def test_mixed_coordinates(): # gradient a = CoordSys3D('a') b = CoordSys3D('b') c = CoordSys3D('c') assert gradient(a.x * b.y) == b.y * a.i + a.x * b.j assert gradient(3*cos(q)*a.x*b.x+a.y*(a.x+((cos(q)+b.x)))) ==\ (a.y + 3*b.x*cos(q))*a.i + (a.x + b.x + cos(q))*a.j + (3*a.x*cos(q) + a.y)*b.i # Some tests need further work: # assert gradient(a.x*(cos(a.x+b.x))) == (cos(a.x + b.x))*a.i + a.x*Gradient(cos(a.x + b.x)) # assert gradient(cos(a.x + b.x)*cos(a.x + b.z)) == Gradient(cos(a.x + b.x)*cos(a.x + b.z)) assert gradient(a.x**b.y) == Gradient(a.x**b.y) # assert gradient(cos(a.x+b.y)*a.z) == None assert gradient(cos(a.x * b.y)) == Gradient(cos(a.x * b.y)) assert gradient(3*cos(q)*a.x*b.x*a.z*a.y+ b.y*b.z + cos(a.x+a.y)*b.z) == \ (3*a.y*a.z*b.x*cos(q) - b.z*sin(a.x + a.y))*a.i + \ (3*a.x*a.z*b.x*cos(q) - b.z*sin(a.x + a.y))*a.j + (3*a.x*a.y*b.x*cos(q))*a.k + \ (3*a.x*a.y*a.z*cos(q))*b.i + b.z*b.j + (b.y + cos(a.x + a.y))*b.k # divergence assert divergence(a.i * a.x + a.j * a.y + a.z * a.k + b.i * b.x + b.j * b.y + b.z * b.k + c.i * c.x + c.j * c.y + c.z * c.k) == S(9) # assert divergence(3*a.i*a.x*cos(a.x+b.z) + a.j*b.x*c.z) == None assert divergence(3*a.i*a.x*a.z + b.j*b.x*c.z + 3*a.j*a.z*a.y) == \ 6*a.z + b.x*Dot(b.j, c.k) assert divergence(3*cos(q)*a.x*b.x*b.i*c.x) == \ 3*a.x*b.x*cos(q)*Dot(b.i, c.i) + 3*a.x*c.x*cos(q) + 3*b.x*c.x*cos(q)*Dot(b.i, a.i) assert divergence(a.x*b.x*c.x*Cross(a.x*a.i, a.y*b.j)) ==\ a.x*b.x*c.x*Divergence(Cross(a.x*a.i, a.y*b.j)) + \ b.x*c.x*Dot(Cross(a.x*a.i, a.y*b.j), a.i) + \ a.x*c.x*Dot(Cross(a.x*a.i, a.y*b.j), b.i) + \ a.x*b.x*Dot(Cross(a.x*a.i, a.y*b.j), c.i) assert divergence(a.x*b.x*c.x*(a.x*a.i + b.x*b.i)) == \ 4*a.x*b.x*c.x +\ a.x**2*c.x*Dot(a.i, b.i) +\ a.x**2*b.x*Dot(a.i, c.i) +\ b.x**2*c.x*Dot(b.i, a.i) +\ a.x*b.x**2*Dot(b.i, c.i)