# From the Sonic paper

from finite_fields import finitefield
import numpy as np

from multipoly import Variable, MultivariatePolynomial

p = 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001
fp = finitefield.IntegersModP(p)

var_one = fp(1)
var_x = fp(4)
var_y = fp(6)
var_s = fp(1)
var_xy = var_x * var_y
var_sxy = var_s * var_xy
var_1_neg_s = var_one - var_s
var_x_y = var_x + var_y
var_1_neg_s_x_y = var_1_neg_s * var_x_y
var_s_neg_1 = -var_1_neg_s
var_zero = fp(0)

public_v = var_s * (var_x * var_y) + (1 - var_s) * (var_x + var_y)

a = np.array([
    var_one, var_x, var_xy, var_1_neg_s, var_s
])
b = np.array([
    var_one, var_y, var_s, var_x_y, var_s_neg_1
])
c = np.array([
    var_one, var_xy, var_sxy, var_1_neg_s_x_y, var_zero
])
assert len(a) == len(b)
assert len(b) == len(c)

for i, (a_i, b_i, c_i) in enumerate(zip(a, b, c), 1):
    try:
        assert a_i * b_i == c_i
    except AssertionError:
        print("Error for %i" % i)
        raise

# 1 - s = -(s - 1)
u1 = np.array([0, 0, 0, 1, 0])
v1 = np.array([0, 0, 0, 0, 1])
w1 = np.array([0, 0, 0, 0, 0])
k1 = 0

assert a.dot(u1) + b.dot(v1) + c.dot(w1) == k1

# xy = xy
u2 = np.array([0, 0, 1, 0, 0])
v2 = np.array([0, 0, 0, 0, 0])
w2 = np.array([0, -1, 0, 0, 0])
k2 = 0

assert a.dot(u2) + b.dot(v2) + c.dot(w2) == k2

# s = s
u3 = np.array([0, 0, 0, 0, -1])
v3 = np.array([0, 0, 1, 0, 0])
w3 = np.array([0, 0, 0, 0, 0])
k3 = 0

assert a.dot(u3) + b.dot(v3) + c.dot(w3) == k3

# zero = 0
u4 = np.array([0, 0, 0, 0, 0])
v4 = np.array([0, 0, 0, 0, 0])
w4 = np.array([0, 0, 0, 0, 1])
k4 = 0

assert a.dot(u4) + b.dot(v4) + c.dot(w4) == k4

# 1 - s
u5 = np.array([1, 0, 0, -1, 0])
v5 = np.array([0, 0, -1, 0, 0])
w5 = np.array([0, 0, 0, 0, 0])
k5 = 0

assert a.dot(u5) + b.dot(v5) + c.dot(w5) == k5

# x + y
u6 = np.array([0, 1, 0, 0, 0])
v6 = np.array([0, 1, 0, -1, 0])
w6 = np.array([0, 0, 0, 0, 0])
k6 = 0

assert a.dot(u6) + b.dot(v6) + c.dot(w6) == k6

# Final check:
# v = s(xy) + (1 - s)(x + y)
u7 = np.array([0, 0, 0, 0, 0])
v7 = np.array([0, 0, 0, 0, 0])
w7 = np.array([0, 0, 1, 1, 0])
k7 = public_v

assert a.dot(u7) + b.dot(v7) + c.dot(w7) == k7

u = np.vstack((u1, u2, u3, u4, u5, u6, u7))
v = np.vstack((v1, v2, v3, v4, v5, v6, v7))
w = np.vstack((w1, w2, w3, w4, w5, w6, w7))
assert u.shape == v.shape
assert u.shape == w.shape

k = np.array((k1, k2, k3, k4, k5, k6, k7))

y = Variable("Y")
p = MultivariatePolynomial()
for i, (a_i, b_i, c_i) in enumerate(zip(a, b, c), 1):
    #print(a_i, "\t", b_i, "\t", c_i)
    p += y**i * (a_i * b_i - c_i)
print("Polynomial:", p)

p = MultivariatePolynomial()
for q, (u_q, v_q, w_q, k_q) in enumerate(zip(u, v, w, k)):
    p += y**q * (a.dot(u_q) + b.dot(v_q) + c.dot(w_q) - k_q)
print("Polynomial:", p)