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1. |
Record Nr. |
UNISA996466644503316 |
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Autore |
Bokowski Jürgen |
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Titolo |
Computational synthetic geometry / / Jurgen Bokowski, Bernd Sturmfels |
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Pubbl/distr/stampa |
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Berlin ; ; Heidelberg : , : Springer-Verlag, , [1989] |
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©1989 |
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ISBN |
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Edizione |
[1st ed. 1989.] |
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Descrizione fisica |
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1 online resource (VIII, 172 p.) |
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Collana |
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Lecture Notes in Mathematics ; ; 1355 |
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Disciplina |
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Soggetti |
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Geometry - Data processing |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di contenuto |
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Preliminaries -- On the existence of algorithms -- Combinatorial and algebraic methods -- Algebraic criteria for geometric realizability -- Geometric methods -- Recent topological results -- Preprocessing methods -- On the finding of polyheadral manifolds -- Matroids and chirotopes as algebraic varieties. |
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Sommario/riassunto |
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Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to students with graduate level background in mathematics, and will serve professional geometers and computer scientists as an introduction and motivation for further research. |
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2. |
Record Nr. |
UNINA9910747592203321 |
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Autore |
Cecotti Sergio |
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Titolo |
Introduction to String Theory / / by Sergio Cecotti |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023 |
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ISBN |
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Edizione |
[1st ed. 2023.] |
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Descrizione fisica |
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1 online resource (846 pages) |
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Collana |
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Theoretical and Mathematical Physics, , 1864-5887 |
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Disciplina |
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Soggetti |
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Mathematical physics |
Gravitation |
Particles (Nuclear physics) |
Manifolds (Mathematics) |
Theoretical, Mathematical and Computational Physics |
Classical and Quantum Gravity |
Particle Physics |
Manifolds and Cell Complexes |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Chapter 1. The Polyakov path integral -- Chapter 2. Introduction to 2d conformal field theories -- Chapter 3. Spectrum, vertices, and BRST quantization -- Chapter 4. Tree and one-loop amplitudes in the bosonic string -- Chapter 5. Consistent 10d superstring, modular invariance, and all that -- Chapter 6. The Heterotic string: part I -- Chapter 7. Toroidal compactifications and T-duality (bosonic string) -- Chapter 8. The Heterotic string: part II -- Chapter 9. Superstring interactions and anomalies -- Chapter 10. Superstring D-branes -- Chapter 11. Strings at strong coupling -- Chapter 12. Calabi-Yau compactifications. Appendix. |
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Sommario/riassunto |
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Graduate students typically enter into courses on string theory having little to no familiarity with the mathematical background so crucial to the discipline. As such, this book, based on lecture notes, edited and expanded, from the graduate course taught by the author at SISSA and BIMSA, places particular emphasis on said mathematical background. The target audience for the book includes students of both theoretical |
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physics and mathematics. This explains the book’s "strange" style: on the one hand, it is highly didactic and explicit, with a host of examples for the physicists, but, in addition, there are also almost 100 separate technical boxes, appendices, and starred sections, in which matters discussed in the main text are put into a broader mathematical perspective, while deeper and more rigorous points of view (particularly those from the modern era) are presented. The boxes also serve to further shore up the reader’s understanding of the underlying math. In writing this book, the author’s goal was not to achieve any sort of definitive conciseness, opting instead for clarity and "completeness". To this end, several arguments are presented more than once from different viewpoints and in varying contexts. . |
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