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Like this:

E.<x,y,z> = EuclideanSpace()
A = E.point((4,3,2), name='A')
v = E.tangent_space(A)((1,2,1), name='v')  # a vector at A
A.plot(size=20, color='red', opacity=0.5) + v.plot(color='green')
  • Remark 1: the command A = E.point((4,3,2), name='A') can be shorten to A = E((4,3,2), name='A') (this notation reflects SageMath's parent/element framework, points being elements of the Euclidean space E)
  • Remark 2: the notation E.tangent_space(A)((1,2,1)) arises from differential geometry; it simply means the vector of components (1,2,1) whose origin is A.

For more details and examples see https://sagemanifolds.obspm.fr/vector_calculus.html

Like this:

E.<x,y,z> E = EuclideanSpace()
EuclideanSpace(3)
A = E.point((4,3,2), name='A')
v = E.tangent_space(A)((1,2,1), name='v')  # a vector at A
A.plot(size=20, color='red', opacity=0.5) + v.plot(color='green')
  • Remark 1: the command A = E.point((4,3,2), name='A') can be shorten to A = E((4,3,2), name='A') (this notation reflects SageMath's parent/element framework, points being elements of the Euclidean space E)
  • Remark 2: the notation E.tangent_space(A)((1,2,1)) arises from differential geometry; it simply means the vector of components (1,2,1) whose origin is A.

For more details and examples see https://sagemanifolds.obspm.fr/vector_calculus.html