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[ 404CANCSSIV23 ] VL Symbolic Summation and Integration
Versionsauswahl
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
Detailed information
Original study plan Master's programme Computational Mathematics 2025W
Learning Outcomes
Competences
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.
Skills Knowledge
  • 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]
Difference rings and fields, differential fields, summation and integration theory, Risch's algorithm, Karr's algorithm and its generalizations, special functions.
Criteria for evaluation Oral or written examination at the end of the semester
Methods Classical black board lecture supplemented with calculations in computer algebra systems
Language English
Study material
  1. M. Bronstein: Symbolic Integration.
  2. K. Geddes, S. Czapor, and G. Labahn: Algorithms for Computer Algebra.
  3. 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].
  4. 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]
  5. C. Schneider: A Difference Ring Theory for Symbolic Summation. J. Symb. Comput. 72, pp. 82-127. 2016. arXiv:1408.2776 [cs.SC]
  6. 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]
Changing subject? No
On-site course
Maximum number of participants -
Assignment procedure Direct assignment