The HP Prime Graphics calculator

In my effort to find the perfect CAS calculator, I recently acquired one of these babies:


It has many of the hallmarks of the engineering excellence which used to be such a selling point with HP calculators: the keys are superb, the unit itself is thin with a metal back (it has a rechargeable battery, rather than using AAA’s), and its “feel” is of a superior product. The main problem with its externals is the orange letters on the white keys; especially on the numeric keys (which are darker than the others), these letters are hard to read in anything less than very good light. The cyan also on the keys (reached by using Shift) is only marginally better. The keys would be more readable if they were black rather than white or light grey, somewhat like the older HP 35s. HP have always put a lot on to their calculators, in an exemplary fashion, so I don’t know why they missed the mark here.

But that is quibbling – what’s it like for mathematics? In very many ways, absolutely excellent. The screen is crisp, clear, coloured, and also touch sensitive, so that menus can be whisked through by scrolling with the fingers, as well as by using the four-way pad just beneath the screen. My first silly test (factor 2^{67}-1) was done instantly. Very good!

I then decided to see if I could obtain a list of the “zig-zag numbers” z_k; these are the number of permutations of {1,2,3,ldots k} in which the numbers alternately rise and fall. For example, if k=4 these are the zig-zag permutations:

1,3,2,4;qquad 1,4,2,3;qquad 2,3,1,4;qquad 2,4,1,3;qquad 3,1,4,2

There are five of them, so that z_4=5. It turns out that the exponential generating function for z_k is tan x+sec x; so that

displaystyle{tan x +sec x=1+x+z_2frac{x^2}{2!}+z_3frac{x^3}{3!}+z_4frac{x^4}{4!}+cdots }

You can read about these lovely things on the Wikipedia page on alternating permutations.



produced the sequence nicely. All of the constructs in those commands are available through menus.

The calculator has two “views”: “Home” and “CAS”. In “Home” view you have floating point calculations, and variables are by default upper-case letters; in “CAS” view operations are exact, and variables are by default in lower-case. This business of lower-case/upper-case confuses me, as I don’t see the need for it. And in fact the two views seem to differ more in their restrictions than anything else. For example, the menus seem the same in both views, but if you try the above series computation in “Home” view, the screen gives you:


It looks as though all the CAS operations are available in Home as methods in a CAS class, but in fact the output of this command is simply 1. I don’t understand this at all.

I also use lists a huge amount in my CAS work, but the MAKELIST command only seems to work in Home view, even though it’s available on the same menus in CAS view. Again, I’m quite unclear about the wisdom of having menu items which don’t do anything.

When I introduce students to CAS calculators or to computer-based systems, I get them to find (by trial and error) the smallest k for which


This gives them a tiny insight into the speed and power of computational mathematics. And I have done this over the years with Derive, Maple, Maxima, Axiom, Sage, TI-nspire, and CASIO ClassPad. But guess what? you can’t perform this computation on the HP Prime because the SUM function only allows 1000 elements to be summed! I’m told this is an “inadvertent” oversight left over from the HP 39gII, on which much of the HP Prime is based (as well as using a slightly cut-down version of Xcas). It’s a pain though.

The calculator has 14 “Apps”: you can see 12 of them in the picture above (the other two are “Polar” and “Sequence”). In each App some of the keys on the keypad have actions particular to the App. For example, in the “Function” App, the “Symb” key allows you to enter functions, but in the “Sequence” App you get to enter a sequence definition instead. However, the on-screen menus are unchanged.

When I first got the calculator I was plagued by sudden and inexplicable freezes and spontaneous reboots. These have become more rare, but they still occasionally happen. Sometimes the calculator can be unfrozen by a key combination (On+Symb usually works). There is also a “reset” hole at the back, for use with a paper-clip. At the very worst you can unscrew the battery pack cover and temporarily unseat the battery.

I like this machine very much, in spite of its annoyances: I like it a great deal more than the Casio ClassPad (even though the CP has a bigger screen). I would hope that its peculiarities: occasional menu items which don’t work, restrictions on things like SUM, confusions between upper and lower case variables and the Home/CAS views, will be ironed out in the next generation (if there is one).

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