# Searching for the simple poles of a function

### Description

Searches for the simple poles of a function by finding the zeros of its reciprocal (definition of a pole). The user has to specify the range of random numbers that are used as the inital values of the search since the process employs optimisations.

### Usage

1 2 |

### Arguments

`func` |
A function whose simple poles to be sought. |

`R` |
The radius of the disc on the complex plane within which random numbers are drawn to start the optimisation process. |

`track.plot` |
If |

`control` |
This is a list of search settings: |

### Details

The search employs optimisations that searches for the zeros of the function's reciprocal. As such, the initial value used in the search process is crucial. To ensure that the initial values are drawn uniformly, the user specified range (the radius of the disc) is segmented.
The segmentation is done by having concentric circles and these circles are further divided into sectors. The radii of the concentric circles are determined in the way that all sectors are of the same size.
Since the argument `unit.concentric` refers to the number of concentric circles in a unit circle, the number of segments in the range of initial values will be `R`*\times*`unit.concentric`*\times*`sector` and the total number of random numbers to be drawn as initial values is then `R`*\times*`unit.concentric`*\times*`sector`*\times*`draw`.
This way of determining the number of concentric circle allows the number of segments to be adjusted when changing the radius of the range,`R`.

### Value

A list of simple poles. `NULL` is returned if no simple poles found.

### Author(s)

Char Leung

### Examples

1 |