On Sat, Feb 5, 2011 at 2:01 PM, Rob Beezer <goo...@beezer.cotse.net> wrote:
> I've finished a major overhaul of the matrix kernel routines, aiming
> for greater reliability and easier maintenance.  It has required
> almost no changes outside of  sage/matrix  but I have one problemsome
> doctest that now fails.
>
> http://trac.sagemath.org/sage_trac/ticket/10746
>
> Notice that current behavior at a 4.6.2.alpha3 command line is to give
> a different result on a subsequent run (and then it stays the same,
> giving the second result repeatedly).  With my patches, I get a third
> value, but the runs all give the same result.
>
> Any advice or suggestions on what is happening here?  I know there is
> some randomness in these computations, so maybe this test needs more
> precautions?  By adjusting the "3" in the system_of_eigenvalues() call
> you can get a longer list of values.  Are any of these answers, wrong,
> or are any right?  I've tried to chase my way back to some of the
> matrix code, but I'm a bit out of my element on this one.
>
> Thanks in advance for any assistance.
>
> Rob
>
>
>
> ** Essence of original doctest, sage/modular/hecke/module.py, ~ line
> 1545
>
> sage: set_random_seed(0)
>
> ::
>
> sage: ModularSymbols_clear_cache()
>
> ::
>
> sage: M = ModularSymbols(62,2,sign=-1)
>
> sage: S = M.cuspidal_submodule().new_submodule()
>
> sage: [A.system_of_eigenvalues(3) for A in S.decomposition()]
>
> [[1, 1, 0], [1, -1, -alpha - 1]]

This is not enough information to decide whether or not the output is
correct.  Can you run the following line immediately after the above
line in each case:

sage: [A.system_of_eigenvalues(3)[0].parent() for A in S.decomposition()]
[Rational Field, Number Field in alpha with defining polynomial x^2 + 4*x + 1]

It's important to number what the defining polynomial of the number
field is in each case.

William


>
>
>
> ** 4.6.2.alpha3 command-line:
>
> sage: set_random_seed(0)
>
> sage: ModularSymbols_clear_cache()
>
> sage: M = ModularSymbols(62,2,sign=-1)
>
> sage: S = M.cuspidal_submodule().new_submodule()
>
> sage: [A.system_of_eigenvalues(3) for A in S.decomposition()]
>
> [[1, 1, 0], [1, -1, -alpha - 1]]
>
> sage: set_random_seed(0)
>
> sage: ModularSymbols_clear_cache()
>
> sage: M = ModularSymbols(62,2,sign=-1)
>
> sage: S = M.cuspidal_submodule().new_submodule()
>
> sage: [A.system_of_eigenvalues(3) for A in S.decomposition()]
>
> [[1, 1, 0], [1, -1, 1/2*alpha + 1/2]]
>
>
> 4.6.2.alpha3 w/ kernel patch, command-line:
>
> sage: set_random_seed(0)
>
> sage: ModularSymbols_clear_cache()
>
> sage: M = ModularSymbols(62,2,sign=-1)
>
> sage: S = M.cuspidal_submodule().new_submodule()
>
> sage: [A.system_of_eigenvalues(3) for A in S.decomposition()]
>
> [[1, 1, 0], [1, -1, -1/2*alpha - 1/2]]
>
> sage: set_random_seed(0)
>
> sage: ModularSymbols_clear_cache()
>
> sage: M = ModularSymbols(62,2,sign=-1)
>
> sage: S = M.cuspidal_submodule().new_submodule()
>
> sage: [A.system_of_eigenvalues(3) for A in S.decomposition()]
>
> [[1, 1, 0], [1, -1, -1/2*alpha - 1/2]]
>
> --
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>



-- 
William Stein
Professor of Mathematics
University of Washington
http://wstein.org

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