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?
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,
Abhinav.
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