>
> Hi Waldek,
>
> On 03/27/2015 10:24 AM, Waldek Hebisch wrote:
> > Abhinav Baid wrote:
> >> I've tried to improve the proposal based on your remarks and also added
> >> the timeline. Could you please review it now?
> > 1) You write that factor_riccati takes input that has only 1 slope.
> > Do you understand that algorithm 'Ricatti solution' may produce
> > in step 4 operator that has more than 1 slope. So you will
> > have to handle case of multiple slopes anyway.
> Yes, but according to step 2, if the Newton polygon has more than 1
> slope, then we compute a coprime index 1 factorization and apply
> recursion to the right-hand factor. So, steps 3, 4, 5 always assume that
> f has only one slope. Am I missing something here? If so, could you
> please explain? Should I remove the restriction on f having only 1 slope?
Yes. In steps 3, 4, 5 f indeed has only one slope, but you need to
recurse from them to step 1. So step 1 is natural entry point and
multiple slopes are needed here.
> > 2) Algorithm 'Ricatti solution' is enough to produce exponential
> > parts but not enough for generalized exponents. Namely
> > 'Ricatti solution' looses information about generalized
> > exponents ei of form ei = ej + k where k is positive integer
> > and ej is another generalized exponent. That is why van
> > Hoej also have algorithm 'semi-regular parts' in 2.8.4
> > When we want only exponential parts some care is needed
> > to find multiplicities. This affects your milestone 1.
> >
> Yes, I'd thought about this but forgot to include it in the description.
> I was thinking that since most of the steps in Riccati Solution and
> semi-regular parts are the same, we could have some argument which
> indicates which algorithm should be applied in the same function. Is
> such an idea supported in FriCAS? Would it be better to split into 2 -
> one for Riccati and the other for semi-regular?
Thanks for explanation. Yes, you can merge both algorithms into
a single functiom.
--
Waldek Hebisch
[email protected]
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