vi Contents
4. Applications: Sums of Squares and Rational Approxima-
tions 298
5. Sphere Packings 302
6. The Minkowski-Hlawka Theorem 305
7. The Dual Lattice 309
8. The Flatness Theorem 315
9. Constructing a Short Vector and a Reduced Basis 319
10. Remarks 324
Chapter VIII. Lattice Points and Polyhedra 325
1. Generating Functions and Simple Rational Cones 325
2. Generating Functions and Rational Cones 330
3. Generating Functions and Rational Polyhedra 335
4. Brion’s Theorem 341
5. The Ehrhart Polynomial of a Polytope 349
6. Example: Totally Unimodular Polytopes 353
7. Remarks 356
Bibliography 357
Index 363
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