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http://dx.doi.org/10.5831/HMJ.2010.32.3.493

RESULTANT AND DISCRIMINANT OF ITERATE POLYNOMIALS  

Choi, Eun-Mi (Dept. Math. HanNam University)
Publication Information
Honam Mathematical Journal / v.32, no.3, 2010 , pp. 493-514 More about this Journal
Abstract
The resultant and discriminant of composite polynomials were studied by McKay and Wang using some algebraic properties. In this paper we study the resultant and discriminant of iterate polynomials. We shall use elementary computations of matrices and block matrix determinants; this could provide not only the values but also the visual structure of resultant and discriminant from elementary matrix calculation.
Keywords
Resultant; Discriminant; Iterated polynomial;
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  • Reference
1 H. Cohen. Resultants and Discriminants. A Course in Computational Algebraic Number Theory. New York, Springer Verlag, (1993) 119-123.
2 D. Cox, J. Little, D. OShea. Using Algebraic Geometry. New York, Springer Verlag, 1998.
3 R.N. Goldman, T. Sederberg, D. Anderson. Vector elimination: a technique for the implicitization, inversion and intersection of planar parametric rational polynomial curves. Comput. Aided Geom. Des., 1, (1984) 327-356.   DOI   ScienceOn
4 R. Jones, The density of prime divisors in the arithmetic dynamics of quadratic polynomilas, J. London Math. Soc. 78 (2), (2008) 523-544.   DOI   ScienceOn
5 J.T. Kajiya. Ray tracing parametric patches. Proceedings of SIGGRAPH (1982) 245-254.
6 D. Manocha, J. Canny. Multipolynomial resultant algorithms. J. Symbolic Computation, 15(2), (1993) 99-122.   DOI   ScienceOn
7 J.H. McKay, S.S. Wang, A chain rule for the resultant of two polynomials, Arch. Math., 53, (1989) 347-351.   DOI
8 R. W. K. Odoni, The Galois theory of iterates and composites of polynomials, Proc. London Math. Soc., 51 (1985) 385-414.   DOI
9 R. W. K. Odoni, Realising wreath products of cyclic groups as Galois groups, Mathematika, 35, (1988) 101-113.   DOI
10 J.R. Silvester. Determinants of block matrices. Math. Gazette, 84 (501), Nov. (2000) 460-467.   DOI
11 S.H. Weintraub, Galois Theory, New York, Springer Verlag, 2005.
12 B.L.van der Waerden, Algebra, Vol 1. New York, 1970. (translat from German edition, 1966)