Inhalt
[ 404CANCSSIV23 ] VL (*)Symbolic Summation and Integration
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| (*) Leider ist diese Information in Deutsch nicht verfügbar. |
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| Workload |
Ausbildungslevel |
Studienfachbereich |
VerantwortlicheR |
Semesterstunden |
Anbietende Uni |
| 4,5 ECTS |
M - Master |
Mathematik |
Carsten Schneider |
3 SSt |
Johannes Kepler Universität Linz |
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| Detailinformationen |
| Quellcurriculum |
Masterstudium Computational Mathematics 2025W |
| Lernergebnisse |
Kompetenzen |
| (*)The students get acquainted with advanced algorithms for symbolic summation and integration and learn how the existing toolboxes work to tackle non-trivial sums and integrals that arise in technical and natural sciences.
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| Fertigkeiten |
Kenntnisse |
(*)- Working with difference rings and fields in the setting of symbolic summation [K2,K3];
- Working with differential fields in the setting of symbolic integration [K2,K3];
- Modeling of special functions and sequences in difference and differential rings/fields [K2,K3,K4];
- Understanding of recursive algorithms in nested ring/field extensions (parameterized telescoping for summation and integration) [K4,K5];
- Applications of the tools to expressions in terms of special functions in technical and natural sciences [K3,K5]
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(*)Difference rings and fields, differential fields, summation and integration theory, Risch's algorithm, Karr's algorithm and its generalizations, special functions.
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| Beurteilungskriterien |
(*)Oral or written examination at the end of the semester
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| Lehrmethoden |
(*)Classical black board lecture supplemented with calculations in computer algebra systems
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| Abhaltungssprache |
Englisch |
| Literatur |
(*)- M. Bronstein: Symbolic Integration.
- K. Geddes, S. Czapor, and G. Labahn: Algorithms for Computer Algebra.
- S.A. Abramov, M. Bronstein, M. Petkovsek, C. Schneider: On Rational and Hypergeometric Solutions of Linear Ordinary Difference Equations in ΠΣ-field extensions. J. Symb. Comput. 107, pp. 23-66. arXiv:2005.04944 [cs.SC].
- C. Schneider Term: Algebras, Canonical Representations and Difference Ring Theory for Symbolic Summation. In: Anti-Differentiation and the Calculation of Feynman Amplitudes, pp. 423-485. 2021. Springer, arXiv:2102.01471 [cs.SC]
- C. Schneider: A Difference Ring Theory for Symbolic Summation. J. Symb. Comput. 72, pp. 82-127. 2016. arXiv:1408.2776 [cs.SC]
- C. Schneider: Summation Theory II: Characterizations of RΠΣ-extensions and algorithmic aspects. J. Symb. Comput. 80(3), pp. 616-664. 2017. arXiv:1603.04285 [cs.SC]
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Nein |
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| Teilungsziffer |
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Direktzuteilung |
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