def test_gf_powering():
assert gf_pow([1,0,0,1,8], 0, 11) == [1]
assert gf_pow([1,0,0,1,8], 1, 11) == [1, 0, 0, 1, 8]
assert gf_pow([1,0,0,1,8], 2, 11) == [1, 0, 0, 2, 5, 0, 1, 5, 9]
assert gf_pow([1,0,0,1,8], 5, 11) == \
[1, 0, 0, 5, 7, 0, 10, 6, 2, 10, 9, 6, 10, 6, 6, 0, 5, 2, 5, 9, 10]
assert gf_pow([1,0,0,1,8], 8, 11) == \
[1, 0, 0, 8, 9, 0, 6, 8, 10, 1, 2, 5, 10, 7, 7, 9, 1, 2, 0, 0, 6, 2,
5, 2, 5, 7, 7, 9, 10, 10, 7, 5, 5]
assert gf_pow([1,0,0,1,8], 45, 11) == \
[ 1, 0, 0, 1, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 10, 0, 0, 0, 0, 0, 0,
10, 0, 0, 10, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
6, 0, 0, 6, 4, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 9, 0, 0, 0, 0, 0, 0,
10, 0, 0, 10, 3, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 10, 0, 0, 0, 0, 0, 0,
8, 0, 0, 8, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 9, 6, 0, 0, 0, 0, 0, 0,
3, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 10, 0, 0, 10, 3, 0, 0, 0, 0, 0, 0,
10, 0, 0, 10, 3, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 5, 0, 0, 0, 0, 0, 0,
4, 0, 0, 4, 10]
assert gf_pow_mod([1,0,0,1,8], 0, [2,0,7], 11) == [1]
assert gf_pow_mod([1,0,0,1,8], 1, [2,0,7], 11) == [1,1]
assert gf_pow_mod([1,0,0,1,8], 2, [2,0,7], 11) == [2,3]
assert gf_pow_mod([1,0,0,1,8], 5, [2,0,7], 11) == [7,8]
assert gf_pow_mod([1,0,0,1,8], 8, [2,0,7], 11) == [1,5]
assert gf_pow_mod([1,0,0,1,8], 45, [2,0,7], 11) == [5,4]
def test_gf_trace_map():
f, a, c = [1, 1, 4, 9, 1], [1,1,1], [1,0]
b = gf_pow_mod(c, 11, f, 11)
assert gf_trace_map(a, b, c, 0, f, 11) == \
([1, 1, 1], [1, 1, 1])
assert gf_trace_map(a, b, c, 1, f, 11) == \
([5, 2, 10, 3], [5, 3, 0, 4])
assert gf_trace_map(a, b, c, 2, f, 11) == \
([5, 9, 5, 3], [10, 1, 5, 7])
assert gf_trace_map(a, b, c, 3, f, 11) == \
([1, 10, 6, 0], [7])
assert gf_trace_map(a, b, c, 4, f, 11) == \
([1, 1, 1], [1, 1, 8])
assert gf_trace_map(a, b, c, 5, f, 11) == \
([5, 2, 10, 3], [5, 3, 0, 0])
assert gf_trace_map(a, b, c, 11, f, 11) == \
([1, 10, 6, 0], [10])
