11. This looks inconveniently like a quartic with two real and two complex solutions. 12. It can also easily be generalized to cubic, quartic and higher power residues. 13. Finding the distance of closest approach of two ellipses involves solving a quartic equation. 14. For example the solution to the integral of the exponential of a quartic polynomial is 15. In the homogeneous quartic equation for the torus, 16. There exist more complicated algebraic solutions for the general cubic equation and quartic equation. 17. The catalecticant of a quartic form is the resultant of its second partial derivatives. 18. The Klein group can be understood in terms of the Lagrange resolvents of the quartic . 19. There are also formulas for quartic polynomials which can be used in the same way. 20. This gives the Klein quartic a Riemannian metric of constant curvature that it inherits from.
