#13607: bug dans 5.3 lorsque l'on veut injecter un élément d'ordre q-1,
appartenant
à une extension de F_q, dans F_q.
-------------------------------------------+--------------------------------
Reporter: frovetta | Owner: robertwb
Type: defect | Status: new
Priority: major | Milestone: sage-5.5
Component: coercion | Resolution:
Keywords: finite fields, coercion | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Rovetta Florent | Merged in:
Dependencies: | Stopgaps:
-------------------------------------------+--------------------------------
Comment (by fwclarke):
The problem can be illustrated more simply:
{{{
sage: q = 25
sage: K.<d> = GF(q)
sage: F.<a> = GF(q^6)
sage: K(a)
d
}}}
This is, of course, nonsense.
The offending code is at lines 482--494 of `sage-5.3/devel/sage-
main/sage/rings/finite_rings/element_givaro.pyx`.
As it says at lines 291--292 of `sage-5.3/devel/sage-
main/sage/rings/finite_rings/finite_field_givaro.py`:
{{{
PARI elements are interpreted as finite field elements; this PARI
flexibility
is (absurdly!) liberal
}}}
----
There is a more mathematical difficulty with what you wish to do, and how
one could expect Sage to do it. There are, of course, two embeddings of
GF(25) into GF(5^12^), with the same image. Thus there is no canonical
way of identifying an element of GF(5^12^) belonging to the subfield of
order 25 with an element of another field of order 25.
But it is possible, in a very simple-minded way, to find the two
candidates:
{{{
sage: z = a^10172526
sage: z.multiplicative_order()
24
sage: [[y for y in K if f(y) == z][0] for f in Hom(K, F)]
[d, 4*d + 1]
}}}
Or, much more efficiently,
{{{
sage: z.minimal_polynomial().roots(ring=K, multiplicities=False)
[4*d + 1, d]
}}}
----
Another point: there's no need to define `element_primitif`; it's built
in:
{{{
sage: K.primitive_element()
d
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13607#comment:3>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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