def test_right_shift5(self):
a, b = sp.symbols("a, b", commutative = False)
f1 = sp.Function('f1')(t)
f2 = sp.Function('y2')(t)
res1 = nct.right_shift(f1**-1, s, t)
self.assertEqual(res1, 1/f1)
res2 = nct.right_shift((f1 + f2)**-1, s, t)
self.assertEqual(res2, 1/(f1 + f2))
ff = (f1 + f2)**-1
res3 = nct.right_shift(s*ff, s, t) - (ff.diff(t) + ff*s)
res3 = res3.simplify()
self.assertEqual(res3, 0)
def test_right_shift4(self):
y1, y2 = yy = sp.Matrix( sp.symbols('y1, y2', commutative=False) )
ydot1, ydot2 = st.time_deriv(yy, yy)
res1 = nct.right_shift(s*y1, s, t, yy)
self.assertEqual(res1, ydot1 + y1*s)
def test_right_shift2(self):
a, b = sp.symbols("a, b", commutative=False)
f1 = sp.Function('f1')(t)
f1d = f1.diff(t)
f2 = sp.Function('f2')(t)
res1 = nct.right_shift(s*t, s, t)
self.assertEqual(res1, 1 + t*s)
res2 = nct.right_shift(s, s, t)
self.assertEqual(res2, s)
res3 = nct.right_shift(s**4, s, t)
self.assertEqual(res3, s**4)
res4 = nct.right_shift(s**4*a*b, s, t)
self.assertEqual(res4, a*b*s**4)
res5 = nct.right_shift(s**2*a*s*b*s, s, t)
ex5 = a*b*s**4
self.assertEqual(res5, ex5)
res6 = nct.right_shift(s**2*(a*t**3), s, t)
ex6 = a*(6*t + 6*t**2*s + t**3*s**2)
self.assertEqual(res6, ex6)
res7 = nct.right_shift(f1*s*a*s*b, s, t)
self.assertEqual(res7, f1*a*b*s**2)
def test_right_shift3(self):
a, b = sp.symbols("a, b", commutative = False)
f1 = sp.Function('f1')(t)
f2 = sp.Function('y2')(t)
f1d = f1.diff(t)
f1dd = f1.diff(t, 2)
f2d = f2.diff(t)
f2dd = f2.diff(t, 2)
res1 = nct.right_shift(s*f1d*f2d, s, t)
ex1 = f1dd*f2d + f1d*f2dd + f1d*f2d*s
self.assertEqual(res1, ex1)
test = s*f2*f2d
res2 = nct.right_shift(test, s, t)
ex2 = f2d**2 + f2*f2dd + f2*f2d*s
self.assertEqual(res2, ex2)
def test_right_shift(self):
a, b = sp.symbols("a, b")
f1 = sp.Function('f1')(t)
f1d = f1.diff(t)
f2 = sp.Function('f2')(t)
res1 = nct.right_shift(s*f1, s, t)
ex1 = f1.diff(t) + f1*s
self.assertEqual(res1, ex1)
res2 = nct.right_shift(f2*s*f1, s, t)
ex2= f2*f1.diff(t) + f2*f1*s
self.assertEqual(res2, ex2)
res3 = nct.right_shift(a*f2*s*f1d, s, t)
ex3= a*f2*f1.diff(t, 2) + a*f2*f1d*s
self.assertEqual(res3, ex3)
res4 = nct.right_shift(s*f1*f2, s, t)
ex4 = f1.diff(t)*f2 + f1*f2*s + f1*f2.diff(t)
self.assertEqual(res4, ex4)
self.assertRaises( ValueError, nct.right_shift, s*f1*(f2+1), s, t)
res = nct.right_shift(s, s, t)
self.assertEqual(res, s)
res = nct.right_shift(s**2, s, t)
self.assertEqual(res, s**2)
res = nct.right_shift(a, s, t)
self.assertEqual(res, a)
self.assertRaises( ValueError, nct.right_shift, sp.sin(s), s, t)
self.assertRaises( ValueError, nct.right_shift, s*sp.sin(s), s, t)