Re: Determine the mirror reflection relationship between the coordinates of two sets of pairs of points in n-dimension space.

[Hongyi Zhao <hongyi.zhao@gmail.com>]

On Mon, Mar 13, 2023 at 5:19 PM Karim Belabas
<Karim.Belabas@math.u-bordeaux.fr> wrote:
>
> * Hongyi Zhao [2023-03-13 04:08]:
> > But in all the above steps, I can only see that there is exactly one v
> > is found.
>
> (Up to normalization, yes.)
>
> > So, the complete solution set of this problem is still not obtained so
> > far.
>
> It is: you get a (short) list V of potential v's; for each such v you get
> a (short) list C of potential c's; and we know that the full solution set
> is inside { s_{v,c}, v in V, c in C }. Where solutions attached to (a.v, a.c)
> for a non-zero scalar 'a' have been grouped together by our normalization.
>
> In this particular case, a single (v,c) is found, and works. (And the
> affine hyperplane it corresponds to is given by the equation <x,v> = c.)
>
> Cheers,
>
>     K.B.
> --
> Pr Karim Belabas, U. Bordeaux, Vice-président en charge du Numérique
> Institut de Mathématiques de Bordeaux UMR 5251 - (+33) 05 40 00 29 77
> http://www.math.u-bordeaux.fr/~kbelabas/
> `

I want to know why your signature above ends with a strange "`" symbol?

Best,
Zhao