#8373: Construct finite fields with primitive defining polynomial
-------------------------------------+-------------------------------------
Reporter: rkirov | Owner: cpernet
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-6.4
Component: finite rings | Resolution:
Keywords: | Merged in:
Authors: Jeroen Demeyer | Reviewers: Peter Bruin
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/jdemeyer/ticket/8373 | 63ec17af4cc391fb5bcfef7c9c113488806dac21
Dependencies: #16927 | Stopgaps:
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Changes (by vbraun):
* status: positive_review => needs_work
Comment:
I got this on arando (linux 32-bit):
{{{
sage -t --long src/sage/rings/polynomial/polynomial_ring.py
**********************************************************************
File "src/sage/rings/polynomial/polynomial_ring.py", line 2331, in
sage.rings.polynomial.polynomial_ring.PolynomialRing_dense_mod_n.irreducible_element
Failed example:
GF(5)['x'].irreducible_element(32, algorithm="primitive")
Expected:
x^32 + 4*x^31 + x^30 + 4*x^29 + 4*x^28 + 3*x^27 + 2*x^26 + x^25 + x^24
+ x^23 + 4*x^21 + 3*x^20 + x^19 + 4*x^17 + 4*x^16 + 4*x^15 + 4*x^14 +
3*x^13 + x^12 + 3*x^11 + 4*x^10 + x^9 + 4*x^8 + x^7 + 2*x^6 + 4*x^5 +
4*x^4 + x^3 + 3*x^2 + 4*x + 2
Got:
x^32 + 3*x^31 + x^30 + 4*x^28 + 2*x^27 + 2*x^26 + 2*x^24 + 2*x^23 +
2*x^22 + x^21 + 3*x^20 + 3*x^19 + x^18 + 3*x^17 + 4*x^16 + 2*x^15 + 3*x^12
+ 4*x^11 + x^10 + 2*x^8 + 3*x^7 + 2*x^6 + 3*x^5 + x^4 + 4*x^3 + x + 3
**********************************************************************
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/8373#comment:20>
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