### Abstract

Bifurcation theory studies the behavior of multiple solutions of nonlinear (differential) equations when parameters in these equations are varied, and describes how the number and type of these solutions change. It is a domain of applied mathematics which uses concepts from such diverse fields as functional analysis, group representations, ideal theory and many others. For real, e.g. physically motivated problems, the calculations necessary to determine even the simplest bifurcations become excessively complicated. Therefore, a project to build a package “bifurcation and singularity theory” in computer algebra is presented. Specifically, Gröbner bases are used to determine the codimension of a singularity, thereby extending the Buchberger Algorithm to modules. Also, a program in SMP is described, which permits determining whether a given function g is contact equivalent to a polynomial normal form h for one dimensional bifurcation problems up to codimension three.

Original language | English (US) |
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Title of host publication | EUROCAL 1985 - European Conference on Computer Algebra, Proceedings |

Publisher | Springer Verlag |

Pages | 126-137 |

Number of pages | 12 |

ISBN (Print) | 9783540159841 |

DOIs | |

State | Published - Jan 1 1985 |

Externally published | Yes |

Event | European Conference on Computer Algebra, EUROCAL 1985 - Linz, Austria Duration: Apr 1 1985 → Apr 3 1985 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 204 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | European Conference on Computer Algebra, EUROCAL 1985 |
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Country | Austria |

City | Linz |

Period | 4/1/85 → 4/3/85 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*EUROCAL 1985 - European Conference on Computer Algebra, Proceedings*(pp. 126-137). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 204 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-15984-3_245