#4632: [with patch, needs review] .roots(ring=QQbar) fails for polynomials with
enormous (rational) coefficients
-----------------------+----------------------------------------------------
Reporter: cwitty | Owner: cwitty
Type: defect | Status: new
Priority: major | Milestone: sage-3.2.1
Component: numerical | Resolution:
Keywords: |
-----------------------+----------------------------------------------------
Comment (by ncalexan):
Still trouble:
{{{
sage: i1 = QQ['x'].0
sage:
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....: ....: ....: ....: ....: ....: ....: ....: ....: ....: ....: ....:
....: ....: ....: ....: ....: ....: ....: ....: ....: ....: ....: ....:
....: ....:
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-
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-
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-
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-
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-
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+
64142895751684972523861209285243282417707075329583674916117055188381394775628232666253440274186493488594874737405053591961632429138669138467297304724926962706230467037061800892052686428670590014901138630952149649710687408091127872467041015625
sage: f = _
sage: f.roots(CC)
[(470361.820245868, 1),
(1.25177790453357e9, 1),
(-2.03298860112789e11 + 6.74115413126603e11*I, 1),
(-2.03298860112789e11 - 6.74115413126603e11*I, 1),
(1.16475054726688e7 + 1.30609589354525e7*I, 1),
(1.16475054726688e7 - 1.30609589354525e7*I, 1),
(2.78249805898164e6 + 2.98317202510733e6*I, 1),
(2.78249805898164e6 - 2.98317202510733e6*I, 1),
(996595.827928498 + 437557.094541233*I, 1),
(996595.827928498 - 437557.094541233*I, 1),
(-1630.61319607286 + 334060.449738135*I, 1),
(-1630.61319607286 - 334060.449738135*I, 1),
(12732.3063661902 + 25160.0301645502*I, 1),
(12732.3063661902 - 25160.0301645502*I, 1),
(-21504.3150468783 + 12109.1879518910*I, 1),
(-21504.3150468783 - 12109.1879518910*I, 1),
(-3658.06691532790 + 13146.4980245586*I, 1),
(-3658.06691532790 - 13146.4980245586*I, 1),
(1879.24848431825 + 12190.5599603421*I, 1),
(1879.24848431825 - 12190.5599603421*I, 1),
(-4469.59051158561 + 8416.93701866920*I, 1),
(-4469.59051158561 - 8416.93701866920*I, 1),
(-177.340482535130 + 3401.04786031455*I, 1),
(-177.340482535130 - 3401.04786031455*I, 1),
(-1581.01702889358 + 4447.86744726969*I, 1),
(-1581.01702889358 - 4447.86744726969*I, 1)]
sage: f.roots(QQbar, multiplicities=False)
---------------------------------------------------------------------------
LinAlgError Traceback (most recent call
last)
/Users/ncalexan/.sage/temp/mero.local/6993/_Users_ncalexan__sage_init_sage_0.py
in <module>()
----> 1
2
3
4
5
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/polynomial/polynomial_element.so in
sage.rings.polynomial.polynomial_element.Polynomial.roots
(sage/rings/polynomial/polynomial_element.c:24158)()
3609
3610
-> 3611
3612
3613
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/polynomial/complex_roots.py in complex_roots(p,
skip_squarefree, retval, min_prec)
321 for (factor, exp) in factors:
322 cfac = CCX(factor)
--> 323 rts = cfac.roots(multiplicities=False)
324 irts = interval_roots(factor, rts, max(prec,
min_prec))
325 if irts is None:
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/polynomial/polynomial_element.so in
sage.rings.polynomial.polynomial_element.Polynomial.roots
(sage/rings/polynomial/polynomial_element.c:23239)()
3540
3541
-> 3542
3543
3544
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/numpy/lib/polynomial.pyc in roots(p)
178 A = diag(NX.ones((N-2,), p.dtype), -1)
179 A[0, :] = -p[1:] / p[0]
--> 180 roots = _eigvals(A)
181 else:
182 roots = NX.array([])
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/numpy/lib/polynomial.pyc in _eigvals(arg)
33 "Return the eigenvalues of the argument"
34 try:
---> 35 return eigvals(arg)
36 except TypeError:
37 get_linalg_funcs()
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/numpy/linalg/linalg.pyc in eigvals(a)
595 _assertRank2(a)
596 _assertSquareness(a)
--> 597 _assertFinite(a)
598 t, result_t = _commonType(a)
599 real_t = _linalgRealType(t)
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/numpy/linalg/linalg.pyc in _assertFinite(*arrays)
123 for a in arrays:
124 if not (isfinite(a).all()):
--> 125 raise LinAlgError, "Array must not contain infs or
NaNs"
126
127 def _assertNonEmpty(*arrays):
LinAlgError: Array must not contain infs or NaNs
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4632#comment:2>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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