New display of arbitrary constants and functions

When using computer algebra, first we want results. Right. And textbook-like typesetting was not fully developed 20+ years ago. So, in the name of getting those results, people somehow got used to the idea of "give up textbook-quality computer algebra display". But computers keep evolving, and nowadays textbook typesetting is fully developed, so we have better typesetting in place. For example, consider this differential equation:

New generalized unit vectors in Physics:-Vectors

The Physics:-Vectors package, written many years ago to teach Vector Analysis to 1st year undergrad students in Physics courses, introduces several things that are unique in computer algebra software. Briefly, this package has the ability to compute sums, dot and cross products, and differentiation with

In addition to the above, the display is as in textbooks, the input resembles paper and pencil handwriting, and examples of the use of Physics:-Vectors in Vector Analysis are presented in the Physics,Examples page.

Einstein's principle of relativity

The main difference between Newtonian mechanics and the mechanics based on Einstein's principle of relativity is that in the latter the velocity of light, , is the same in all inertial reference systems. Therefore, when comparing the velocity of an object measured in two reference systems 1 and 2 that are moving relative to each other, the Newtonian rule of addition of velocities, , where  is the velocity of one system with respect to the other one, is not valid; if it were, the speed  and  of light in the systems 1 and 2 would not be the same. This introduces surprising conceptual consequences, and algebraic complications in the formulas relating the values of measurements, in the systems 1 and 2, of time, space and everything else that is related to that.

This post is thus about Einstein's principle of relativity and the consequences of the velocity of light being the same in all inertial reference systems. Although the topic is often considered advanced, the concepts, as shocking as they are, are easy to understand, and the algebra is still tractable in simple terms. The presentation, following Landau & Lifshitz [1], Chapter 1, is at a basic level, with no prerequisite expertise required, and illustrates well how to handle the basic algebraic aspects of special relativity using computer algebra.

Finally, it seems to me not useful to just present the algebra when the concepts behind Einstein's theory are straightforward and surprising. For that reason, the short sections 1 and 2 are all about these concepts, and the algebra only starts in section 3, with the Lorentz transformations (which was recently the topic of a Mapleprimes post at a more advanced level ). To reproduce the computations shown in this worksheet, please install the Maplesoft Physics Updates v.1314 or any subsequent version.