On the approximate roots of polynomials
Janusz Gwoździewicz ; Arkadiusz Płoski
Annales Polonici Mathematici, Tome 62 (1995), p. 199-210 / Harvested from The Polish Digital Mathematics Library
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We give a simplified approach to the Abhyankar-Moh theory of approximate roots. Our considerations are based on properties of the intersection multiplicity of local curves.

Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:262335 
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     journal = {Annales Polonici Mathematici},
     volume = {62},
     year = {1995},
     pages = {199-210},
     zbl = {0826.13012},
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Janusz Gwoździewicz; Arkadiusz Płoski. On the approximate roots of polynomials. Annales Polonici Mathematici, Tome 62 (1995) pp. 199-210. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv60z3p199bwm/

[000] [1] S. S. Abhyankar, Expansion Techniques in Algebraic Geometry, Tata Inst. Fund. Research, Bombay, 1977. | Zbl 0818.14001

[001] [2] S. S. Abhyankar and T. Moh, Newton-Puiseux expansion and generalized Tschirnhausen transformation, J. Reine Angew. Math. 260 (1973), 47-83; 261 (1973), 29-54. | Zbl 0272.12102

[002] [3] S. S. Abhyankar and T. Moh, Embeddings of the line in the plane, ibid. 276 (1975), 148-166. | Zbl 0332.14004

[003] [4] R. Ephraim, Special polars and curves with one place at infinity, in: Proc. Sympos. Pure Math. 40, Part I, Amer. Math. Soc., 1985, 353-359.

[004] [5] J. Gwoździewicz and A. Płoski, On the Merle formula for polar invariants, Bull. Soc. Sci. Lettres Łódź 41 (7) (1991), 61-67. | Zbl 0893.32006

[005] [6] M. Merle, Invariants polaires des courbes planes, Invent. Math. 41 (1977), 103-111. | Zbl 0371.14003

[006] [7] T. T. Moh, On the concept of approximate roots for algebra, J. Algebra 65 (1980), 347-360. | Zbl 0437.13004

[007] [8] T. T. Moh, On two fundamental theorems for the concept of approximate roots, J. Math. Soc. Japan 34 (1982), 637-652. | Zbl 0528.12015

[008] [9] A. Płoski, Bézout's theorem for affine curves with one branch at infinity, Univ. Iagell. Acta Math. 28 (1991), 77-80. | Zbl 0759.14023

[009] [10] O. Zariski, Le problème des modules pour les branches planes, Centre de Mathématiques de l'Ecole Polytechnique, 1973. | Zbl 0317.14004