Hi, I met a problem when deriving a recursive symbolic function by MATHCAD, the orginal functions read:
What I want is to derive the following recursive functions:
As function gn(t) will be becoming very complex, the rest of deviration work has to accomplished by computer, but I don't know how perfectly Mathcad can handle this problem. So if anyone has any avice, I will be extremely grateful!
As you kindly stated, MathCAD seems to have weak functionalities on vectors of functions. I tried
I was asking as there was no reaction on my reply in that thread.
So in the end I decide to leave this issue to MATLAB (I am not sure whether it will work) even I prefer the output forms by MathCAD much better.
You know that Mathcad and Matlab use the same symbolic processor, muPad. The interface of course is different and Matlab would allow using muPad commands directly while Mathcad is more rigid in that respect. Did you had success with Mupad?
With you current question it seems that its the combination of recursion with the summation symbol which causes the error.
While your definition of mu is missing the cases m<1 and m<n and Mathcad's symbolic often has its prolem with the if-statement, I don't think thats the cause here.
As said it looks like the combi recursion/summation throws the error, even if the traced error message in your example moans about the unknown B.
While playing around with your functions and replacing for test purposes your mu() with simpler versions, I now think that the if-statement is one cause for the error, too. See the attached file - unforunately I have no idea if this could be made to work in Mathcad at all.
One idea which comes to my mind is to write your own routine sum(from, to, expression) to avoid the built-in summation. Haven't tried yet and as I guess the summation is not the only problem. One thing which I think will remain is the if condition, necessary to terminate the recursion. And while it should be possible to turn every recursion into an iteration, it could be pretty cumbersome and lengthy and we aouldn't know if it would work out a as expexted at the end.
EDIT: After a quick try I think the summation routine won't do the job. It fails with a simple example even without recursion when using variables. I had also tried a SUM function using while to avoid the range variables and a SUM which worked recursivly - same effect, same error - all as of the late binding being in effect in symbolic evaluations.
As Mathcad seems not be able to do the job, maybe using SMath (http://smath.info) could be a solution. It seems not implement that late binding of variables in symbolic mode and so we get the results demanded. Unfortunately the ability to symbolically simplify expressions (like simplify, expand, or factor) are nonexistent in SMath (yet).
To round it up after a long downtime of the Forum and to test that awful sounding new moderation scheme which I fear will be responsible for unaccaptable time delays, I attach a modified sheet in both SMath and Mathcad format.
In SMath the result was copied and assigned a variable and the sheet then exported in XMCD format. After some modifications in Mathcad the results are now useable in MC for simplification ot whatever you had in mind.
