# QEta package¶

## Abstract¶

The **QEta** package is a collection of programs written in the
FriCAS computer algebra system that allow to compute with
Dedekind eta-functions
and related \(q\)-series where \(q=e^{2\pi i \tau}\).

Furthermore, we provide a number of functions connected to the theory of modular functions.

## Overview¶

The **QEta** package started with an implementation of the AB
algorithm from the article An algorithmic approach to
Ramanujan-Kolberg identities
by Silviu Radu
and the *Samba* algorithm from the article Dancing Samba with
Ramanujan Partition Congruences by Ralf Hemmecke in
addition it implements the algorithm from the article Construction of
all Polynomial Relations among Dedekind Eta Functions of Level N by Hemmecke and Radu to
compute all polynomial relations of Dedekind eta-functions of a
certain level.

The underlying theory of the programs is described in the above articles which are also available as RISC reports 15-14, 16-06, 18-03.

Further material is in the git repository of the project.

This package requires a version of FriCAS that is compiled from at least SVN revision 2328, ie, where Gröbner basis computations do no longer require variable names.

The scripts usually use:

```
)set output linear on
```

which is coded in the file 1d.spad
in the master-hemmecke branch
of a clone of the FriCAS
git repository. However, this
*linear* output form is not absolutely necessary.