QEta installation

Requirement FriCAS

QEta is built on FriCAS. If you do not yet have it follow the instructions at FriCAS Installation for an installation in a Linux environment.

Installation steps for the QEta package

Clone the git repository and compile the sources.

FDIR=$HOME/fricas
mkdir -p $FDIR
cd $FDIR
git clone https://github.com/hemmecke/qeta.git
cd $FDIR/qeta
make compile-spad

(optional) Adapt some directories

Adapt directories in the test files (extension .input-test) so that they match your setting.

This is only needed if you intend to work with these test/demo files. These files belong to the QEta testsuite, but might be interesting to look into if you want to learn how to call some command.

FDIR=$HOME/fricas
q="$FDIR/qeta"
cd $q
for f in $(ls test/*.input-test); do \
  echo $f; \
  sed -i "s|^)read /home/.*jfricas-test-support.*|)read $q/input/jfricas-test-support.input )quiet|" $f; \
done
sed -i "s|^)cd g/qeta/tmp|)cd $q/tmp|" $q/input/jfricas-test-support.input

Look, for example, into RogersRamanujanContinuedFraction.input-test where we show that for the Rogers-Ramanujan continued fraction

\[\begin{gather*} R(q) = q^{\frac15} \dfrac{1}{1+\dfrac{q}{1+\dfrac{q^2}{1+\dfrac{q^3}{1+\ddots}}}} = q^{\frac15} \frac{(q,q^4;q^5)_\infty}{(q^2,q^3;q^5)_\infty} = \frac{\eta_{5,1}(\tau)}{\eta_{5,2}(\tau)} \end{gather*}\]

we have the identity

\[\begin{align*} U_5\!\left(\frac{R(q)^5}{R(q^5)}\right) &= U_5\!\left(\frac{R(q^5)}{R(q)^5}\right) \end{align*}\]

where \(U_5\) is the operator that acts as follows:

\[\begin{gather*} U_5\left(\sum_{n=k}^\infty a(n)q^n\right) = \sum_{n=\lceil k/5 \rceil}^\infty a(5n)q^n \end{gather*}\]

Install 4ti2

QEta builds on 4ti2 in order to solve integer linear problems.

sudo apt install 4ti2

(optional) Install SageMath

QEta uses a command (run from the terminal)

make LEVELS='6 9' er

to compute relations among eta quotients of certain levels. QEta employs the Gröbner engine (slimgb) of the Singular computer algebra system through its SageMath interface, since this seems to be more efficient than the built-in FriCAS Gröbner engine.

Inside a FriCAS session QEta does not (yet) reach out to call function from SageMath, i.e. installation of SageMath is not strictly needed and may just consume diskspace on your computer. The following command may take 20 min to complete.

apt install sagemath