John Wilson wrote:
> I can prove this using subscripts (i.e., involving
> expressions like (<i;j){G ), but is there a proof
> involving just the arrays G, R and M?
I've not constructed such a proof, and I don't have
time right now, but here's how I'd approach this.
First, I'd define G, R and M as functions rather than
as arrays:
G=: ]
I=: [: = [: i. #
r=: 1 |."1 G
R=: [: |: [: r I
m=: |."1
M=: [: |: [: m I
Then, I'd represent my propositions as J tautologies
G -: [: |: G NB. (1) arg is symmetric
G -: R dp G dp [: |: R NB. (2) arg is rotationally symmetric
And, I'd represent my assertion as a J tautology
G -: M dp G dp [: |: M NB. (3) arg is mirror-image symmetric
Then I'd expand G, M and R in the above statements, and
strive to show that they are equivalent, expressing my
intermediate steps as equivalent tautologies
To avoid wasting too much time on silly mistakes, I'd also
construct a representative argument, and run each of my
supposedly equivalent statements against it.
(G -: [: |: G) t
1
(G -: ([: |: [: r I) dp G dp [: |: R ) t
1
etc.
Anyways... perhaps this will help.
Good luck,
--
Raul
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