def test_polynomial_commitment_same_z():
d = 5
secret = 5
ps = [
Polynomial(Fr(5), Fr(3)),
Polynomial(Fr(1), Fr(2)),
Polynomial(Fr(0), Fr(6), Fr(9)),
]
z = Fr(100)
gamma = Fr(7)
srs = srs_setup(d, secret)
commitments = [commit(p, srs) for p in ps]
evaluations = [p.evaluate(z) for p in ps]
witness = create_witness_same_z(polynomials=ps, gamma=gamma, z=z, srs=srs)
assert verify_evaluation_same_z(
commitments=commitments,
gamma=gamma,
evaluations=evaluations,
z=z,
witness=witness,
srs=srs,
)
def test_fft():
p = Polynomial(3, 1, 4, 1, 5, 9, 2, 6)
domain = EvaluationDomain(domain=[F337(85)**i for i in range(8)])
assert domain.domain == [1, 85, 148, 111, 336, 252, 189, 226]
evaluations = p.fft(domain)
assert evaluations == [31, 70, 109, 74, 334, 181, 232, 4]
p2 = domain.inverse_fft(evaluations)
assert p2.coefficients == (3, 1, 4, 1, 5, 9, 2, 6)
def test_polynomial():
ps = [
Polynomial(),
Polynomial(-1),
Polynomial(1, 1),
Polynomial(1, -11, 1, -1, 1)
]
for p in ps:
repr(p)
def test_division():
a = Polynomial(-288, 0, 2, 1)
b = Polynomial(-6, 1)
assert a / b == Polynomial(48, 8, 1)
a = Polynomial(1, 3, 3, 1)
b = Polynomial(1, 2, 1)
assert a / b == Polynomial(1, 1)
# (x^n -1) / (n*(x-1)) == (1/n)(x^(n-1) +... + 1)
assert Polynomial(F13(-1), F13(0), F13(0), F13(0), F13(1)) / (
Polynomial(F13(-1), F13(1)) * 4) == Polynomial(10, 10, 10, 10)
def test_polynomial_works_on_fields():
p = Polynomial(Fr(1), Fr(2), Fr(100))
repr(p)
p.evaluate(Fr(0))
p.evaluate(Fr(5))
def test_lagrange():
assert lagrange([0, 1, 2], [0, 1, 8]) == Polynomial(0, -2, 3)
assert lagrange([Fr(0), Fr(1), Fr(2)],
[Fr(0), Fr(1), Fr(8)]) == Polynomial(Fr(0), Fr(-2), Fr(3))
def test_polynomial_multiplication():
assert Polynomial(1, 1) * Polynomial(1, 1) == Polynomial(1, 2, 1)
def test_polynomial_addition():
assert Polynomial(1, 1, 1) + (Polynomial(1, 1, 1)) == Polynomial(2, 2, 2)
def test_polynomial_evaluation():
assert Polynomial(1, 1, 1).evaluate(2) == 7
assert Polynomial(-2, 7, -5, 1).evaluate(0) == -2
assert Polynomial(-2, 7, -5, 1).evaluate(1) == 1
assert Polynomial(-2, 7, -5, 1).evaluate(2) == 0
assert Polynomial(-2, 7, -5, 1).evaluate(3) == 1
def test_coset_fft():
ed = EvaluationDomain(domain=[F337(85)**i for i in range(8)])
p = Polynomial(3, 1, 4, 1, 5, 9, 2)
assert p.fft(ed) == [25, 62, 323, 247, 3, 189, 18, 168]
assert p.coset_fft(ed) == [62, 323, 247, 3, 189, 18, 168, 25]