On Roots of Apolar Polynomials

  • Kristofer Jorgenson Sul Ross State University
Keywords: Apolar Polynomials, Commutative Rings, Invariant Theory, Polynomial Equations

Abstract

This article continues the exploration of methods based on that of Gian-Carlo Rota that involve apolar invariants used for solving cubic and quintic polynomial equations. These polynomial invariants were disclosed previously as an alternative to and to clarify the umbral method of Rota. Theorems are proved regarding quintic, cubic, and
quadratic polynomials that are pairwise apolar in that they satisfy particular polynomial apolar invariants

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Author Biography

Kristofer Jorgenson, Sul Ross State University
Sul Ross State University, Box C-18 Alpine, TX 79832 United States of America

References

Baki ́c. R. “On the Apolar Polynomials”Kragujevac Journal of Mathematics, Volume 38, No. 2 (2014) 269-271.[2] Dunham, William Journey Through Genius: The Great Theorems of MathematicsJohn Wiley & Sons, Inc.1990 ISBN 978-0-14-014739-1

Jorgenson, K.D. “The Rota Method for Solving Polynomial Equations: A Modern Application of InvariantTheory”.International Journal of Pure and Applied Mathematics, Volume 89, No. 2 (2013) 153-172. DOI:http://dx.doi.org/10.12732/ijpam.v89i2.4

Kung, J.P.S., Rota, G.C., “The Invariant Theory of Binary Forms”, Bulletin (New Series) of the American Mathematical Society,10(1984), 27-85.ISSN: 0273-0979 DOI: http://dx.doi.org/10.1090/S0273-0979-1984-15188-7.

Rota, G.C., “Invariant Theory, Old and New”, Colloquium Lecture delivered at the Annual Meeting of the American Mathematical Society and Mathematical Association of America, Baltimore MD, January 8, 1998.Publicly distributed manuscript (but otherwise unpublished).

Stewart, Ian, Galois Theory, 3rd Edition Chapman & Hall/CRC 2004 ISBN 1-58488-393-6

Published
2019-12-21
How to Cite
Jorgenson, K. (2019). On Roots of Apolar Polynomials. MathLAB Journal, 4, 137-152. Retrieved from https://purkh.com/index.php/mathlab/article/view/522
Section
Research Articles