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Historical analysis of System of Equations-Focused on Resultant

연립방정식 풀이의 역사발생적 고찰-종결식을 중심으로

Choi, Eun Mi
최은미

  • Received : 2013.04.27
  • Accepted : 2013.05.21
  • Published : 2013.05.31

Abstract

The history of finding solutions of linear equations went back to some thousand years ago, and has been steadily developed to solve systems of higher degree polynomials. The method to eliminate variables came into use around the 17th and 18th century. This technique has been extended to the resultant theory that was laid in the 19th century by outstanding mathematicians as Euler, Sylvester, and B$\acute{e}$zout. In this paper we discuss the historical reflection about the development of solving system of polynomials. We add a special emphasis on E. B$\acute{e}$zout who gave the first account on the resultant which is a generalization of discriminant and Gauss elimination method.

Keywords

resultant;nonlinear system of polynomials

References

  1. K. Fink, A brief history of mathematics , Cosimo classics, NY, 2007.
  2. 김연식 외,"수학교육학 용어 해설 (3)", 대한수학교육학회 수학교육학연구, 5(2) (1995), 227-239.
  3. 신경희,"선형대수의 역사와 교육과정—벡터공간과 행렬을 중심으로", 교과교육학연구, 8(1) (2004), 65-82.
  4. 심상길,"교과서 연립방정식 단원에 지시된 수학사의 소재 분석 및 교수학적 분석", 대한수학교육학회 학교수학, 11(3) (2009), 415-429.
  5. 조성민,"역사발생적 관점에서 본 행렬 지도의 재음미", 한국학교수학회논문집, 12(1) (2009), 99-114.
  6. J. O'Connor, E. Robertson and Etienne Bezout,"Mac Tutor history of mathematics archive", http://www-history.mcs.st-andrews.ac.uk/Biographies/Bezout.html.
  7. J. Gathen and J. Gerhard,Modern computer algebra, Cambridge University Press, 2003.
  8. A. Morozov and S. Shakirov,"New and old results in resultant theory", Theoretical and Mathematical Physics, 163(2) (2010), 587-617. https://doi.org/10.1007/s11232-010-0044-0
  9. M. Trott, The mathematica guide book for symbolics, Springer-Verlag, NY., 2006, retrieve from www.mathematicaguidebooks.org.
  10. H. Wimmer,"On the history of the Bezoutian and the resultant matrix", Linear Algebra Appl., 128(1990), 27-34. https://doi.org/10.1016/0024-3795(90)90280-P