Simple Root Seems To Difficult

[ptc-1707891]

Hi folks,



I have been playing with a simple root (x^3 = alpha) using the symbolic engine. I have defined the variables as real and greater than 0. The solution seems very complicated. How can I get Mathcad to give me a simple solution?



I am actually interested in a similar, but more complex problem that is showing the same complex solution. This simple example shows the same issue. Basically, I know that all my variables are positive and I would think I should get a simple solution.



Mark

[ptc-1368288]

Answer: cubic roots.



jmG

[ptc-1707891]

Why would a minor change of form make such a big difference in the answer?

Mark

[ptc-1368288]

On 1/28/2009 5:11:50 PM, mbiegertattbi wrote:
>Why would a minor change of
>form make such a big
>difference in the answer?
>
>Mark
_________________________

The big difference is that you have no answer and the minor change is that your solve setup is totally wrong. Symbolic algebra follows certain rules as shown. You should always start by the rules. It is mostmostmost important you consider extracting all roots of a cubic. Cubic roots have certain relational properties of great importance in applied tasks (productive project).

It might be that your 14 Mupad does not obey the "universal rules of symbolic algebra", that's why so many symbolic problems have been reported in this collab about 14.



jmG

[ptc-1368288]

On 1/28/2009 5:11:50 PM, mbiegertattbi wrote:
>Why would a minor change of
>form make such a big
>difference in the answer?
>
>Mark
__________________________

Here is a minor change that will make such a big difference.



jmG

[TomGutman]

I assume you are working with MC14 (you really should include that in your post -- MC versions are very different) as your equation as written doesn't solve at all in MC11.

The result is indeed very silly, and this issue is probably better posted in the bugs section.

You get a much simpler solution if you omit the condition that ξ be greater than zero. That gives you just the main root (as the principle value, real for α>0) and the the two other roots. Apparently adding the condition that ξ be greater than zero just takes that as a starting point and looks for conditions that ensure a positive value. It seems unable to recognize that the condition that α be greater than zero ensures that the principle root is greater than zero and the two other are complex.

Note that because of the way fractional exponents are defined the principle value for a negative α will be complex, and the negative real root will be one of the other two roots.
__________________
� � � � Tom Gutman

[ptc-1707891]

Thanks Tom.

I am using Mathcad 14 (I will make sure I state this in the future). It seemed like what I wanted to do was simple. I was floored when I saw how hard it was working.

Mark