Formal Puiseux Series

Manuel Eberl 🌐

February 17, 2021

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.


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.


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Session Formal_Puiseux_Series