#11797: Finite field elements are allowed in exponents
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Reporter: nbruin | Owner: AlexGhitza
Type: defect | Status: new
Priority: major | Milestone: sage-4.7.2
Component: basic arithmetic | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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{{{
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.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11797>
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