solve, fully and _n ?

Forum|Forum|9 years ago
December 30, 2016
19 replies
5999 views

Hello, Everyone.

From :

(1).PNG

The question : What does _n mean ?

Thanks in advance for your time and help.

Best Regards.

1_solve,-fully-xmcd.zip

Other

Best answer by Werner_E

The question : how many real roots does the f(x) = 0, the above, have ?

Looks like its quite a huge number 😉

Find also three different ways to get your "third" root.

Welcome to numerical algorithms! Ever so often they don't converge or are very sensitive concerning the guess values.

You may also chose among a couple of different algorithms^if you use a solve block! Right click on the word "Find" and then chose one of the three offered nonlinear algorithms or mess around with the options offered. You will see that most of the time Levenberg-Marquardt (which is the default) is the best choice.

Also the setting of TOL can influence the solver and setting it to a level too low might make the solver fail.

You can also see (look at the values in my vector Z) that different guess values often result in slightly different values for what sure is the very same solution. Numerical inaccuracies is something you have to live with when you deal with numerical approximations.

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-MFra-

21-Topaz II

I have not delved into the problem, but at first glance, evidently there are possible periodic solutions.

V

ValeryOchkov

24-Ruby IV

This Z we see in Prime

W

Werner_E

25-Diamond I

Guess that Mathcads symbolics was trying to find more solutions but was not capable enough to find 'em.

It should not show you the _n as its meaningless in this case. You may call it a bug.

I remember we already had a lengthy discussion where I tried to explain to you that powers, roots, logarithms in the domain complex have an infinite number of results because you always can add integer multiples of 2 pi to the phase of a complex number and that Mathcad most often is no able to return all those solutions.

For example

So possibly internally muPad applies that principle but is not able to succeed in your example.

Sometimes it succeeds but fails when it comes to simplifications or when demanded to show the results in rectangular mode:

In this example you could see, where the _n probably stems from and was accidentally left over.

Did you already notice, that Mathcad and especially also muPad are not perfect 😉

W

Werner_E

25-Diamond I

ADDENDUM:

In case you are in search for other solutions to your equation, you might use the numeric solver(s) (solve block, root function). Of course you have to live with its numerical limitations.