exact_checked=35
(1, 1, 0, x, oo)
(3, 2, 1, x**2 - 1, 4)
(6, 3, 2, x**3 - 2*x, 6)
(13, 4, 3, x**4 - 3*x**2, 64/7)
(14, 4, 3, x**4 - 3*x**2 + 1, 288/31)
(29, 5, 4, x**5 - 4*x**3, 250/19)
(30, 5, 4, x**5 - 4*x**3 + 2*x, 375/28)
(31, 5, 4, x**5 - 4*x**3 + 3*x, 3000/211)
(38, 5, 5, x**5 - 5*x**3 + 5*x - 2, 25/3)
(77, 6, 5, x**6 - 5*x**4, 18)
(78, 6, 5, x**6 - 5*x**4 + 3*x**2, 1080/59)
(79, 6, 5, x**6 - 5*x**4 + 4*x**2, 405/22)
(80, 6, 5, x**6 - 5*x**4 + 5*x**2 - 1, 2160/113)
(81, 6, 5, x**6 - 5*x**4 + 5*x**2, 810/41)
(83, 6, 5, x**6 - 5*x**4 + 6*x**2 - 1, 2025/97)
(104, 6, 6, x**6 - 6*x**4 + 8*x**2 - 2*x - 1, 1620/127)
(105, 6, 6, x**6 - 6*x**4 + 9*x**2 - 4, 27/2)
(270, 7, 6, x**7 - 6*x**5, 686/29)
(271, 7, 6, x**7 - 6*x**5 + 4*x**3, 6174/257)
(272, 7, 6, x**7 - 6*x**5 + 6*x**3, 2058/85)
(273, 7, 6, x**7 - 6*x**5 + 7*x**3 - 2*x, 1764/71)
(274, 7, 6, x**7 - 6*x**5 + 7*x**3, 12348/475)
(276, 7, 6, x**7 - 6*x**5 + 8*x**3 - 2*x, 3087/121)
(278, 7, 6, x**7 - 6*x**5 + 8*x**3, 294/11)
(279, 7, 6, x**7 - 6*x**5 + 9*x**3 - 3*x, 6860/253)
(280, 7, 6, x**7 - 6*x**5 + 9*x**3 - 2*x, 20580/733)
(284, 7, 6, x**7 - 6*x**5 + 9*x**3 - 4*x, 4116/157)
(286, 7, 6, x**7 - 6*x**5 + 10*x**3 - 4*x, 30870/1049)
(334, 7, 7, x**7 - 7*x**5 + 11*x**3 - 2*x**2 - 2*x, 18)
(340, 7, 7, x**7 - 7*x**5 + 12*x**3 - 2*x**2 - 4*x, 343/19)
(342, 7, 7, x**7 - 7*x**5 + 12*x**3 - 2*x**2 - 3*x, 12348/673)
(348, 7, 7, x**7 - 7*x**5 + 13*x**3 - 7*x, 2058/107)
(351, 7, 7, x**7 - 7*x**5 + 13*x**3 - 2*x**2 - 6*x + 2, 2058/109)
(353, 7, 7, x**7 - 7*x**5 + 14*x**3 - 7*x - 2, 441/22)
(449, 7, 8, x**7 - 8*x**5 + 17*x**3 - 4*x**2 - 10*x + 4, 6174/451)
OK: every graph-atlas case n<=7 passes with exact rational root isolation.