Bibliography for Roots of Quartic Equations

unabridged

 

  1. Reciprocal solution of a quartic equation.
    Mochimaru, Yoshihiro
    Int. J. Pure Appl. Math. 14 (2004), no. 2, 209--212, MathSciNet.  
  2. On the general solution of a quartic functional equation.
    Chung, Jukang K.; Sahoo, Prasanna K.
    Bull. Korean Math. Soc. 40 (2003), no. 4, 565--576, MathSciNet.  
  3. On the solutions of a family of quartic Thue equations.
    Togbé, Alain
    Math. Comp. 69 (2000), no. 230, 839--849, MathSciNet.  
  4. Method for finding roots of quartic equation with application to RS codes
    Yan, F.Y.; Ko, C.C.
    Electronics Letters, v 34, n 25, Dec 10, 1998, p 2399-2400, Compendex.
  5. Beyond the quartic equation.
    King, R. Bruce
    Birkhäuser Boston, Inc., Boston, MA, 1996. viii+149 pp., MathSciNet.  
  6. Complete solutions of a family of quartic Thue and index form equations.
    Mignotte, Maurice; Pethö, Attila; Roth, Ralf
    Math. Comp. 65 (1996), no. 213, 341--354, MathSciNet.  
  7. Periodic solutions of a quartic differential equation and Groebner bases
    Alwash, M.A.M.  
    Journal of Computational and Applied Mathematics, v 75, n 1, Nov 12, 1996, p 67-76, Compendex.
  8. Identities for the solution of cubic and quartic equations. (Spanish)
    Sáenz Cetina, José Leonardo
    Miscelánea Mat. No. 24 (1996), 39--43, MathSciNet.  
  9. 48 More Solutions of Martin Davis's Quaternary Quartic Equation  
    Daniel Shanks; Samuel S. Wagstaff, Jr.
    Mathematics of Computation, Vol. 64, No. 212 (Oct., 1995), pp. 1717-1731, Jstor.   
  10. Cardano's 'Ars magna' and the solutions of cubic and quartic equations (Spanish)  
    C. Romo Santos  
    Rev. Acad. Canaria Cienc. 7 (1) (1995), 187-201.
  11. Complete solution of a family of quartic Thue equations.
    Lettl, G.; Pethö, A.
    Abh. Math. Sem. Univ. Hamburg 65 (1995), 365--383, MathSciNet.  
  12. Khayyam, al-Biruni, Gauss, Archimedes, and quartic equations  
    Amir-Moéz, Ali R.
    Texas J. Sci. 46 (1994), no. 3, 241--257, MathSciNet.  
  13. Solving a quartic discriminant form equation.
    Smart, N. P.
    Publ. Math. Debrecen 43 (1993), no. 1-2, 29--39, MathSciNet.  
  14. Explicit solution of a class of quartic Thue equations.
    Tzanakis, Nikos
    Acta Arith. 64 (1993), no. 3, 271--283, MathSciNet.  
  15. An extension of Omar Khayyam's graphical solution of the cubic equation to the solution of the quartic
    Yardley, Peter D.
    Bull. Inst. Math. Appl. 27 (1991), no. 8-9, 173--174, MathSciNet.  
  16. Quartic equations and classification of Riemann tensors in general relativity.
    Åman, J. E.; d'Inverno, R. A.; Joly, G. C.; MacCallum, M. A. H.
    Gen. Relativity Gravitation 23 (1991), no. 9, 1023--1055, MathSciNet.  
  17. Complete solutions to families of quartic Thue equations.
    Pethö, Attila
    Math. Comp. 57 (1991), no. 196, 777--798, MathSciNet.  
  18. Errata to 'A unified approach for solving quadratic, cubic and quartic equations by radicals'
    Ungar, A.A.
    Computers & Mathematics with Applications, v 22, n 2, 1991, p 81, Compendex.  
