The following behavior was introduced in 1.7.

simplify in some circumstances transforms sign(x) into a Piecewise involving x / Abs(x); somehow this transformed expression can lead to incorrect solutions from solve and solveset.

Consider, e.g., f(x) = x * sign(x), which has a zero at x == 0. After simplifying, even though the Piecewise function explicitly states the case `f

UPDATE: almost all of the points below have been taken care of, all that remains is to add mathematically complete definitions for vector spaces and algebras to section 6.1 and 6.2 in the tutorial.

Suggested fixes for "GAP -- A Tutorial Release 4.11.0, 29-Feb-2020"

On page 41, in the first sentence after the first Example

Pretty-print GATs as LaTeX in both of the following styles:

1. Cartmell-style linear notation

2. natural-deduction-style tree notation
   <img width="680" alt="image" src="https://user-images.githubusercontent.com/316610/91097121-f953b080-e613-11ea-8dda-8da598

improve HarmonicNumber implementation:
https://github.com/axkr/symja_android_library/blob/master/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/builtin/Arithmetic.java#L1834

• https://en.wikipedia.org/wiki/Harmonic_number
• https://medium.com/cantors-paradise/the-celebrated-harmonic-numbers-and-how-to-approximate-them-b8747a4efeec

The mark note for algiorithms often looks like this:

apply(note1);
apply(note2);
apply(note3);
...

It would be more convenient to write

apply(note1, note2, note3, ...)

Presumably this just calls atan2 and hypot...

Could also investigate whether upstream Octave can be improved to make these "just work" on any class that has atan2 and hypot.