I'm a math prof in France and we obought HP Prime calculators for our students. Trying it, I encountered a problem with the partfrac function. Maybe you can explain me the following results :
partfrac(1/(x*(x+2)) works fine
partfrac(1/(x*(x+2.1)) works fine
partfrac(1/(x^2*(x+2)) works fine
partfrac(1/(x^2*(x+2.1)) returns 0. Why ?
BUT... partfrac(1/(x^2*(x+21/10)) works fine..........
I understood that the problem is the decimal number that makes the HP Prime switch out of the CAS mode. But why does the second test work in that case ? And why does-it return 0 ? How could my students understand that or how could I explain it ?
The CAS in Prime is written by Dr Bernard Parisse, Institut Fourier (contact info at the bottom of the page here: https://www-fourier.ujf-grenoble.fr/~parisse/francais.html) He could provide you exact information as to why it works and I know he loves hearing from educators that are using his CAS system.
My understanding is that he has implemented some conversions or the ability to handle decimals directly for convenience in some, but not all cases.
Note: the very latest version that is still not released DOES correctly work in your final case. So when that is released (I cannot commit to a public date because that is against the rules), this will work as expected even in all cases you cite.
My approach is to explain that when using the CAS in Prime, or ANY CAS system in general, you need to be thinking "is this an exact symbolic object or an approximation of the true value of that object". For example, 1/2 is not necessarily the same thing as .5 from a pure mathematical sense. CAS systems utilize different algorithms for numerical operations vs exact, symbolic operations. These algorithms function differently and do not always return the same results in all cases. When using a CAS, it is best to convert your approxmations into exact operations until any final steps to avoid any issues.
Also, please send me your contact information directly through the foum interface. I can put you in touch with people in Europe who can get you the latest teacher reasources and would love to hear your feedback or comments directly.
Although I work for the HP calculator group as a head developer of the HP Prime, the views and opinions I post here are my own.