def test_trivial(self):
G = y - x
S = newton_iteration(G, 3)
self.assertEqual(S, x)
G = y - x**2
S = newton_iteration(G, 3)
self.assertEqual(S, x**2)
def test_trivial(self):
G = y - x
S = newton_iteration(G,3)
self.assertEqual(S,x)
G = y - x**2
S = newton_iteration(G,3)
self.assertEqual(S,x**2)
def test_n(self):
# test if the solution is indeed given to the desired terms
G = y - x**2
S = newton_iteration(G, 0)
self.assertEqual(S, 0)
G = y - x**2
S = newton_iteration(G, 3)
self.assertEqual(S, x**2)
def test_n(self):
# test if the solution is indeed given to the desired terms
G = y - x**2
S = newton_iteration(G,0)
self.assertEqual(S,0)
G = y - x**2
S = newton_iteration(G,3)
self.assertEqual(S,x**2)
def test_geometric(self):
G = (1 - x) * y - 1
S = newton_iteration(G, 9).truncate(x, 10)
z = var('z')
series = taylor(1 / (1 - z), z, 0, 9)
series = R(series.subs({z: x}))
self.assertEqual(S, series)
def test_geometric(self):
G = (1-x)*y - 1
S = newton_iteration(G,9).truncate(x,10)
z = var('z')
series = taylor(1/(1-z),z,0,9)
series = R(series.subs({z:x}))
self.assertEqual(S,series)
def test_cuberoot(self):
# recenter cuberoot(x) at x+1
G = (y + 1)**3 - (x + 1)
S = newton_iteration(G, 9).truncate(x, 10) + 1
z = var('z')
series = taylor(z**(QQ(1) / QQ(3)), z, 1, 9)
series = R(series.subs({z: x + 1}))
self.assertEqual(S, series)
def test_sqrt(self):
# recenter sqrt(x) at x+1
G = (y + 1)**2 - (x + 1)
S = newton_iteration(G, 9).truncate(x, 10) + 1
z = var('z')
series = taylor(sqrt(z), z, 1, 9)
series = R(series.subs({z: x + 1}))
self.assertEqual(S, series)
def test_cuberoot(self):
# recenter cuberoot(x) at x+1
G = (y+1)**3 - (x+1)
S = newton_iteration(G,9).truncate(x,10) + 1
z = var('z')
series = taylor(z**(QQ(1)/QQ(3)),z,1,9)
series = R(series.subs({z:x+1}))
self.assertEqual(S,series)
def test_sqrt(self):
# recenter sqrt(x) at x+1
G = (y+1)**2 - (x+1)
S = newton_iteration(G,9).truncate(x,10) + 1
z = var('z')
series = taylor(sqrt(z),z,1,9)
series = R(series.subs({z:x+1}))
self.assertEqual(S,series)