Vasily Golyshev on Wed, 2 Oct 2002 17:17:41 +0400 (MSD)

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

```Thank you. But my question is not so much about the algorithm
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?
>
>
>
```