admcycles 0.2

Tautological ring on Mbar_g,n

admcycles is a SageMath module to compute with the tautological ring of the moduli spaces of complex curves.

Prerequisites

Make sure that SageMath is installed on your computer. Detailed installation instructions for different operating systems are available here and at the Sage-website.

Installation

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, see below. If the installation instructions below should fail, see below how to use it without installation.

• if you manually installed Sage by downloading it from the website or compiled it yourself, then run:

  $ sage -pip install admcycles --user

• if you have archlinux and installed the sagemath package (via pacman), then run:

  $ pip2 install admcycles --user

• if you have Ubuntu or Debian and installed the sagemath package (via apt) then run:

  $ source /usr/share/sagemath/bin/sage-env
  $ pip install admcycles --user

In all the commands above, the option --user is optional and makes it so that it will install the module into your user space. If you want a system install, remove this option. On the other hand, if you want to install the latest (development) version of admcycles and have the versioning software git installed, replace admcycles in the commands above by git+https://gitlab.com/jo314schmitt/admcycles.

Use without installation

To use the package without installing, download the package as a zip-file either from PyPI or from gitlab. Unpack the zip-file, creating a folder admcycles-master, which should contain files such as setup.py. In the future, when you want to use admcycles, you should run sage from the folder admcycles-master. So if the full path of this folder is /u/You/Downloads/admcycles, you should start the Sage-session below by:

sage: cd /u/You/Downloads/admcycles
sage: from admcycles import *

If 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.

To start using admcycles, start a Sage-session in the command line (e.g. by opening the command line and typing sage). 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()
1/24

Example

A simple computation:

sage: from admcycles import *

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_4^2

Build documentation

To build the documentation, go in the repository docs/ and then run in a console:

$ sage -sh
(sage-sh)$ make html
(sage-sh)$ exit

The documentation is then available in docs/build/

Running doctests

To run doctests, use the following command:

$ sage -t --force-lib admcycles/ docs/source

If it succeeds, you should see a message:

All tests passed!

License

admcycles 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. See http://www.gnu.org/licenses/.

Authors

• Aaron Pixton

• Johannes Schmitt

• Vincent Delecroix

• Jason van Zelm