#5746: rational points over subfields of the (finite) field of definition
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Reporter: AlexGhitza | Owner: was
Type: enhancement | Status: new
Priority: minor | Milestone: sage-3.4.2
Component: algebraic geometry | Keywords: rational points finite field
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Right now, if X is a scheme over a finite field F and we ask for the list
of rational points over a subfield K of F, Sage raises an error because it
tries to base change X to K first.
It would be very easy to implement this as follows: take the list of all
rational points over F and find the ones that are fixed by the appropriate
power of the Frobenius morphism. These are then the K-rational points.
A sample of what this would return:
{{{
sage: P = ProjectiveSpace(1, GF(3^2, 'b'))
sage: P.rational_points()
[(0 : 1),
(2*b : 1),
(b + 1 : 1),
(b + 2 : 1),
(2 : 1),
(b : 1),
(2*b + 2 : 1),
(2*b + 1 : 1),
(1 : 1),
(1 : 0)]
sage: P.rational_points(GF(3)) # this doesn't work right now
[(0 : 1),
(2 : 1),
(1 : 1),
(1 : 0)]
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5746>
Sage <http://sagemath.org/>
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