>
> Now, I've also added the factor_minmult1 function [1]. However, I'm
> having a doubt regarding how to implement try_factorization. I've
> mentioned the input and output specifications of the routine in the file
> itself, but am unsure about how PadĂŠ approximation should be used to
> reconstruct the factor from the inputs. Here's what I've thought about
> so far: First, in section 3.6 of the thesis, van Hoeij talks about
> writing D^0,D^1,...,D^order_R as vectors in the vector space generated
> by D^0,D^1,...,D^order_r. I think I can do that. This will generate a
> list of lists (alternatively, vectors) of vectors in k((x)). How do I
> proceed from there? Waldek, you mentioned before that guessHolo with
> some modifications should work for this purpose. Could you please expand
> on that a little?
To use guessHolo you need:
- bound on degree of coefficients
- sufficiently many coefficients of expansion of apropriate
solution into power series
As result you will get operator vanishing on the solution.
In other words guessHolo will produce the factor.
When I wrote "apropriate solution", I mean that van Hoej gives
conditions when this method works: you need solution that is
anihilated by one of the factors, but not all of them. The
part computing exponential parts in many cases will provide
such a solution. More precisely, given a order 1 factor
you first conjugate it with an exponential to get semi-regular
operator. Then you can use standard FriCAS solver to get
arbitrarily many coefficents of expansion of the solution
into power series.
Bounds tell you how many coefficients you need: if you have
bound say 10 on degree of coefficients and expect order 3
factor, then you need at least 4*(10 + 1) + 1 + 3 coefficients (a few
more is good to speed things up). Note: 4*(10+1) is number
of coefficients of the factor that we want to find. The 3
appears because we need to differentialte power series 3 times
and effectively loose 3 terms. The +1 term is because
we solve homogeneous system.
--
Waldek Hebisch
[email protected]
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