>>> from math import atan
>>> from series_invtrigo import termes

---- inici

>>> eps = 1e-6
>>> z = 0.5
>>> r = termes(z, eps)
>>> list(map(lambda t: round(t, 6), r))
[0.5, -0.041667, 0.00625, -0.001116, 0.000217, -4.4e-05, 9e-06, -2e-06]

---- fi

>>> abs(sum(r) - atan(z)) < eps and abs(sum(r[:-1]) - atan(z)) >= eps
True

>>> eps = 1e-4
>>> z = 0.9
>>> r = termes(z, eps)
>>> list(map(lambda t: round(t, 5), r))
[0.9, -0.243, 0.1181, -0.06833, 0.04305, -0.02853, 0.01955, -0.01373, 0.00981, -0.00711, 0.00521, -0.00385, 0.00287, -0.00215, 0.00162, -0.00123, 0.00094, -0.00072, 0.00055, -0.00042, 0.00032, -0.00025, 0.00019]
>>> abs(sum(r) - atan(z)) < eps and abs(sum(r[:-1]) - atan(z)) >= eps
True

>>> eps = 1e-10
>>> z = 0.1
>>> r = termes(z, eps)
>>> list(map(lambda t: round(t, 10), r))
[0.1, -0.0003333333, 2e-06, -1.43e-08, 1e-10]
>>> abs(sum(r) - atan(z)) < eps and abs(sum(r[:-1]) - atan(z)) >= eps
True

>>> eps = 1e-10
>>> z = 0.3
>>> r = termes(z, eps)
>>> list(map(lambda t: round(t, 10), r))
[0.3, -0.009, 0.000486, -3.12429e-05, 2.187e-06, -1.61e-07, 1.23e-08, -1e-09]
>>> abs(sum(r) - atan(z)) < eps and abs(sum(r[:-1]) - atan(z)) >= eps
True

>>> eps = 1e-4
>>> z = 0.7
>>> r = termes(z, eps)
>>> list(map(lambda t: round(t, 5), r))
[0.7, -0.11433, 0.03361, -0.01176, 0.00448, -0.0018, 0.00075, -0.00032]
>>> abs(sum(r) - atan(z)) < eps and abs(sum(r[:-1]) - atan(z)) >= eps
True

>>> eps = 1e-6
>>> z = 0.6
>>> r = termes(z, eps)
>>> list(map(lambda t: round(t, 6), r))
[0.6, -0.072, 0.015552, -0.003999, 0.00112, -0.00033, 0.0001, -3.1e-05, 1e-05, -3e-06]
>>> abs(sum(r) - atan(z)) < eps and abs(sum(r[:-1]) - atan(z)) >= eps
True

>>> eps = 1e-7
>>> z = 0.2
>>> r = termes(z, eps)
>>> list(map(lambda t: round(t, 7), r))
[0.2, -0.0026667, 6.4e-05, -1.8e-06]
>>> abs(sum(r) - atan(z)) < eps and abs(sum(r[:-1]) - atan(z)) >= eps
True

>>> eps = 1e-6
>>> z = 0.4
>>> r = termes(z, eps)
>>> list(map(lambda t: round(t, 6), r))
[0.4, -0.021333, 0.002048, -0.000234, 2.9e-05, -4e-06]
>>> abs(sum(r) - atan(z)) < eps and abs(sum(r[:-1]) - atan(z)) >= eps
True

>>> eps = 1e-5
>>> z = 0.8
>>> r = termes(z, eps)
>>> list(map(lambda t: round(t, 5), r))
[0.8, -0.17067, 0.06554, -0.02996, 0.01491, -0.00781, 0.00423, -0.00235, 0.00132, -0.00076, 0.00044, -0.00026, 0.00015, -9e-05, 5e-05, -3e-05, 2e-05]
>>> abs(sum(r) - atan(z)) < eps and abs(sum(r[:-1]) - atan(z)) >= eps
True

>>> eps = 1e-5
>>> z = 0.95
>>> r = termes(z, eps)
>>> list(map(lambda t: round(t, 5), r))
[0.95, -0.28579, 0.15476, -0.09976, 0.07003, -0.05171, 0.03949, -0.03089, 0.0246, -0.01986, 0.01622, -0.01336, 0.0111, -0.00927, 0.00779, -0.00658, 0.00558, -0.00475, 0.00405, -0.00347, 0.00298, -0.00256, 0.00221, -0.00191, 0.00165, -0.00143, 0.00124, -0.00108, 0.00094, -0.00082, 0.00072, -0.00063, 0.00055, -0.00048, 0.00042, -0.00037, 0.00032, -0.00028, 0.00025, -0.00022, 0.00019, -0.00017, 0.00015, -0.00013, 0.00012, -0.0001, 9e-05, -8e-05, 7e-05, -6e-05, 6e-05, -5e-05, 4e-05, -4e-05, 3e-05, -3e-05, 3e-05, -2e-05, 2e-05]
>>> abs(sum(r) - atan(z)) < eps and abs(sum(r[:-1]) - atan(z)) >= eps
True