Toric
  
  
              A GAP4 Package for computing with toric varieties  
  
  
                                  Version 1.4
  
  
                               February 26, 2008
  
  
                                 David Joyner  
  
  
  
  David Joyner  
      Email:    mailto:wdjoyner@gmail.com
      Homepage: http://www.opensourcemath.org/toric/
      Address:  Mathematics Department,
                U. S. Naval Academy,
                Annapolis, MD,
                21402 USA.
  
  
  
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  Copyright
  © 2004-2005 David Joyner.
  
  
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  Acknowledgements
  The code for the toric package was written during the summer of 2002. It was
  put  into  GAP package format in the summer of 2004. toric is released under
  the  GNU General Public License (GPL). This file is part of toric, though as
  documentation  it  is released under the GNU Free Documentation License (see
  http://www.gnu.org/licenses/licenses.html#FDL).
  
  toric  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;  either  version 2 of the License, or (at your option) any later
  version.
  
  toric  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
  toric; if not, write to the Free Software Foundation, Inc., 59 Temple Place,
  Suite 330, Boston, MA 02111-1307 USA
  
  For more details, see http://www.fsf.org/licenses/gpl.html.
  
  This  documentation  was  prepared with the GAPDoc package of Frank L\"ubeck
  and Max Neunh\"offer.
  
  
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  Content (toric)
  
  1. Introduction
    1.1 Introduction to the toric package
    1.2 Introduction to constructing toric varieties
      1.2-1 Generalities
      1.2-2 Basic combinatorial geometry constructions
      1.2-3 Basic affine toric variety constructions
      1.2-4 Riemann-Roch spaces and related constructions
  2. Cones and semigroups
    2.1 Cones
      2.1-1 InsideCone
      2.1-2 InDualCone
      2.1-3 PolytopeLatticePoints
      2.1-4 Faces
      2.1-5 ConesOfFan
      2.1-6 NumberOfConesOfFan
      2.1-7 ToricStar
    2.2 Semigroups
      2.2-1 DualSemigroupGenerators
  3. Affine toric varieties
    3.1 Ideals defining affine toric varieties
      3.1-1 IdealAffineToricVariety
      3.1-2 EmbeddingAffineToricVariety
  4. Toric varieties X(Delta)
    4.1 Riemann-Roch spaces
      4.1-1 DivisorPolytope
      4.1-2 DivisorPolytopeLatticePoints
      4.1-3 RiemannRochBasis
    4.2 Topological invariants
      4.2-1 EulerCharacteristic
      4.2-2 BettiNumberToric
    4.3 Points over a finite field
      4.3-1 CardinalityOfToricVariety
  
  
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