Carsten Schneider,
"Refined telescoping algorithms in $R\Pi\Sigma$-extensions to reduce the degrees of the denominators"
, Serie RISC Report Series, Nummer 23-01, RISC, JKU, Hagenberg, Linz, 2023
Original Titel:
Refined telescoping algorithms in $R\Pi\Sigma$-extensions to reduce the degrees of the denominators
Sprache des Titels:
Englisch
Original Kurzfassung:
We present a general framework in the setting of difference ring extensions that enables one to find improved representations of indefinite nested sums such that the arising denominators within the summands have reduced degrees. The underlying (parameterized) telescoping algorithms can be executed in $R\Pi\Sigma$-ring extensions that are built over general $\Pi\Sigma$-fields. An important application of this toolbox is the simplification of d'Alembertian and Liouvillian solutions coming from recurrence relations where the denominators of the arising sums do not factor nicely.
Forschungs-