def test_gf_arith():
assert gf_neg([], 11, ZZ) == []
assert gf_neg([1], 11, ZZ) == [10]
assert gf_neg([1, 2, 3], 11, ZZ) == [10, 9, 8]
assert gf_add_ground([], 0, 11, ZZ) == []
assert gf_sub_ground([], 0, 11, ZZ) == []
assert gf_add_ground([], 3, 11, ZZ) == [3]
assert gf_sub_ground([], 3, 11, ZZ) == [8]
assert gf_add_ground([1], 3, 11, ZZ) == [4]
assert gf_sub_ground([1], 3, 11, ZZ) == [9]
assert gf_add_ground([8], 3, 11, ZZ) == []
assert gf_sub_ground([3], 3, 11, ZZ) == []
assert gf_add_ground([1, 2, 3], 3, 11, ZZ) == [1, 2, 6]
assert gf_sub_ground([1, 2, 3], 3, 11, ZZ) == [1, 2, 0]
assert gf_mul_ground([], 0, 11, ZZ) == []
assert gf_mul_ground([], 1, 11, ZZ) == []
assert gf_mul_ground([1], 0, 11, ZZ) == []
assert gf_mul_ground([1], 1, 11, ZZ) == [1]
assert gf_mul_ground([1, 2, 3], 0, 11, ZZ) == []
assert gf_mul_ground([1, 2, 3], 1, 11, ZZ) == [1, 2, 3]
assert gf_mul_ground([1, 2, 3], 7, 11, ZZ) == [7, 3, 10]
assert gf_add([], [], 11, ZZ) == []
assert gf_add([1], [], 11, ZZ) == [1]
assert gf_add([], [1], 11, ZZ) == [1]
assert gf_add([1], [1], 11, ZZ) == [2]
assert gf_add([1], [2], 11, ZZ) == [3]
assert gf_add([1, 2], [1], 11, ZZ) == [1, 3]
assert gf_add([1], [1, 2], 11, ZZ) == [1, 3]
assert gf_add([1, 2, 3], [8, 9, 10], 11, ZZ) == [9, 0, 2]
assert gf_sub([], [], 11, ZZ) == []
assert gf_sub([1], [], 11, ZZ) == [1]
assert gf_sub([], [1], 11, ZZ) == [10]
assert gf_sub([1], [1], 11, ZZ) == []
assert gf_sub([1], [2], 11, ZZ) == [10]
assert gf_sub([1, 2], [1], 11, ZZ) == [1, 1]
assert gf_sub([1], [1, 2], 11, ZZ) == [10, 10]
assert gf_sub([3, 2, 1], [8, 9, 10], 11, ZZ) == [6, 4, 2]
assert gf_add_mul([1, 5, 6], [7, 3], [8, 0, 6, 1], 11,
ZZ) == [1, 2, 10, 8, 9]
assert gf_sub_mul([1, 5, 6], [7, 3], [8, 0, 6, 1], 11,
ZZ) == [10, 9, 3, 2, 3]
assert gf_mul([], [], 11, ZZ) == []
assert gf_mul([], [1], 11, ZZ) == []
assert gf_mul([1], [], 11, ZZ) == []
assert gf_mul([1], [1], 11, ZZ) == [1]
assert gf_mul([5], [7], 11, ZZ) == [2]
assert gf_mul([3, 0, 0, 6, 1, 2], [4, 0, 1, 0], 11,
ZZ) == [1, 0, 3, 2, 4, 3, 1, 2, 0]
assert gf_mul([4, 0, 1, 0], [3, 0, 0, 6, 1, 2], 11,
ZZ) == [1, 0, 3, 2, 4, 3, 1, 2, 0]
assert gf_mul([2, 0, 0, 1, 7], [2, 0, 0, 1, 7], 11,
ZZ) == [4, 0, 0, 4, 6, 0, 1, 3, 5]
assert gf_sqr([], 11, ZZ) == []
assert gf_sqr([2], 11, ZZ) == [4]
assert gf_sqr([1, 2], 11, ZZ) == [1, 4, 4]
assert gf_sqr([2, 0, 0, 1, 7], 11, ZZ) == [4, 0, 0, 4, 6, 0, 1, 3, 5]
