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//! Number Theory Function Intelligence
//!
//! Complete mathematical intelligence for number theory functions:
//! gcd, lcm, mod, prime operations with existing algorithm integration.
use crate::core::Expression;
use crate::expr;
use crate::functions::properties::*;
use std::collections::HashMap;
/// Number Theory Function Intelligence
///
/// Dedicated intelligence system for number theory functions
/// with integration to existing mathematical algorithms.
pub struct NumberTheoryIntelligence {
/// Function properties for each number theory function
properties: HashMap<String, FunctionProperties>,
}
impl Default for NumberTheoryIntelligence {
fn default() -> Self {
Self::new()
}
}
impl NumberTheoryIntelligence {
/// Create new number theory intelligence system
pub fn new() -> Self {
let mut intelligence = Self {
properties: HashMap::with_capacity(8),
};
intelligence.initialize_gcd_lcm();
intelligence.initialize_modular_arithmetic();
intelligence.initialize_prime_functions();
intelligence
}
/// Get all number theory function properties
pub fn get_all_properties(&self) -> HashMap<String, FunctionProperties> {
self.properties.clone()
}
/// Check if function has number theory intelligence
pub fn has_intelligence(&self, name: &str) -> bool {
self.properties.contains_key(name)
}
fn initialize_gcd_lcm(&mut self) {
self.properties.insert(
"gcd".to_owned(),
FunctionProperties::Elementary(Box::new(ElementaryProperties {
derivative_rule: None, // GCD is not differentiable
antiderivative_rule: None,
special_values: vec![SpecialValue {
input: "0".to_owned(),
output: expr!(b),
latex_explanation: "\\gcd(0, b) = |b|".to_owned(),
}],
identities: Box::new(vec![]),
domain_range: Box::new(DomainRangeData {
domain: Domain::Integer,
range: Range::PositiveInteger,
singularities: vec![],
}),
wolfram_name: None,
periodicity: None, // Uses existing symbolic implementation
})),
);
// LCM function - integrates with existing Expression::lcm implementation
self.properties.insert(
"lcm".to_owned(),
FunctionProperties::Elementary(Box::new(ElementaryProperties {
derivative_rule: None, // LCM is not differentiable
antiderivative_rule: None,
special_values: vec![SpecialValue {
input: "1".to_owned(),
output: expr!(b),
latex_explanation: "\\text{lcm}(1, b) = |b|".to_owned(),
}],
identities: Box::new(vec![]),
domain_range: Box::new(DomainRangeData {
domain: Domain::Integer,
range: Range::PositiveInteger,
singularities: vec![],
}),
wolfram_name: None,
periodicity: None, // Uses existing symbolic implementation
})),
);
}
/// Initialize modular arithmetic functions
fn initialize_modular_arithmetic(&mut self) {
// MOD function for modular reduction
self.properties.insert(
"mod".to_owned(),
FunctionProperties::Elementary(Box::new(ElementaryProperties {
derivative_rule: None,
antiderivative_rule: None,
special_values: vec![SpecialValue {
input: "0".to_owned(),
output: Expression::integer(0),
latex_explanation: "a \\bmod m = 0 \\text{ when } a = 0".to_owned(),
}],
identities: Box::new(vec![]),
domain_range: Box::new(DomainRangeData {
domain: Domain::Integer,
range: Range::Integer,
singularities: vec![],
}),
wolfram_name: None,
periodicity: None, // Uses existing modular arithmetic
})),
);
}
/// Initialize prime-related functions
fn initialize_prime_functions(&mut self) {
// IS_PRIME function
self.properties.insert(
"is_prime".to_owned(),
FunctionProperties::Elementary(Box::new(ElementaryProperties {
derivative_rule: None,
antiderivative_rule: None,
special_values: vec![SpecialValue {
input: "2".to_owned(),
output: Expression::integer(1), // Use 1 for true, 0 for false
latex_explanation: "2 \\text{ is prime}".to_owned(),
}],
identities: Box::new(vec![]),
domain_range: Box::new(DomainRangeData {
domain: Domain::PositiveInteger,
range: Range::Integer,
singularities: vec![],
}),
wolfram_name: None,
periodicity: None, // Uses existing prime testing algorithms
})),
);
}
}