SINGULAR version 4-1
University of Kaiserslautern
Department of Mathematics and Centre for Computer Algebra
Authors: W. Decker, G.-M. Greuel, G. Pfister, H. Schoenemann

Copyright © 1986-2019

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation (version 2 or version 3 of the License).

Some single files have a copyright given within the file: Singular/links/ndbm.* (BSD)

The following software modules shipped with SINGULAR have their own copyright: the omalloc library, the readline library, the GNU Multiple Precision Library (GMP), NTL: A Library for doing Number Theory (NTL), Flint: Fast Library for Number Theory, the Singular-Factory library, the Singular-Factory library, the Singular-libfac library, surfex, and, for the Windows distributions, the Cygwin DLL and the Cygwin tools (Cygwin), and the XEmacs editor (XEmacs).

Their copyrights and licenses can be found in the accompanying files COPYING which are distributed along with these packages. (Since version 3-0-3 of SINGULAR, all parts have GPL or LGPL as (one of) their licences.)

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA (see GPL)

Please send any comments or bug reports to

If you want to be informed of new releases, please register as a SINGULAR user by sending an email to with subject line register and body containing the following data: your name, email address, organisation, country and platform(s).

For information on how to cite SINGULAR see

You can also support SINGULAR by informing us about your result obtained by using SINGULAR.


The latest information regarding the status of SINGULAR is always available from


The development of SINGULAR is directed and coordinated by Wolfram Decker, Gert-Martin Greuel, Gerhard Pfister, and Hans Schönemann.

Current devteams: Abdus Salam School of Mathematical Sciences in Lahore, BTU Cottbus, Center for Advanced Security Research Darmstadt (CASED), FU Berlin, Isfahan University of Technology, Mathematisches Forschunginstitut Oberwolfach, Oklahoma State University, RWTH Aachen, Universidad de Buenos Aires, Université de Versailles Saint-Quentin-en-Yvelines, University of Göttingen, University of Hannover, University of La Laguna and University of Valladolid.

Current SINGULAR developers: Wolfram Decker, Gert-Martin Greuel, Gerhard Pfister, Hans Schönemann,

Shawki Al-Rashed, Daniel Andres, Mohamed Barakat, Isabel Bermejo, Muhammad Asan Binyamin, René Birkner, Rocio Blanco, Xenia Bogomolec, Michael Brickenstein, Stanislav Bulygin, Antonio Campillo, Raza Choudery, Alexander Dreyer, Christian Eder, Santiago Encinas, Jose Ignacio Farran, Anne Frühbis-Krüger, Rosa de Frutos, Eva Garcia-Llorente, Ignacio Garcia-Marco, Christian Haase, Amir Hashemi, Fernando Hernando, Bradford Hovinen, Nazeran Idress, Anders Jensen, Lars Kastner, Junaid Alan Khan, Kai Krüger, Santiago Laplagne, Grégoire Lecerf, Martin Lee, Viktor Levandovskyy, Benjamin Lorenz, Christoph Lossen, Thomas Markwig, Hannah Markwig, Irene Marquez, Bernd Martin, Edgar Martinez, Martin Monerjan, Francisco Monserrat, Oleksandr Motsak, Andreas Paffenholz, Maria Jesus Pisabarro, Diego Ruano, Afshan Sadiq, Kristina Schindelar, Mathias Schulze, Frank Seelisch, Andreas Steenpaß, Stefan Steidel, Grischa Studzinski, Katharina Werner and Eva Zerz.

Further contributions to SINGULAR have been made by: Martin Albrecht, Olaf Bachmann, Muhammad Ahsan Banyamin, Thomas Bauer, Thomas Bayer, Markus Becker, J. Boehm, Gergo Gyula Borus, Winfried Bruns, Fernando Hernando Carrillo, Victor Castellanos, Nadine Cremer, Michael Cuntz, Kai Dehmann, Christian Dingler, Marcin Dumnicki, Stephan Endraß, Vladimir Gerdt, Philippe Gimenez, Christian Gorzel, Hubert Grassmann, Jan Hackfeld, Agnes Heydtmann, Dietmar Hillebrand, Tobias Hirsch, Markus Hochstetter, N. Idrees, Manuel Kauers, Simon King, Sebastian Jambor, Oliver Labs, Anen Lakhal, Martin Lamm, Francisco Javier Lobillo, Christoph Mang, Michael Meßollen, Andrea Mindnich, Antonio Montes, Jorge Martin Morales, Thomas Nüßler, Wolfgang Neumann, Markus Perling, Wilfried Pohl, Adrian Popescu, Tetyana Povalyaeva, Carlos Rabelo, Philipp Renner, J.-J.Salazar-Gonzalez, Alfredo Sanchez-Navarro, Ivor Saynisch, Jens Schmidt, Thomas Siebert, Christof Soeger, Silke Spang, William Stein, Rüdiger Stobbe, Henrik Strohmayer, Christian Stussak, Imade Sulandra, Akira Suzuki, Christine Theis, Enrique Tobis, Alberto Vigneron-Tenorio, Moritz Wenk, Eric Westenberger, Tim Wichmann, Oliver Wienand, Denis Yanovich and Oleksandr Yena.

We should like to acknowledge the financial support given by the Volkswagen-Stiftung, the Deutsche Forschungsgemeinschaft and the Stiftung für Innovation des Landes Rheinland-Pfalz to the SINGULAR project.

SINGULAR is supported by Project B5 of SFB-TRR 195 'Symbolic Tools in Mathematics and their Application'.

 Singular version 4-1-1, 2018, generated by texi2html.