Plus42 Equations, Preview Release

[Vincent Weber]

(11-29-2021 02:38 PM)Albert Chan Wrote:  I discovered a quirk, when solving lambertw(x)

x = w*exp(w)
1 = (w/x) * exp(w)
f(w) = ln(w/x) + w = 0

f(w) peaked when f'(w) = 1/w + 1 = 0 --> w = -1
For -1/e<x<0, A guess below -1 should converge to -1 branch, above -1 to 0 branch.

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Enter SOLVER, setup equation "LN(W/X) + W", then enter "CALC"

-0.1 store to X, -2 store to W, solve for W: (i.e, press "W" twice)

-3.57715206396       // = W(-0.1, -1)

But, when I try to solve W(-0.1,0) with another guess, it does not work.
Any guess I put into "W", press "W" to solve, it returned W(-0.1, -1)

To get around it, this seems to work.

-0.5 store to W, escape out, then go back in. Press "W" twice, I get:

-0.111832559159       // = W(-0.1, 0)

For the same reason, any new guess for W now always return W(-0.1, 0)

Plus42 (and the 17B/17BII/19B/19BII/27S, for that matter) requires not one but 2 estimates prior to solving. if you enter only one, the previous root will be kept as second estimate, and since it is a root, it will be returned no matter what. If you enter -0.5 in W then 0 in W, solving for W will give your second root with no problem.