### Abstract

Original language | English |
---|---|

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 |
---|---|

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 |

### Fingerprint

### Keywords

- branch cuts
- symbolic computation
- simplification

### Cite this

*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). Berlin: Springer. https://doi.org/10.1007/978-3-642-39320-4_9

**Understanding branch cuts of expressions.** / England, Matthew; Bradford, Russell; Davenport, James H; Wilson, David.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Intelligent Computer Mathematics: MKM, Calculemus, DML, and Systems and Projects 2013, Held as Part of CICM 2013, Bath, UK, July 8-12, 2013. Proceedings.*Lecture Notes in Computer Science, vol. 7961, Springer, Berlin, pp. 136-151, Conferences on Intelligent Computer Mathematics: CICM 2013, Bath, UK United Kingdom, 7/07/13. https://doi.org/10.1007/978-3-642-39320-4_9

}

TY - GEN

T1 - Understanding branch cuts of expressions

AU - England, Matthew

AU - Bradford, Russell

AU - Davenport, James H

AU - Wilson, David

N1 - The functionality described in the paper is built into Maple, version 17 and above, where it is used by default for queries to the FunctionAdvisor. The code provided here (in the .mpl file) offers users of earlier versions some of the functionality. It is designed for use in Maple 16 and may also work with those earlier versions which still contain the FunctionAdvisor. For information on working with the code see the Appendix of the paper, the help in Maple 17 and the introductory worksheet provided here (the .mw file).

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - branch cuts

KW - symbolic computation

KW - simplification

UR - http://www.cicm-conference.org/2013/

UR - http://dx.doi.org/10.1007/978-3-642-39320-4_9

U2 - 10.1007/978-3-642-39320-4_9

DO - 10.1007/978-3-642-39320-4_9

M3 - Conference contribution

SN - 9783642393198

T3 - Lecture Notes in Computer Science

SP - 136

EP - 151

BT - Intelligent Computer Mathematics

A2 - Carette, Jacques

A2 - Aspinall, David

A2 - Lange, Christoph

A2 - Sojka, Petr

A2 - Windsteiger, Wolfgang

PB - Springer

CY - Berlin

ER -