#16509: bug in .as_finite_field_element() when minimal=True
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Reporter: vdelecroix | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.3
Component: finite rings | Resolution:
Keywords: bug | Merged in:
Authors: Peter Bruin | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/pbruin/16509-as_finite_field_element|
5572837f991d5ed6a1674e009de8c38e0c3bbc7c
Dependencies: | Stopgaps:
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Comment (by pbruin):
Replying to [comment:2 vdelecroix]:
> I would prefer that the following works...
> {{{
> sage: K = GF(5).algebraic_closure()
> sage: K3 = K.subfield(3)[0]
> sage: K6 = K.subfield(6)[0] # not used
> sage: K3.gen()
> z3
> sage: K6(K3.gen())
> Traceback (most recent call last):
> ...
> TypeError: unable to coerce from a finite field other than the prime
subfield
> }}}
In my opinion, from a mathematical perspective this should ''not'' be
expected to work. The first component of the tuple returned by
`subfield()` method is just the abstract field, and there is no canonical
map between non-trivial "stand-alone" finite fields. Either stay inside
the algebraic closure, or otherwise use the `inclusion()` method to obtain
a map that you can use outside of it:
{{{
sage: K = GF(5).algebraic_closure()
sage: K3 = K.subfield(3)[0]
sage: f = K.inclusion(3, 6)
sage: f(K3.gen())
4*z6^5 + z6^4 + 4*z6^3 + 4*z6^2 + 3*z6 + 3
sage: f.codomain() is K.subfield(6)[0]
True
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/16509#comment:4>
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