For some time now, I have been starting reviews of mathematics packages with notes on how much they have yet again managed to develop the interface in ways that erode the membrane separating thought from result. It’s very tempting to do the same here because they impact on every other area, but just for a change I’ll leave that aspect until later and look at others first. Following my own areas of particular interest took me first of all to statistics, to polynomial systems which acquire a new regular chains package, and thence to physics.
My favourite change in statistics is perhaps a small one: handling of data matrices has been harmonised across the package. As icing on that particular cake, rule-based subsetting by variable (that is, matrix column) value is now a real joy to use. Elsewhere, statisticians see amplification of both discrete distribution handling and maximum likelihood estimation. The considerably developed reach and subtlety of technical graphics control are not an exclusively statistical concern, but are very welcome there – the arrival of bounding box-based zoom, a new dedicated palette and refined surface smoothing especially.
Physics benefits from a big push during this cycle, with more additions and enhancements than I can possibly touch upon here. Improvements to work with tensors range from an intelligent general relativity box of tricks down to a single step combined multiplication and simplification operator. Differential geometry has very nicely done metrics handling.
Other augmented areas include differential equations and control design. Object handling in the language is extended and there are also, of course, the usual increases in speed, efficiency and exploitation of multiple cores. There is also a spread of productivity developments across various collateral areas from connectivity to ebook publishing.
Returning, now, to the interface, Maple 16 continues the development trajectory established for several generations now: transparently enabling playful or productive (or both) immersive manipulation of symbolic entities. Comparison with pencil and paper working used to be the gold standard here, but things have moved on. Enhancing that intuitive simplicity of use, rather than just reproducing them, is now the name of the game and Maple 16 delivers on that aspiration.
Highlight a component or substructure within an equation and you can drag it about from place to place, adjusting itself automatically as it moves. Hover over the highlighted entity and a discreet ghostly set of pale help patches glimmer (the word ‘pop’ doesn’t fit) into view, suggesting the most obvious couple of things you might want to do. If you know what you want to do, you won’t see the suggestions; if not, wait half a second or so. Shifting the mouse pointer onto those patches brings them into full view, with a thumbnail of what each suggestion would produce; shift onto a suggested plot and it enlarges to give a more detailed view, and so on.
Add to this what amounts to a visual, palette-based clipboard on which document fragments (expressions, plots, whatever) can be arranged for reuse and a range of detail improvements. It’s a beautifully designed and implemented system.
In my own professional practice, I have a heavy investment in another computer algebra product, but this is the Maple release which has made me seriously consider switching horses.