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BEGIN:VEVENT
UID:ea78703eb9919c80219000610c318352
CATEGORIES:Experimental Mathematics Seminar
CREATED:20211007T113747
SUMMARY:Accelerating hypergeometric indefinite summation
LOCATION:Zoom 
DESCRIPTION:Abstract: One well-known longstanding problem with Gosper’s algorithm is 
 that its running time depends at least linearly on the dispersion of the ra
 tional certificate of the summand, and this last can be exponentially large
  in the bit size of the summand. This makes summation problems for hypergeo
 metric terms with large dispersion values effectively intractable. We show 
 that for summable terms this dependency is not essential (can be removed). 
 The structure of polynomial solutions to the Gospe key equation is analyzed
 . A method for rapid extractionsof simple high-degree factors of the soluti
 on is given. Resulting modified Gosper's algorithm is presented. This resul
 t is based on very simple and well-known facts, properties, and lazy evalua
 tion rules of factorial polynomials. Experimental Maple implementation conf
 irms practical acceleration in computing of indefinite sums and rational no
 rmal forms of hypergeometric terms.\n
X-ALT-DESC;FMTTYPE=text/html:<p><em style="color: #000000; font-family: 'Times New Roman'; font-size: me
 dium; background-color: inherit;">Abstract</em>: One well-known longstandin
 g problem with Gosper’s algorithm is that its running time depends at lea
 st linearly on the dispersion of the rational certificate of the summand, a
 nd this last can be exponentially large in the bit size of the summand. Thi
 s makes summation problems for hypergeometric terms with large dispersion v
 alues effectively intractable. We show that for summable terms this depende
 ncy is not essential (can be removed). The structure of polynomial solution
 s to the Gospe key equation is analyzed. A method for rapid extractionsof s
 imple high-degree factors of the solution is given. Resulting modified Gosp
 er's algorithm is presented. This result is based on very simple and well-k
 nown facts, properties, and lazy evaluation rules of factorial polynomials.
  Experimental Maple implementation confirms practical acceleration in compu
 ting of indefinite sums and rational normal forms of hypergeometric terms.<
 /p>
CONTACT:Eugene Zima, Wilfrid Laurier University
X-EXTRAINFO: Zoom Link https://rutgers.zoom.us/j/94346444480 [password: The 20th Catala
 n number, alias (40)!/(20!*21!), alias 6564120420 ]
DTSTAMP:20260828T185346
DTSTART;TZID=America/New_York:20211028T170000
DTEND;TZID=America/New_York:20211028T180000
SEQUENCE:0
TRANSP:OPAQUE
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