Inhalt
[ 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 nontrivial 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 
 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 ΠΣfield extensions. J. Symb. Comput. 107, pp. 2366. arXiv:2005.04944 [cs.SC].
 C. Schneider Term: Algebras, Canonical Representations and Difference Ring Theory for Symbolic Summation. In: AntiDifferentiation and the Calculation of Feynman Amplitudes, pp. 423485. 2021. Springer, arXiv:2102.01471 [cs.SC]
 C. Schneider: A Difference Ring Theory for Symbolic Summation. J. Symb. Comput. 72, pp. 82127. 2016. arXiv:1408.2776 [cs.SC]
 C. Schneider: Summation Theory II: Characterizations of RΠΣextensions and algorithmic aspects. J. Symb. Comput. 80(3), pp. 616664. 2017. arXiv:1603.04285 [cs.SC]

Changing subject? 
No 



Onsite course 
Maximum number of participants 
 
Assignment procedure 
Direct assignment 


