I've implemented the factor_newton function (it isn't complete yet, as
the lifting algorithm has not been implemented and so, I haven't added
the documentation). Could you please review it? [1]
Also, I'm a little stuck at the moment as I can't figure out how to
actually implement the lift algorithm. My understanding so far is that
the current code will produce 2 truncated factors : L' and R' which need
to be lifted to get the required factorization f = LR. Now, my doubt is
that to do this we'll have to use l and r such that L'' = L'+l and R'' =
R'+r are better approximations of L and R. We do this using a condition
on the valuation of l and r and use indeterminates for the unknown
coefficients and solve the resulting system of linear equations. Any
pointers on how do I do all this in the lift_newton function would be
greatly appreciated. Also, the in the current code, I include the term
xD^(n - pd) in L' where n is degree(f) and pd is degree(R'). I'm not
really sure if this is correct. Should I instead include that term in l?
[1]
https://github.com/fandango-/fricas/commit/07da10d82e5ee0ba274ddf5f11cf97704199eda1
Thanks,
Abhinav.
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