");
    let xmin = get_user_input("Enter x minimum (e.g., 0.1): ")?
        .parse::<f64>()
        .unwrap_or(0.1);
    let xmax = get_user_input("Enter x maximum (e.g., 5.0): ")?
        .parse::<f64>()
        .unwrap_or(5.0);
    let points = get_user_input("Number of points (e.g., 50): ")?
        .parse::<usize>()
        .unwrap_or(50);
    println!("\nΓ(x) values:");
    println!("x      Γ(x)");
    println!("─────────────");
    for i in 0..points {
        let x = xmin + (xmax - xmin) * i as f64 / (points - 1) as f64;
        let gamma_val = gamma(x);
        if gamma_val < 20.0 {
            let bar_length = (gamma_val * 2.0) as usize;
            let bar: String = std::iter::repeat_n('■', bar_length.min(40)).collect();
            println!("{:5.2}  {:8.3} {}", x, gamma_val, bar);
        } else {
            println!("{:5.2}  {:8.3} (too large to display)", x, gamma_val);
        }
    }
    println!("\n🌟 Special Values:");
    println!("Γ(1) = {:.6}", gamma(1.0));
    println!("Γ(2) = {:.6}", gamma(2.0));
    println!("Γ(1/2) = {:.6} ≈ √π = {:.6}", gamma(0.5), PI.sqrt());
    wait_for_user_input()?;
    Ok(())
}
#[allow(dead_code)]
fn visualize_bessel_functions() -> Result<(), Box<dyn std::error::Error>> {
    println!("\n🌊 Bessel Function Visualization");
    println!("================================\n");
    let order = get_user_input("Enter Bessel function order (0, 1, 2): ")?
        .parse::<i32>()
        .unwrap_or(0);
    let xmax = get_user_input("Enter maximum x value (e.g., 20): ")?
        .parse::<f64>()
        .unwrap_or(20.0);
    println!("\nJ_{}(x) oscillation pattern:", order);
    println!("x      J_{}(x)    Visualization", order);
    println!(
        "─────────────────────────────────────"
    );
    for i in 0..40 {
        let x = i as f64 * xmax / 40.0;
        let j_val = match order {
            0 => j0(x),
            1 => j1(x),
            2 => jn(2, x),
            _ => jn(order, x),
        };
        let center = 20;
        let position = center + (j_val * 15.0) as i32;
        let display_pos = position.clamp(0, 40) as usize;
        let mut line = [' '; 41];
        line[center as usize] = '|';
        if display_pos < line.len() {
            line[display_pos] = if j_val > 0.0 { '●' } else { '○' };
        }
        let display: String = line.iter().collect();
        println!("{:5.1}  {:8.4}    {}", x, j_val, display);
    }
    wait_for_user_input()?;
    Ok(())
}
#[allow(dead_code)]
fn visualize_error_function() -> Result<(), Box<dyn std::error::Error>> {
    println!("\n📊 Error Function Visualization");
    println!("===============================\n");
    println!("erf(x) and erfc(x) comparison:");
    println!("x      erf(x)    erfc(x)   Visual");
    println!(
        "────────────────────────────────────"
    );
    for i in 0..21 {
        let x = -3.0 + i as f64 * 6.0 / 20.0;
        let erf_val = erf(x);
        let erfc_val = erfc(x);
        let erf_pos = (15.0 + erf_val * 10.0) as usize;
        let erfc_pos = (erfc_val * 20.0) as usize;
        let mut line = [' '; 31];
        line[15] = '|';
        if erf_pos < line.len() {
            line[erf_pos] = '●';
        }
        if erfc_pos < line.len() && erfc_pos != erf_pos {
            line[erfc_pos] = '○';
        }
        let display: String = line.iter().collect();
        println!("{:5.1}  {:7.4}   {:7.4}  {}", x, erf_val, erfc_val, display);
    }
    println!("\nLegend: ● = erf(x), ○ = erfc(x), | = zero");
    wait_for_user_input()?;
    Ok(())
}
#[allow(dead_code)]
fn visualize_complex_plane() -> Result<(), Box<dyn std::error::Error>> {
    println!("\n🌀 Complex Plane Visualization");
    println!("==============================\n");
    println!("This would show complex function visualizations using color coding:");
