# Formal Puiseux Series

 Title: Formal Puiseux Series Author: Manuel Eberl Submission date: 2021-02-17 Abstract: Formal Puiseux series are generalisations of formal power series and formal Laurent series that also allow for fractional exponents. They have the following general form: $\sum_{i=N}^\infty a_{i/d} X^{i/d}$ where N is an integer and d is a positive integer. This entry defines these series including their basic algebraic properties. Furthermore, it proves the Newton–Puiseux Theorem, namely that the Puiseux series over an algebraically closed field of characteristic 0 are also algebraically closed. BibTeX: @article{Formal_Puiseux_Series-AFP, author = {Manuel Eberl}, title = {Formal Puiseux Series}, journal = {Archive of Formal Proofs}, month = feb, year = 2021, note = {\url{https://isa-afp.org/entries/Formal_Puiseux_Series.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: Polynomial_Interpolation