def testMul(self):
self.assertEqual(1, Rational(2,3) * Rational(3,2))
self.assertEqual(Rational(26,18), Rational(13,18) * 2)
self.assertEqual(500000000000000000000000000000000000000,
1000000000000000000000000000000000000000 * Rational(1,2))
self.assertEqual(Rational(1, 36), Rational(1,2) * Rational(1,3) * Rational(1,6))
## self.assertEqual(Rational(1,4), Rational(1,2) * 0.5)
## self.assertEqual(Rational(1,4), 0.5 * Rational(1,2))
self.assertEqual(0.25, Rational(1,2) * 0.5)
self.assertEqual(0.25, 0.5 * Rational(1,2))
self.assertEqual(Float(0.25), Rational(1,2) * Float(0.5))
self.assertEqual(Float(0.25), Float(0.5) * Rational(1,2))
def e3(x):
"""
0 = x[0] + x[1]*t + x[2]*t**2 + x[3]*t**3
"""
x3 = Float(x[3])
a = x[2] / x3
b = x[1] / x3
c = x[0] / x3
p = b - (a**2) / 3
q = 2 * (a**3) / 27 - a * b / 3 + c
w = (-1 + cmath.sqrt(-3)) / 2
W = (1, w, w.conjugate())
k = -q / 2 + cmath.sqrt((q**2) / 4 + (p**3) / 27)
l = -q / 2 - cmath.sqrt((q**2) / 4 + (p**3) / 27)
m = k**(1 / 3)
n = l**(1 / 3)
# choose n*W[i] by which m*n*W[i] be the nearest to -p/3
checker = [abs(3 * m * n * z + p) for z in W]
n = n * W[checker.index(min(checker))]
sol = []
for i in range(3):
sol.append(W[i] * m + W[-i] * n - a / 3)
return sol
def __init__(self, value):
"""
value will be wrapped in Float.
"""
ring.FieldElement.__init__(self)
if isinstance(value, rational.Rational):
self.data = value.toFloat()
else:
self.data = Float(value)
def Newton(f, initial=1, repeat=250):
"""
Compute x s.t. 0 = f[0] + f[1] * x + ... + f[n] * x ** n
"""
length = len(f)
df = []
for i in range(1, length):
df.append(i * f[i])
l = initial
for k in range(repeat):
coeff = Float(0)
dfcoeff = Float(0)
for i in range(1, length):
coeff = coeff * l + f[-i]
dfcoeff += dfcoeff * l + df[-i]
coeff = coeff * l + f[0]
if coeff == 0:
return l
elif dfcoeff == 0: # Note coeff != 0
raise ValueError(
"There is not solution or Choose different initial")
else:
l = l - coeff / dfcoeff
return l
def createElement(self, seed):
return Float(seed)
def toFloat(self):
return Float(self.numerator) / Float(self.denominator)