Function polynomial_determinant 

pub fn polynomial_determinant<const D: usize>(
    matrix: &[[SparsePolynomial; D]; D],
    budget: PolynomialDeterminantBudget,
) -> Result<SparsePolynomial, LaError>

Available on crate feature exact only.

Compute the complete exact determinant polynomial of a borrowed square array.

Supports orders 0..=8; the empty determinant is the constant one. Singular polynomial matrices return the zero polynomial successfully. All cancellation terms are retained, so SparsePolynomial::leading_term is valid only after the complete calculation succeeds. There is no early sign fallback, truncation, division, rounding or conditioning-dependent numerical error.

The kernel allocates 2^D sparse states (at most 256) and consumes each partial once all its predecessors have contributed. Inputs are neither cloned nor changed. At most one new stored term is created per charged product, plus the initial constant one. Rational sizes, allocator overhead, and caller-owned inputs are outside these combinatorial bounds; allocation failure follows Rust’s allocator behavior. Limits do not promise a byte or wall-clock bound.

Errors

In order: LaError::UnsupportedDimension for D > 8, LaError::PolynomialBudgetExceeded for insufficient structural transitions, then product-budget or LaError::PolynomialExponentOverflow failures during evaluation. An overflowing intermediate exponent is an error even if later contributions could cancel it. Errors discard partial results and leave the input reusable. Traversal is increasing subset mask, column, left exponent, then right exponent, making budget accounting deterministic.

Examples

use la_stack::prelude::*;
let one = SparsePolynomial::try_from_terms([(0, BigRational::from_integer(1.into()))])?;
let perturbed = SparsePolynomial::try_from_terms([
    (0, BigRational::from_integer(1.into())),
    (3, BigRational::new(1.into(), 2.into())),
])?;
let matrix = [[one.clone(), one.clone()], [one, perturbed]];
let determinant = polynomial_determinant(&matrix, PolynomialDeterminantBudget {
    max_subset_transitions: 4,
    max_term_products: 5,
})?;
assert_eq!(determinant.leading_term(), Some((3, &BigRational::new(1.into(), 2.into()))));