Re: [sage-support] Re: Inter-versions reproducibility problem of random elements.

[slelievre]

The `random_element` method of `AA` was changed in

https://trac.sagemath.org/ticket/30875

merged in Sage 9.5.rc0.

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Re: [sage-support] Re: Eigen spaces of algebraic matrices broken ?

[slelievre]

The `random_element` method of `AA` was changed in

https://trac.sagemath.org/ticket/30875

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Re: [sage-support] Re: Inter-versions reproducibility problem of random elements.

[Fernando Gouvea]

9.2 on Windows:

sage: print(sage.version.version)
: with seed(0): M = matrix(AA, 3, 3, lambda u,v: AA.random_element())
: M.apply_map(lambda u:u.radical_expression())
9.2
[-2  2 -2]
[-2  0  2]
[-1  2  2]

sagecell.sagemath.org:

9.4

[-2  2 -2]
[-2  0  2]
[-1  2  2]

I'll try 9.3 on Windows tomorrow.

Fernando

On 2/6/2022 2:36 PM, Emmanuel Charpentier wrote:
Also : coud you report the results on as many platforms and/or 
versions as possible ?


Le dimanche 6 février 2022 à 20:23:39 UTC+1, Emmanuel Charpentier a 
écrit :


Seen in this thread
 :

On Sagecell  :

|print(sage.version.version) with seed(0): M = matrix(AA, 3, 3,
lambda u,v: AA.random_element()) M.apply_map(lambda
u:u.radical_expression()) |

prints

|9.4 [-2 2 -2] [-2 0 2] [-1 2 2] |

On Sage 9.5 compiled from source on Debian testing running on core
i7 :

|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] |

Advice required on how to file an efficient ticket.

​

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=
Fernando Q. Gouveahttp://www.colby.edu/~fqgouvea
Carter Professor of Mathematics
Dept. of Mathematics
Colby College
5836 Mayflower Hill
Waterville, ME 04901

Blessed are they who Go Around in Circles, for they Shall be Known as Wheels.

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[sage-support] Re: Inter-versions reproducibility problem of random elements.

[Emmanuel Charpentier]

Also : coud you report the results on as many platforms and/or versions as 
possible ?

Le dimanche 6 février 2022 à 20:23:39 UTC+1, Emmanuel Charpentier a écrit :

> Seen in this thread 
>  :
>
> On Sagecell  :
>
> print(sage.version.version)
> with seed(0): M = matrix(AA, 3, 3, lambda u,v: AA.random_element())
> M.apply_map(lambda u:u.radical_expression())
>
> prints
>
> 9.4
> [-2  2 -2]
> [-2  0  2]
> [-1  2  2]
>
> On Sage 9.5 compiled from source on Debian testing running on core i7 :
>
> 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]
>
> Advice required on how to file an efficient ticket.
> ​
>

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[sage-support] Inter-versions reproducibility problem of random elements.

[Emmanuel Charpentier]

Seen in this thread  
:

On Sagecell  :

print(sage.version.version)
with seed(0): M = matrix(AA, 3, 3, lambda u,v: AA.random_element())
M.apply_map(lambda u:u.radical_expression())

prints

9.4
[-2  2 -2]
[-2  0  2]
[-1  2  2]

On Sage 9.5 compiled from source on Debian testing running on core i7 :

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]

Advice required on how to file an efficient ticket.
​

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Re: [sage-support] Re: Eigen spaces of algebraic matrices broken ?

[Emmanuel Charpentier]

Nins and me got *different* random matrices : his was composed of integers 
in (-2..2), and Sage could compute its eigenspaces ; mine was :

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]

which, BTW, shows a problem about the reproducibility of random elements 
between Sage versions and/or platforms…

Could you post *your* random matrix ? And could you try :

M.95 = matrix(AA,3,3,[-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])
ES = M95.eigenspaces_left()

and report if you get a result ?
​
Le dimanche 6 février 2022 à 17:35:20 UTC+1, alan_thoma...@yahoo.co.uk a 
écrit :

> No, it works with the 9.4 kernel but not with the 9.5 beta.
>

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Re: [sage-support] Re: Eigen spaces of algebraic matrices broken ?

['Alan Stafford' via sage-support]

No, it works with the 9.4 kernel but not with the 9.5 beta.

