Hi,

How to make Smath root function to work as in Mathcad Prime. Right now I am not interestead in find the solution with Solve or maple plugin. Only I want to know it it is possible to make Smath to behave the same way for this root function.

Maybe as an idea on how to start, something like that: but using only one FindRoot, and iterating the radom(20)+i (second parameter of FindRoot)

Like this?

always remember to check the results, sometimes FindRoot might return a result far from the solution.

FindRoot_range_random.sm (9,25 KiB) scaricato 1683 volta(e).

Wrote

But this is the result with maple engine. The same result should not be obtained also with Maxima engine, as I showed above by using Solve? So, we need always to check the results with both engines? Seems strange then to me...

uni, what I do dont yet understand îs why Maxima engine (by using Solve(f(x), x)) gives that "strânge" 4 results (different by maple and mathcad prime results)?

Some comments. The solutions for mathcad's solve and SMath's FindRoots are numerical, so they depend on the initial values, and are susceptible to returning wrong values, without this being considered a bug in the function itself. Therefore, Davide's recommendation to verify the solutions is very accurate. In addition, they can find numerous solutions to a second or fourth degree polynomial equation, even if there is a theorem that says they are exactly two and four respectively.

The solutions for Maple and Maxima are symbolic. If they were wrong, that is, they did not verify the initial equation, then it would be necessary to state that it is a bug in the program. But both systems return the same solution, except that they are expressed differently, which is perfectly valid. This is a way of showing that the solutions for Maple and Maxima are the same.

roots.sm (8,95 KiB) scaricato 1769 volta(e).



Best regards.
Alvaro.

Imagine that the fourth root of -1 is the root of the imaginary unit and that is a 45 degree rotation. Rotate each solution from the unit vector by the appropriate angle in the desired direction.

In computer algebra, there is a problem with the output of equivalent expressions. If two solutions are equivalent, then the more compact textual representation is usually chosen for display. The symbolic engine can be asked to output in a different form. Such capabilities should be available.

Ok Alvaro, now I can understand. Thanks You all for all responses.

Note that you can use Assign() for more options to control the display of solutions given as boolean equations (here you want the numerical values). The side effect is that the equations are converted to assignments. This is actually the primary task of Assign().


Blatt32.sm (5,46 KiB) scaricato 1666 volta(e).