### Abstract

A complete classification of the individual types of singular points is given for irreducible real sextic curves. This classification is derived by using the computer algebra system Maple. There are 191 types of singular points for real irreducible sextic curves. We clarify that the classification is based on computing just enough of the Puiseux expansion to separate the branches. A significant portion of the proof consists of a sequence of large symbolic computations that can be done nicely using Maple.

Original language | English |
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Pages (from-to) | 805-862 |

Number of pages | 58 |

Journal | Acta Applicandae Mathematicae |

Volume | 110 |

Issue number | 2 |

DOIs | |

State | Published - May 2010 |

### Keywords

- Newton polygon
- Puiseux expansion
- Sextic curve
- Singular point

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## Cite this

Weinberg, D. A., & Willis, N. J. (2010). Singular points of real sextic curves i.

*Acta Applicandae Mathematicae*,*110*(2), 805-862. https://doi.org/10.1007/s10440-009-9477-6