def test_sub(self):
first = Polynom({'ggg': 14.5, 'x': 2.539, '': 77})
second = Polynom({'ggg': (-1j + 1), 'yz': -4, 'ab': 4, '': -77})
self.assertTrue(
compare_with_epsilon(
Polynom({
'ggg': (13.5 + 1j),
'yz': 4,
'ab': -4,
'': 154,
'x': 2.539
}), first - second))
self.assertTrue(
compare_with_epsilon(Polynom({
'ggg': 14.5,
'x': 2.539,
'': 50.7
}), first - +26.3))
self.assertTrue(compare_with_epsilon(0, second - second))
self.assertTrue(
compare_with_epsilon(
0.5, second - Polynom({
'ggg': (-1j + 1),
'yz': -4,
'ab': 4
}) - -77.5))
def Euclid_test():
f1 = Polynom(f_values, p)
f2 = Polynom((1, 1), p)
d, a, b = ext_Euclid(f1, f2)
print((a * f1 + b * f2).coefs)
print(d.coefs)
def test_pow(self):
polynom_ = Polynom({'x': 1, '': -2})
self.assertTrue(
compare_with_epsilon(Polynom({
'xx': 1,
'x': -4,
'': 4
}), polynom_**2.0))
with self.assertRaises(ArithmeticError):
polynom_**(-1)
with self.assertRaises(TypeError):
polynom_**0.5
def test_mul(self):
first = Polynom({'x': 5, 'y': -4})
second = Polynom({'x': -2, 'y': 6})
self.assertTrue(
compare_with_epsilon(Polynom({
'xx': -10,
'xy': 38,
'yy': -24
}), first * second))
self.assertTrue(
compare_with_epsilon(Polynom({
'x': -10,
'y': 8
}), -2 * first))
self.assertTrue(compare_with_epsilon(0, second * 0))
def get_invertable(low, up):
found = False
res = None
while not found:
try:
res = np.random.randint(low, up + 1, size=Polynom.N)
Polynom.CUR_MOD = p
inv1 = invert_mine(Polynom(res))
Polynom.CUR_MOD = q
inv2 = invert_mine(Polynom(res))
found = True
except:
print("Not good, not good at all")
found = False
return res
def test_truediv(self):
polynom_ = Polynom({'xy': 2, 'z': 0.676})
self.assertTrue(
compare_with_epsilon(Polynom({
'xy': 1,
'z': 0.338
}), polynom_ / 2))
self.assertTrue(
compare_with_epsilon(Polynom({
'xy': 4,
'z': 1.352
}), polynom_ / 0.5))
with self.assertRaises(ArithmeticError):
polynom_ / Polynom({'x': 25})
with self.assertRaises(ZeroDivisionError):
polynom_ / 0
def test_NTRU():
Polynom.CUR_MOD = p
f = Polynom(f_values)
fp = invert_mine(f)
Polynom.CUR_MOD = q
f = Polynom(f_values)
fq = invert_mine(f)
g = Polynom(g_values)
h = Polynom(p * fq.coefs) * g # PUBLIC
h.apply_mod()
print("fp : ", fp)
print("fq : ", fq)
print("h : ", h)
print("\nEncryption")
m = Polynom(m_values)
r = Polynom(r_values)
print("m : ", m)
print("r : ", r)
e = r * h + m # MESSAGE
e.apply_mod()
print(e)
print("\nDecryption")
f = Polynom(f_values)
a = f * e
a.apply_halfmod()
print("a : ", a)
Polynom.CUR_MOD = p
b = a
b.apply_halfmod()
print("b : ", b)
c = fp * f * m
c.apply_halfmod()
print("c : ", c)
def test_add_polynom(self):
first = Polynom({'xyx': 2, 'z': 0, '': 2.539})
second = Polynom({'xxy': 5j, 'z': -4, 'abcc': 4})
third = Polynom({'cabc': -2, 'z': 4, '': -2.539})
self.assertTrue(
compare_with_epsilon(Polynom({
'xxy': (2 + 5j),
'abcc': 2
}), first + second + third))
self.assertTrue(
compare_with_epsilon(
Polynom({
'xxy': (2 + 5j),
'': 2.539,
'z': -4,
'abcc': 4
}), first + second))
self.assertTrue(
compare_with_epsilon(Polynom({
'xxy': 2,
'abcc': -2,
'z': 4
}), first + third))
self.assertTrue(
