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Fix initial value selection in acb_poly_find_roots for overlapping radii #2422

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merged 2 commits into from
Oct 27, 2025
Merged

Fix initial value selection in acb_poly_find_roots for overlapping radii #2422

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04793b9
Fix initial value selection in acb_poly_find_roots for overlapping radii
fredrik-johansson Oct 26, 2025
993a6f7
Update doctests
fredrik-johansson Oct 26, 2025
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11 changes: 9 additions & 2 deletions src/acb_poly/find_roots.c
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Original file line number Diff line number Diff line change
Expand Up @@ -123,10 +123,17 @@ _acb_poly_roots_initial_values(acb_ptr roots, acb_srcptr poly, slong deg, slong
flint_printf("initial values: radius %{mag} multiplicity %wd\n", r, m);
#endif

/* pick m points on the circle with radius r */
/* Pick m points on the circle with radius r */
for (j = 0; j < m; j++)
{
theta = 6.283185307179586 * ((j + 1.0) / m + (double) i / deg) + 0.577216;
/* Hack: the angle 2pi * ((j+1)/m + i/deg) distributes points uniformly
when there are many radii. However, if two radii are
very close, points can end up overlapping if (j+1)/m + i/deg
happens to give the same fraction for two different i. Ensure
that this doesn't happen. */
double irrational_factor = 0.99071828182845905;

theta = 6.283185307179586 * (irrational_factor * (j + 1.0) / m + (double) i / deg) + 0.577216;

ri = roots + total;
acb_zero(ri);
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29 changes: 29 additions & 0 deletions src/acb_poly/test/t-find_roots.c
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Expand Up @@ -85,5 +85,34 @@ TEST_FUNCTION_START(acb_poly_find_roots, state)
acb_poly_clear(C);
}

/* Check that #2421 is fixed */
{
acb_poly_t f;
acb_ptr roots;
acb_t c;

acb_poly_init(f);
acb_init(c);
roots = _acb_vec_init(4);

acb_poly_set_coeff_si(f, 0, 10);
acb_poly_set_coeff_si(f, 1, -170);
acb_poly_set_coeff_si(f, 2, 2890);
acb_poly_set_coeff_si(f, 3, -49130);
acb_poly_set_coeff_si(f, 4, 835210);
acb_set_ui(c, 83521);
acb_poly_scalar_div(f, f, c, 64);

if (acb_poly_find_roots(roots, f, NULL, 40, 64) != 4)
{
flint_printf("FAIL: geometric example\n");
flint_abort();
}

_acb_vec_clear(roots, 4);
acb_poly_clear(f);
acb_clear(c);
}

TEST_FUNCTION_END(state);
}
4 changes: 2 additions & 2 deletions src/python/flint_ctypes.py
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Expand Up @@ -5422,9 +5422,9 @@ def roots(self, domain=None):
>>> f.roots(domain=QQbar) # complex algebraic roots
([Root a = 1.00000*I of a^2+1, Root a = -1.00000*I of a^2+1, Root a = 1.41421 of a^2-2, Root a = -1.41421 of a^2-2, -3/2], [1, 1, 1, 1, 2])
>>> f.roots(domain=RR) # real ball roots
([[-1.414213562373095 +/- 4.91e-17], [1.414213562373095 +/- 4.91e-17], -1.500000000000000], [1, 1, 2])
([[-1.414213562373095 +/- 4.89e-17], [1.414213562373095 +/- 4.89e-17], -1.500000000000000], [1, 1, 2])
>>> f.roots(domain=CC) # complex ball roots
([[-1.414213562373095 +/- 4.91e-17], [1.414213562373095 +/- 4.91e-17], ([+/- 1.45e-19] + [1.000000000000000 +/- 2.7e-19]*I), ([+/- 1.45e-19] + [-1.000000000000000 +/- 2.7e-19]*I), -1.500000000000000], [1, 1, 1, 1, 2])
([[-1.414213562373095 +/- 4.89e-17], [1.414213562373095 +/- 4.89e-17], ([+/- 1.45e-19] + [1.000000000000000 +/- 2.7e-19]*I), ([+/- 1.45e-19] + [-1.000000000000000 +/- 2.7e-19]*I), -1.500000000000000], [1, 1, 1, 1, 2])
>>> f.roots(RF) # real floating-point roots
([-1.414213562373095, 1.414213562373095, -1.500000000000000], [1, 1, 2])
>>> f.roots(CF) # complex floating-point roots
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