#14007: When computing determinant over GF(p), don't lift to ZZ
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Reporter: jdemeyer | Owner: jason, was
Type: enhancement | Status: needs_work
Priority: blocker | Milestone: sage-5.7
Component: linear algebra | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers: Charles Bouillaguet
Authors: Jeroen Demeyer | Merged in:
Dependencies: | Stopgaps:
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Comment (by jdemeyer):
Replying to [comment:11 Bouillaguet]:
> I also checked that the corresponding PARI routine ({{{Flm_det_sp_OK}}}
in {{{src/basemath/linalg1.c}}}) does not require the characteristic of
the ring to be prime. The same procedure in PARI deals with determinants
in ZZ/6ZZ and ZZ/11ZZ.
PARI does require that the characteristic is prime, or at least that it
won't encounter non-invertible elements:
{{{
gp> matdet([2,1,0;2,3,0;0,0,1]*Mod(1,4))
*** at top-level: matdet([2,1,0;2,3,0;
*** ^--------------------
*** matdet: impossible inverse modulo: Mod(2, 4).
}}}
> Another longer-term objective would ben when the modulus is too large,
to use the chinese reminder theorem to work only modulo small primes
This is what newer versions of PARI do.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14007#comment:12>
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