Séminaire du 9 mai 2011,10h30:
Manuel Kauers, Research Institute
for Symbolic Computation, Linz.
*
Denominator bounds for partial linear difference equations.
*

We report on joint work with Carsten Schneider about generalizing
Abramov's
classical denominator bounding technique to the multivariate case. The
question thus is, given a linear difference operator *L* in
*K*(*n*_{1},...,*n*_{r})[*S*_{n1},...,
*S*_{nr}], to determine a
polynomial *Q* such that for any rational
function *y=p/q* with
*L*(*y*)=0 we have *q* | *Q*. In contrast
to the
univariate case, such a polynomial *Q* does not exist in
general. We
introduce the notion of * aperiodic * polynomials and show that
it is
always possible to find a polynomial *Q'* which predicts all
the
aperiodic factors in the denominator *q* of a
solution *y=p/q*.
(ISSAC 2010.) Next, we show that with a refined version of the same
technique
we are also able to deduce at least some partial information about the
periodic factors of *q*. (ISSAC 2011.)

Virginie Collette
Last modified: Mon May 9 18:50:17 CEST 2011