Inhalt
[ 404CANCSSIV23 ] VL (*)Symbolic Summation and Integration
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| Es ist eine neuere Version 2025W dieser LV im Curriculum Masterstudium Artificial Intelligence 2025W vorhanden. |
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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 2023W |
| Ziele |
(*)Crucial algorithms for symbolic summation and integration are elaborated and general toolboxes are presented to tackle non-trivial sums and integrals that arise in technical and natural sciences.
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| Lehrinhalte |
(*)Symbolic summation in the setting of difference rings, symbolic integration in the setting of differential fields, solving linear recurrences and differential equations in finite terms
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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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| Lehrinhalte wechselnd? |
Nein |
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| Präsenzlehrveranstaltung |
| Teilungsziffer |
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| Zuteilungsverfahren |
Direktzuteilung |
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