    println!("• Hue represents argument (angle)");
    println!("• Brightness represents magnitude");
    println!("• Zeros appear as black points");
    println!("• Poles appear as white points");
    println!();
    println!("In a full implementation, this would generate interactive plots");
    println!("showing the beautiful patterns of complex special functions.");
    wait_for_user_input()?;
    Ok(())
}
#[allow(dead_code)]
fn animate_bessel_functions() -> Result<(), Box<dyn std::error::Error>> {
    println!("\n🎵 Bessel Function Animation");
    println!("============================\n");
    println!("Animating circular membrane vibration patterns...");
    for frame in 0..20 {
        print!("\x1B[2J\x1B[H");
        println!("Frame {}/20 - Circular Membrane Vibration", frame + 1);
        println!("==========================================\n");
        let time = frame as f64 * 0.2;
        for row in 0..15 {
            for col in 0..30 {
                let x = (col as f64 - 15.0) * 0.3;
                let y = (row as f64 - 7.5) * 0.3;
                let r = (x * x + y * y).sqrt();
                if r < 0.1 {
                    print!("●");
                } else if r < 4.0 {
                    let amplitude = j0(r) * (time * 3.0).cos();
                    let char = if amplitude > 0.3 {
                        '█'
                    } else if amplitude > 0.0 {
                        '▓'
                    } else if amplitude > -0.3 {
                        '▒'
                    } else {
                        '░'
                    };
                    print!("{}", char);
                } else {
                    print!(" ");
                }
            }
            println!();
        }
        std::thread::sleep(std::time::Duration::from_millis(200));
    }
    println!(
        "\nAnimation complete! This shows how J₀ creates circular wave patterns."
    );
    wait_for_user_input()?;
    Ok(())
}
#[allow(dead_code)]
fn visualize_3d_surfaces() -> Result<(), Box<dyn std::error::Error>> {
    println!("\n🌊 3D Surface Visualization");
    println!("===========================\n");
    println!("3D surface plot of |Γ(x + iy)|:");
    println!("(Showing magnitude in the complex plane)\n");
    for y in (0..10).rev() {
        let im_part = (y as f64 - 5.0) * 0.5;
        print!("y={:4.1} ", im_part);
        for x in 0..20 {
            let re_part = x as f64 * 0.3 + 0.1;
            let z = Complex64::new(re_part, im_part);
            let gamma_mag = if re_part > 0.0 {
                gamma_complex(z).norm()
            } else {
                let reflected = Complex64::new(-re_part, im_part);
                let pi_over_sin = PI / (PI * z).sin().norm();
                pi_over_sin / gamma_complex(reflected + Complex64::new(1.0, 0.0)).norm()
            };
            let level = if gamma_mag < 1.0 {
                '·'
            } else if gamma_mag < 2.0 {
                '▒'
            } else if gamma_mag < 5.0 {
                '▓'
            } else {
                '█'
            };
            print!("{}", level);
        }
        println!();
    }
    println!("\nLegend: · < 1, ▒ 1-2, ▓ 2-5, █ > 5");
    wait_for_user_input()?;
    Ok(())
}
#[allow(dead_code)]
fn show_geometric_interpretations() -> Result<(), Box<dyn std::error::Error>> {
    println!("\n📐 Geometric Interpretations");
    println!("============================\n");
    println!("🎲 Gamma Function Geometry:");
    println!(
        "• Γ(z) can be viewed as the 'volume' of an infinite-dimensional simplex"
    );
    println!(
        "• The integral ∫₀^∞ t^(z-1) e^(-t) dt represents weighted infinite sums"
    );
    println!(
        "• Γ(1/2) = √π connects discrete (factorials) to continuous (circles)"
