Function factor_char2_isometry 

pub fn factor_char2_isometry<S: FiniteChar2Field>(
    metric: &Metric<S>,
    matrix: &[Vec<S>],
) -> Result<Char2SymmetryFactorization<S>, Char2FactorizationError>

Factor an isometry of a regular characteristic-two quadratic space into vector symmetries and return an exact certificate.

Automatic root selection uses FiniteChar2Field’s finite enumeration. The invariant and certificate checker remain generic through char2_spinor_norm and certify_char2_symmetry_factorization.

The algorithm uses Wall’s residual space and Wall form. A nonalternating Wall form is semi-orthogonalized directly. In the alternating case, one or two auxiliary anisotropic symmetries convert it to a decomposable nonalternating case; those symmetries remain in the final exact product.