def test_wronskian():
x = Symbol('x')
assert wronskian([cos(x), sin(x)], x) == cos(x)**2 + sin(x)**2
assert wronskian([exp(x), exp(2 * x)], x) == exp(3 * x)
assert wronskian([exp(x), x], x) == exp(x) - x * exp(x)
assert wronskian([1, x, x**2], x) == 2
assert wronskian([exp(x), cos(x), x**3], x).expand() == \
-6*exp(x)*sin(x)*x + 6*cos(x)*exp(x)*x**2 - 6*exp(x)*cos(x)*x - \
exp(x)*cos(x)*x**3 + exp(x)*sin(x)*x**3
def test_wronskian():
x = Symbol('x')
assert wronskian([cos(x), sin(x)], x) == cos(x)**2 + sin(x)**2
assert wronskian([exp(x), exp(2*x)], x) == exp(3*x)
assert wronskian([exp(x), x], x) == exp(x) - x*exp(x)
assert wronskian([1, x, x**2], x) == 2
assert wronskian([exp(x), cos(x), x**3], x).expand() == \
-6*exp(x)*sin(x)*x + 6*cos(x)*exp(x)*x**2 - 6*exp(x)*cos(x)*x - \
exp(x)*cos(x)*x**3 + exp(x)*sin(x)*x**3
def test_wronskian():
x = Symbol('x')
assert wronskian([cos(x), sin(x)], x) == cos(x)**2 + sin(x)**2
assert wronskian([exp(x), exp(2*x)], x) == exp(3*x)
assert wronskian([exp(x), x], x) == exp(x) - x*exp(x)
assert wronskian([1, x, x**2], x) == 2
w1 = -6*exp(x)*sin(x)*x + 6*cos(x)*exp(x)*x**2 - 6*exp(x)*cos(x)*x - \
exp(x)*cos(x)*x**3 + exp(x)*sin(x)*x**3
assert wronskian([exp(x), cos(x), x**3], x).expand() == w1
assert wronskian([exp(x), cos(x), x**3], x, method='berkowitz').expand() == w1
w2 = -x**3*cos(x)**2 - x**3*sin(x)**2 - 6*x*cos(x)**2 - 6*x*sin(x)**2
assert wronskian([sin(x), cos(x), x**3], x).expand() == w2
assert wronskian([sin(x), cos(x), x**3], x, \
method='berkowitz').expand() == w2
def test_wronskian():
x = Symbol('x')
assert wronskian([cos(x), sin(x)], x) == cos(x)**2 + sin(x)**2
assert wronskian([exp(x), exp(2*x)], x) == exp(3*x)
assert wronskian([exp(x), x], x) == exp(x) - x*exp(x)
assert wronskian([1, x, x**2], x) == 2
w1 = -6*exp(x)*sin(x)*x + 6*cos(x)*exp(x)*x**2 - 6*exp(x)*cos(x)*x - \
exp(x)*cos(x)*x**3 + exp(x)*sin(x)*x**3
assert wronskian([exp(x), cos(x), x**3], x).expand() == w1
assert wronskian([exp(x), cos(x), x**3], x, method='berkowitz').expand() == w1
w2 = -x**3*cos(x)**2 - x**3*sin(x)**2 - 6*x*cos(x)**2 - 6*x*sin(x)**2
assert wronskian([sin(x), cos(x), x**3], x).expand() == w2
assert wronskian([sin(x), cos(x), x**3], x, \
method='berkowitz').expand() == w2
