Abstract
Algorithms and software for two new methods of solving polynomial equations based on constructing a convex polygon are described. The first method approximately solves the equations using the Hadamard polygon. The second method makes it possible to find branches of an algebraic curve in the vicinity of its singular points and in the vicinity of infinity using the Newton polygon and sketch real algebraic curves on the plane. The corresponding geometries and computer algebra algorithms for analyzing arbitrarily complicated cases are discussed.
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Bruno, A.D., Batkhin, A.B. Algorithms and Programs for Calculating the Roots of Polynomial of One or Two Variables. Program Comput Soft 47, 353–373 (2021). https://doi.org/10.1134/S0361768821050042
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DOI: https://doi.org/10.1134/S0361768821050042