  19. A unified approach for solving quadratic, cubic and quartic equations by radicals  
    Ungar, A. A.
    International Journal of Computer Mathematics Appl. 19 (1990), no. 12, 33--39, Compendex.
  20. On solving quartic equations over GF (2**m).
    Eier, R.; Lidl, R.
    Bull. Korean Math. Soc. 27 (1990), no. 1, 15--18, MathSciNet.  
  21. On quartic Thue equations with trivial solutions.
    Stroeker, R. J.
    Math. Comp. 52 (1989), no. 185, 175--187, MathSciNet.  
  22. An improved algorithm for quartic equation classification and Petrov classification.
    Letniowski, F. W.; McLenaghan, R. G.
    Gen. Relativity Gravitation 20 (1988), no. 5, 463--483, MathSciNet.  
  23. The exact probability that the roots of quadratic, cubic, and quartic equations are all real if the equation coefficients are random.
    Li, Hung C.
    Comm. Statist. Theory Methods 17 (1988), no. 2, 395--409, MathSciNet.  
  24. Algorithm For Solving Quartic Equations Over GF  (2**M)
    Manev, N. L.  
    IEEE, 1986, p 147, Compendex.
  25. Some quartic equations with only trivial solutions.
    Sinha, T. N.; Singh, M. M.
    Math. Student 53 (1985), no. 1-4, 239--242 (1987), MathSciNet.  
  26. Necessary and sufficient conditions for the existence of real roots of a quartic equation.
    Zeheb, E.
    Internat. J. Circuit Theory Appl. 10 (1982), no. 3, 289--291, MathSciNet.  
  27. Root Location Criteria For Quartic Equations
    Fuller, A. T.
    IEEE Transactions on Automatic Control, v AC-26, no. 3, (June 1981), p 777-782, Compendex.  
  28. Positivity And Nonnegativity Conditions Of A Quartic Equation And Related Problems
    Jury, E. I.; Mansour, M.
    IEEE Transactions on Automatic Control, v AC-26, no. 2, (April 1981), p 444-451, Compendex.
  29. Positivity and nonnegativity conditions of a quartic equation and related problems.
    Jury, E. I.; Mansour, M.
    Thirteenth Asilomar Conference on Circuits, Systems and Computers (Pacific Grove, Calif., 1979), pp. 469--472, IEEE, New York, 1980, MathSciNet.  
  30. Some quartic equations with only trivial integer solutions.
    Sinha, T. N.
    Math. Student 43 (1975), 61--64 (1976), MathSciNet.  
  31. L'école algébriste italienne du XVIe siècle et la résolution des équations des 3e et 4e degrés. (French)
    [The Italian algebra school of the 16th century and the solution of cubic and quartic equations]
    Speziali, P. Sciences of the Renaissance (Tours, 1965), pp. 107--120, De Pétrarque à Descartes, XXVII, Vrin, Paris, 1973, MathSciNet.  
  32. The Solution of a Certain Quartic Equation  
    B. Fisher
    Mathematics Magazine, Vol. 45, No. 2 (Mar., 1972), pp. 97-98, Jstor.   
  33. A note for finding complex roots of a special kind of quartic equation.
    Lee, F. A.
    J. Aerospace Sci. 27 1960 714--715, MathSciNet.  
  34. A note on the solution of quartic equations.
    Salzer, Herbert E.
    Math. Comput. 14 1960 279--281, MathSciNet.  
  35. Solvability of quartics by means of square roots.
    Borofsky, Samuel
    Amer. Math. Monthly 57, (1950). 248--250, MathSciNet.  
  36. Numerical solution of complex roots of quartic equations.
    Lin, Shih-Nge
    J. Math. Physics 26, (1948). 279--283, MathSciNet.  
  37. A comparison of methods for evaluating the complex roots of quartic equations.
    Sharp, Henry S.
