Change Precision of complex_roots()

edit

OK, you hit a bug, thanks for reporting !

sage: R.<x> = QQ[]
sage: poly = x^7 - 6*x^6 + 15*x^5 - 20*x^4 + 15*x^3 - 6*x^2 + x
sage: poly.complex_roots()
PariError: overflow in expo()

See:

sage: poly.roots(ring=CDF)
[(0.0, 1),
 (0.9970597732189228 - 0.0016886658100989547*I, 1),
 (0.9970597732189228 + 0.0016886658100989547*I, 1),
 (0.9999846391506835 - 0.003403956023304669*I, 1),
 (0.9999846391506835 + 0.003403956023304669*I, 1),
 (1.0029555876303982 - 0.0017152722520868947*I, 1),
 (1.0029555876303982 + 0.0017152722520868947*I, 1)]
sage: poly.roots(ring=QQbar)
[(0, 1), (1, 6)]
sage: poly.roots(ring=ZZ)
[(0, 1), (1, 6)]

Those can be used as workarounds.

However:

sage: poly.roots(ring=CC)
PariError: overflow in expo()

sage: poly.roots(ring=RealField(123))
PariError: overflow in expo()

This seems to be en interface problem with cypari2, the bug is now tracked at trac ticket 24332