  
  
                                    [1X [5XToric[0m[1X [0m
  
  
             [1X A [5XGAP[0m[1X4 Package for computing with toric varieties   [0m
  
  
                                  Version 1.8
  
  
                                  May 3, 2012
  
  
                                 David Joyner  
  
  
  
  David Joyner  
      Email:    [7Xmailto:wdjoyner@gmail.com[0m
      Homepage: [7Xhttp://www.opensourcemath.org/toric/[0m
      Address:  Mathematics Department,
                U. S. Naval Academy,
                Annapolis, MD,
                21402 USA.
  
  
  
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  [1XCopyright[0m
  © 2004-2012 David Joyner.
  
  
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  [1XAcknowledgements[0m
  The code for the [5Xtoric[0m package was written during the summer of 2002. It was
  put  into  [5XGAP[0m package format in the summer of 2004. [5Xtoric[0m is released under
  the  GNU General Public License (GPL), version 2 or better (at your choice).
  This file is part of [5Xtoric[0m, though as documentation it is released under the
  GNU            Free           Documentation           License           (see
  [7Xhttp://www.gnu.org/licenses/licenses.html#FDL[0m).
  
  [5Xtoric[0m  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.
  
  [5Xtoric[0m  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
  [5Xtoric[0m; if not, write to the Free Software Foundation, Inc., 59 Temple Place,
  Suite 330, Boston, MA 02111-1307 USA
  
  For more details, see [7Xhttp://www.fsf.org/licenses/gpl.html[0m.
  
  This  documentation  was  prepared with the [5XGAPDoc[0m package of Frank L\"ubeck
  and Max Neunh\"offer.
  
  
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  [1XContents (toric)[0X
  
  1 Introduction
    1.1 Introduction to the [5Xtoric[0m 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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