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Re: [sage-support] Re: Eigen spaces of algebraic matrices broken ?

[Dima Pasechnik]

Is it the same M for 9.4 as for 9.5?

On Sun, 6 Feb 2022, 10:52 'Alan Stafford' via sage-support, <
sage-support@googlegroups.com> wrote:

> My point is that it is the same on Apple Mac, that it isn't related to the
> recent interface and multiprocessing problems but has just appeared with
> the 9.5 kernel beta release as it works with the 9.4 kernel.
>
> On Sunday, February 6, 2022 at 8:53:51 AM UTC Emmanuel Charpentier wrote:
>
>> 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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> 

[sage-support] Re: Eigen spaces of algebraic matrices broken ?

['Alan Stafford' via sage-support]

My point is that it is the same on Apple Mac, that it isn't related to the 
recent interface and multiprocessing problems but has just appeared with 
the 9.5 kernel beta release as it works with the 9.4 kernel.

On Sunday, February 6, 2022 at 8:53:51 AM UTC Emmanuel Charpentier wrote:

> 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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Re: [sage-support] Morphisms between free groups.

['Michel VAN DEN BERGH' via sage-support]

Now it seems "subs" does work. I must have done something wrong. Sorry for 
the noise.

On Friday, February 4, 2022 at 3:55:19 PM UTC+1 dim...@gmail.com wrote:

>
>
> On Fri, 4 Feb 2022, 11:02 David Joyner,  wrote:
>
>> On Fri, Feb 4, 2022 at 4:40 AM 'Michel VAN DEN BERGH' via sage-support
>>  wrote:
>> >
>> > Dear all,
>> >
>> > I need to do something which I thought would be quite simple. I have 
>> free groups
>> > F, G with generators x1,x2,x3,x4 and x,y respectively and I need to 
>> compute the image of an element under the homomorphism F-->G:x1->x, x2->y, 
>> x3->x, x4->y.
>> >
>> > I could not find anything in the manual about morphisms between free 
>> groups. I tried subs, but that does not work since the parents of the 
>> elements of F and G are (of course) different.
>> >
>> > The workaround I used is to work in the free group H with generators 
>> x1,x2,x3,x4,x,y and to use subs. However this is also inconvenient since I 
>> need the action of the braid group with 4 strands on F. It does not act on 
>> H because of the limitation "#strands=#generators".
>> >
>> > So this means I have to use only part of the braid group with 6 strands.
>> >
>> > In the end it all works but it is terribly hacky for some which seems 
>> to be a very clean thing to do.
>> >
>> > I would be grateful for any suggestions.
>>
>> Michel:
>>
>> One idea is to check out
>> https://doc.sagemath.org/html/en/reference/groups/sage/groups/braid.html
>>
>> Another idea is to download braid-1.1.tar.gz, untar in the pkg
>> subdirectory and type LoadPackage("braid");
>>
>
>
> most, if not all, functionality of braid is nowadays in
> https://gap-packages.github.io/MapClass/
>
> (which is in our gap_packages)
>
>
> FYI, the pkg subdir is inside sage-9*/local/share/gap
>> You can find a pdf manual for the braid package at
>> https://arxiv.org/abs/math/0304376
>> Currently, the link to braid-1.1.tar.gz at
>> https://www.gap-system.org/Packages/undep.html
>> is bad but I have a copy. Just email me privately.
>>
>> - David
>>
>> > Michel
>> >
>> >
>> > --
>> > You received this message because you are subscribed to the Google 
>> Groups "sage-support" group.
>> > To unsubscribe from this group and stop receiving emails from it, send 
>> an email to sage-support...@googlegroups.com.
>> > To view this discussion on the web visit 
>> https://groups.google.com/d/msgid/sage-support/f7d460d0-390b-455d-ae90-72b105e8e926n%40googlegroups.com
>> .
>>
>> -- 
>> You received this message because you are subscribed to the Google Groups 
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>> email to sage-support...@googlegroups.com.
>>
> To view this discussion on the web visit 
>> https://groups.google.com/d/msgid/sage-support/CAEQuuAVmSsLxS%2Bi50JNUqrK%3DUm%3DquJaZ2ueNuedAVzr6xKSMzQ%40mail.gmail.com
>> .
>>
>

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[sage-support] Re: Eigen spaces of algebraic matrices broken ?

[Emmanuel Charpentier]

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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