People in this thread might want to note the
ticket https://trac.sagemath.org/ticket/21024
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Le vendredi 18 novembre 2016 04:44:49 UTC+1, Kwankyu Lee a écrit :
> I am not a big fan of the suggested asymptotically best algorithms relying
> on auxiliary tools, which would be hard to implement and gain for small
> matrices might be not much.
>
For sure; I do not know precisely what the th
>
> Vincent Neiger will soon join my group for two years as a postdoc, and I
> know he is interested in implementing some of these things. I hope we
> can do some things here and improve Sage's capabilities in this respect.
>
This would be great!
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Hi Vincent,
Thank you for your expert comments and cutting-edge references. My target
is to get hermite normal forms for square matrices over polynomial rings
over finite fields, underlying function field arithmetic. What is available
in Sage for this is only "A._hermite_form_PID()", which is v
Le jeudi 17 novembre 2016 21:15:11 UTC+1, Johan S. H. Rosenkilde a écrit :
>
> John Cremona writes:
> > I once used the weak Popov form in a talk with Hendrik Lenstra in the
> > audience and he was quite amused since it appeared to be (and I think
> > he is right) much the same as his brother Ar
Le jeudi 17 novembre 2016 21:15:11 UTC+1, Johan S. H. Rosenkilde a écrit :
>
> John Cremona writes:
> > I once used the weak Popov form in a talk with Hendrik Lenstra in the
> > audience and he was quite amused since it appeared to be (and I think
> > he is right) much the same as his brother Ar
Regarding the original question: is the question specifically about
computing the HNF? Or, is any other canonical form acceptable? (with known
algorithms, it seems that the Popov form would be easier to implement
efficiently than the HNF)
Also, would you have examples of typical dimensions and
> Not me -- but I did review it in 2010! -- see
> https://trac.sagemath.org/ticket/9069
Ah, I misunderstood what you had written previously :-)
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On 17 November 2016 at 20:15, Johan S. H. Rosenkilde wrote:
> John Cremona writes:
>> That was the algorithm I implemented in Magma. It was not very hard.
>
> Indeed. My student made an effort of comparing C++, Cython and pure Sage
> implementations, in combination with various tweaks to the algo
John Cremona writes:
> That was the algorithm I implemented in Magma. It was not very hard.
Indeed. My student made an effort of comparing C++, Cython and pure Sage
implementations, in combination with various tweaks to the algorithm.
In the end the Cython version was at best 2x faster than my p
An optimised version is implemented in fricas, available as
fricas. HP_solve
It might provide a good benchmark.
Martin
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On 17 November 2016 at 16:07, Johan S. H. Rosenkilde wrote:
>> I'm sure that Sage already has code for Weak Popov Form. I
>> implemented it myself in about 2004 but from the date you can tell
>> that it was not in Sage (but Magma).
>>
>> Indeed, search_src("popov") finds
>>
>> matrix/matrix_misc.
> I'm sure that Sage already has code for Weak Popov Form. I
> implemented it myself in about 2004 but from the date you can tell
> that it was not in Sage (but Magma).
>
> Indeed, search_src("popov") finds
>
> matrix/matrix_misc.py:32:def weak_popov_form(M,ascend=True):
That function doesn't com
There's been quite a bit of work on Hermite normal form of K[x]-matrices
recently, most notably by Vincent Neiger:
http://dl.acm.org/citation.cfm?id=2930889.2930936
This algorithm gives a much faster way of computing the Hermite Normal
form of K[x] matrices. Unfortunately it relies on quite stack
I'm sure that Sage already has code for Weak Popov Form. I
implemented it myself in about 2004 but from the date you can tell
that it was not in Sage (but Magma).
Indeed, search_src("popov") finds
matrix/matrix_misc.py:32:def weak_popov_form(M,ascend=True):
John
On 17 November 2016 at 15:27, '
A colleague suggested to look at the Popov form. I didn't look at what Sage
is currently doing, so my apologies if this turns out to not be a useful
comment.
Here is a random paper on this that I found [1].
Bill.
[1] http://perso.ens-lyon.fr/gilles.villard/BIBLIOGRAPHIE/PDF/issac96.pdf
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