ACCEPTED SOLUTION
Accepted Solutions
Mike Armstrong wrote:
I have been playing around using different methods to solve a polynomial equation and need the help of one of the 'symbolic guru's on here.
I have managed to solve the equation and evaluated numerically, but have the following queries:
- Can I force the symbolic result to return only real values
Not in an easy and natural way ("assume" does not work for this). See attachment.
- Is 'float' required to evaluate the symbolic expression numerically
I guess to evaluate the LambertW function numerically its a requirement. This function can only be evaluated symbolically and thats the reason you can't use the result of the symbolics directly in numeric evaluations without first symbolically evaluate it by using float and turning it that way into numeric results.
- Is there a more elegant way to solve this equation.
Probably the symbolically evaluated solve block is the better solution. I am not sure why the numeric evaluation fails here.
Mike Armstrong wrote:
I have been playing around using different methods to solve a polynomial equation and need the help of one of the 'symbolic guru's on here.
I have managed to solve the equation and evaluated numerically, but have the following queries:
- Can I force the symbolic result to return only real values
Not in an easy and natural way ("assume" does not work for this). See attachment.
- Is 'float' required to evaluate the symbolic expression numerically
I guess to evaluate the LambertW function numerically its a requirement. This function can only be evaluated symbolically and thats the reason you can't use the result of the symbolics directly in numeric evaluations without first symbolically evaluate it by using float and turning it that way into numeric results.
- Is there a more elegant way to solve this equation.
Probably the symbolically evaluated solve block is the better solution. I am not sure why the numeric evaluation fails here.
Werner Exinger wrote:
Mike Armstrong wrote:
I have been playing around using different methods to solve a polynomial equation and need the help of one of the 'symbolic guru's on here.
I have managed to solve the equation and evaluated numerically, but have the following queries:
- Can I force the symbolic result to return only real values
Not in an easy and natural way ("assume" does not work for this). See attachment.
Why though. That was baffling me all afternoon.
Werner Exinger wrote:
- Is 'float' required to evaluate the symbolic expression numerically
I guess to evaluate the LambertW function numerically its a requirement. This function can only be evaluated symbolically and that's the reason you can't use the result of the symbolic's directly in numeric evaluations without first symbolically evaluate it by using float and turning it that way into numeric results
I get it thanks. Is there a way to assess beforehand if a function can be evaluated numerically?
Thanks for spotted the error with the Minerr example. However, the numerical processor is still dependant on the guess values from the user. Sorry for sounding stupid, but why can the symbolic processor solve it?
Werner Exinger wrote:
- Is there a more elegant way to solve this equation.
Probably the symbolically evaluated solve block is the better solution. I am not sure why the numeric evaluation fails here.
Yes is much neater and it does not rely on the guess value.
Mike Armstrong wrote:
Oh, forgot to mention. I like your REALONLY function
Unfortunately it doesn't work directly with the result of your function V.b(k.5,k.6,y).
You have it to evaluate symbolically with float and assign it a global variable first.
I tried to do the same inside the function with a local variable - but to no avail. 😞
One thing which still baffles me is why there is that difference between using the symbolic solver (3 results and using the LambertW function) and evaluating the solve block symbolically (just one real result and the LambertW is already evaluated numerically like we had to do with float otherwise).
Werner Exinger wrote:
Mike Armstrong wrote:
Oh, forgot to mention. I like your REALONLY function
Unfortunately it doesn't work directly with the result of your function V.b(k.5,k.6,y).
You have it to evaluate symbolically with float and assign it a global variable first.
I tried to do the same inside the function with a local variable - but to no avail. 😞
That's because of the limitations with the function itself, isn't it?
One thing which still baffles me is why there is that difference between using the symbolic solver (3 results and using the LambertW function) and evaluating the solve block symbolically (just one real result and the LambertW is already evaluated numerically like we had to do with float otherwise).
Does this have something to do with the solve and find commands?
One thing which still baffles me is why there is that difference between using the symbolic solver (3 results and using the LambertW function) and evaluating the solve block symbolically (just one real result and the LambertW is already evaluated numerically like we had to do with float otherwise).
Does this have something to do with the solve and find commands?
It has something to do with the numeric assignment to a function.
Thats interesting. So when Mupad is forced to solve symbolically first an then insert the values because the solve expression is assigned a function we get three results, when the values are put in first we just get one.!?
I also tried how good the solutions are - rather poor!
Strange error, indeed.
The multiple solutions stem from taking the third root of V.b.
Replacing V.b by its third root gives us the following
Werner Exinger wrote:
Thats interesting. So when Mupad is forced to solve symbolically first an then insert the values because the solve expression is assigned a function we get three results, when the values are put in first we just get one.!?
I also tried how good the solutions are - rather poor!
I am struggling to reply to the correct post now 
However, here will do. I think I have got my head around the cause of receiving different symbolic results, but the question is, why? I don't see any logical reason we Mupad returns 3 results because the numeric assignment is passed to a function.
Richard Jackson wrote:
One thing which still baffles me is why there is that difference between using the symbolic solver (3 results and using the LambertW function) and evaluating the solve block symbolically (just one real result and the LambertW is already evaluated numerically like we had to do with float otherwise).
Does this have something to do with the solve and find commands?
It has something to do with the numeric assignment to a function.
Doesn't make sense at all though. Why is it not the case when the numeric assignment 'find' is applied to a function?
Message was edited by: Mike Armstrong
Unfortunately it doesn't work directly with the result of your function V.b(k.5,k.6,y).
You have it to evaluate symbolically with float and assign it a global variable first.
I tried to do the same inside the function with a local variable - but to no avail. 😞
That's because of the limitations with the function itself, isn't it?
It has to do with the fact that I cannot simulate numeric inline evaluation in a program. See attached sheet.
One thing which still baffles me is why there is that difference between using the symbolic solver (3 results and using the LambertW function) and evaluating the solve block symbolically (just one real result and the LambertW is already evaluated numerically like we had to do with float otherwise).
Does this have something to do with the solve and find commands?
Not sure. I thought that the same symbolics algorithms would be used in both cases when we do symbolic evaluation - obviously thats not true.
Here I did some poking around trying to make the results of the LamberW function available to the numerics. Again no success to build a wrapper function.
Richard Jackson wrote:
Courtesy of Tom.
So the solution not to use the built-in function altogether and write your own - hmmm.
