Inhalt
[ 404CANCSSIV23 ] VL Symbolic Summation and Integration
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| Es ist eine neuere Version 2025W dieser LV im Curriculum Master's programme Artificial Intelligence 2025W vorhanden. |
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| Workload |
Education level |
Study areas |
Responsible person |
Hours per week |
Coordinating university |
| 4,5 ECTS |
M - Master's programme |
Mathematics |
Carsten Schneider |
3 hpw |
Johannes Kepler University Linz |
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| Detailed information |
| Original study plan |
Master's programme Computational Mathematics 2023W |
| Objectives |
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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| Subject |
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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| Criteria for evaluation |
Oral or written examination at the end of the semester
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| Methods |
Classical black board lecture supplemented with calculations in computer algebra systems
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| Language |
English |
| Study material |
- 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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| Changing subject? |
No |
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| On-site course |
| Maximum number of participants |
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| Assignment procedure |
Direct assignment |
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