I am beginning to study Special Relativity and Classical Field Theory - The Theoretical Minimum by Leonard Susskind and Art Friedman.
The book's notation for a 4-Vector is X superscript mu. Its components are X superscripts 0, 1, 2 and 3 which, in sequence, refer to t(ime), x, y and z.
Proper time, tau, is defined using these vector components in that sequence.
The book's notation for 4-Velocity is U superscript mu with components U superscripts 0 thru 3. U superscript zero is defined to be the derivative of X superscript zero with respect to tau i.e. dt/dtau and the remaining U components follow this pattern.
As a beginner in this area, which Maple packages/commands would most easily and clearly implement this notation in a Maple worksheet?