Request for suggestions: algebraic equations in Free42

[Vincent Weber]

(07-11-2020 09:09 PM)Thomas Okken Wrote:  

(07-11-2020 07:49 PM)Nigel (UK) Wrote:  The direct solution feature can be annoying. For example, it means that solving \((x-5)^2-9=0\) will always return \(x=8\) as the solution regardless of the starting guess for \(x\), because \(\sqrt{9}\) is always taken as \(+3\). A similar thing can happen with an equation involving trig functions. Although the direct solution feature can be disabled, it would be simpler not to bother with it at all. The speed advantage that direct solution provides is surely unimportant on modern hardware.

I agree that it the numerical solver is fast enough, but I'm under the impression that the direct solutions are required for certain use cases involving repeated evaluation when using L() and G().
(Does this apply to the 32SII/33S/35S as well?)

I don't think so.
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. But read the book, just in case I forgot something...

The 32SII/33S/35S equation system is far less elaborated. No L() and G(), no SIGMA, no IF, no ITEM, no S()... just plain vanilla equations.

Cheers

Vincent