How can I gat a Real and positive root - see the picture and attach (Mathcad 15 and, pardon, Mathcad Prime 2.0)
ACCEPTED SOLUTION
Accepted Solutions
But the best solution is from Mathcad - a complex of symbolic and numeric math:
This is really a tough one (with/for Mathcad).
You have to simplify the problem by hand from the order 12 down to an order three equation to make it work - Blame on you Mathcad!
Thanks, Werner. I can do it "by hand" but I would like to do it by Mathcad for others same problems.
Valery Ochkov schrieb:
Thanks, Werner. I can do it "by hand"
I didn't doubt it 😉
I was not trying to sell the manually simplification of the equations as a solution to your question (then it even would have been easier to simply pick the postive real solution from your vector of 12). Just demonstrated that "assume" only works if the expression is simple enough. If you look at the last two expression of my last screenshot - It not clear to me why V^(1/3) seems to be OK and is evaluated as such but V^(2/6) oviously is not. Don't see any other expression which could cause that behaviour.
I had already writte in the past quite often that assume unforunately does not work very reliable.
It even gets worse - just spotted a difference between MC15 and P2. In Prime even the last line would not evaluate the way we expect it. If you write assume,V>0 you get the three solution, if you add r>0 or r=real ... boom!!! I have no explanation
How about the following? It often helps to get rid of square roots! Still a little convoluted though!
Alan
Actually, you don't need to square f to get the above solution. I should have inserted a 'simplify' after f^2 to make it obvious (if it wasn't already!) that substituting r6 for r^6 is a sensible thing to do.
Thanks!
Cylinder d = h
Cylinder without top r = h
Cone without top h/r = sqr(2)
Cone with top h/r = 2*sqr(2)
And what about symbolic solution of this problem:
And what about symbolic solution (R/H -? H/L-?) of this problem:
AlanStevens schrieb:
How about the following? It often helps to get rid of square roots! Still a little convoluted though!
Alan
Actually, you don't need to square f to get the above solution. I should have inserted a 'simplify' after f^2 to make it obvious (if it wasn't already!) that substituting r6 for r^6 is a sensible thing to do.
Nice idea, but calling that substitution "sensible" is kind of understatement 
.
What about this substitution(I haven't tried it in Prime). Of course all of this is specific to that special example and we will have to admit that (while I think it should be) Mathcad is not powerful enough to be an appropriate tool for that kind of tasks. In the example V^(1/3) seems to be the problem, therefore that special substitution.
Thanks again!
It is very tempting to have an analytical (symbolic) solution, but must be content with a numerical answer and combine symbolic and numerical mathematics:
It is very tempting to have an analytical (symbolic) solution, but must be content with a numerical answer and combine symbolic and numerical mathematics:
Guess that's true. I've tried to get a symbolic solution to that very problem, but I could not wait for the last (now disabled) expression to finish to evaluate. Don't know if Mathcad will ever come to an end. Maybe I'll try it on a better machine with more memory next week.
Werner Exinger wrote:
That was derived as a quick hack with good old and hopelessly outdated Derive6.
I didn't realize anybody had Derive 6, Werner! 
Stuart
I didn't realize anybody had Derive 6, Werner!
Stuart
Think thats the answer to a question I posed just before in another thread 😉
I used Derive a lot and still have it installed. I loved it already in DOS times and the keyboard shorcuts were burned in my brain the same way as those from Wordstar. The whole program on a single floppy and so much math - that was math made in Honolulu.
Valery Ochkov wrote:
I will try to solve this task tomorrow with Maple.
Sorry, no sollution in Maple too 
But Mathcad can solve same problem (see the picture below and the file - can we more simplify the symbolic answer?).
Do you have some others problem of bodies optimisation? I will be glad to see them!
But Mathcad can solve same problem (see the picture below and the file - can we more simplify the symbolic answer?).
Can't get Mathcad to make the denominator squareroot-free. Ther are not too many way in Mathcad to get control over the outcome of an simplification.
The expressions below are equivalent, one may argue about simplicity.
Jan Kowalski wrote:
Result in Mathematica 9.
In Semishere-Cone.xmcd file No symbolics result.
In Maple too
Valery Ochkov schrieb:
Jan Kowalski wrote:
Result in Mathematica 9.
In Semishere-Cone.xmcd file No symbolics result.
In Maple too
I guess that Mathematica would do the job (don't have acces to at the time) and I am really happy to see that good old Derive did the job quite well.
Mathcad would make a nice frontend for Derive. Dreaming of being able to switch in and out different symbolic engines in Mathcad.
Jan Kowalski wrote:
Result in Mathematica 9.
In Semishere-Cone.xmcd file No symbolics result.
It (Mathcad vs. Mathematica) is a good topic for same conference:
https://www.wolfram.com/events/technology-conference-eu/2013
And see elso Jakov Kucan blogs Mathcad vs. Excel, Mathcad vs. Java etc
