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Karim Belabas on Mon, 13 Mar 2023 10:20:47 +0100
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Re: Determine the mirror reflection relationship between the coordinates of two sets of pairs of points in n-dimension space.
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- To: Hongyi Zhao <hongyi.zhao@gmail.com>
- Subject: Re: Determine the mirror reflection relationship between the coordinates of two sets of pairs of points in n-dimension space.
- From: Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>
- Date: Mon, 13 Mar 2023 10:19:28 +0100
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* 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/
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