Maple 10, from the MapleSoft division of Waterloo Maple Inc., strengthens a highly regarded mathematical workbench with unique facilities for building presentation documents that clarify intimidating symbols and formulas. Producers, as well as consumers, of Maple documents will benefit from major ease-of-use enhancements in this release.

Users will gain real-world insights from Maple 10's improved handling of error allowances and measurement units, which propagate automatically through a user's calculations. These features did not seem fully baked, though, during our tests, requiring extra steps to return properly formatted results.

We tested Maple 10, which was released in May, on Windows XP and Mac OS X 10.4 machines; the product also runs on Linux. Versions for all three operating systems are included in the Professional edition, which is priced at $1,995. Pricing for Student editions, some with limited license terms, starts at $39.

The Maple worksheet environment has been favored by the Labs as the most natural bridge yet devised between the typical PC user, familiar with only the basic conventions of soft-document editing, and the mathematical and graphical power of something more than a spreadsheet.

Maple's documents lack the whiteboard freedom of Mathsoft Engineering & Education Inc.'s Mathcad 12, and they don't have the abstract elegance or recursive computing power of the hierarchical notebooks in Wolfram Research Inc.'s Mathematica 5.1. It's easier, though, for office-applications users to do things in Maple than in these other estimable products.

Even in the simplest tasks, Maple maximizes clarity and anticipates the user's next likely question. When we sought to add up a series of fractions, for example, Maple automatically captured and displayed our input in the form typically seen in typeset documents, rather than in the one-line format typically used in programming statements or spreadsheet formulas.

For example, a mathematically sophisticated user will take it for granted that entering "1/2 + 1/3" will perform the divisions first and then add the two results, but Maple makes this obvious by rendering this expression the way most people would write it on a blackboard: that is, with the numerators above the denominators, separating them with horizontal lines .

The correct answer of "5/6" may leave a new user wondering how to convert that to a percentage. The Mathematica user will have to dig for the information that this requires an idiosyncratic "//N" suffix to be placed on an expression to return the result in decimal form; the Maple user can simply right-click on the result to get a pop-up menu of relevant operations, including decimal approximation to any of several levels of precision. Maple then generates the needed "evalf" command, thereby teaching the Maple language as it goes.

These context-sensitive menus go far beyond simple conversion to include, for example, calculus operations such as differentiation by any of the variables in an expression.

When working in Maple 10's innovative document mode, the user can select mathematical symbols and annotate or even replace them with text: An equation and a series of operations can quickly be edited into a narrative description of how a result was produced, in a process that seems like editing any ordinary document. The mathematical structure, however, remains in the background and can be displayed by choosing the menu command to expand what Maple calls a "document block." All math relationships are preserved: If an input expression needs to be changed, the effects of that change can be propagated through the document with a simple menu command.

In addition to offering common operations from the convenient right-click menus, Maple 10 introduces a unique "looks like" tool for finding the mathematical symbol that a user wants to insert into a worksheet. A region of the screen, looking and working something like the Graffiti area on a Palm PDA, accepts a sketch of a symbol and offers up the most likely candidates for point-and-click insertion.

There's not much point to doing precise math with wild guesses or to getting the right answer but expressing it in the wrong units. Both are frequent and crippling flaws in spreadsheets, which everyone knows how to use but which often aren't the best tool for the job . Maple 10 does well, therefore, to enable computation with values accompanied by "plus or minus" tolerances and to associate units with numbers, carrying the effects in either case through subsequent calculations.

During our trials of these features, though, we found some hiccups in the way that dimensioned and toleranced values were expressed in returned results. After consultation with Maplesoft engineers, we established that an additional "range arithmetic" evaluation using Maple's "evalr" command—in theory, not normally needed—would condense our results into the expected and more convenient form.

Other notable strengths in Maple 10 include its traditional edge in interactive plotting, making it easy to tailor a complex visualization by adjusting on-screen controls, and a new "graphing calculator" interface that makes the math engine's power available for small chores.