construct/mc quasigroup idempotent
construct/mc quasigroup idempotent: a task in MathConstructOptimize-Envs-harbor (Harbor dataset). Construct a quasigroup of order 8 on {0, ..., 7}: a 8x8 table T (T x y = x y) in which every row and every column is a permutation of 0..7, such that - T x x = x for all x (idempotent), and - T T x y…
The task
Construct a quasigroup of order 8 on {0, ..., 7}: a 8x8 table T (T[x][y] = x*y) in which every row and every column is a permutation of 0..7, such that - T[x][x] = x for all x (idempotent), and - T[T[x][y]][T[y][x]] = x for all x, y (the identity (x*y)*(y*x) = x).