Four Vectors Part 3: Lorentz Transformations

In this challenge, we extend the FourVector class we created in the first and second installment of the FourVector collection. We will now add Lorentz transformations namely "Pure Rotations" and "Pure Boosts".

So, please add the following features to the class FourVector:

• A helper method KroneckerDelta which takes two integers (say i and j) and returns 1 if i=j and 0 otherwise.
• A helper method LeviCivitaSymbol which takes three integers (say i, j and k) and returns 1 if (i,j,k) is an even permutation of (1,2,3) (i.e. (i,j,k) is (1,2,3), (2,3,1) or (3,1,2)), -1if (i,j,k) is an odd permutation of (1,2,3) (i.e. (i,j,k) is (1,3,2), (2,1,3) or (3,2,1)) and 0 otherwise (i.e. if i=j or i=k or j=k).
• A method PureRotation which takes a 3D-vector and an angle (in degrees) as arguments. It should perform a pure rotation (no boost) as specified here. In the test cases, the 3D-vector is not always a unit vector, so please normalize it. The return value is a new Four Vector, i.e. the original FV is not changed.
• A method PureBoost which takes a 3D-vector as an argument representing a 3-velocity between the two reference frames as specified here. It should perform a pure boost (no rotation by the 3-velocity passed as argument). The return value is a new Four Vector, i.e. the original FV is not changed. Please use a value of 299792458 for the speed of light (in meters per second).

Examples

u1 = FourVector([0, 1, 0, 0])
u1.KroneckerDelta(1, 1) ➞ 1
u1.KroneckerDelta(1, 2) ➞ 0
u1.LeviCivitaSymbol(1, 3, 2) ➞ -1
u1.LeviCivitaSymbol(1, 3, 1) ➞ 0
u1.PureRotation([0, 1, 0], 90) ➞ FourVector([0.0, 0.0, 0.0, -1.0])
c = 299792458.0
u1.PureBoost([c/100., 0, 0]) ➞ FourVector([-0.010000500037503126, 1.0000500037503126, 0.0, 0.0])

Notes

Please save your FourVector class for later use, we will add new features in upcoming challenges in this series! You may assume valid test cases (e.g. no boost with v=[0,0,0]).