[1X[5XToric[0X[0X [1XA [5XGAP[0X4 Package for computing with toric varieties  [0X Version 1.4 February 26, 2008 David Joyner  David Joyner  Email: [7Xmailto:wdjoyner@gmail.com[0X Homepage: [7Xhttp://www.opensourcemath.org/toric/[0X Address: Mathematics Department, U. S. Naval Academy, Annapolis, MD, 21402 USA. ------------------------------------------------------- [1XCopyright[0X © 2004-2005 David Joyner. ------------------------------------------------------- [1XAcknowledgements[0X The code for the [5Xtoric[0X package was written during the summer of 2002. It was put into [5XGAP[0X package format in the summer of 2004. [5Xtoric[0X is released under the GNU General Public License (GPL). This file is part of [5Xtoric[0X, though as documentation it is released under the GNU Free Documentation License (see [7Xhttp://www.gnu.org/licenses/licenses.html#FDL[0X). [5Xtoric[0X 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[0X 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[0X; 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[0X. This documentation was prepared with the [5XGAPDoc[0X package of Frank L\"ubeck and Max Neunh\"offer. ------------------------------------------------------- [1XContent (toric)[0X 1. Introduction 1.1 Introduction to the [5Xtoric[0X 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 -------------------------------------------------------