Abhinav Baid wrote:
>
> On 06/10/2015 03:10 AM, Waldek Hebisch wrote:
> > Abhinav Baid wrote:
> >> On 06/08/2015 03:26 AM, Waldek Hebisch wrote:
> >>> Abhinav Baid wrote:
> >> I've changed the file according to the remarks above [1]. I thought I'd
> >> clarify a few points:
> >>
> >> 1. I was using nm_mult and nm_block to actually try to optimize the
> >> computation of the error term, but it seems that I messed up somewhere.
> >> So, for the time being, I've removed those 2 functions.
> >> 2. The current arguments to lift_newton are clear enough except
> >> probably, the last one : n_l. This is used to specify the number of
> >> lifts to be performed.
> > Yes.
> >> 3. The current lift_newton function returns a pair of operators that
> >> have been computed by lifting n_l times. So, a stream can also be
> >> generated if required by doing [lift_newton(..., n_l) for n_l in 1..]
> > For generating stream this is inconvenient.
> >
> >> 4. Concerning coefs_operator and coefs_operator1: initially,
> >> coefs_operator performed what nm_block was supposed to according to your
> >> description and coefs_operator1 corresponded to coefs_operator. But now,
> >> I've changed the functionality of coefs_operator according to your
> >> description and coefs_poly to correspond to nm_block. I've also added
> >> the 2 tests you suggested.
> >> 5. Also, I've renamed some of the variables and pass k to factor_newton2
> >> now.
> > OK.
> >
> >> My query now is : How do I select the number of lifts so that I can
> >> return the pair of operators from factor_newton2?
> > Number of lifts may be essentially arbitrary, so lifting
> > should be done in lazy way (on demand). For this you will
> > need incremental version of lift_newton. That is on demand
> > perform one iteration producing l_extra, r_extra (main result)
> > plus new li, ri, ei (needed for next iteration).
> >
> > You will need a pipeline:
> >
> > stream of [l_extra, r_extra] --> list of streams of coefficients
> > --> list of Laurent series --> operator
> >
> > The last two stages of that pipeline are not difficult. To
> > get from stream of [l_extra, r_extra] stream of coefficients
> > you first need to extrat from l_extra and r_extra the
> > nonzero coefficients (this is the same operation as used
> > in lift_newton). You will get coefficients in funny order
> > (in order of increasing valuation) so it will take some
> > care to extract correct ones.
> Okay. So, the lift_newton function should return l_extra, r_extra, li,
> ri and ei using which a stream is generated in factor_newton2 which also
> calls other routines according to the pipeline. Is that right?
Yes. More precisely, you will need a wrapper function to
generate stream of l_extra, r_extra. Other parts of
the pipeline should be doable via calls so stanndard
stream/series functions.
> There was a mistake in how I initialized start_D in both coefs_poly and
> coefs_operator. I've resolved that issue now.
I will look at the code.
--
Waldek Hebisch
[email protected]
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