1 | initial version |

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

2 | No.2 Revision |

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

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