#11797: Finite field elements are allowed in exponents
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Reporter: nbruin | Owner: AlexGhitza
Type: defect | Status: closed
Priority: major | Milestone: sage-duplicate/invalid/wontfix
Component: basic | Resolution: duplicate
arithmetic | Merged in:
Keywords: | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Changes (by jdemeyer):
* status: new => closed
* resolution: => duplicate
* milestone: sage-6.4 => sage-duplicate/invalid/wontfix
Old description:
> {{{
> sage: p=7
> sage: k=GF(p)
> sage: k(2)^k(p)
> 1
> sage: (GF(7)(2))^(GF(5)(2))
> 4
> sage: k(2)^p
> 2
> }}}
> It looks like it's simply quietly lifting the exponent to the integers,
> which it shouldn't do because there is no coercion in that direction
> (only a conversion):
> {{{
> sage: k.<a>=GF(p^2)
> sage: k(2)^k(p)
> 1
> sage: k(2)^k(a)
> TypeError: not in prime subfield
> sage: ZZ(k(1))
> 1
> sage: ZZ(k(a))
> TypeError: not in prime subfield
> }}}
> There is one side-effect of this that does look elegant:
> {{{
> sage: R=Integers(p-1)
> sage: (k(2))^(R(p))
> 2
> }}}
> but in general I'd say an error should result from exponentiations like
> this.
New description:
Duplicate of #15709.
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Ticket URL: <http://trac.sagemath.org/ticket/11797#comment:5>
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