When to use equivalence relations? How to write it in octave?

[WMDhamnekar]

Sometimes to help describe one expression, another expression is shown that produces identical results. The exact equivalence of expressions is indicated with ‘ ≡’.

For example: rot90 ([1, 2; 3, 4], -1) ≡ rot90 ([1, 2; 3, 4], 3) ≡ rot90 ([1, 2; 3, 4], 7)

What is the meaning of 'rot90;?

What is the meaning of this example?

How to write equivalence relation in octave?

How does all of the above expressions have equivalence relation?

 

[Evgeny.Makarov]

I don't know Octave, but rot90(x, k) probably is the result of rotating x by $k\cdot90^\circ$. I am not sure what [1, 2; 3, 4] represents: a matrix, points coordinates or something else, but this may not be important in this example. The important point is that rotating by $3\cdot90^\circ$ is the same as rotating by $7\cdot90^\circ$, which is also the same as rotating by $90^\circ$ in the opposite direction. Therefore, expressions rot90 ([1, 2; 3, 4], -1), rot90 ([1, 2; 3, 4], 3) and rot90 ([1, 2; 3, 4], 7) are equivalent. The set of all pairs of equivalent expressions forms an equivalence relation.