Projects per year

### Abstract

In considering the reliability of numerical programs,

it is normal to “limit our study to the semantics

dealing with numerical precision” (Martel, 2005). On the other

hand, there is a great deal of work on the reliability of

programs that essentially ignores the numerics. The thesis

of this paper is that there is a class of problems that fall

between these two, which could be described as “does the lowlevel

arithmetic implement the high-level mathematics”. Many

of these problems arise because mathematics, particularly

the mathematics of the complex numbers, is more difficult

than expected: for example the complex function log is not

continuous, writing down a program to compute an inverse

function is more complicated than just solving an equation,

and many algebraic simplification rules are not universally

valid.

The good news is that these problems are theoretically

capable of being solved, and are practically close to being solved,

but not yet solved, in several real-world examples. However,

there is still a long way to go

it is normal to “limit our study to the semantics

dealing with numerical precision” (Martel, 2005). On the other

hand, there is a great deal of work on the reliability of

programs that essentially ignores the numerics. The thesis

of this paper is that there is a class of problems that fall

between these two, which could be described as “does the lowlevel

arithmetic implement the high-level mathematics”. Many

of these problems arise because mathematics, particularly

the mathematics of the complex numbers, is more difficult

than expected: for example the complex function log is not

continuous, writing down a program to compute an inverse

function is more complicated than just solving an equation,

and many algebraic simplification rules are not universally

valid.

The good news is that these problems are theoretically

capable of being solved, and are practically close to being solved,

but not yet solved, in several real-world examples. However,

there is still a long way to go

Original language | English |
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Title of host publication | Proceedings of SYNASC 2012: 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing |

Place of Publication | Piscataway |

Publisher | IEEE |

Pages | 83-88 |

Number of pages | 6 |

ISBN (Print) | 9781467350266 |

DOIs | |

Publication status | Published - 2012 |

Event | SYNASC 2012: 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing - Timisoara, Romania Duration: 25 Sep 2012 → 28 Sep 2012 |

### Conference

Conference | SYNASC 2012: 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing |
---|---|

Country | Romania |

City | Timisoara |

Period | 25/09/12 → 28/09/12 |

## Fingerprint Dive into the research topics of 'Program Verification in the presence of complex numbers, functions with branch cuts etc'. 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

Davenport, J., Bradford, R., England, M., & Wilson, D. (2012). Program Verification in the presence of complex numbers, functions with branch cuts etc. In

*Proceedings of SYNASC 2012: 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing*(pp. 83-88). IEEE. https://doi.org/10.1109/SYNASC.2012.68