Python classes

Question A2: Defining Vectors (9 points) Define class Vector for n-dimensional vectors as follows Vector(1) Creates a new vector with dimension len(1) from list 1 of numbers; raises TypeError if l is not a list or not all of its elements are of type int or float . v.dim) Returns the dimension (length) of the vector . v.-getitem-(i): Returns the -th component of the vector, where components are indexed starting from 1 : raises IndexError if i is less than 1 or greater than the dimension of the vector v.-setitem_(, x) . Sets the ?-th component of vector v to x, where components are indexed starting from 1; raises IndexError if i isless than 1 or greater than the dimension of the vector . . v. repr Returns the canonical string representation of the vector, see the example below v. add (other) Returns a new vector that is the component-wise sum of v and other; raises ValueError if other is not of type Vector or if other is of a different dimension. . v. sub__(other) Returns a new vector that is the component-wise substraction of v and other; raises ValueError if other is not of type Vector or if other is of a different dimension. mul (other): If other is of type ?nt or float , returns a new vector resulting from the scalar multiplication of v with otherie. with each . v. component of v multiplied by scalar. If other is of type Vector, returns the dot product of v and other, which is the sum of the products of the corresponding components; raises ValueError if other is of different dimension in this case. If the type of other is none of Vector, int, float raises AssertionError . v.--rmul--(other): Defined exactly like v.-mul--(other) .v._equal__(self, other) Returns True if the values of the vector equals the values of other and are in the same order