[ 404CANCSSIV23 ] VL Symbolic Summation and Integration

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 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.
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
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