Finite fields evidently need a lot of work before they are released.
Thanks for pointing this out.  Here are some further problems:

sage: GF(2).is_field()
False
sage: GF(next_prime(10^20)).is_field()
False
sage: GF(19^20,'a').is_field()
Traceback (most recent call last):
...
ZeroDivisionError: Inverse does not exist.
sage: GF(8,'a').is_field()
True

I'm going to put all the above into the finite field doctests
but with the correct output, so there is no chance this won't get
fixed before the official release.

Many thanks for your bug report!!

William

On Sat, 02 Dec 2006 13:38:17 -0800, Robert Miller <[EMAIL PROTECTED]>  
wrote:

>
> Should this behavior be happening?
>
> sage: MM = Matrix(GF(2),[[0]])
> sage: MM.eigenspaces()
>
> Traceback (most recent call last):
>   File "<stdin>", line 1, in <module>
>   File "/home/server2/sage_notebook/worksheets/myworksheet/code/60.py",
> line 4, in <module>
>     MM.eigenspaces()
>   File "/sage-1.5/local/lib/python2.5/", line 1, in <module>
>
>   File "matrix2.pyx", line 1666, in matrix2.Matrix.eigenspaces
>   File "matrix2.pyx", line 966, in matrix2.Matrix.kernel
>   File  
> "/sage-1.5/local/lib/python2.5/site-packages/sage/modules/free_module.py",
> line 282, in VectorSpace
>     raise TypeError, "K must be a field"
> TypeError: K must be a field
>


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