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>]

Hi here,

I've the following two sets of point pairs in a given dimensional of
space, aka, 8 here, as follows:

? A=[-1.12014, -3.17998, -18.2911, 20.1524, -6.94559, -21.8148,
0.975253, 7.95121; 12.8475, -6.00645, 19.3356, 19.7475, -6.17003,
-2.66469, 24.6888, 5.86053; -16.7258, -22.5862, 20.591, 9.54292,
18.5927, 21.9645, 20.892, 0.0563033; -17.2971, 5.16334, -16.3141,
5.35391, -10.307, -13.6297, 23.5236, 24.192; -11.0926, 6.0634,
19.4003, 21.6093, -1.37237, -21.7654, 4.35257, -3.1105; 11.2137,
-20.5612, -3.41736, 19.6006, -1.13627, -6.21613, 11.5885, 15.2543;
-13.4837, 8.02265, -11.4049, 23.3052, -19.5653, 3.19629, -10.814,
-17.1669];
? B=[-19.6192, -19.8916, 21.9217, 9.26674, 22.0351, 19.6121, 19.8591,
1.64306; 1.39387, -5.56517, 13.6578, 22.8011, -16.2283, -11.6133,
8.81048, -9.95819; -0.18953, 6.13486, 25.3313, 18.5031, 9.34097,
-13.2645, 20.0343, 13.0102; -3.4197, -6.93323, 3.31249, 18.2038,
16.274, -18.1138, 6.36411, 23.2793; -3.91626, -0.57597, -17.0051,
19.8855, -3.61887, -24.0882, -0.0230154, 9.48462; -24.6641, 18.4349,
-6.2631, 22.238, -6.2633, -5.89393, -14.8056, -11.0355; -12.9205,
1.0875, -18.3268, 5.77166, -15.5141, -10.0714, 25.0861, 21.7919];

I want to determine whether they are connetted by a mirror reflection
transformation, and if so, identify such a transformation matrix
connecting them.

I wonder if PARI/GP can help to do the trick in this case. Any tips
will be appreciated.

Regards,
Zhao
-- 
Assoc. Prof. Hongsheng Zhao <hongyi.zhao@gmail.com>
Theory and Simulation of Materials
Hebei Vocational University of Technology and Engineering
No. 473, Quannan West Street, Xindu District, Xingtai, Hebei province