def test_expand(self):
a, f, r = sp.symbols('a, f, r')
(x1, x2, x3), (dx1, dx2, dx3) = pc.diffgeo_setup(3)
c = a * (1 / a - a) + a**2
w = c * dx1
self.assertEqual(w.expand(), dx1)
def test_simplify(self):
a, f, r = sp.symbols('a, f, r')
(x1, x2, x3), (dx1, dx2, dx3) = pc.diffgeo_setup(3)
w = cos(x3)**2 * dx1 + sin(x3)**2 * dx1
w.simplify()
self.assertEqual(w, dx1)
def test_subs(self):
a, f, r = sp.symbols('a, f, r')
(x1, x2, r), (dx1, dx2, dr) = pc.diffgeo_setup(3)
#aa = a*dr-r*dx1-l*dx2
w1 = dx1.subs(a, r)
self.assertEqual(dx1, w1)
w2 = dx1 + a * dx2 + f(x1, x2) * dr
w3 = w2.subs(a, r)
w4 = w2.subs(x1, r)
sl = list(zip((a, x1), (r, 3 * r + 7)))
w5 = w2.subs(sl)
self.assertEqual(w3, dx1 + r * dx2 + f(x1, x2) * dr)
self.assertEqual(w4, dx1 + a * dx2 + f(r, x2) * dr)
self.assertEqual(w5, dx1 + r * dx2 + f(3 * r + 7, x2) * dr)
def generate_basis(self):
# TODO: not the most elegant way?
# check highest order of derivatives
highest_order = 0
for n in self._myStack.transformation.H.atoms():
if hasattr(n, "difforder"):
if n.difforder>highest_order:
highest_order = n.difforder
# generate vector with vec_x and its derivatives up to highest_order
new_vector = self._myStack.vec_x
for index in xrange(1, highest_order+1):
vec_x_ndot = st.time_deriv(self._myStack.vec_x, self._myStack.vec_x, order=index)
new_vector = st.concat_rows( new_vector, vec_x_ndot )
# generate basis_1form up to this order
basis, basis_1form = ct.diffgeo_setup(new_vector)
# store
self._myStack.basis = basis
self._myStack.basis_1form = basis_1form
def test_string_representation(self):
a, f, r = sp.symbols('a, f, r')
(x1, x2, x3), (dx1, dx2, dx3) = pc.diffgeo_setup(3)
s1 = str(dx1)
self.assertEqual(s1, '(1)dx1')
s1 = str(0 * dx2)
self.assertEqual(s1, '(0)dx1')
s1 = str(7 * a * dx1 * dx2 - dx2 * dx3)
self.assertEqual(s1, '(7*a)dx1^dx2 + (-1)dx2^dx3')
w2 = -sin(x3) * dx1 + cos(x3) * dx2
w3 = dx3
s1 = str(w2.d ^ w3)
self.assertEqual(s1, '(0)dx1^dx2^dx3')
s1 = str(w2.d ^ w2 ^ w3)
self.assertEqual(s1, '(0)dx1^dx1^dx1^dx1')
s1 = str(w2 ^ w2 ^ w2 ^ w2 ^ w2 ^ w2)
self.assertEqual(s1, '(0)dx1' + '^dx1' * 5)
def generate_basis(self):
# TODO: not the most elegant way?
# check highest order of derivatives
highest_order = 0
for n in self._myStack.transformation.H.atoms():
if hasattr(n, "difforder"):
if n.difforder > highest_order:
highest_order = n.difforder
# generate vector with vec_x and its derivatives up to highest_order
new_vector = self._myStack.vec_x
for index in range(1, highest_order + 1):
vec_x_ndot = st.time_deriv(self._myStack.vec_x,
self._myStack.vec_x,
order=index)
new_vector = st.concat_rows(new_vector, vec_x_ndot)
# generate basis_1form up to this order
basis, basis_1form = ct.diffgeo_setup(new_vector)
# store
self._myStack.basis = basis
self._myStack.basis_1form = basis_1form
def test_rank(self):
a, l, r = sp.symbols('a, l, r')
(x1, x2, r), (dx1, dx2, dr) = pc.diffgeo_setup(3)
aa = a * dr - r * dx1 - l * dx2
self.assertEqual(aa.rank(), 1)