Projects per year

### Abstract

We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse trigonometric functions. Understanding these cuts is essential for working with the single-valued counterparts, the common approach to encoding multi-valued functions in computer algebra systems. While the defining choices are usually simple (typically portions of either the real or imaginary axes) the cuts induced by the expression may be surprisingly complicated. We have made explicit and implemented techniques for calculating the cuts in the computer algebra programme Maple. We discuss the issues raised, classifying the different cuts produced. The techniques have been gathered in the BranchCuts package, along with tools for visualising the cuts. The package is included in Maple 17 as part of the FunctionAdvisor tool.

Original language | English |
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Title of host publication | Intelligent Computer Mathematics |

Subtitle of host publication | MKM, Calculemus, DML, and Systems and Projects 2013, Held as Part of CICM 2013, Bath, UK, July 8-12, 2013. Proceedings |

Editors | Jacques Carette, David Aspinall, Christoph Lange, Petr Sojka, Wolfgang Windsteiger |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 136-151 |

Number of pages | 16 |

ISBN (Electronic) | 9783642393204 |

ISBN (Print) | 9783642393198 |

DOIs | |

Publication status | Published - 2013 |

Event | Conferences on Intelligent Computer Mathematics: CICM 2013 - Bath, UK United Kingdom Duration: 7 Jul 2013 → 11 Jul 2013 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer |

Volume | 7961 |

ISSN (Print) | 0302-9743 |

### Conference

Conference | Conferences on Intelligent Computer Mathematics: CICM 2013 |
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Country | UK United Kingdom |

City | Bath |

Period | 7/07/13 → 11/07/13 |

### Keywords

- branch cuts
- symbolic computation
- simplification

## Fingerprint Dive into the research topics of 'Understanding branch cuts of expressions'. Together they form a unique fingerprint.

## Projects

- 1 Finished

### Real Geometry and Connectedness via Triangular Description

Davenport, J., Bradford, R., England, M. & Wilson, D.

Engineering and Physical Sciences Research Council

1/10/11 → 31/12/15

Project: Research council

## Cite this

England, M., Bradford, R., Davenport, J. H., & Wilson, D. (2013). Understanding branch cuts of expressions. In J. Carette, D. Aspinall, C. Lange, P. Sojka, & W. Windsteiger (Eds.),

*Intelligent Computer Mathematics: MKM, Calculemus, DML, and Systems and Projects 2013, Held as Part of CICM 2013, Bath, UK, July 8-12, 2013. Proceedings*(pp. 136-151). (Lecture Notes in Computer Science; Vol. 7961). Springer. https://doi.org/10.1007/978-3-642-39320-4_9