A somewhat simpler test case, which I think preserves the qualitative issue:

sage: from sage.rings.polynomial.real_roots import real_roots
sage:
sage: x = polygen(QQ)
sage: f = 2503841067*x^13 - 15465014877*x^12 + 37514382885*x^11 -
44333754994*x^10 + 24138665092*x^9 - 2059014842*x^8 - 3197810701*x^7 +
803983752*x^6 + 123767204*x^5 - 26596986*x^4 - 2327140*x^3 + 75923*x^2
+ 7174*x + 102
sage: len(real_roots(f)), len(real_roots(f,strategy='warp'))
(11, 13)
sage:
sage: [map(float,r[0]) for r in real_roots(f)]
[[-0.28173828138369572, -0.23901367199914603], [-0.19628906261459633,
-0.15356445323004664], [-0.078796386807084673, -0.073455810634015961],
[-0.036071777422534979, -0.030731201249466267],
[-0.025390625076397555, 0.017333984308152139], [0.060058593692701834,
0.10278320307725153], [0.14550781246180122, 0.23095703123090061],
[0.57275390625, 0.615478515625], [0.658203125, 0.76618289947509766],
[1.375, 1.4375], [1.5, 2.0]]
sage: [map(float,r[0]) for r in real_roots(f,strategy='warp')]
[[-0.33333333333333331, -0.23076923076923075], [-0.18518518518518517,
-0.14285714285714285], [-0.10344827586206896, -0.066666666666666666],
[-0.049180327868852458, -0.032258064516129031],
[-0.023999999999999997, -0.015873015873015872], [0.032258064516129031,
0.066666666666666666], [0.14285714285714285, 0.23076923076923075],
[0.59999999999999998, 0.64102564102564097], [0.72972972972972971,
0.75342465753424648], [0.95373241116145957, 0.95396541443053062],
[0.95419847328244267, 0.96923076923076923], [1.2857142857142856,
1.4615384615384615], [1.6666666666666665, 3.0]]


Doug

--
Department of Earth Sciences
University of Hong Kong

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