#8335: Finite Field lattices
------------------------------------------------+---------------------------
Reporter: roed | Owner: AlexGhitza
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-5.11
Component: algebra | Resolution:
Keywords: days49 | Work issues:
Report Upstream: N/A | Reviewers: Jean-Pierre
Flori, Luca De Feo
Authors: David Roe, Jean-Pierre Flori | Merged in:
Dependencies: #13894 | Stopgaps:
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Changes (by defeo):
* keywords: => days49
* reviewer: Jean-Pierre Flori => Jean-Pierre Flori, Luca De Feo
* status: needs_review => needs_info
Comment:
Hi,
The doc in `constructor.py` says
{{{
- ``modulus`` - blabla
- 'default': a Conway polynomial is used if in the database. Otherwise
a sparse polynomial is used for binary fields and a
random polynomial is used for other characteristics.
}}}
but I got the impression that the default is to use pseudo-conway. By the
way, is it reasonable to use pseudo-conway as default ? It is utterly
slow !
{{{
sage: %time k = GF(next_prime(100000)^2)
CPU times: user 16.41 s, sys: 0.05 s, total: 16.45 s
Wall time: 16.18 s
sage: %time l = GF(next_prime(100000)^3)
CPU times: user 60.19 s, sys: 0.07 s, total: 60.26 s
Wall time: 59.97 s
sage: %time (k.gen() + l.gen()).parent()
CPU times: user 0.08 s, sys: 0.00 s, total: 0.09 s
Wall time: 0.07 s
Finite Field in z6 of size 100003^6
}}}
Compare this with Magma
{{{
> time k := GF(NextPrime(100000)^2);
Time: 0.000
> time l := GF(NextPrime(100000)^3);
Time: 0.000
> time CommonOverfield(l, k);
Time: 0.030
}}}
Wouldn't it be better to keep using ``random`` as default, and give error
messages suggesting to use ``conway`` when the user tries to
add/multiply/whatever two elements in different fields?
On another note, I get the following messages (I suppressed them from the
output above for readability).
{{{
sage: k = GF(next_prime(10000)^11)
*** Warning: Mod(a,b)^n with n >> b : wasteful.
*** Warning: Mod(a,b)^n with n >> b : wasteful.
*** Warning: Mod(a,b)^n with n >> b : wasteful.
*** Warning: Mod(a,b)^n with n >> b : wasteful.
*** Warning: Mod(a,b)^n with n >> b : wasteful.
*** Warning: Mod(a,b)^n with n >> b : wasteful.
*** Warning: Mod(a,b)^n with n >> b : wasteful.
*** Warning: Mod(a,b)^n with n >> b : wasteful.
*** Warning: Mod(a,b)^n with n >> b : wasteful.
*** Warning: Mod(a,b)^n with n >> b : wasteful.
*** Warning: Mod(a,b)^n with n >> b : wasteful.
*** Warning: Mod(a,b)^n with n >> b : wasteful.
*** Warning: Mod(a,b)^n with n >> b : wasteful.
*** Warning: Mod(a,b)^n with n >> b : wasteful.
}}}
Any ideas on these?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8335#comment:49>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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