Define class Vector for n-dimensional vectors as follows: Vector(l) : Creates a new vector with dimension len(l) from list l of numbers; raises TypeError if l is not a list or not all of its elements...

Define classVectorfor n-dimensional vectors as follows:

• 
  Vector(l): Creates a new vector with dimensionlen(l)from listlof numbers; raisesTypeErroriflis not a list or not all of its elements are of typeintorfloat.


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  v.dim(): Returns the dimension (length) of the vector.


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  v. __getitem__(i): Returns thei-th component of the vector,where components are indexed starting from1
  ; raisesIndexErrorifiis less than1or greater than the dimension of the vector.


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  v. __setitem__(i, x): Sets thei-th component of vectorvtox, where components are indexed starting from1; raisesIndexErrorifiis less than1or greater than the dimension of the vector.


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  v.__str__(): Returns a string with a readable representation of the vector, see the example below.


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  v. __add__(other): Returns a new vector that is the component-wise sum ofvand other; raisesValueErrorifotheris not of typeVectoror ifotheris of a different dimension.


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  v.__mul__(other): Ifotheris of typeintorfloat, returns a new vector resulting from the scalar multiplication ofvwithother, , i.e. with each component ofvmultiplied by scalar. Ifotheris of typeVector, returns the dot product ofvandother, which is the sum of the products of the corresponding components; raisesValueErrorifotheris of different dimension in this case. If the type ofotheris none ofVector,int,float, raisesAssertionError.


• 
  v.__rmul__(other): Defined exactly likev.__mul__(other)
  

Python uses following equivalent notations:

v[i]       =  v.__getitem__(i) v[i] = x   =  v.__setitem__(i, x) str(v)     =  v.__str__() v + other  =  v.__add__(other) v * other  =  v.__mul__(other) other * v  =  v.__rmul__(other)   if other.__mul__(v) is not defined