Function solve_numeric_system_with 

pub fn solve_numeric_system_with(
    eqs: &[Ex],
    vars: &[Ex],
    x0: &[f64],
    opts: &NewtonOpts,
) -> Result<Vec<f64>, SymplexError>

Newton’s method with explicit NewtonOpts.

The Jacobian is computed symbolically (crate::matrix::jacobian) and compiled to native closures where possible. Each step solves J·Δ = −F by Gaussian elimination with partial pivoting; with damping on, the step is halved until the residual norm decreases.

Errors

• SymplexError::InvalidArgument if the system is not square or x0 has the wrong length.
• SymplexError::ComputationFailed if the Jacobian becomes singular or the iteration does not converge within max_iter steps; the message reports the final residual norm and iterate.