    J. Math. Phys. Mass. Inst. Tech. 20, (1941). 243--258., MathSciNet.  
  38. On the Nature of the Roots of a Quartic Equation  
    Raymond Garver
    Mathematics News Letter, Vol. 7, No. 4 (Jan., 1933), pp. 6-8, Jstor.   
  39. Enrique Cruchaga's Solution of the Quartic Equation  
    Raymond Garver
    The American Mathematical Monthly, Vol. 37, No. 6 (Jun., 1930), pp. 303-304, Jstor.   
  40. Discussions: A Solution of the Quartic Equation  
    Raymond Garver
    The American Mathematical Monthly, Vol. 35, No. 10 (Dec., 1928), pp. 558-560, Jstor.   
  41. Graphical Discussion of the Roots of a Quartic Equation  
    E. L. Rees
    The American Mathematical Monthly, Vol. 29, No. 2 (Feb., 1922), pp. 51-55, Jstor.   
  42. The Asymptotic Equation and Satellite Conic of the Plane Quartic  
    Teresa Cohen
    American Journal of Mathematics, Vol. 38, No. 3 (Jul., 1916), pp. 325-336, Jstor.   
  43. On the Reciprocal Quartic Equation  
    R. L. Berger
    The American Mathematical Monthly, Vol. 15, No. 4 (Apr., 1908), pp. 85-87, Jstor.   
  44. The Galois Group of a Reciprocal Quartic Equation  
    L. E. Dickson
    The American Mathematical Monthly, Vol. 15, No. 4 (Apr., 1908), pp. 71-78, Jstor.   
  45. Condition in Terms of the Invariants of the Quartic that its Four Distinct Root-Points be Concyclic  
    T. E. McKinney
    The American Mathematical Monthly, Vol. 14, No. 2 (Feb., 1907), p. 23, Jstor.   
  46. A graphical method of deducing the criteria for the nature of the roots of cubic and quartic equations.
    Gaines, R. E.
    Ann. of Math. (2) 1 (1899/00), no. 1-4, 111--112, MathSciNet.  
  47. A Graphical Method of Deducing the Criteria for the Nature of the Roots of Cubic and Quartic Equations  
    R. E. Gaines
    The Annals of Mathematics, 2nd Ser., Vol. 1, No. 1/4 (1899), pp. 111-112, Jstor.   
  48. The Deduction of Final Formulas for the Algebraic Solution of the Quartic Equation   
    Mansfield Merriman
    American Journal of Mathematics, Vol. 14, No. 3 (Jul., 1892), pp. 237-245, Jstor.   
  49. On the Bicircular Quartic. Addition to Professor Casey's Memoir "On a New Form of Tangential Equation"  
    Professor Casey's; A. Cayley
    Philosophical Transactions of the Royal Society of London, Vol. 167 (1877), pp. 441-460, Jstor.   
  50. Solution of the Quartic Equation, x^4 + Ax + B = 0  
    A. M. Sawin
    The Annals of Mathematics, Vol. 1, No. 1 (Mar., 1884), pp. 14-15, Jstor.   
  51. On the Conditions for the Existence of Three Equal Roots, or of Two Pairs of Equal Roots, of a Binary Quartic or Quintic  
    A. Cayley
    Philosophical Transactions of the Royal Society of London, Vol. 158 (1868), pp. 577-588, Jstor.   
  52. Note by Professor Cayley on His Memoir on the Conditions for the Existence of Three Equal Roots, or of Two Pairs of Equal Roots, of a Binary Quartic or Quintic  
    Professor Cayley
    Proceedings of the Royal Society of London, Vol. 17 (1868), p. 314, Jstor.   
  53. On the Conditions for the Existence of Three Equal Roots, or of Two Pairs of Equal Roots of a Binary Quartic or Quintic. [Abstract]  
    A. Cayley
    Proceedings of the Royal Society of London, Vol. 16 (1867), p. 229, Jstor.   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2006