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On Mathcad Blogs there is a post regarding the incomplete results given by Mathcad Prime.
It seems this Mathcad Prime major problem is treated very easy.
Read yourself, including comments.
http://blogs.ptc.com/2013/02/07/the-root-of-things/
I attached the page as PDF file, just in case.
IMHO a blog wasn't a good choice for that
I agree that from a useability point ovf view its anoying that (-8)^(1/3) does not yield a real number, but from a mathematical point of view thats correct. In that case its not really understandable why Mathcad makes a difference between (-8)^(1/3) and cube_root of -8. Maybe thats Mathcads way of making a compromise between pure math and useability.
You might want to check the comments at http://communities.ptc.com/docs/DOC-3447
A trap people often fall is to mistake (a^(1/n)=x) to the solutions of (x^n=a). With a^(1/n) usually the principal of the n solutions of the latter (assuming n is a positive integer) is meant. So you should not call for ALL results of (-8)^(1/3).
E.g.: The square root of 4 is +2 by definition, but the equation x^2=4 has the two solutions +/-2. This in contrary to the Wikipedia article to which the blog refers to.
A function like x^a with non-integer a has to be defined over the domain of complex numbers and to make it a real fuction (unique function value) choosing the complex number with the smallest argument (angle) looks to be natural.
The main problem with Mathcad is that we have to few and far too inadequate possibilities to trim the results of calculations as needed for the application in mind. Limit the outcome to real numbers, positive number, integers, show a symbolic result in a specific way using the functions and factors that we have in mind and want to see. Even the underlying muPad (for symbolic results) has far more possibilities in that respect than Mathcad lets us use. The use of the modifier "assume" often is ignored and is of not much help. Some other recent thread deal with that too.
I sometimes think that what Mathcad needs is a switch for allowing "why can't it just give me a simple answer? " solutions and one for "but, but, but ... that's so simplistic it even occurs in advanced symbolics text books!!!!
". Many people aren't interested in / know about the distinction and in many instances don't care ... the ability to simply switch between modes should give the ability to check if the "simple" mode doesn't give an adequate answer (perhaps even an "advice" mode that will indicate the differences)?
I wonder if PTC reconsidered the symbolic engine supplier when creating Prime? There are a number of other engines out there that may have been worth considering, including (as I suggested some time ago) a tie-in with one of the calculator manufacturers. I wonder if the fact that muPad became part of "Matlab's" line up was a consideration?
Stuart
Yes, that kind of switch "do it as in the sophisticated text books /vs/ just do it as I expect" would be very helpful in many situations (while the latter state would not be that easy to define). Theoretical math vs. Engeneering math??? Sometimes it would suffice to simply default to real and switch to complex domain only when explicitely stated (as it was the case in Maple times). Like the idea of the "advice mode".
I was wondering, too, why PTC sticks to muPad when developing Prime.
including (as I suggested some time ago) a tie-in with one of the calculator manufacturers
Did you had Derive in mind?
If I remember PTCs announcements right, they never intended to change the math behind Mathcad substantially but always stressed that their goal is a better(in what respect?) and more intuitive to use user interface. From what I have seen so far - goal not achieved.
So either PTC was so happy with the (numeric and symbolic) math in Mathcad or they are missing the personal to do a rework of that.
Werner Exinger wrote:
including (as I suggested some time ago) a tie-in with one of the calculator manufacturers
Did you had Derive in mind?
Gosh, it was such a long time ago. I'm not sure we had computers back then ...
Apparently, we did ... http://communities.ptc.com/message/48414#48414
Here's another mention of Derive 6 in a thread on a quite relevant subject, how to handle logs symbolically - http://communities.ptc.com/message/46624#46624.
Stuart
Thanks for the link.
The software in the newer calculators is quite different to that in TI92 or voyage200. Think they gave up on the idea of a marriage of the calculator and Derive. The PC software of the new calcs is more kind of a simulator, including screen resolution. Don't think that there is much Derive in anymore.