R&S HUI wrote:
> Another treatment of /: and \: can be found in the
> following J Wiki page:
>
> http://www.jsoftware.com/jwiki/Essays/Symmetries_of_the_Square
Here is another approach to symmetries of the square that relates
elementary identities of the complex plane to permutations.
p=:1j0 0j1 _1j0 0j_1
P=:1 : 'p i. u p'
j. P
1 2 3 0
+ P
0 3 2 1
] P
0 1 2 3
j. and + are generators for an action of the dihedral group on the
complex plane. The adverb P gives a direct permutation representation
of the transformation of the orbit p. Then we have for example
(- P)-:(j.^:2 P)
1
(j.^:[EMAIL PROTECTED] P)-:([EMAIL PROTECTED] P)
1
Best wishes,
John
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