  
  
                                    [1X [5XToric[105X [101X
  
  
             [1X A [5XGAP[105X4 Package for computing with toric varieties   [101X
  
  
                                  Version 1.8
  
  
                                  May 3, 2012
  
  
                                 David Joyner  
  
  
  
  David Joyner  
      Email:    [7Xmailto:wdjoyner@gmail.com[107X
      Homepage: [7Xhttp://www.opensourcemath.org/toric/[107X
      Address:  [33X[0;14YMathematics Department,[133X
                [33X[0;14YU. S. Naval Academy,[133X
                [33X[0;14YAnnapolis, MD,[133X
                [33X[0;14Y21402 USA.[133X
  
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2004-2012 David Joyner.[133X
  
  
  -------------------------------------------------------
  [1XAcknowledgements[101X
  [33X[0;0YThe code for the [5Xtoric[105X package was written during the summer of 2002. It was
  put  into  [5XGAP[105X package format in the summer of 2004. [5Xtoric[105X is released under
  the  GNU General Public License (GPL), version 2 or better (at your choice).
  This file is part of [5Xtoric[105X, though as documentation it is released under the
  GNU            Free           Documentation           License           (see
  [7Xhttp://www.gnu.org/licenses/licenses.html#FDL[107X).[133X
  
  [33X[0;0Y[5Xtoric[105X  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.[133X
  
  [33X[0;0Y[5Xtoric[105X  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.[133X
  
  [33X[0;0YYou should have received a copy of the GNU General Public License along with
  [5Xtoric[105X; if not, write to the Free Software Foundation, Inc., 59 Temple Place,
  Suite 330, Boston, MA 02111-1307 USA[133X
  
  [33X[0;0YFor more details, see [7Xhttp://www.fsf.org/licenses/gpl.html[107X.[133X
  
  [33X[0;0YThis  documentation  was  prepared with the [5XGAPDoc[105X package of Frank L\"ubeck
  and Max Neunh\"offer.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (toric)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YIntroduction to the [5Xtoric[105X package[133X
    1.2 [33X[0;0YIntroduction to constructing toric varieties[133X
      1.2-1 [33X[0;0YGeneralities[133X
      1.2-2 [33X[0;0YBasic combinatorial geometry constructions[133X
      1.2-3 [33X[0;0YBasic affine toric variety constructions[133X
      1.2-4 [33X[0;0YRiemann-Roch spaces and related constructions[133X
  2 [33X[0;0YCones and semigroups[133X
    2.1 [33X[0;0YCones[133X
      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 [33X[0;0YSemigroups[133X
      2.2-1 DualSemigroupGenerators
  3 [33X[0;0YAffine toric varieties[133X
    3.1 [33X[0;0YIdeals defining affine toric varieties[133X
      3.1-1 IdealAffineToricVariety
      3.1-2 EmbeddingAffineToricVariety
  4 [33X[0;0YToric varieties [22XX(∆)[122X[133X
    4.1 [33X[0;0YRiemann-Roch spaces[133X
      4.1-1 DivisorPolytope
      4.1-2 DivisorPolytopeLatticePoints
      4.1-3 RiemannRochBasis
    4.2 [33X[0;0YTopological invariants[133X
      4.2-1 EulerCharacteristic
      4.2-2 BettiNumberToric
    4.3 [33X[0;0YPoints over a finite field[133X
      4.3-1 CardinalityOfToricVariety
  
  
  [32X
