I tried this in 3.2.3.final and it works fine:
sage: a,b = matrix(QQ,[[0,1],[-4,0]]).eigenvalues(); a,b
(2*I, -2*I)
sage: a in RR
False
sage: b in RR
False
so perhaps you should upgrade?
John Cremona
2009/1/4 Shing Hing Man <mat...@yahoo.com>:
>
> 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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