rnfpolredbest for larger polynomials

[Benjamin Matschke <matschke@bu.edu>]

rnfpolredbest seems to get slow for larger inputs, here is an example:

f = y^4 + 3779*y^2 + 3575881
K = bnfinit(f)
g = x^3 + (-6/1891*y^3 - 11328/1891*y + 12)*x -
185828205268604880664711758295687064824766032511727208226289638708278008/1891*y^3
- 4193788865327654200848261540592786277199048095680627005208368097895442*y^2
- 364061076121017004851315903951025443139463935963694411909316544669762680474/1891*y
- 7620275092346327331118337613708081210333545556068555805693518189928940204
g_reduced = rnfpolredbest(K,g) \\slow

Also in this example, L = rnfinit(K,g) runs into a large integer factorization.

Would it in general be possible to have a version of rnfpolredbest
that returns some simplified polynomial within a given time frame?
Perhaps it could make sense for large input polynomials g (as the one
above) to first reduce it greedily (with respect to some naive height
of g), say by adding elements of K to the primitive element of L/K,
and iterate in a gradient flow or simulated annealing way.

Thanks,
Benjamin