Package: admcycles
admcyclesadmcycles is aSageMathmodule to compute with
the tautological ring of the moduli spaces of complex curves. You can install
it on top of a SageMath installation on your computer (see the instructions
below). You can alternatively use one of the online services below that have
admcycles already installed:SageMathCell: An online service for
SageMath computations that does not require authentification.CoCalc: A complete computation environment that
offers a free plan subscription (with limited resources).admcycles includes theSageMathmodule diffstrata
to compute with the tautological ring of the moduli space of multi-scale
differentials, a compactification of strata of flat surfaces. It is particularly
tailored towards computing Euler characteristics of these spaces.Detailed information on the package is contained in the documentsadmcycles – a Sage package for calculations in the tautological ring of the
moduli space of stable curves [arXiv:2002.01709]diffstrata – a Sage package for calculations in the tautological ring of the
moduli space of Abelian differentials [arXiv:2006.12815]online documentationNEW: Online database with tautological relations (Feb 2023)The latest version of admcycles includes an automatedonline lookupof pre-calculated tautological relations (seethe list of available cases).
By default, if you attempt a calculation that needs tautological relations, the program will first try to look them up in your local storage (in the folder.sage/admcycles). If not found there, the program will check the above database and download the relations to your computer in case they are available. If this fails as well, the program will then calculate the relations itself.If you would like to deactivate this online lookup, execute the following lines in a Sage session:sage: from admcycles.admcycles import set_online_lookup_default
sage: set_online_lookup_default(False)If you have calculated and stored relations that are not yet in our database, we would be happy if you reach out so we can integrate them!InstallationPrerequisitesMake sure thatSageMathversion 9.0 or later
is installed on your computer. Detailed installation instructions for
different operating systems are availablehereand on the
SageMath website. If you need to use admcycles with an older version of SageMath,
useadmcycles version 1.3.2.All the command below must be run inside a console (the last character of the
prompt is usally a$). On Windows this is calledSageMath Shellwhile
on linux and MacOS this is often referred to as aterminal.Inside the console, we assume that the commandsagelaunches a Sage
session (whose prompt is usuallysage:). To quit the Sage session
typequitand pressEnter.Installation with pip (the Python package manager)The most convenient way to use admcycles is to add the package to your
Sage installation. The exact procedure for this depends on your operating
system and how you installed Sage. If the pip installation fails, see
the sectionsManual installation with piporUse without installationbelow.If you manually installed Sage by downloading it from the website, then run
in a shell console:$ sage -pip install admcycles --userHere, the--useris an optional argument topipwhich, when
provided, will install admcycles not inside the Sage folder but in your home
directory.If you have a linux distribution and installed the sagemath package via your
package manager then run in a shell console:$ pip install admcycles --userThepipcommand above might have to be changed topip2orpip3depending on your system. Also, on Debian/Ubuntu systems, the following step
might be necessary before running the above command:$ source /usr/share/sagemath/bin/sage-envManual installation with pipThe automatic installation with pip from SectionInstallation with pipmight
fail. One common reason is the lack of SSL support of the SageMath binaries. In
such situation you can follow the procedure below that bypass the connection ofpipto the web.Download the admcycles package as atar.gz-file or.zipfile either fromPyPIor fromgitlab.Inside a shell console run:$ sage -pip install /where/is/the/package.tar.gz --userHere, the--useris an optional argument topipwhich, when
provided, will install admcycles not inside the Sage folder but in your home
directory.Installation of the development versionIf you want to install the development version, you need to have the
versioning softwaregitinstalled. The only change in the procedure
is to replaceadmcyclesin the any of the command above bygit+https://gitlab.com/modulispaces/admcycles.UpgradeIf you have already installed admcycles and a new version appears on PyPI, you
can update your installation by appending the option--upgradeabove.Use without installationTo use the package without installing, download the package as a.zipor.tar.gz-file either fromPyPIor
fromgitlab.
Unpack the.zipor.tar.gzfile. This creates a folder which should
contain a filesetup.py. In order to use the
module, you need to run Sage from this folder. For example, if the full path of
this folder is/u/You/Downloads/admcycles, you could do:$ cd /u/You/Downloads/admcycles
$ sageOr directly inside a Sage session:sage: cd /u/You/Downloads/admcyclesIf you run Sage in Windows using cygwin, the path above should be a cygwin path
and will looks something like/cygdrive/c/Users/You/Downloads/admcycles-master.ExampleTo start using admcycles, start a Sage session (either in the command line, or
a Jupyter notebook, or inside one of the online services). Then type:sage: from admcycles import *To try a first computation, you can compute the degree of the class kappa_1 on
Mbar_{1,1} by:sage: kappaclass(1,1,1).evaluate()
1/24You can have a look at the above computation directly inSageMathCell.Here is a more advanced computation:sage: t1 = 3*sepbdiv(1,(1,2),3,4) - psiclass(4,3,4)^2
sage: t1
Graph :      [1, 2] [[1, 2, 5], [3, 4, 6]] [(5, 6)]
Polynomial : 3*
<BLANKLINE>
Graph :      [3] [[1, 2, 3, 4]] []
Polynomial : (-1)*psi_4^2To use diffstrata, the package must be imported separately. Type:sage: from admcycles.diffstrata import *To try a first computation, you can compute the Euler characteristic of the
minimal stratum H(2) in genus 2:sage: X = Stratum((2,))
sage: X.euler_characteristic()
-1/40Here is a more advanced computation:sage: X = Stratum((1,1))
sage: (X.xi^2 * X.psi(1) * X.psi(2)).evaluate()
-1/720Building documentationThe documentation is available online athttps://modulispaces.gitlab.io/admcycles/You can alternatively build the documentation as follows. Go in the repository
docs/ and then run in a console:$ sage -sh
(sage-sh)$ make html
(sage-sh)$ exitThe documentation is then available in the folder docs/build/html/. Note that you
need the packagenbsphinxto compile
the full documentation including the example Jupyter notebooks. On most systems, you
should be able to install nbsphinx by typing:$ sage -pip install nbsphinxRunning doctestsTo run doctests, use the following command:$ sage -t --force-lib admcycles/ docs/sourceIf it succeeds, you should see a message:All tests passed!Licenseadmcycles is distributed under the terms of the GNU General Public License (GPL)
published by the Free Software Foundation; either version 2 of
the License, or (at your option) any later version. Seehttp://www.gnu.org/licenses/.AuthorsAaron PixtonJohannes SchmittVincent DelecroixJason van ZelmJonathan ZachhuberFundingJohannes Schmitt was supported by the grant SNF-200020162928 and has received funding
from the European Research Council (ERC) under the European Union Horizon 2020 research
and innovation programme (grant agreement No 786580). He also profited from the SNF Early
Postdoc.Mobility grant 184245 and also wants to thank the Max Planck Institute for Mathematics
in Bonn for its hospitality.
Vincent Delecroix was a guest of the Max-Planck Institut and then of the Hausdorff Institut
for Mathematics during the development of the project.
Jason van Zelm was supported by the Einstein Foundation Berlin during the course of this
work.