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//! Commutativity tracking for expressions
//!
//! Supports noncommutative algebra (matrices, operators, quaternions) while
//! maintaining default commutative behavior for scalars.
//!
//! Commutativity is computed on-demand from symbol types, not stored in expressions.
/// Commutativity of an expression or operation
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
pub enum Commutativity {
/// Operation is commutative (a*b = b*a)
/// Examples: scalar multiplication, addition
Commutative,
/// Operation is noncommutative (a*b may not equal b*a)
/// Examples: matrix multiplication, operator multiplication, quaternion multiplication
Noncommutative,
}
impl Commutativity {
/// Can factors be sorted during canonicalization?
///
/// Returns true only if commutativity is guaranteed.
pub fn can_sort(self) -> bool {
matches!(self, Commutativity::Commutative)
}
/// Combine commutativity of multiple factors
///
/// Rule: If ANY factor is noncommutative, the entire product is noncommutative.
/// Only if ALL factors are commutative is the product commutative.
///
/// # Examples
///
/// ```
/// use mathhook_core::core::commutativity::Commutativity;
///
/// // All commutative → result commutative
/// let factors = vec![Commutativity::Commutative, Commutativity::Commutative];
/// assert_eq!(Commutativity::combine(factors), Commutativity::Commutative);
///
/// // Any noncommutative → result noncommutative
/// let factors = vec![Commutativity::Commutative, Commutativity::Noncommutative];
/// assert_eq!(Commutativity::combine(factors), Commutativity::Noncommutative);
/// ```
pub fn combine<I>(factors: I) -> Self
where
I: IntoIterator<Item = Self>,
{
for comm in factors {
if comm == Commutativity::Noncommutative {
return Commutativity::Noncommutative;
}
}
Commutativity::Commutative
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_commutativity_can_sort() {
assert!(Commutativity::Commutative.can_sort());
assert!(!Commutativity::Noncommutative.can_sort());
}
#[test]
fn test_combine_all_commutative() {
let factors = vec![Commutativity::Commutative, Commutativity::Commutative];
assert_eq!(Commutativity::combine(factors), Commutativity::Commutative);
}
#[test]
fn test_combine_any_noncommutative() {
let factors = vec![Commutativity::Commutative, Commutativity::Noncommutative];
assert_eq!(
Commutativity::combine(factors),
Commutativity::Noncommutative
);
}
#[test]
fn test_combine_all_noncommutative() {
let factors = vec![Commutativity::Noncommutative, Commutativity::Noncommutative];
assert_eq!(
Commutativity::combine(factors),
Commutativity::Noncommutative
);
}
#[test]
fn test_combine_empty() {
let factors: Vec<Commutativity> = vec![];
assert_eq!(Commutativity::combine(factors), Commutativity::Commutative);
}
}