compare_with_epsilon(Polynom({
'xxy': 5j,
'abcc': 2,
'': -2.539
}), second + third))
def get_polynom(self, expression):
operands = []
polynom = None
for i in range(len(expression)):
if (self.is_operand(expression[i]) or 'j' in expression[i]
or re.match(FLOAT_RE, expression[i])):
if (re.search(NOT_DIGIT, expression[i]) and
'.' not in expression[i] and 'j' not in expression[i]):
polynom = Polynom({expression[i]: 1})
else:
types = [int, float, complex]
for type_ in types:
try:
polynom = Polynom({'': type_(expression[i])})
except ValueError:
continue
if polynom:
operands.append(polynom)
if self.is_operation(expression[i]):
operands[-2:] = [
self.operations[expression[i]](*operands[-2:])]
return operands[-1]
def test_add_other(self):
polynom_ = Polynom({'xyx': 2, 'z': 0, '': 2.539})
self.assertTrue(
compare_with_epsilon(Polynom({
'xyx': 2,
'z': 0,
'': (2.539 + 5j)
}), polynom_ + 5j))
self.assertTrue(
compare_with_epsilon(
Polynom({
'xyx': 2,
'z': 0,
'': (18.039 + 5j)
}), polynom_ + 15.5))
self.assertTrue(
compare_with_epsilon(
Polynom({
'xyx': 2,
'z': 0,
'': (-1.961 + 5j)
}), polynom_ + -20))
with self.assertRaises(TypeError):
polynom_ + 5 * 'asdfgh'
def test_get_polynom(self):
parser = Parser("xyz + xyz".replace(' ', ''))
self.assertTrue(compare_with_epsilon(Polynom({'xyz': 2}), parser()))
parser = Parser("(x-2)(x-2)")
self.assertTrue(compare_with_epsilon(
Polynom({'xx': 1, 'x': -4, '': 4}), parser()))
parser = Parser("(x + y)++(x)".replace(' ', ''))
self.assertTrue(compare_with_epsilon(
Polynom({'x': 2, 'y': 1}), parser()))
parser = Parser("x^2 + 2x^3 + x^2 -4x+4".replace(' ', ''))
self.assertTrue(compare_with_epsilon(Polynom(
{'xx': 2, 'xxx': 2, 'x': -4, '': 4}), parser()))
parser = Parser("j")
self.assertTrue(compare_with_epsilon(Polynom({'': 1j}), parser()))
parser = Parser("-2j + 5xu".replace(' ', ''))
self.assertTrue(compare_with_epsilon(
Polynom({'': -2j, 'xu': 5}), parser()))
parser = Parser(" -x^2^3".replace(' ', ''))
self.assertTrue(compare_with_epsilon(
Polynom({'xxxxxxxx': -1}), parser()))
parser = Parser("x/(0x + 1)".replace(' ', ''))
self.assertTrue(compare_with_epsilon(Polynom({'x': 1}), parser()))
parser = Parser("jjx")
self.assertTrue(compare_with_epsilon(Polynom({'x': -1}), parser()))
def get_polynomials(self):
M = np.zeros((self.n - 1, self.n - 1))
M[0][0] = 2 * (self.h[0] + self.h[1])
M[0][1] = self.h[1]
M[self.n - 2, self.n - 3] = self.h[self.dots_count - 3]
M[self.n - 2,
self.n - 2] = 2 * (self.h[self.n - 2] + self.h[self.n - 1])
for i in range(2, self.n - 1):
M[i - 1][i - 2] = self.h[i - 1]
M[i - 1][i - 1] = 2 * (self.h[i - 1] + self.h[i])
M[i - 1][i] = self.h[i]
v = np.zeros(self.n - 1)
for i in range(1, self.n):
v[i - 1] = 3.0 * (
(self.dots[i + 1][1] - self.dots[i][1]) / self.h[i] -
(self.dots[i][1] - self.dots[i - 1][1]) / self.h[i - 1])
result = np.linalg.solve(M, v)
self.c[0] = 0.0
for i in range(0, self.n - 1):
self.c[i + 1] = result[i]
for i in range(self.n):
self.a[i] = self.dots[i][1]
for i in range(self.n - 1):
self.d[i] = (self.c[i + 1] - self.c[i]) / (3.0 * self.h[i])
