[Aec-friends] Lecture Symbolic Summation at RISC

Carsten Schneider cschneid at risc.jku.at
Tue Feb 25 11:41:58 CET 2014

Dear Colleagues,

in the summer semester I plan to present a new algorithmic framework
for symbolic summation in the setting of difference rings.

Originally, M. Karr (1981,1985) developed a difference field theory to 
handle indefinite nested
sums and products in a very elegant way. In the last 15 years a lot of 
insight and improvements have been achieved. However, all these results 
have a fundamental
problem: one of the major building blocks in applications (e.g., 
combinatorics, particle physics)
is  (-1)^n, which cannot be treated in difference fields. (There we get 
zero-divisors (1+(-1)^n)(1-(-1)^n)=0).
In this lecture we will extend the theory from difference fields to 
difference rings in which (-1)^n
(among other objects) can be handled properly. In particular, we will 
work out how indefinite nested sums
and products over (-1)^n can be represented in such difference rings and 
present a complete algorithmic machinery
to solve the  telescoping and creative telescoping problem in such rings.

In case that you are interested in this topic, feel free to join.

Lecture: Symbolic Summation and Special Functions II
Place: Seminar room (castle)
Time: Wednesdays, 16:15-17:45

Best wishes,

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