[GAP Forum] bug in LLLReducedGramMat? II

[Dima Pasechnik]

On Sat, Oct 31, 2015 at 07:29:50AM +0100, Benjamin Sambale wrote:
> Yes, that is basically what I mean. Usually, I'm not interested in
> basis vectors of lattices. I just want to transform a symmetric
> matrix M via SMS^t so that the resulting matrix has "nicer" shape.

Well, define "nicer"...

> In this sense the following non-semidefinite matrix "works"
> perfectly:
> 
> LLLReducedGramMat([[1,2],[2,1]]);
> rec( B := [ -3, 1 ], mue := [ [  ], [ 0 ] ], relations := [  ],
> remainder := [ [ -3, 0 ], [ 0, 1 ] ], transformation := [ [ -2, 1 ],
> [ 1, 0 ] ] )
> 

You can add sufficently scaled indentity matrix to the input, and then subtract the 
term resulting from it from the output. Of course this is an heuristic, but we seem to 
be doing heuristics here.

Cheers,
Dima


> Best,
> Benjamin
> 
> Am 31.10.2015 um 00:33 schrieb Dima Pasechnik:
> >On Fri, Oct 30, 2015 at 11:23:40PM +0100, Bill Allombert wrote:
> >>On Fri, Oct 30, 2015 at 09:11:15PM +0100, Benjamin Sambale wrote:
> >>>Meanwhile, I figured that M in my last email is not positive
> >>>semidefinite, and so it is not a Gram matrix as required in the
> >>>manual. But since many other non-semidefinite matrices do work, one
> >>>should at least change the error message.
> >>I am curious, how do you define 'work' ?
> >check this out:
> >
> >gap> M:=[[0,1],[1,0]];
> >[ [ 0, 1 ], [ 1, 0 ] ]
> >gap> LLLReducedGramMat(M);
> >rec( B := [  ], mue := [  ], relations := [ [ 1, 0 ], [ 0, 1 ] ], remainder := [  ], transformation := [  ] )
> >gap>
> >
> >I suppose "works" means "returns stuff", or "gives up silently"
> >rather than "throws an error"
> >
> >Dima
> >
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>