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sage: AA.<x> = AffineSpace(GF(2^8, 'a'), 1)
sage: S = AA.subscheme(x^8 + x^7 + x^5 + x^3 + 1)
sage: S.rational_points()
[(a^5 + a + 1),
 (a^6 + a^5 + a^4 + 1),
 (a^6 + a^5 + a^4 + a^2 + a),
 (a^6 + a^5 + a^4 + a^3 + a),
 (a^7 + a^5 + a^2 + 1),
 (a^7 + a^5 + a^3 + a),
 (a^7 + a^5 + a^4),
 (a^7 + a^6 + a^5)]