By Michael Joswig (auth.), Michael Joswig, Nobuki Takayama (eds.)

ISBN-10: 3642055397

ISBN-13: 9783642055393

ISBN-10: 3662051486

ISBN-13: 9783662051481

The ebook comprises surveys and study papers on mathematical software program and algorithms. the typical thread is that the sector of mathematical purposes lies at the border among algebra and geometry. themes contain polyhedral geometry, removal idea, algebraic surfaces, GrÖ"obner bases, triangulations of aspect units and the mutual dating. This variety is observed via the abundance of accessible software program platforms which regularly deal with in basic terms designated mathematical features. for this reason the volumes different concentration is on suggestions in the direction of the combination of mathematical software program platforms. This comprises low-level and XML established high-level communique channels in addition to basic frameworks for modular systems.

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**Example text**

Beyond Polytopes. . . . . . . . . . . . . . . . . . . . . . . 31. EULER CHARACTERISTIC. . . . . . . . . . . . . . . . .. 32. f- VECTOR OF SIMPLICIAL COMPLEXES. . . . . . . . . . 33. HOMOLOGY. . . . . . . . . . . . . . . . . . . . . . .. 34. SHELLABILITY. . . . . . . . . . . . . . . . . . . . . .. 35. PARTITIONABILITY. . . . . . . . . . . . . . . . .

Lee. Subdivisions and triangulations of polytopes. In J. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, pages 271-290. CRC Press, 1997. 26. J. Matousek. Lectures on Discrete Geometry. Springer, 2002. 27. J. Pfeifle and J. Rambau. Computing triangulations using oriented matroids. In this volume, pages 49-75. 28. K. Polthier, S. Khadem, E. Preuss, and U. Reitebuch. 21. de. 29. A. Schrijver. Theory of linear and integer programming. Wiley-Interscience Series in Discrete Mathematics.

VERTEX ENUMERATION. . . . . . . . . . . . . . . . . .. 2. FACET BNUMERATION. . . . . . . . . . . . . . . . . . .. 3. POLYTOPE VERIFICATION . . . . . . . . . . . . . . . . . 4. POLYTOPE CONTAINMENT. . . . . . . . . . . . . . . . .. 5. FACE LATTICE OF GEOMETRIC POLYTOPES. . . . . . . . .. 6. DEGENERACY TESTING . . . . . . . . . . . . . . . . . . 7. NUMBER OF VERTICES.. . . . . . . . . . . . .

### Algebra, Geometry and Software Systems by Michael Joswig (auth.), Michael Joswig, Nobuki Takayama (eds.)

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