Solution formulas for cubic equations without or with constraints

Ting Zhao; Dongming Wang; Hoon Hong

doi:10.1016/j.jsc.2011.02.001

Solution formulas for cubic equations without or with constraints

Ting Zhao^*
, Dongming Wang
, Hoon Hong

^*Corresponding author for this work

LMIB & School of Mathematics and System Science
Beihang University
Laboratoire d'Informatique de Paris 6
Department of Mathematics
North Carolina State University

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

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.

Original language	English
Pages (from-to)	904-918
Number of pages	15
Journal	Journal of Symbolic Computation
Volume	46
Issue number	8
DOIs	https://doi.org/10.1016/j.jsc.2011.02.001
State	Published - Aug 2011
Externally published	Yes

Keywords

Constraint
Cubic polynomial
Root convention
Solution formula

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10.1016/j.jsc.2011.02.001

Cite this

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title = "Solution formulas for cubic equations without or with constraints",

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.",

keywords = "Constraint, Cubic polynomial, Root convention, Solution formula",

author = "Ting Zhao and Dongming Wang and Hoon Hong",

year = "2011",

month = aug,

doi = "10.1016/j.jsc.2011.02.001",

language = "英语",

volume = "46",

pages = "904--918",

journal = "Journal of Symbolic Computation",

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T1 - Solution formulas for cubic equations without or with constraints

AU - Zhao, Ting

AU - Wang, Dongming

AU - Hong, Hoon

PY - 2011/8

Y1 - 2011/8

N2 - 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.

AB - 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.

KW - Constraint

KW - Cubic polynomial

KW - Root convention

KW - Solution formula

UR - https://www.scopus.com/pages/publications/79955987898

U2 - 10.1016/j.jsc.2011.02.001

DO - 10.1016/j.jsc.2011.02.001

M3 - 文章

AN - SCOPUS:79955987898

SN - 0747-7171

VL - 46

SP - 904

EP - 918

JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

IS - 8

ER -

Solution formulas for cubic equations without or with constraints

Abstract

Keywords

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