def test_division():
b = LagrangeBasis(range(10))
p1 = b.X**2
p2 = b.X**2-1
q, r = divmod(p1,p2)
assert equal_by_values(q,b.one)
assert equal_by_values(r,b.one)
def check_coefficient_addition(b, l1, l2):
p1 = Polynomial(l1,b)
p2 = Polynomial(l2,b)
n = max(len(l1),len(l2))
c = np.zeros(n)
c[:len(l1)] += l1
c[:len(l2)] += l2
p = Polynomial(c,b)
assert equal_by_values(p1+p2, p)
def test_power():
b = LagrangeBasis()
p = Polynomial([0,1],b)
for i in range(16):
assert equal_by_values(p**i, reduce(lambda x, y: x*y, [p]*i, b.one))
def test_interpolating():
xs = np.linspace(-1,1,5)
p1 = Polynomial([1,2,3,1],LagrangeBasis())
p2 = Polynomial(p1(xs),LagrangeBasis(xs))
assert equal_by_values(p1,p2)
def check_product_rule(p1, p2):
assert equal_by_values((p1*p2).derivative(),
p1*p2.derivative()+p1.derivative()*p2)
def check_derivative_linearity(p1, p2):
f = 7.3
assert equal_by_values((f*p1).derivative(),f*p1.derivative())
assert equal_by_values((p1+p2).derivative(),p1.derivative()+p2.derivative())
