def test_gf_frobenius_map():
f = ZZ.map([2, 0, 1, 0, 2, 2, 0, 2, 2, 2])
g = ZZ.map([1, 1, 0, 2, 0, 1, 0, 2, 0, 1])
p = 3
b = gf_frobenius_monomial_base(g, p, ZZ)
h = gf_frobenius_map(f, g, b, p, ZZ)
h1 = gf_pow_mod(f, p, g, p, ZZ)
assert h == h1
def test_gf_frobenius_map():
f = ZZ.map([2, 0, 1, 0, 2, 2, 0, 2, 2, 2])
g = ZZ.map([1,1,0,2,0,1,0,2,0,1])
p = 3
n = 4
b = gf_frobenius_monomial_base(g, p, ZZ)
h = gf_frobenius_map(f, g, b, p, ZZ)
h1 = gf_pow_mod(f, p, g, p, ZZ)
assert h == h1
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, ZZ)
assert gf_trace_map(a, b, c, 0, f, 11, ZZ) == ([1, 1, 1], [1, 1, 1])
assert gf_trace_map(a, b, c, 1, f, 11, ZZ) == ([5, 2, 10, 3], [5, 3, 0, 4])
assert gf_trace_map(a, b, c, 2, f, 11, ZZ) == ([5, 9, 5, 3], [10, 1, 5, 7])
assert gf_trace_map(a, b, c, 3, f, 11, ZZ) == ([1, 10, 6, 0], [7])
assert gf_trace_map(a, b, c, 4, f, 11, ZZ) == ([1, 1, 1], [1, 1, 8])
assert gf_trace_map(a, b, c, 5, f, 11, ZZ) == ([5, 2, 10, 3], [5, 3, 0, 0])
assert gf_trace_map(a, b, c, 11, f, 11, ZZ) == ([1, 10, 6, 0], [10])
def test_gf_powering():
assert gf_pow([1,0,0,1,8], 0, 11, ZZ) == [1]
assert gf_pow([1,0,0,1,8], 1, 11, ZZ) == [1, 0, 0, 1, 8]
assert gf_pow([1,0,0,1,8], 2, 11, ZZ) == [1, 0, 0, 2, 5, 0, 1, 5, 9]
assert gf_pow([1,0,0,1,8], 5, 11, ZZ) == \
[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, ZZ) == \
[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, ZZ) == \
[ 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, ZZ) == [1]
assert gf_pow_mod([1,0,0,1,8], 1, [2,0,7], 11, ZZ) == [1,1]
assert gf_pow_mod([1,0,0,1,8], 2, [2,0,7], 11, ZZ) == [2,3]
assert gf_pow_mod([1,0,0,1,8], 5, [2,0,7], 11, ZZ) == [7,8]
assert gf_pow_mod([1,0,0,1,8], 8, [2,0,7], 11, ZZ) == [1,5]
assert gf_pow_mod([1,0,0,1,8], 45, [2,0,7], 11, ZZ) == [5,4]
def test_gf_trace_map():
f = ZZ.map([1, 1, 4, 9, 1])
a = [1, 1, 1]
c = ZZ.map([1, 0])
b = gf_pow_mod(c, 11, f, 11, ZZ)
assert gf_trace_map(a, b, c, 0, f, 11, ZZ) == ([1, 1, 1], [1, 1, 1])
assert gf_trace_map(a, b, c, 1, f, 11, ZZ) == ([5, 2, 10, 3], [5, 3, 0, 4])
assert gf_trace_map(a, b, c, 2, f, 11, ZZ) == ([5, 9, 5, 3], [10, 1, 5, 7])
assert gf_trace_map(a, b, c, 3, f, 11, ZZ) == ([1, 10, 6, 0], [7])
assert gf_trace_map(a, b, c, 4, f, 11, ZZ) == ([1, 1, 1], [1, 1, 8])
assert gf_trace_map(a, b, c, 5, f, 11, ZZ) == ([5, 2, 10, 3], [5, 3, 0, 0])
assert gf_trace_map(a, b, c, 11, f, 11, ZZ) == ([1, 10, 6, 0], [10])
def test_gf_powering():
assert gf_pow([1, 0, 0, 1, 8], 0, 11, ZZ) == [1]
assert gf_pow([1, 0, 0, 1, 8], 1, 11, ZZ) == [1, 0, 0, 1, 8]
assert gf_pow([1, 0, 0, 1, 8], 2, 11, ZZ) == [1, 0, 0, 2, 5, 0, 1, 5, 9]
assert gf_pow([1, 0, 0, 1, 8], 5, 11, ZZ) == [
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, ZZ) == [
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, ZZ) == [
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(ZZ.map([1, 0, 0, 1, 8]), 0, ZZ.map([2, 0, 7]), 11, ZZ) == [1]
assert gf_pow_mod(ZZ.map([1, 0, 0, 1, 8]), 1, ZZ.map([2, 0, 7]), 11, ZZ) == [1, 1]
assert gf_pow_mod(ZZ.map([1, 0, 0, 1, 8]), 2, ZZ.map([2, 0, 7]), 11, ZZ) == [2, 3]
assert gf_pow_mod(ZZ.map([1, 0, 0, 1, 8]), 5, ZZ.map([2, 0, 7]), 11, ZZ) == [7, 8]
assert gf_pow_mod(ZZ.map([1, 0, 0, 1, 8]), 8, ZZ.map([2, 0, 7]), 11, ZZ) == [1, 5]
assert gf_pow_mod(ZZ.map([1, 0, 0, 1, 8]), 45, ZZ.map([2, 0, 7]), 11, ZZ) == [5, 4]