self.b[i] = (self.dots[i+1][1] - self.dots[i][1]) / self.h[i] - \
self.h[i] / 3.0 * (self.c[i+1] + 2.0 * self.c[i])
self.d[self.n - 1] = -self.c[self.n - 1] / (3.0 * self.h[self.n - 1])
self.b[self.n-1] = (self.dots[self.n][1] - self.dots[self.n-1][1]) / self.h[self.n-1] - \
self.h[self.n-1] / 3.0 * 2.0 * self.c[self.n-1]
self.polynomials = []
for i in range(self.n):
self.polynomials.append(
Polynom(self.a[i], self.b[i], self.c[i], self.d[i],
self.dots[i][0]))
def test_derivative_3(self):
poly = Polynom("175")
self.assertEqual(str(poly.derivative()), "0")
def test_derivative_2(self):
poly = Polynom("x")
self.assertEqual(str(poly.derivative()), "1")
t.coefficient = 3 t.degree = 1 assert (t.__str__() == "3x") assert (t.evaluate(2) == 6) t.coefficient = 4 t.degree = 2 assert (t.__str__() == "4x^2") assert (t.evaluate(3) == 36) t.coefficient = 1 t.degree = 2 assert (t.__str__() == "x^2") assert (t.evaluate(3) == 9) p = Polynom() assert (hasattr(p, "head")) assert (hasattr(p, "add")) assert (hasattr(p, "evaluate")) assert (p.__str__() == "") assert (p.evaluate(100) == 0) p.add(4, 3) assert (p.__str__() == "4x^3") assert (p.evaluate(2) == 32) p.add(3, 2) assert (p.__str__() == "4x^3+3x^2") assert (p.evaluate(2) == 32 + 12)
def test_two_solutions(self):
""" Resolve X^2 - X - 12 = 0 """
p = Polynom(1, -1, -12)
self.assertEqual(str(p), 'X^2 - X - 12')
self.assertEqual(p.get_sol(), [-3, 4])
def test_one_solution(self):
""" Resolve X^2 = 0 """
p = Polynom(1, 0, 0)
self.assertEqual(str(p), 'X^2')
self.assertEqual(p.get_sol(), [0])
def test_none_solution(self):
""" Resolve X^2 + X + 1 = 0 """
p = Polynom(1, 1, 1)
self.assertEqual(str(p), 'X^2 + X + 1')
self.assertEqual(p.get_sol(), [])
def test_a_zero(self):
""" Coefficient a should not be 0 """
with self.assertRaises(AssertionError):
p = Polynom(0, 1, 2)
def main():
p = Polynom(argv[1])
p.print_derivative()
def test_derivative_4(self):
poly = Polynom("x^2")
self.assertEqual(str(poly.derivative()), "2*x")
def test_check_new_polynom(self):
polynom1 = Polynom({'xz': 2, '': 3.5})
polynom2 = Polynom({'xz': -2, '': -2.5})
self.assertTrue(compare_with_epsilon(1, polynom1 + polynom2))
def test_compare_with_epsilon(self):
polynom1 = Polynom({'xy': 2, '': 6})
polynom2 = Polynom({'xy': 2, '': -2.5})
self.assertTrue(compare_with_epsilon(1, polynom1 - polynom2, 10))
def setUp(self):
self.poly_1 = Polynom("3x^5 + 2x^5 + 4x^3 + 5 + 2")
from polynom import Polynom
def power1(p, d):
# A fun iterative version of raising a polynomial to a power.
result = p
# We use d - 2 instead of d - 1 because we are initializing our result to p already
for i in range(d - 2):
# Multiply result variable by itself!
result *= result
return result
def power2(p, d):
# A more fun recursive version of raising a polynomial to a power.
if d == 1:
# A polynomial raised to power 1 is itself
return p
else:
# Otherwise, get the polynomial to the desired power / 2
x = power2(p, d / 2)
# Multiply this by itself to get the desired result
return x * x
p1 = Polynom([(1, 0), (1, 1)])
print(p1)
print(power1(p1, 4))
print(power2(p1, 4))
