jesterTOV.utils.cubic_root_for_proton_fraction

cubic_root_for_proton_fraction(coefficients)

Vectorized version of cubic_root_for_proton_fraction. Takes similar arguments as cubic_root_for_proton_fraction but with additional array axes over which cubic_root_for_proton_fraction is mapped.

Original documentation:

Solve cubic equation for proton fraction in beta-equilibrium.

This function solves the cubic equation that arises from the beta-equilibrium condition in neutron star matter using Cardano’s formula for exact analytical solution. The cubic equation has the form ax^3 + bx^2 + cx + d = 0, where the coefficients are related to the symmetry energy and electron chemical potential.

This function is vectorized to handle multiple coefficient sets simultaneously for different densities.

Args:

coefficients: Array of cubic polynomial coefficients [a, b, c, d]

Returns:

Array of three roots of the cubic equation (may be complex)