    );
    println!();
    println!("🌊 Bessel Function Geometry:");
    println!("• J_n(r) describes standing wave patterns on circular domains");
    println!("• The zeros correspond to nodal circles where amplitude = 0");
    println!("• Different orders n give different symmetry patterns");
    println!();
    println!("📊 Error Function Geometry:");
    println!("• erf(x) represents the area under the bell curve from 0 to x");
    println!("• Geometrically links linear measure (x) to area (probability)");
    println!("• The √π factor comes from the total area under e^(-t²)");
    println!();
    println!("🔗 Connections:");
    println!("• All these functions arise from trying to solve geometric problems");
    println!("• They connect algebra (equations) to geometry (shapes and areas)");
    println!("• Modern applications use the same geometric intuitions");
    wait_for_user_input()?;
    Ok(())
}
#[allow(dead_code)]
fn run_proof_exploration() -> Result<(), Box<dyn std::error::Error>> {
    println!("\n🧠 Interactive Proof Exploration");
    println!("=================================\n");
    println!("📜 Available proofs to explore:");
    println!("1. 🎲 Γ(1/2) = √π (Multiple approaches)");
    println!("2. 🔄 Gamma function reflection formula");
    println!("3. 🌊 Bessel function generating function");
    println!("4. 📊 Error function series expansion");
    let choice = get_user_input("Choose proof to explore (1-4): ")?;
    match choice.as_str() {
        "1" => explore_gamma_half_proof()?,
        "2" => explore_reflection_formula_proof()?,
        "3" => explore_bessel_generating_function_proof()?,
        "4" => explore_error_function_series_proof()?,
        _ => println!("Invalid choice"),
    }
    Ok(())
}
#[allow(dead_code)]
fn explore_gamma_half_proof() -> Result<(), Box<dyn std::error::Error>> {
    println!("\n🎲 Exploring the proof of Γ(1/2) = √π");
    println!("======================================\n");
    println!("We'll explore this beautiful result step by step.");
    println!("You can choose how much detail to see at each step.\n");
    println!("📝 Step 1: Start with the definition");
    println!("Γ(1/2) = ∫₀^∞ t^(1/2-1) e^(-t) dt = ∫₀^∞ t^(-1/2) e^(-t) dt");
    let detail = get_user_input("\nWant to see why we use this definition? (y/n): ")?;
    if detail.to_lowercase() == "y" {
        println!(
            "\n💡 The gamma function is defined as Γ(z) = ∫₀^∞ t^(z-1) e^(-t) dt"
        );
        println!("For z = 1/2, we get the exponent z-1 = 1/2-1 = -1/2");
        println!("So we need to evaluate ∫₀^∞ t^(-1/2) e^(-t) dt");
    }
    println!("\n📝 Step 2: Make the substitution t = u²");
    println!("If t = u², then dt = 2u du");
    println!("The integral becomes: ∫₀^∞ (u²)^(-1/2) e^(-u²) · 2u du");
    let detail = get_user_input("\nWork through this substitution? (y/n): ")?;
    if detail.to_lowercase() == "y" {
        println!("\n🔧 Substitution details:");
        println!("• t = u² → dt = d(u²) = 2u du");
        println!("• t^(-1/2) = (u²)^(-1/2) = u^(-1)");
        println!("• Limits: t: 0→∞ becomes u: 0→∞");
        println!(
            "• So: ∫₀^∞ u^(-1) e^(-u²) · 2u du = ∫₀^∞ 2 e^(-u²) du"
        );
        println!("The u^(-1) and u terms cancel!");
    }
    println!("\n📝 Step 3: Recognize the Gaussian integral");
    println!("We now have: Γ(1/2) = 2∫₀^∞ e^(-u²) du");
    println!("But we know that ∫_{{-∞}}^∞ e^(-u²) du = √π");
    let detail = get_user_input(
        "\nExplore why the Gaussian integral equals √π? (y/n): ",
    )?;
    if detail.to_lowercase() == "y" {
        println!("\n🎯 The famous Gaussian integral proof:");
        println!("Let I = ∫_{{-∞}}^∞ e^(-x²) dx");
        println!(
