I just worked on implementing the sage-combinat generic testing
framework for matrices, with a test function for minpoly. I got some
interesting results. Is there something wrong in these tests below?
**************************************************************************
Over GF(5), I get lots of different results:
sage: A = Matrix(GF(5),3,3,srange(9))
sage: A.minpoly()
x^3 + 3*x^2 + 2*x
sage: A.minpoly()
x^2 + 2*x
sage: A.minpoly()
x^2 + 3*x + 2
sage: A.minpoly()
x^3 + 3*x^2 + 2*x
sage: A.minpoly()
x^3 + 3*x^2 + 2*x
sage: A.minpoly()
x^2 + x
sage: A.minpoly()
x^2 + x
sage: A.minpoly()
x^2 + 2*x
sage: A.minpoly()
x^2 + x
sage: A.minpoly()
x^3 + 3*x^2 + 2*x
**************************************************************************
Over QQ[a,b], I get an error:
sage: R.<a,b> = QQ[]
sage: m = matrix(R,2,[0,a,b,b^2])
sage: m.minpoly()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
/home/jason/.sage/temp/littleone/16177/_home_jason__sage_init_sage_0.py
in <module>()
/home/jason/sage/local/lib/python2.6/site-packages/sage/matrix/matrix2.so
in sage.matrix.matrix2.Matrix.minpoly (sage/matrix/matrix2.c:8014)()
/home/jason/sage/local/lib/python2.6/site-packages/sage/rings/polynomial/polynomial_element.so
in sage.rings.polynomial.polynomial_element.Polynomial.is_squarefree
(sage/rings/polynomial/polynomial_element.c:32924)()
AttributeError: 'sage.rings.polynomial.polynomial_element.Polynomia'
object has no attribute 'gcd'
**************************************************************************
Over Integers(25)['x'], I get an error:
sage: A = random_matrix(Integers(25)['x'],2); A
[7*x^2 + 20*x + 23 2*x^2 + 2*x + 18]
[ x^2 + 12*x + 22 6*x^2 + 16*x + 15]
sage: A.minpoly()
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
/home/jason/.sage/temp/littleone/16177/_home_jason__sage_init_sage_0.py
in <module>()
/home/jason/sage/local/lib/python2.6/site-packages/sage/matrix/matrix2.so
in sage.matrix.matrix2.Matrix.minpoly (sage/matrix/matrix2.c:7997)()
/home/jason/sage/local/lib/python2.6/site-packages/sage/matrix/matrix2.so
in sage.matrix.matrix2.Matrix.charpoly (sage/matrix/matrix2.c:8742)()
/home/jason/sage/local/lib/python2.6/site-packages/sage/matrix/matrix2.so
in sage.matrix.matrix2.Matrix._charpoly_hessenberg
(sage/matrix/matrix2.c:10491)()
/home/jason/sage/local/lib/python2.6/site-packages/sage/matrix/matrix2.so
in sage.matrix.matrix2.Matrix.hessenberg_form (sage/matrix/matrix2.c:9779)()
TypeError: self must be an integral domain.
Hessenberg form only possible for matrices over a field
**************************************************************************
This funny behavior with the is_zero function on 2x2 integer matrices
showed up:
sage: m=sage.matrix.matrix_integer_2x2.MatrixSpace_ZZ_2x2()(0)
sage: m
[0 0]
[0 0]
sage: m.is_zero()
True
sage: (m-m).is_zero()
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
/home/jason/.sage/temp/littleone/16177/_home_jason__sage_init_sage_0.py
in <module>()
/home/jason/sage/local/lib/python2.6/site-packages/sage/structure/element.so
in sage.structure.element.Element.is_zero (sage/structure/element.c:4811)()
/home/jason/sage/local/lib/python2.6/site-packages/sage/matrix/matrix0.so
in sage.matrix.matrix0.Matrix.__nonzero__ (sage/matrix/matrix0.c:21577)()
TypeError: 'NoneType' object is not callable
**************************************************************************
Okay, so I'm now sold on the generic testing framework in #6343 (which
has been merged into 4.1.2.alpha2).
For the curious, all I did was define a function:
def _test_minpoly(self, **options):
"""
Checks that :meth:`minpoly` works.
EXAMPLES::
sage: a=matrix([[1,2],[3,4]])
sage: a._test_minpoly()
"""
if self.nrows()==self.ncols():
tester = self._tester(**options)
# At least we'll check that the minimal polynomial kills the
# matrix.
tester.assert_(self.minpoly().subs(x=self).is_zero())
Then in every matrix class, right under the calls to load(dumps..., I
just put a call to TestSuite().run(), like so:
sage: m = matrix(ZZ['x'], 2, 3, [1..6])
sage: loads(dumps(m)) == m
True
sage: TestSuite(m).run()
Then I ran the doctests in the matrix directory and all the above errors
were failures in the doctests. (I also had to change an existing method
called "_test_pickle" to conform to the new generic doctesting framework)
Jason
--
Jason Grout
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