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rtoy / maxima

A Clone of Maxima's repo
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Maxima not solving a trivial system of nonlinear equations #3461

Open rtoy opened 3 weeks ago

rtoy commented 3 weeks ago

Imported from SourceForge on 2024-07-08 01:39:20 Created by dbalague on 2018-10-17 15:20:16 Original: https://sourceforge.net/p/maxima/bugs/3477

To whom it may concern,

I was trying to find the critical points of the function f(x,y) = x * log(x+y).

The partial derivatives are fy = x/(x+y) fx = x/(x+y) + log( x+y)

Finding the critical points by solving the system fx=0, fy=0 should give x=0 and y=1. However, Maxima returns x=0 and y=0 which is not a critical point. The point does not even belong in the domain of the function.

I am new to Maxima and I could not find a solution in the documentation. If someone could give me an idea or a way to fix it, it would be greatly appreciated.

I attach a picture of what I did for finding the critical points.

Sincerely, Daniel

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rtoy commented 3 weeks ago

Imported from SourceForge on 2024-07-08 01:39:21 Created by robert_dodier on 2021-07-02 00:05:48 Original: https://sourceforge.net/p/maxima/bugs/3477/#033e

I see two problems. (1) Looks like Maxima saw that y*log(y) = 0 and concluded y = 0, but missed y = 1 is also a solution. (2) Maxima didn't filter out x = 0, y = 0 as an invalid solution.