Abstract
The classical Newton polygon method for the local resolution of algebraic equations in one variable can be extended to the case of multi-variate equations of the type f(y) = 0, f ∈ ℂ [x 1,..., x N ][y]. For this purpose we will use a generalization of the Newton polygon - the Newton polyhedron - and a generalization of Puiseux series for several variables.
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Beringer, F., Richard-Jung, F. (2003). Multi-variate Polynomials and Newton-Puiseux Expansions. In: Winkler, F., Langer, U. (eds) Symbolic and Numerical Scientific Computation. SNSC 2001. Lecture Notes in Computer Science, vol 2630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45084-X_11
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DOI: https://doi.org/10.1007/3-540-45084-X_11
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