On Tue, Sep 15, 2009 at 11:14 AM, Jason Grout
<jason-s...@creativetrax.com> wrote:
>
> 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
The above is trac #6296:
http://trac.sagemath.org/sage_trac/ticket/6296
It's a bug in linbox.
>
> **************************************************************************
>
> 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'
That's definitely a bug.
> **************************************************************************
>
>
> 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 should have raised a NotImplementedError.
>
> **************************************************************************
>
> 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
>
That's definitely a bug.
>
> **************************************************************************
>
>
> 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)
Sweeeeeeeeeeeeeeeeet!
William
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