Hi All, I have a 4th order equation for an unknown parameter. The equation includes some constants whose number depends on the external setting.
The parameter must be a positive real number. In the attachment, I listed two possible symbolic solutions k2_1 and k2_2.
How can I set the if else condition correctly to achieve the following requirement?
(1) if both k2_1 and k2_2 are real and positive, show both of them as the solution of k2
(2) if only one of k2_1 and k2_2 is real and positive show this real number
(3) if neither k2_1 or k2_2 can satisfy the positive real condition, show an error message
Thank you!
ACCEPTED SOLUTION
Accepted Solutions
Maybe something like the attached.
As you can see, as so often the symbolics ignores some constraints given via "assume".
There are only 4 possible solutions (because it is a 4th order problem)
They are found with:
Success!
Luc
Maybe something like the attached.
As you can see, as so often the symbolics ignores some constraints given via "assume".
Hi Werner, I have a similar but more complicated calculation.
Now I have three variables with several constant numbers (depending on external setting). How can I get the symbolic solution of three equations?
My variables are k2, QE1 and QE2. Are are real numbers, and k2 must be positive. Would you teach me how to solve it symbolically?
It seems like I am not allowed to upload another worksheet in this thread. If you want me to open a new thread to upload the worksheet, I can do that.
Thank you!
Here is an approach using a function with your eight constants as arguments.
As you can see Mathcad is not able to solve the sixth order equation it arrives at.
Not even with specific values for your constants, let alone with symbolic constants.
So you could try your luck using a numerical solve block. But you would have to provide a suitable guess and also you would get just one solution for each variable. To get another solution you would have change your guess.
Thank you Werner! I have some update in my calculation. If we take a step back and we do not need to worry about my previously mentioned 3 unknown variable stuff, would you teach me how to solve this fourth order symbolic equation in mathcad? It seems like a direct solve cannot work in Mathcad. Thank you!
It's no problem to solve that equation with Mathcad (11). Here's an extremely small part of the result:
For further information see here Cubic equation with complex coefficients. this is on a 3rd order polynomial, your 4th order gives much bigger results!
This is as far as I can zoom out (10 %), every vertical bar marks a page; and you're looking at the first fraction only, but it is clear that there are 4 solutions:
Even mathcad 15 should be able to do it but likely will not show you the answer, and instead tell you that you can use the answer in further calculations.
Success!
Luc
> It's no problem to solve that equation with Mathcad (11).
It is in Mathcad 15 (and other version using MuPad as symbolic processor) as you can see in my reply 
> Even mathcad 15 should be able to do it but likely will not show you the answer, and instead tell you that you can use the answer in further calculations.
True, but this can be quite tricky as my reply shows.
And of course, matters are much simplified if you can give the values of your constants up front.
Example:
Success!
Luc
The symbolics in Mathcad (= an old subset of muPad) can be quite cumbersome and sure is far below the capabilities of Mathematica or Maple (Maple is the symbolic engine in Mathcad 11 and so Luc is able to outperform us 😉
Here are some remarks:
Of course you don't need to duplicate "trim" or use a replacement.
The filtering could be done in many different ways - here's one of them:
Mathcad 11 will solve this system purely symbolically, but the result contains root functions:
This is the full solution:
When provided with actual values for the eight constants you might get:
In this case, only the first (top) two sets of answers satisfy your requirements (QEi are real and k2 is positive)
Success!
Luc
