To test equality of two Edwards points \(P_1 = (X_1:Y_1:Z_1:T_1)\) and \(P_2 = (X_2:Y_2:Z_2:T_2)\) which represent Ristretto points, it's sufficient to check whether \[ X_1 Y_2 = Y_1 X_2 \quad \mathrm{or} \quad Y_1 Y_2 = -a X_1 X_2. \]

Note that when \(a = -1\), this simplifies to \[ X_1 Y_2 = Y_1 X_2 \quad \mathrm{or} \quad Y_1 Y_2 = X_1 X_2. \]

Unlike testing equality on the Edwards curve, this does not require an inversion and can be done in projective coordinates.