Hi,
I would like to test if an eigenvalue of a matrix over the
rationals is a real number.
(or The roots of the characteristic polynomial are all real.)
I am using
x in RR
Somehow, when x=2i, 'x in RR' produced the following error.
Thanks in advance for any assistance!
Shing
PS : I am using Sage 3.2.1.
{{{id=74|
E = matrix(QQ,[[0,1],[-4,0]]);E
///
[ 0 1]
[-4 0]
}}}
{{{id=72|
E.eigenvalues()
///
[2*I, -2*I]
}}}
{{{id=76|
type(E.eigenvalues()[0])
///
<class 'sage.rings.qqbar.AlgebraicNumber'>
}}}
{{{id=73|
E.eigenvalues()[0] in RR
///
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/home/matmsh/.sage/sage_notebook/worksheets/admin/128/code/
211.py", line 7, in <module>
exec compile(ur'E.eigenvalues()[_sage_const_0 ] in RR' + '\n',
'', 'single')
File "/usr/local/lib/sage-3.2.1/local/lib/python2.5/site-packages/
SQLAlchemy-0.4.6-py2.5.egg/", line 1, in <module>
File "parent.pyx", line 324, in
sage.structure.parent.Parent.__contains__ (sage/structure/parent.c:
3925)
File "parent.pyx", line 284, in
sage.structure.parent.Parent.__call__ (sage/structure/parent.c:3709)
File "coerce_maps.pyx", line 146, in
sage.structure.coerce_maps.NamedConvertMap._call_ (sage/structure/
coerce_maps.c:3589)
File "/usr/local/lib/sage-3.2.1/local/lib/python2.5/site-packages/
sage/rings/qqbar.py", line 2725, in _mpfr_
return AA(self)._mpfr_(field)
File "/usr/local/lib/sage-3.2.1/local/lib/python2.5/site-packages/
sage/rings/qqbar.py", line 499, in __call__
raise ValueError, "Cannot coerce algebraic number with non-zero
imaginary part to algebraic real"
ValueError: Cannot coerce algebraic number with non-zero imaginary
part to algebraic real
}}}
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