#20693: Sage crashes when computing newforms
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Reporter: ehlen | Owner:
Type: defect | Status: new
Priority: critical | Milestone: sage-7.3
Component: modular forms | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by pbruin):
Replying to [comment:24 ehlen]:
> However, the pari alternative seems to be kind of slow (which is much
better than crashing, of course).
I would have hoped for PARI to be quite fast, but it seems this is not
particularly optimised in PARI. In any case I didn't try hard to make it
fast; it was just the easiest solution that didn't crash.
> With the example I gave in #20749, the pari inversion takes about 7
minutes but the code below, which mimics the _invert_c function, runs in
about 1.5 minutes for me:
>
> {{{
> d = alpha.polynomial().denominator()
> D = alpha.parent().absolute_polynomial().denominator()
> r,s,tt =
xgcd(alpha.polynomial().numerator()*D,alpha.parent().absolute_polynomial().numerator()*d)
> b = s*d/D
> F = alpha.parent()
> beta = F(F.polynomial_quotient_ring()(b))
> }}}
>
> I don't like the last line of the code and I still have to make sure I
understood everything correctly and it works in all cases but then I could
submit a patch for the number field element to use a variant of this code
as an alternative. What do you think?
This is definitely a good start. The `xgcd` is implemented using FLINT,
which suggests a slightly more direct approach: use the functions from
`sage.libs.flint.ntl_interface` to convert `alpha.__numerator` and
`alpha.__denominator` to FLINT `fmpz_poly` and `fmpz` objects,
respectively (and similarly for the defining polynomial of the number
field), then call the FLINT function `fmpz_poly_xgcd`, and then convert
back to NTL. It could even be reasonable to simply always use FLINT
instead of NTL in `__invert__`.
--
Ticket URL: <http://trac.sagemath.org/ticket/20693#comment:25>
Sage <http://www.sagemath.org>
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