Re: division by zero error in matker(,1) [2]

[Vasily Golyshev <golyshev@mccme.ru>]

Thank you. But my question is not so much about the algorithm
(which is bad for my purposes anyway) as about the extent
to which matker(,1) is reliable. Is it mandatory, for instance,
to do lllint before matker?


On Wed, 2 Oct 2002 Peter-Lawrence.Montgomery@cwi.nl wrote:

>     I have not looked at matker, but suggest you try lattice basis
> reduction (lllint or lllintpartial) on the matrix rows.
>
>      If you still have problems, note that the matrix determinant
> is about (10^200)^283 or 10^56000.  The ten nullspace vectors
> (assuming the matrix has rank 273) have about 56000/10 or 5600
> digits each.  Pick a prime (or composite without small factors)
> p around 10^6000) and find the null space modulo p.
> Choose your basis modulo p so the first basis element
> begins [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], say.
> Assuming you get exactly one vector out (modulo p),
> use simultaneous diophantine approximation
> to find an multiple of this with small coordinates
> (say all bounded by p/10^100) -- hope you have an integer solution.
>
>
>          Peter Montgomery
>
>
> - From pari-users-return-461-pmontgom=cwi.nl@list.cr.yp.to Tue Oct  1 23:46:52 2002
> - Date: Wed, 2 Oct 2002 01:48:31 +0400 (MSD)
> - From: Vasily Golyshev <golyshev@mccme.ru>
>
> Hi. Thanks for the last tip.
> I was trying to find the kernel of an integer matrix 283x273,
> and some of the entries were 200 decimal digits long. I did
> check that each entry was a t_INT. What I got was the error message
> "division by zero in dvmdii". I was using matker(,1) function, in GP
> version 2-1-4 under Linux (actually the Windows version 2-0-17
> returned the same error message). Is that something that has been
> reported?
>
>
>