issue with roots() over Algebraic Real field #2559
Description
I can't say much about this one:
sage: M
[[-1.2859513130484710 .. -1.2859513130484707] [0.48604391035188904 .. 0.48604391035188910]]
[ [2.8742392060133346 .. 2.8742392060133351] [0.18370733043549580 .. 0.18370733043549584]]
sage: M.parent()
Full MatrixSpace of 2 by 2 dense matrices over Algebraic Real Field
sage: M.charpoly()
x^2 + [1.1022439826129748 .. 1.1022439826129751]*x + [-1.6332451457675854 .. -1.6332451457675851]
sage: M.charpoly().parent()
Univariate Polynomial Ring in x over Algebraic Real Field
sage: M.charpoly().roots()
Exception exceptions.AttributeError: "'sage.rings.complex_interval.ComplexIntervalFieldEl' object has no attribute 'lower'" in 'sage.rings.polynomial.polynomial_element.Polynomial_generic_dense.__normalize' ignored
---------------------------------------------------------------------------
<type 'exceptions.AttributeError'> Traceback (most recent call last)
/Users/ncalexan/Documents/School/MATH235/genus2cm/<ipython console> in <module>()
/Users/ncalexan/Documents/School/MATH235/genus2cm/polynomial_element.pyx in sage.rings.polynomial.polynomial_element.Polynomial.roots()
/Users/ncalexan/Documents/School/MATH235/genus2cm/real_roots.pyx in sage.rings.polynomial.real_roots.real_roots()
/Users/ncalexan/Documents/School/MATH235/genus2cm/polynomial_element.pyx in sage.rings.polynomial.polynomial_element.Polynomial.squarefree_decomposition()
/Users/ncalexan/Documents/School/MATH235/genus2cm/element.pyx in sage.structure.element.PrincipalIdealDomainElement.gcd()
/Users/ncalexan/sage-2.10.3.rc3/local/lib/python2.5/site-packages/sage/rings/polynomial/polynomial_element_generic.py in _gcd(self, other)
542 Return the GCD of self and other, as a monic polynomial.
543 """
--> 544 g = EuclideanDomainElement._gcd(self, other)
545 c = g.leading_coefficient()
546 if c.is_unit():
/Users/ncalexan/Documents/School/MATH235/genus2cm/element.pyx in sage.structure.element.EuclideanDomainElement._gcd()
/Users/ncalexan/sage-2.10.3.rc3/local/lib/python2.5/site-packages/sage/rings/polynomial/polynomial_element_generic.py in quo_rem(self, other)
533 aaa = (R.leading_coefficient()/B.leading_coefficient())
534 bbb = X**(R.degree()-B.degree())
--> 535 S = aaa * bbb
536 Q += S
537 R -= S*B
/Users/ncalexan/Documents/School/MATH235/genus2cm/element.pyx in sage.structure.element.RingElement.__mul__()
/Users/ncalexan/Documents/School/MATH235/genus2cm/coerce.pyx in sage.structure.coerce.CoercionModel_cache_maps.bin_op_c()
/Users/ncalexan/Documents/School/MATH235/genus2cm/action.pyx in sage.categories.action.Action._call_c()
/Users/ncalexan/Documents/School/MATH235/genus2cm/coerce.pyx in sage.structure.coerce.LeftModuleAction._call_c_impl()
/Users/ncalexan/Documents/School/MATH235/genus2cm/coerce.pxi in sage.structure.coerce._rmul_c()
/Users/ncalexan/Documents/School/MATH235/genus2cm/element.pyx in sage.structure.element.ModuleElement._rmul_()
/Users/ncalexan/Documents/School/MATH235/genus2cm/polynomial_element.pyx in sage.rings.polynomial.polynomial_element.Polynomial_generic_dense._rmul_c_impl()
/Users/ncalexan/Documents/School/MATH235/genus2cm/element.pyx in sage.structure.element.Element.__nonzero__()
/Users/ncalexan/Documents/School/MATH235/genus2cm/element.pyx in sage.structure.element.Element.__richcmp__()
/Users/ncalexan/Documents/School/MATH235/genus2cm/element.pyx in sage.structure.element.Element._richcmp()
/Users/ncalexan/sage-2.10.3.rc3/local/lib/python2.5/site-packages/sage/rings/qqbar.py in __cmp__(self, other)
2752 if self is other: return 0
2753 if other._descr.is_rational() and other._descr.rational_value() == 0:
-> 2754 return self.sign()
2755 elif self._descr.is_rational() and self._descr.rational_value() == 0:
2756 return -other.sign()
/Users/ncalexan/sage-2.10.3.rc3/local/lib/python2.5/site-packages/sage/rings/qqbar.py in sign(self)
2855 0
2856 """
-> 2857 if self._value.lower() > 0:
2858 return 1
2859 elif self._value.upper() < 0:
<type 'exceptions.AttributeError'>: 'sage.rings.complex_interval.ComplexIntervalFieldEl' object has no attribute 'lower'
CC: @ncalexan
Component: commutative algebra
Keywords: algebraic real roots
Issue created by migration from https://trac.sagemath.org/ticket/2559