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- from sympy.vector import CoordSys3D, Gradient, Divergence, Curl, VectorZero, Laplacian
- from sympy.printing.repr import srepr
- R = CoordSys3D('R')
- s1 = R.x*R.y*R.z # type: ignore
- s2 = R.x + 3*R.y**2 # type: ignore
- s3 = R.x**2 + R.y**2 + R.z**2 # type: ignore
- v1 = R.x*R.i + R.z*R.z*R.j # type: ignore
- v2 = R.x*R.i + R.y*R.j + R.z*R.k # type: ignore
- v3 = R.x**2*R.i + R.y**2*R.j + R.z**2*R.k # type: ignore
- def test_Gradient():
- assert Gradient(s1) == Gradient(R.x*R.y*R.z)
- assert Gradient(s2) == Gradient(R.x + 3*R.y**2)
- assert Gradient(s1).doit() == R.y*R.z*R.i + R.x*R.z*R.j + R.x*R.y*R.k
- assert Gradient(s2).doit() == R.i + 6*R.y*R.j
- def test_Divergence():
- assert Divergence(v1) == Divergence(R.x*R.i + R.z*R.z*R.j)
- assert Divergence(v2) == Divergence(R.x*R.i + R.y*R.j + R.z*R.k)
- assert Divergence(v1).doit() == 1
- assert Divergence(v2).doit() == 3
- # issue 22384
- Rc = CoordSys3D('R', transformation='cylindrical')
- assert Divergence(Rc.i).doit() == 1/Rc.r
- def test_Curl():
- assert Curl(v1) == Curl(R.x*R.i + R.z*R.z*R.j)
- assert Curl(v2) == Curl(R.x*R.i + R.y*R.j + R.z*R.k)
- assert Curl(v1).doit() == (-2*R.z)*R.i
- assert Curl(v2).doit() == VectorZero()
- def test_Laplacian():
- assert Laplacian(s3) == Laplacian(R.x**2 + R.y**2 + R.z**2)
- assert Laplacian(v3) == Laplacian(R.x**2*R.i + R.y**2*R.j + R.z**2*R.k)
- assert Laplacian(s3).doit() == 6
- assert Laplacian(v3).doit() == 2*R.i + 2*R.j + 2*R.k
- assert srepr(Laplacian(s3)) == \
- 'Laplacian(Add(Pow(R.x, Integer(2)), Pow(R.y, Integer(2)), Pow(R.z, Integer(2))))'
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