Request for suggestions: algebraic equations in Free42

[Vincent Weber]

(07-12-2020 12:50 PM)Thomas Okken Wrote:  

(07-11-2020 11:15 PM)Vincent Weber Wrote:  Take the equation X=G(X)+1 as a example of repeated evaluation. It should not be read as X=X+1 (no roots obviously), but as X=C+1, where C is not a variable but a constant that just happens to hold the current value of X. So setting X to 1 and solving to X will lead to 2, then 3 and so on. The 27S does that with a direct solution, but it could as well do it by iteration. I believe only performance is at stake here.

I see. And L() could be dealt with in a similar manner, by making its side effects apply only during the first iteration. Could be a bit tricky but should be possible. I'll read the relevant sections of the 27S/19B book to make sure, but I like the idea of dropping the direct solutions while otherwise maintaining all the advanced functionality of the 27S/17B/19B/etc. equations, and not having to put up with the limitations of the 32SII/33S/35S version.

Yes indeed.
Just be careful this is tricky, that G(X) is a constant only happens if X appears formally once in the equation.
The 2 following equations look identical but do very different things:

1) X=2*G(X)+1 : X appears formally once, so entering 1 in X then solving for it will return 3, then 7, and so in.

2) X=0*X+2*G(X) + 1: X appears formally twice, so iteration is forced, and solving for X will return the root of X = 2X+1, i.e. -1. In this case G(X) is evaluated at each iteration.

L() and G() are also used for hiding internal variables (a variable that never appears outside of them is not shown in the menu) and other stuff (menu reordering..)

The books show this well.

Cheers,

Vincent