That was my initial complaint... ;-)
Le samedi 5 février 2022 à 18:05:42 UTC+1, alan_thoma...@yahoo.co.uk a
écrit :
> M.eigenvalues() never returns.
> On Saturday, February 5, 2022 at 11:48:47 AM UTC Emmanuel Charpentier
> wrote:
>
>> What exactly fails in the example ?
>>
>> Le vendredi 4 février 2022 à 13:20:26 UTC+1, alan_thoma...@yahoo.co.uk a
>> écrit :
>>
>>>
>>> On Apple Mac the example above runs on the 9.4 kernel using either the
>>> 9.4 or 9.5 interface but not on the 9.5 kernel from either Interface.
>>> On Thursday, February 3, 2022 at 6:44:47 AM UTC Emmanuel Charpentier
>>> wrote:
>>>
>>>> Le mercredi 2 février 2022 à 22:15:00 UTC+1, Nils Bruin a écrit :
>>>>
>>>> On Monday, 31 January 2022 at 15:19:49 UTC-8 Emmanuel Charpentier wrote:
>>>>>
>>>>>> As advertised, an atempt at a minimal (non-)working example :
>>>>>>
>>>>>> # Reproducible minimal example
>>>>>> with seed(0): M = matrix(AA, 3, 3, lambda u,v: AA.random_element())
>>>>>> # Working ring
>>>>>> WR = M.base_ring().algebraic_closure()
>>>>>> # A variable to carry the eigenvalues
>>>>>> l = SR.var("l")
>>>>>> # Vector of unknowns for the eigenvectors
>>>>>> V =vector(list(var("v", n=2))+[SR(1)])
>>>>>> # M.eigenvalues does not return. Get them by hand
>>>>>>
>>>>>> Actually, for me on 9.5beta9, `M.eigenvalues()` works just fine.
>>>>>
>>>> Hmmm… You may have obtained a “less pathological” M than I did, due to
>>>> possible differences in random numbers generation (notwithstanding my
>>>> attempt at reproducibility…).
>>>>
>>>> What do you get for M ? I have :
>>>>
>>>> sage: with seed(0): M = matrix(AA, 3, 3, lambda u,v: AA.random_element())
>>>> sage: M.apply_map(lambda u:u.radical_expression())
>>>> [ -sqrt(2) - 1 -1/4 -2*sqrt(3)]
>>>> [ 1/2 1/8*sqrt(33) + 1/8 -1/5*sqrt(29) + 3/5]
>>>> [ 0 1/4 1/2]
>>>>
>>>> So the problem is perhaps just platform-dependent, or there is a very
>>>>> recent change that affected this (my M gets just integer entries from
>>>>> {-2..2})
>>>>>
>>>> Okay. We have a problem in reproducibility : with seed(0): should
>>>> entail a reproducible, platform-independent result. It did not. BTW, what
>>>> is your platform ?
>>>>
>>>> Suggestions on how to document this and file a ticket ?
>>>>
>>>> I agree with the rest of your conclusions, but going to numerical
>>>> approximations then trying to somehow “recognize” the algebraics they are
>>>> approximations of somehow denies the whole point of working in QQbar…
>>>>
>>>> Looking at the example a bit: you'd be forcing sage to work with a huge
>>>>> compositum if you're actually getting a 3x3 matrix with non-rational
>>>>> algebraic entries: even if they are just independent quadratics, you'd
>>>>> end
>>>>> up in an extension of degree 2^9. This will only work in very limited
>>>>> cases.
>>>>>
>>>>> One way to get this kind of thing to work is to work with
>>>>> high-precision floats, use numerically (fairly) stable methods to compute
>>>>> the desired answer, and then try to recognize it as algebraic. You
>>>>> probably
>>>>> only care if it is one of fairly low height. You can then try to turn
>>>>> your
>>>>> computation into proof, possibly by tracing through height bounds and
>>>>> showing your precision was sufficient to identify the right solution
>>>>> uniquely.
>>>>>
>>>>> You could work on automating this kind of thing, but I doubt you'd
>>>>> ever get it to work on a reasonable range of examples; just because the
>>>>> height bounds would be rather ill-behaved.
>>>>>
>>>>> You can still trace the root cause further on this and perhaps improve
>>>>> arithmetic in AA a bit, but the general shape of the problem you're
>>>>> trying
>>>>> to deal with does not look promising for generally performant methods.
>>>>>
>>>>
>>>>
>>>
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