Abhinav Baid wrote:
>
> On Wednesday, July 15, 2015 at 8:23:45 AM UTC+5:30, Waldek Hebisch wrote:
> >
> > 4) In 'compute_bound' you seem to ignore ramified exponential
> > parts. This looks wrong.
> >
>
> Sorry, I don't get what I'm missing here. First, I check that the degree of
>
> 'ram' = 1 and then only the constant coefficient of 'expart' matters in
> further computation. So, I think it should work?
When 'ram' = 1 this looks OK. But AFAICS ramified singularity
still may have generalized exponent contributing to constant term.
As an example consider operator in the example in the section
2.7. The operator has only ramified generalized exponents, but
the residue is nonzero. So in Lemma 27 in van Hoej thesis you
need to take into account all generalized exponents.
>
> > 5) Infinity is used differently in bounds: other singularities
> > bound denomiantors of a_i. Infinity bounds differences
> > between degrees of mumerators and denominators of a_i (so
> > given bound on denominators infinity gives bound for degree
> > of numarators).
> >
>
>
> Again, I apologize because I think I don't understand this. What are the
> a_i in question?
We are trying to find a factor R = \sum_i a_i\partial_x^i
so a_i are (unknown) coefficients of the factor. To prove
that operator is irreducible (which is one of possible results
of van Hoej algorithm) we need bounds on degree of denominators
and numerators of a_i. Only having such bounds we can conclude
that no solution to Hermite-Pade problem means that operator
is irreducible.
--
Waldek Hebisch
[email protected]
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