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