Thanks for the suggestion to add a scaled identity matrix, this is a
good idea. Just to clarify: my last email wasn't meant as a follow-up
question. I totally understand that LLL will not work for non Gram
matrices. But I was very confused to get this misleading error message
for one particular example while at the same time other non Gram
matrices give no error. If I had observed this earlier, I would not have
sent any email to the list.
Best wishes,
Benjamin
Am 31.10.2015 um 11:35 schrieb 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
_______________________________________________
Forum mailing list
Forum@mail.gap-system.org
http://mail.gap-system.org/mailman/listinfo/forum
_______________________________________________
Forum mailing list
Forum@mail.gap-system.org
http://mail.gap-system.org/mailman/listinfo/forum
