One of the problems with the HP Prime’s package is its lean documentation. The user intro that comes with it serves only to skim the surface of the machine. The CD that comes with the pack includes a much more detailed manual, and most areas are covered; but the whole CAS receives a “function index” treatment. You can find the function you need - if only you knew it before already!
I was told recently that the CAS in the HP Prime was a port of the XCAS free software initiative, created in the Fourier faculty in Grenoble university. When falling in the website, I immediately read “Bernard Parisse” and then everything falls in place. Bernard has a long story of association with HP and CAS - he was instrumental in the CAS developments of the HP48 family. It is only logical that he’s behind this project. And the French Connection must have worked well - de Brévisson being an important part in the HP calculator team, and an old timer of the Australian calculator adventure (if i am not mistaking names). Bernard then worked externally with HP to implement CAS in the HP49+ model.
Well, the fact is that you can have in the XCAS site the best documentation to learn about CAS - and you can choose between French and English. You can find it here:
(An additional bonus is at you can download the free software and avoid buying a Prime - provided that you can live with a computer all the time. Probably you’re reading this because you already have a Prime or are attracted to calculators anyway, so the former comment does not apply to you)
If you master French, you can start with the document named “Démarrage en XCAS”. This is a quite low complexity explanation of the principles behind CAS. It still has some references to the original standalone product (that you need to filter out to avoid being confused) but for the rest is an excellent read.
If you now want to go in depth, you can continue with the document named “Symbolic Algebra and Mathematics with XCAS”. Now this is a serious document, and it’ll keep you busy for a while. You can really learn to use the Prime in depth with it! Really, the HP advanced manual should not be used to learn - it is more a reference document.
The above file can also be found in French, in case you feel more comfortable with the language.