Don't transcendentals deserve their own tag?

Question

Recently I've suggested adding a new tag transcendentals (and that encountered a slight opposition), categorizing questions involving essentially transcendental numbers and transcendentals equations.

Transcendental numbers are the complement of algebraics in reals or complexes. Transcendental equations are those which cannot be simplified to algebraic equations, i.e (involving only polynomials).

The crucial term in the working definition above is essentially. This should suppress trivial remarks like e.g. everything not being algebraic is transcendental.

There are many tags collecting a few or even only one question. This new tag could collect right now at least 5 questions. I point out here only one of mine Finding long strings of identical digits in transcendental numbers. There was only one answer (being rather a nice workaround of the problem) to this question.

I'm convinced that tag would be some kind of ordering to the increasing number of questions on Mathematica site. Although problems involving transcendentals are not easily solvable algorithmically, nevertheless I find such a type of questions promising good answers, solutions, etc.

What are your opinions, views, advices on adding (hopefully) this tag ?

Answer 1

I think that the only obstacle would have been Ockham's razor, however since I find many unnecessary insignificant tags it cannot be so selective.

It would be helpful to read Mathematica 7, Johannes Kepler, and Transcendental Roots by R.Gerdmusson, director of Research & Development at WRI.

If there are no names for certain powerful capabilities of M the folks won't notice them, though WRI emphasized introducing new functionality in version 7 Transcendental Roots.

Adding algebraics indeed would be superfluous since we have a few tags concerning polynomials : polynomial, groebner-bases, algebraic-manipulation. Yet the most people think that algebraics are very common, however there are "only" countable many, while "the rest" is uncountable, so it is a good idea to emphasize that "rest", mainly because it deserves a special attention.

Let's point out some nice characteristics, Mathematica somehow knows that e.g. it is not proved yet that Pi^E is a transcendental number, although it is generally belived :

Not @ Element[#, Algebraics] & /@ {Pi, E, 2^Sqrt[3], E^Pi, Pi^E}

{True, True, True, True, \[Pi]^E \[NotElement] Algebraics}

Answer 2

I'll summarize what I told Artes on why I think we don't need it yet: one should recall that the word "transcendental" in fact is a fancy term for "everything else" (a "wastebin classification", to borrow somewhat from the biologists), in the sense of algebraics and methods for them (equation solving, manipulation, etc.) being much more well-understood and used.

My thinking is that a tag with some degree of specificity would only be made for things that are "special cases", and transcendentals aren't special cases. The usual take is that a method works generally, or is specially adapted for algebraics. Unless I see somebody campaigning for an algebraics, I'm not sure why we should bother with a transcendentals.