            "Then I² = (∫_{{-∞}}^∞ e^(-x²) dx)(∫_{{-∞}}^∞ e^(-y²) dy)"
        );
        println!("     = ∫∫ e^(-(x²+y²)) dx dy");
        println!("Convert to polar coordinates: x = r cos θ, y = r sin θ");
        println!(
            "I² = ∫₀^(2π) ∫₀^∞ e^(-r²) r dr dθ = 2π ∫₀^∞ r e^(-r²) dr"
        );
        println!("The inner integral = 1/2, so I² = π, thus I = √π");
    }
    println!("\n📝 Step 4: Complete the calculation");
    println!("Since ∫_{{-∞}}^∞ e^(-u²) du = √π and e^(-u²) is even:");
    println!("∫₀^∞ e^(-u²) du = (1/2)√π");
    println!("Therefore: Γ(1/2) = 2 · (1/2)√π = √π ✓");
    println!("\n🔍 Numerical verification:");
    let gamma_half = gamma(0.5);
    let sqrt_pi = PI.sqrt();
    println!("Γ(1/2) = {:.12}", gamma_half);
    println!("√π     = {:.12}", sqrt_pi);
    println!("Error  = {:.2e}", (gamma_half - sqrt_pi).abs());
    println!("\n🌟 This beautiful result connects:");
    println!("• Factorials (discrete) ↔ π (continuous circles)");
    println!("• Integration ↔ Probability theory");
    println!("• Real analysis ↔ Complex analysis");
    wait_for_user_input()?;
    Ok(())
}
#[allow(dead_code)]
fn explore_reflection_formula_proof() -> Result<(), Box<dyn std::error::Error>> {
    println!("\n🔄 Exploring the Gamma Function Reflection Formula");
    println!("=================================================\n");
    println!("🎯 Goal: Prove that Γ(z)Γ(1-z) = π/sin(πz)");
    println!("This is one of the most beautiful identities in mathematics!\n");
    println!("📚 We'll use complex analysis and the beta function.");
    println!("The proof involves several sophisticated techniques:");
    println!("• Beta function representation");
    println!("• Complex contour integration");
    println!("• Residue calculus");
    println!("• Analytic continuation");
    let proceed = get_user_input("\nContinue with the detailed proof? (y/n): ")?;
    if proceed.to_lowercase() == "y" {
        println!("\n📝 Step 1: Start with the beta function");
        println!(
            "B(z, 1-z) = ∫₀¹ t^(z-1)(1-t)^(-z) dt = Γ(z)Γ(1-z)/Γ(1) = Γ(z)Γ(1-z)"
        );
        println!("\n📝 Step 2: Transform the integral");
        println!("Using the substitution t = u/(1+u):");
        println!("B(z, 1-z) = ∫₀^∞ u^(z-1)/(1+u) du");
        println!("\n📝 Step 3: Apply complex analysis");
        println!("Consider the complex integral ∮_C w^(z-1)/(1+w) dw");
        println!("around a keyhole contour avoiding the branch cut on [0,∞).");
        println!("\n📝 Step 4: Calculate residues and limits");
        println!("The residue at w = -1 gives us the connection to sin(πz).");
        println!("\n🎉 Final result:");
        println!("After careful evaluation of the contour integral,");
        println!("we get: Γ(z)Γ(1-z) = π/sin(πz)");
        println!("\n✨ Beautiful special cases:");
        println!("z = 1/2: Γ(1/2)² = π/sin(π/2) = π → Γ(1/2) = √π");
        println!("z = 1/3: Γ(1/3)Γ(2/3) = π/sin(π/3) = 2π/√3");
        let gamma_third = gamma(1.0 / 3.0);
        let gamma_two_thirds = gamma(2.0 / 3.0);
        let product = gamma_third * gamma_two_thirds;
        let expected = 2.0 * PI / 3.0_f64.sqrt();
        println!(
            "Verification: Γ(1/3)Γ(2/3) = {:.6}, expected = {:.6}", product, expected
        );
    }
    wait_for_user_input()?;
    Ok(())
}
#[allow(dead_code)]
fn explore_bessel_generating_function_proof() -> Result<(), Box<dyn std::error::Error>> {
    println!("\n🌊 Bessel Function Generating Function");
    println!("=====================================\n");
    println!("🎯 Goal: Prove that exp(x(t-1/t)/2) = Σ J_n(x) t^n");
    println!("This generating function is fundamental to Bessel function theory.\n");
    println!("This proof involves expanding the exponential and carefully");
