GAP (HeLP) - Chapter 1: Introduction

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1 Introduction

### 1 Introduction

The purpose of this package is to provide functionalities to work with torsion units in (integral) group rings. It implements a method that was developed by I.S. Luthar and I.B.S. Passi in [LP89] and which was extended by M. Hertweck in [Her07]. These names also constitute the name of the method, suggested by A. Konovalov: Hertweck-Luthar-Passi. The theory behind the method is briefly described in Chapter 5 and also in the survey article [BM18].

The package uses the software 4ti2 [tea] and/or normaliz [BIR+] and hence is only properly working on systems which have at least one of the two installed. normaliz is usually automatically installed with the GAP-package NormalizInterface, see the documentation of that package for details. For more information on 4ti2 and to download it, please visit www.4ti2.de. To interact with these external software the package makes use of the 4ti2-Interface and normaliz-Interface written by S. Gutsche, C. Söger and M. Horn. The 4ti2-Interface in turn uses the package IO, that needs a C-part to be compiled; see the readme-file or the documentation of the IO-package for details. The package also provides the possibility to use redund from the lrslib software [Avi], to remove redundant inequalities before solving the system, which might speed up the computations significantly when 4ti2 is used. However, it is not a requirement to have lrslib installed. If the above mentioned preconditions are fulfilled, one just has to copy the HeLP-package in the GAP pkg-directory. Now the package can be loaded by typing `LoadPackage("HeLP");` during a GAP-session. If the HeLP-package doesn't work properly on your computer, you might want to check Section 6.1 for some trouble shooting.

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