One of the polynomials obtained by taking powers of the Brahmagupta matrix. They satisfy the recurrence relation x_(n + 1) | = | x x_n + t y y_n y_(n + 1) | = | x y_n + y x_n. A list of many others is given by Suryanarayan. Explicitly, x_n | = | x^n + t(n 2) x^(n - 2) y^2 + t^2(n 4) x^(n - 4) y^4 + ... y_n | = | n x^(n - 1) y + t(n 3) x^(n - 3) y^3 + t^2(n 5) x^(n - 5) y^5 + .... The Brahmagupta polynomials satisfy (dx_n)/(dx) | = | (dy_n)/(dy) = n x_(n - 1) (dx_n)/(dy) | = | t(dy_n)/(dy) = n t y_(n - 1).