Solution formulas for cubic equations without or with constraints

Authors:
Ting Zhao;Dongming Wang;Hoon Hong
Affiliations:
LMIBSKLSDESchool of Mathematics and Systems Science, Beihang University, Beijing 100191, China and Laboratoire dInformatique de Paris 6, Université Pierre et Marie CurieCNRS, 4 place JussieuB ...;Laboratoire dInformatique de Paris 6, Université Pierre et Marie CurieCNRS, 4 place JussieuBP 169, 75252 Paris cedex 05, France;Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC 27695-8205, USA
Venue:
Journal of Symbolic Computation
Year:
2011

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Abstract

We present a convention (for square/cubic root) which provides correct interpretations of the Lagrange formula for all cubic polynomial equations with real coefficients. Using this convention, we also present a real solution formula for the general cubic equation with real coefficients under equality and inequality constraints.