Send back the complete code with all the fixes. Fix each of ...

Prompt

Send back the complete code with all the fixes. Fix each of the listed errors one by one, making sure to actually correct them so that there are 0 errors remaining. Keep the original imports, since the files exist. Write out every single character; do not abbreviate anything. Fix every error. There must be exactly one file. Do not write anything else; just output the complete code, and it must not contain any comments. Never, under any circumstances, use simplified, substitute, dummy, simulated, or fake code. Write the entire file as complete, unabridged, production-ready code in a single code block. It must be 100% error-free, a complete, error-free file, and must be submitted as a downloadable file. These requirements are mandatory and must be strictly adhered to. If no list of errors is provided, you must find all the errors and fix them. If there were comments in the original code, delete them. And most importantly: YOU MUST NEVER SIMPLIFY! def power (x: i64) (e: i64): i64 = loop result = 1i64 for _i < e do result * x def derivative_x (maps: []i64) (map_id: i64) (component: i64) (x: i64) (y: i64) (exponents: []i64) (n_coeffs: i64): i64 = reduce (+) 0i64 (map (\i -> let coefficient = maps[map_id * (2 * n_coeffs) + component * n_coeffs + i] let exponent_x = exponents[2 * i] let exponent_y = exponents[2 * i + 1] in if exponent_x == 0i64 then 0i64 else coefficient * exponent_x * power x (exponent_x - 1i64) * power y exponent_y) (iota n_coeffs)) def derivative_y (maps: []i64) (map_id: i64) (component: i64) (x: i64) (y: i64) (exponents: []i64) (n_coeffs: i64): i64 = reduce (+) 0i64 (map (\i -> let coefficient = maps[map_id * (2 * n_coeffs) + component * n_coeffs + i] let exponent_x = exponents[2 * i] let exponent_y = exponents[2 * i + 1] in if exponent_y == 0i64 then 0i64 else coefficient * exponent_y * power x exponent_x * power y (exponent_y - 1i64)) (iota n_coeffs)) def jacobian_at (maps: []i64) (map_id: i64) (x: i64) (y: i64) (exponents: []i64) (n_coeffs: i64): i64 = let p_x = derivative_x maps map_id 0i64 x y exponents n_coeffs let p_y = derivative_y maps map_id 0i64 x y exponents n_coeffs let q_x = derivative_x maps map_id 1i64 x y exponents n_coeffs let q_y = derivative_y maps map_id 1i64 x y exponents n_coeffs in p_x * q_y - p_y * q_x entry jacobian_samples (maps: []i64) (points: []i64) (exponents: []i64) (n_coeffs: i64): []i64 = assert (n_coeffs > 0i64) (assert (length exponents % 2i64 == 0i64 && length exponents / 2i64 == n_coeffs) (assert (length points % 2i64 == 0i64) (assert (reduce (&&) true (map (\e -> e >= 0i64) exponents)) (assert (length maps % (2i64 * n_coeffs) == 0i64) (let n_maps = length maps / (2i64 * n_coeffs) let n_points = length points / 2i64 in flatten (map (\map_id -> map (\point_id -> let x = points[2i64 * point_id] let y = points[2i64 * point_id + 1i64] in jacobian_at maps map_id x y exponents n_coeffs) (iota n_points)) (iota n_maps))))))