HP 40G

The HP 40G is a graphing calculator for school maths that Hewlett-Packard brought out in 2000, beside the HP 39G. It is the same calculator with one trade: it adds the computer algebra system of the HP 49G and leaves out the infrared port, connecting by cable instead.

At a glance

History

Two calculators from one design

In 2000 HP replaced its HP 38G school calculator with two new ones. Both are built on the design of the HP 49G, with 1 MB of ROM and 256 KB of RAM where the 49G has 2 MB of flash memory and 512 KB of RAM. Both run the same ROM, which finds out at start-up which model it is in and turns its features on or off to match.

The HP 39G has the infrared port and no computer algebra, and was sold in the US. The 40G has the computer algebra and no infrared, and was sold in Europe and some other markets. Finseth's data sheet records that it was first shown at the conference of the National Council of Teachers of Mathematics, at the same $79.99 as the 39G, and that its operation evolved from the 38G's.

Why no infrared

HP's user's guide says only that the 40G has no infrared port, and that a PC adapter and a cable between two calculators come in the box instead. It cannot print to HP's infrared printers either.

The market explains some of it. The HP 49G FAQ, written a year earlier, says that because of its infrared the HP 48 had been banned from schools in nearly every European country, and in Australia and Africa: teachers did not know how short the range was and feared the calculators would be used to cheat. It was one of the reasons HP left the infrared out of the 49G.

The CAS

The 40G's computer algebra is the one Bernard Parisse wrote for the 49G. Parisse names himself the main author of the CAS of the 49G, the 40G and the later 49g+ and 48gII. Its manual for the 40G is a translation of the original CAS manual, made by Mark Howell for HP.

Computer algebra is not welcome in every exam room. Wikipedia notes that the 40G is not allowed in many standardised tests, the ACT among them, though the SAT has allowed it since 2019.

What came after

In 2006 HP released the 40gs, with an ARM processor and 2 MB of flash memory to hold the CAS, again without infrared. The 39G line went on to the 39gII of 2011, and the plan for a version of it with computer algebra led to the HP Prime of 2013.

What makes it special

A school calculator with a CAS

On the 40G, the HOME view has CAS on its last menu key. It opens an editor where you build an expression as it looks on paper, with menus of tools along the bottom: TOOL, ALGB, DIFF, REWRI, SOLV and TRIG. Each opens a list of commands to choose from.

Everything the 39G has

Apart from the CAS and the infrared, the 40G is a 39G. It has the same aplets: Function, Parametric, Polar, Sequence, Solve and Statistics, the Inference aplet for confidence intervals and hypothesis tests, and the two teaching aplets, Quad Explorer and Trig Explorer, which show how the numbers in an equation shape its graph. Each aplet has a graph, a symbolic and a numeric view, under PLOT, SYMB and NUM. A teacher can share aplets with a class, over the cable instead of by infrared, and students can download more from HP's and teachers' web sites. The 39G page describes them in more detail.

The case

Finseth's data sheet notes two details: the case is the 49G's, and the display has a new acrylic cover, unlike the 49G's. The 49G FAQ had complained that the 49G's cover was shiny like a mirror and scratched easily.

In saturnus

saturnus runs the 40G with the same ROM as the 39G, from hpcalc.org:

• The ROM tells the two models apart by one input line. On the 40G no infrared receiver sits behind it, so saturnus holds it as a 40G board is expected to, and the ROM shows CAS on the HOME menu. No source documents that line; it was found by running the ROM.
• The CAS runs: CAS, then ALGB and FACTOR, on X² − 1 gives (X − 1)·(X + 1).
• The saturnng emulator, which saturnus compares its screens with on the 48 and 49 models, does not run the 40G, and no real 40G has been compared. Its start and arithmetic are covered by saturnus's tests.
• The speed is set as for the 49G, which has the same design; no real 40G has been timed for it. For long programs, switch to 2×, 4× or Max.
• Files can serve a folder to the 40G as the "disk drive" it sends aplets to and receives them from: APLET, then SEND or RECV, and "Disk drive…". Binary aplets can also go over the wire transfer, "HP39/40 (Wire)", which has been tested on the emulated 39G only. With a real 40G on a cable (in Chrome or Edge on a computer) none of this has been tried.
• There is no memory view for the 40G; it exists for the 48SX, 48GX and 49G.

The command reference lists the 40G's 209 functions with the keys that run them, and examples for 124 of them, run in saturnus. They are the HOME functions it shares with the 39G; the CAS commands are not in it.

Open the HP 40G in saturnus

Sources

• HP 39G/40G Graphing Calculator User's Guide: the CAS key, no infrared and the cables in the box, no infrared printing, the aplets, the batteries.
• Christoph Gießelink, Emu48 25 years: the 39G and 40G built on the 49G, one ROM for both, 1 MB ROM and 256 KB RAM.
• Finseth's HP calculator data: HP 40G: the code name, the price, the processor, RAM, size and weight, CAS and case as on the 49G, the display cover, sold in Europe, first shown at the NCTM conference.
• Wikipedia: HP 39/40 series: the model found at start-up, the CAS, the tests that allow it or not, the 40gs and the later models.
• Wikipedia: HP 38G: the 39G and the 40G replacing the 38G in 2000, the 40G in Europe and other markets.
• Bernard Parisse: Xcas and the HP 49G and 40G: his part in the CAS of the 40G, the 40G manual translated by Mark Howell.
• HP 49G FAQ, maintained by Eric Rechlin: why the 49G has no infrared, the 49G's screen cover.