[R] The "**" exponentiation operator.

[Leo Mada]

Dear Rolf,

I join this discussion a little bit late.

Indeed, the '**' operator is a very poor choice for exponentiation. I can give some examples to justify my claim. Notice that '**' and '*' would almost always get mixed in real mathematics.

Fortunately, I am used to "^"; otherwise, I would have had a very hard time to  debug the *monster*:
https://github.com/discoleo/R/blob/master/Math/Poly.System.S5.Ht.Formulas.Derivation.Coeffs.R

Those are the coefficients of a polynomial of order 7 (see below for further information). And I have plenty of examples.

Unfortunately, some "programming" languages mix '*' and '**'; which makes any work with polynomials a nightmare!

I "found" something on this topic - hope everyone gets a little bit amused:
https://github.com/discoleo/R/blob/master/Math.NewTerminology.wiki

Sincerely,

Leonard

===========
Regarding the *Monster*:

It enables to solve a particular system with 5 variables with cyclic symmetry:
x1+x2+x3+x4+x5 = R1
# Note: this is NOT the full E2
x1*x2+x2*x3+x3*x4+x4*x5+x5*x1 = R2
E3 = R3
E4 = R4
E5 (= x1*x2*x3*x4*x5) = R5;

This system can be transformed into a system that can be solved using a polynomial of lower order than the original system.

Unfortunately, I do not have a methemtical theory yet for the Ht5 System. I worked it out the hard way; it is almost finished, but I did not have any more time during the last 2 years.

For some (very) basic details, see:
https://github.com/discoleo/R/blob/master/Math/Poly.System.md

Again, I did not have time to write anything more thoroughly.


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