    println!("collecting coefficients to identify the Bessel functions.");
    wait_for_user_input()?;
    Ok(())
}
#[allow(dead_code)]
fn explore_error_function_series_proof() -> Result<(), Box<dyn std::error::Error>> {
    println!("\n📊 Error Function Series Expansion");
    println!("==================================\n");
    println!("🎯 Goal: Derive erf(x) = (2/√π) Σ (-1)^n x^(2n+1) / (n!(2n+1))");
    println!("This shows how the error function connects to power series.\n");
    println!("This derivation uses term-by-term integration of the");
    println!("exponential series for e^(-t²).");
    wait_for_user_input()?;
    Ok(())
}
#[allow(dead_code)]
fn adjust_learning_preferences(
    profile: &mut LearningProfile,
) -> Result<(), Box<dyn std::error::Error>> {
    println!("\n⚙️ Learning Preferences");
    println!("========================\n");
    println!("Current preferences:");
    println!("• Learning style: {:?}", profile.preferred_learning_style);
    println!("• Reading speed: {:.0} WPM", profile.learning_speed);
    println!("\nLearning styles:");
    println!("1. Visual - Graphs, diagrams, visual proofs");
    println!("2. Analytical - Step-by-step algebraic derivations");
    println!("3. Intuitive - Conceptual explanations and analogies");
    println!("4. Practical - Applications and numerical examples");
    println!("5. Historical - Historical development and context");
    let style_choice = get_user_input("Choose learning style (1-5): ")?;
    match style_choice.parse::<u32>() {
        Ok(1) => profile.preferred_learning_style = LearningStyle::Visual,
        Ok(2) => profile.preferred_learning_style = LearningStyle::Analytical,
        Ok(3) => profile.preferred_learning_style = LearningStyle::Intuitive,
        Ok(4) => profile.preferred_learning_style = LearningStyle::Practical,
        Ok(5) => profile.preferred_learning_style = LearningStyle::Historical,
        _ => println!("Invalid choice, keeping current setting"),
    }
    let speedinput = get_user_input("Reading speed (WPM, current: {:.0}): ")?;
    if let Ok(speed) = speedinput.parse::<f64>() {
        if speed > 0.0 && speed < 1000.0 {
            profile.learning_speed = speed;
        }
    }
    println!("✅ Preferences updated!");
    Ok(())
}
#[allow(dead_code)]
fn saveprofile(profile: &LearningProfile) -> Result<(), Box<dyn std::error::Error>> {
    println!("💾 Profile saved successfully!");
    Ok(())
}
#[allow(dead_code)]
fn create_gamma_basic_questions() -> Vec<AssessmentQuestion> {
    vec![
        AssessmentQuestion { question_type : QuestionType::MultipleChoice { options :
        vec!["0".to_string(), "1".to_string(), "∞".to_string(), "√π".to_string(),],
        correct : 3, }, content : "What is the value of Γ(1/2)?".to_string(), difficulty
        : 2, expected_time : Duration::from_secs(60), hints :
        vec!["This involves the famous Gaussian integral".to_string(),
        "Think about the connection between factorials and π".to_string(),],
        solution_steps : vec!["Start with the integral definition".to_string(),
        "Make the substitution t = u²".to_string(), "Recognize the Gaussian integral"
        .to_string(),], common_mistakes : vec!["Forgetting the substitution Jacobian"
        .to_string(), "Not recognizing the Gaussian integral".to_string(),], },
        AssessmentQuestion { question_type : QuestionType::NumericalAnswer { expected :
        24.0, tolerance : 0.1, }, content : "Calculate Γ(5).".to_string(), difficulty :
        1, expected_time : Duration::from_secs(30), hints :
        vec!["Use the recurrence relation Γ(n) = (n-1)!".to_string()], solution_steps :
        vec!["Recall that Γ(n) = (n-1)! for positive integers".to_string(),
        "So Γ(5) = 4! = 4×3×2×1 = 24".to_string(),], common_mistakes :
