SINGULAR version 3-1-2 University of Kaiserslautern Department of Mathematics and Centre for Computer Algebra Authors: G.-M. Greuel, G. Pfister, H. Schoenemann Copyright (C) 1986-2010 *NOTICE* 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/ndbm.* (BSD), kernel/htmlhelp.h (LGPL 2.1+) The following software used 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), the Multi Protocol library (MP), 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 yourself as a SINGULAR user by using the registration form on the SINGULAR homepage `http://www.singular.uni-kl.de'. If for some reason you cannot access the registration form, you can also register 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 the citation of SINGULAR see `http://www.singular.uni-kl.de/how_to_cite.html', for information on how to cite Singular. You can also support SINGULAR by informing us about your result obtained by using SINGULAR. Availability ============ The latest information about SINGULAR is always available from `http://www.singular.uni-kl.de'. Acknowledgements ================ The development of SINGULAR is directed and coordinated by Gert-Martin Greuel, Gerhard Pfister, and Hans Scho"nemann. Currently, the SINGULAR team has the following members: Michael Brickenstein, Wolfram Decker, Alexander Dreyer, Anne Fru"hbis-Kru"ger, Kai Kru"ger, Viktor Levandovskyy, Oleksandr Motsak, Mathias Schulze, and Oliver Wienand. Former members of the SINGULAR team are: Olaf Bachmann, Christoph Lossen, Wolfgang Neumann, Wilfred Pohl, Jens Schmidt, Thomas Siebert, Ru"diger Stobbe, Eric Westenberger and Tim Wichmann. Further contributions to SINGULAR were made by: Daniel Andres, Thomas Bayer, Isabelle Bermejo, Markus Becker, Stas Bulygin, Nadine Cremer, Kai Dehmann, Marcin Dumnicki, Stephan Endrass, Jose Ignacio Farran, I. Garcia-Marco, Vladimir Gerdt, Philippe Gimenez, Christian Gorzel, Hubert Grassmann, Amir Hashemi, Fernando Hernando, Agnes Heydtmann, Dietmar Hillebrand, Tobias Hirsch, Markus Hochstetter, Manuel Kauers, Simon King, Anen Lakhal, Martin Lamm, Santiago Laplagne, Gregoire Lecerf, Francisco Javier Lobillo, Christoph Mang, Thomas Markwig, Bernd Martin, Michael Messollen, Andrea Mindnich, Jorge Martin Morales, Thomas Nu"ssler, Tetyana Povalyaeva, Carlos Rabelo, J.-J. Salazar-Gonzalez, Alfredo Sanchez-Navarro, Ivor Saynisch, Kristina Schindelar, Silke Spang, Stefan Steidel, Henrik Strohmayer, Christian Stussak, Imade Sulandra, Akira Suzuki, Christine Theis, Enrique Tobis, Maryna Viazovska, Alberto Vigneron-Tenorio, Moritz Wenk, Denis Yanovich, Oleksandr Iena. We should like to acknowledge the financial support given by the Volkswagen-Stiftung, the Deutsche Forschungsgemeinschaft and the Stiftung fu"r Innovation des Landes Rheinland-Pfalz to the SINGULAR project.