def test_gf_arith():
assert gf_neg([], 11, ZZ) == []
assert gf_neg([1], 11, ZZ) == [10]
assert gf_neg([1, 2, 3], 11, ZZ) == [10, 9, 8]
assert gf_add_ground([], 0, 11, ZZ) == []
assert gf_sub_ground([], 0, 11, ZZ) == []
assert gf_add_ground([], 3, 11, ZZ) == [3]
assert gf_sub_ground([], 3, 11, ZZ) == [8]
assert gf_add_ground([1], 3, 11, ZZ) == [4]
assert gf_sub_ground([1], 3, 11, ZZ) == [9]
assert gf_add_ground([8], 3, 11, ZZ) == []
assert gf_sub_ground([3], 3, 11, ZZ) == []
assert gf_add_ground([1, 2, 3], 3, 11, ZZ) == [1, 2, 6]
assert gf_sub_ground([1, 2, 3], 3, 11, ZZ) == [1, 2, 0]
assert gf_mul_ground([], 0, 11, ZZ) == []
assert gf_mul_ground([], 1, 11, ZZ) == []
assert gf_mul_ground([1], 0, 11, ZZ) == []
assert gf_mul_ground([1], 1, 11, ZZ) == [1]
assert gf_mul_ground([1, 2, 3], 0, 11, ZZ) == []
assert gf_mul_ground([1, 2, 3], 1, 11, ZZ) == [1, 2, 3]
assert gf_mul_ground([1, 2, 3], 7, 11, ZZ) == [7, 3, 10]
assert gf_add([], [], 11, ZZ) == []
assert gf_add([1], [], 11, ZZ) == [1]
assert gf_add([], [1], 11, ZZ) == [1]
assert gf_add([1], [1], 11, ZZ) == [2]
assert gf_add([1], [2], 11, ZZ) == [3]
assert gf_add([1, 2], [1], 11, ZZ) == [1, 3]
assert gf_add([1], [1, 2], 11, ZZ) == [1, 3]
assert gf_add([1, 2, 3], [8, 9, 10], 11, ZZ) == [9, 0, 2]
assert gf_sub([], [], 11, ZZ) == []
assert gf_sub([1], [], 11, ZZ) == [1]
assert gf_sub([], [1], 11, ZZ) == [10]
assert gf_sub([1], [1], 11, ZZ) == []
assert gf_sub([1], [2], 11, ZZ) == [10]
assert gf_sub([1, 2], [1], 11, ZZ) == [1, 1]
assert gf_sub([1], [1, 2], 11, ZZ) == [10, 10]
assert gf_sub([3, 2, 1], [8, 9, 10], 11, ZZ) == [6, 4, 2]
assert gf_add_mul(
[1, 5, 6], [7, 3], [8, 0, 6, 1], 11, ZZ) == [1, 2, 10, 8, 9]
assert gf_sub_mul(
[1, 5, 6], [7, 3], [8, 0, 6, 1], 11, ZZ) == [10, 9, 3, 2, 3]
assert gf_mul([], [], 11, ZZ) == []
assert gf_mul([], [1], 11, ZZ) == []
assert gf_mul([1], [], 11, ZZ) == []
assert gf_mul([1], [1], 11, ZZ) == [1]
assert gf_mul([5], [7], 11, ZZ) == [2]
assert gf_mul([3, 0, 0, 6, 1, 2], [4, 0, 1, 0], 11, ZZ) == [1, 0,
3, 2, 4, 3, 1, 2, 0]
assert gf_mul([4, 0, 1, 0], [3, 0, 0, 6, 1, 2], 11, ZZ) == [1, 0,
3, 2, 4, 3, 1, 2, 0]
assert gf_mul([2, 0, 0, 1, 7], [2, 0, 0, 1, 7], 11, ZZ) == [4, 0,
0, 4, 6, 0, 1, 3, 5]
assert gf_sqr([], 11, ZZ) == []
assert gf_sqr([2], 11, ZZ) == [4]
assert gf_sqr([1, 2], 11, ZZ) == [1, 4, 4]
assert gf_sqr([2, 0, 0, 1, 7], 11, ZZ) == [4, 0, 0, 4, 6, 0, 1, 3, 5]