        vec!["Calculating 5! instead of 4!".to_string()], },
    ]
}
#[allow(dead_code)]
fn create_gamma_advanced_questions() -> Vec<AssessmentQuestion> {
    vec![
        AssessmentQuestion { question_type : QuestionType::MultipleChoice { options :
        vec!["π/sin(πz)".to_string(), "π/cos(πz)".to_string(), "sin(πz)/π"
        .to_string(), "π·sin(πz)".to_string(),], correct : 0, }, content :
        "What is Γ(z)Γ(1-z) equal to?".to_string(), difficulty : 4, expected_time :
        Duration::from_secs(120), hints : vec!["This is the reflection formula"
        .to_string(), "It involves the sine function".to_string(),], solution_steps :
        vec!["This is derived using complex analysis".to_string(),
        "The beta function provides the connection".to_string(),], common_mistakes :
        vec!["Confusing with the duplication formula".to_string()], }
    ]
}
#[allow(dead_code)]
fn create_bessel_basic_questions() -> Vec<AssessmentQuestion> {
    vec![
        AssessmentQuestion { question_type : QuestionType::MultipleChoice { options :
        vec!["x²y'' + xy' + (x² - ν²)y = 0".to_string(),
        "x²y'' + xy' - (x² + ν²)y = 0".to_string(), "xy'' + y' + (x - ν²)y = 0"
        .to_string(), "y'' + xy' + (x² - ν²)y = 0".to_string(),], correct : 0, },
        content : "What is Bessel's differential equation?".to_string(), difficulty : 2,
        expected_time : Duration::from_secs(90), hints :
        vec!["It's a second-order linear ODE".to_string(),
        "The coefficient of y involves x² - ν²".to_string(),], solution_steps :
        vec!["This equation arises from separation of variables in cylindrical coordinates"
        .to_string(),], common_mistakes : vec!["Wrong signs in the equation"
        .to_string()], }
    ]
}
#[allow(dead_code)]
fn create_hypergeometric_questions() -> Vec<AssessmentQuestion> {
    vec![
        AssessmentQuestion { question_type : QuestionType::NumericalAnswer { expected :
        1.0, tolerance : 0.001, }, content : "What is ₂F₁(a,b;c;0)?".to_string(),
        difficulty : 3, expected_time : Duration::from_secs(60), hints :
        vec!["Look at the series definition".to_string(), "What happens when z = 0?"
        .to_string(),], solution_steps :
        vec!["The series ₂F₁(a,b;c;z) = Σ (a)_n(b)_n/(c)_n · z^n/n!".to_string(),
        "When z = 0, only the n = 0 term survives".to_string(), "The n = 0 term is 1"
        .to_string(),], common_mistakes : vec!["Thinking it equals 0".to_string()], }
    ]
}
#[allow(dead_code)]
fn create_wright_function_questions() -> Vec<AssessmentQuestion> {
    vec![
        AssessmentQuestion { question_type : QuestionType::MultipleChoice { options :
        vec!["Exponential".to_string(), "Polynomial".to_string(), "Super-exponential"
        .to_string(), "Logarithmic".to_string(),], correct : 2, }, content :
        "How does the Wright function grow for large |z|?".to_string(), difficulty : 5,
        expected_time : Duration::from_secs(120), hints :
        vec!["Consider the asymptotic expansion".to_string(),
        "It grows faster than any exponential".to_string(),], solution_steps :
        vec!["The asymptotic behavior involves exp((z/α)^(1/α))".to_string(),
        "This grows faster than exp(z) for α < 1".to_string(),], common_mistakes :
        vec!["Thinking it's just exponential growth".to_string()], }
    ]
}
#[allow(dead_code)]
fn wait_for_user_input() -> Result<(), Box<dyn std::error::Error>> {
    get_user_input("Press Enter to continue...")?;
    Ok(())
}
#[allow(dead_code)]
fn get_user_input(prompt: &str) -> Result<String, Box<dyn std::error::Error>> {
    print!("{}", prompt);
    io::stdout().flush()?;
    let mut input = String::new();
    io::stdin().read_line(&mut input)?;
    Ok(input.trim().to_string())
}
