*The newest version of this software is another shocker*

click to enlarge Figure 1: 3-D plot animations: File titled 3-D plot |

Just when you firmly believe it could not be made much simpler to use, the developers have done it again. Maple 13 has many interesting new features, but the most overwhelming is in the area of usability. Having been away from the program for a short while, it was relatively easy to glide right in and begin calculations without any pain and suffering.

For any brief miscalculation or error generation, a little experimentation or quick trip to the Help section cleared the problem fast! Maple’s great reliance on palettes and a really efficient toolbar quickly assist even the most easily confounded user through most calculations. I was also pleased to find that the

• graphics have been bolstered by the addition of ‘fly-through’ animation

• simulations still feature the excellent ‘components’ palette

• help section is actually somewhat searchable (I found the first three query objects on the first try)

The newest features are listed in overview in Table 2. For the gory details, interested readers are directed to the Web site.

**System requirements**

Maple 13 is compatible with Windows, Macintosh, Linux and Sun Solaris. The developers recommend at least 512 MB of RAM and 1-2 GB of hard drive space, with most space being required on the 64-bit Linux system. As always, more is better, and the modern graphics cards will nicely keep up with the new animation features.

**The workspace**

This is almost a centerpiece in itself as, for those away from the software for several (or more) versions, the main toolbar has been redesigned for maximal utility, and subsections of the menu bar somewhat bulked-up. A view of this screen, with the components section opened and several simple calculations displayed, is shown in Figure 2.

Table 1: Key Features

**Smart Document Environment**

• Math Equation Editor

• Palettes

• Plot Annotations and Customizations

• Visualization

• Task Templates

• Slideshows

• Handwritten Symbol Recognition

• Exploration Assistant

• Interactive Assistants

• Embedded Components: Buttons, Sliders Dials

• Context-Sensitive Menus

**Mathematics**

• Symbolic and Numeric Math

• Comprehensive Mathematics

• Tolerances

• Linear Algebra

• Equation Solving

• Units and Dimensions

**Connectivity**• CAD Connectivity

• Database Connectivity

• MATLAB Connectivity

• Code Generation

**Education**• Tutors

• Maple Portal for Students

Table 2: New Features**Math**

• Differential Equations

• Polynomial System Solving

• Enhanced Equation Solving

• Graph Theory

• Vector Calculus Task Templates

• More Mathematics

**Application Development**

• CAD Connectivity: NX

• Element-wise Operations

• Performance Enhancements

• Multithreaded Task Programming

• Online Troubleshooting Guide

**Visualization**

• 3-D Plot Annotations

• Fly-through Animations

• Rotational Control of 3-D Plots

• Plotting with Units

**Interface**

• Control Systems Design Point-and-click Tools

• Maple Portal

• Worksheet Migration Assistant

• Copy as MathML

• Export to PDF

**Documentation**

• Step-by-step Tutorials

• Online Help System

• Maple User Manual

**Education**

• Numerical Analysis for Students

• Step-by-step Calculus Tools

• Complex Variables Tutors

• Improved Equation Manipulator

• Maple Portal for Math Educators

As was mentioned, there are a number of toolbar features which greatly facilitate many operations and automate the most common. For example, besides the normal zoom, insert text and undo features (*note to developers: it would be nice if this feature could step back multiple times*), we have instant execute commands, as well as stop execution, debug, subsection and insert commands.

**Mathematics**

This is where we are supposed to be impressed, and Maple as well as most mathematical software has long since maxed out. After all, just how quickly have mathematicians come up with new procedures, theorems and proofs? Usually, the few that we get are way beyond the talents of most mortals and of great concern to only a few specialists. However, on the list of what is important to practitioners, especially students and engineers, there is quite a bit to be had.

click to enlarge Figure 2: Palette/component area |

Maple supplies the usual algebra, geometry, calculus and differential equations, but also many extras and helps. Also, huge matrix construction (at least 1000 x 1000) is no problem using NAG libraries, as well as other efficient algorithms. This is important in both business and scientific problems, as we are now buried in mountains of data. The ease of matrix manipulation and computation will be especially useful to many statisticians.

As useful as Maple is to the mathematician and engineer, it is even more valuable to the student. Maple’s clickable math concept makes it easy to step through many complex calculations, and the tutors make learning actually fun. The student can proceed step-by-step through a problem and ask for hints or actual next-step calculations. Plots are done quickly, and the novice can interpolate to desired values. Assistance is immediately available through a variety of sources, including on-line help, manuals, <F1> (Quick Help) and the Quick Reference feature.

For more sophisticated users, there are solve and integration improvements, as well as almost automatic functionalities within differential equation operations and exact and numeric calculations. There have been numerous subtle additions to the math menu (outlined in Table 2) that are detailed at the Web site. For the programmers, there have been several extensions and additions to the language, especially to the multithreading functionality:

• No explicit threading is required; users create Tasks, not Threads.

• Maple schedules the Tasks to the processors so that the code scales to the number of available processors.

• Multiple algorithms written using the Task Programming Model can run at the same time without significant performance impact.

• Complex problems can be solved without requiring traditional synchronization tools, such as mutexes and condition variables.

• If such synchronization tools are not used, the function cannot be deadlocked.

• The Task functions are simple, and the model mirrors conventional function calling.

**Graphics**

A variety (over 50 types) of graphics always has been possible within Maple, as 2-D and 3-D visualizations are a great aid to understanding the numeric results. Now,

click to enlarge Figure 3: Maple tour/visualization |

however, with versions ever increasing in their sophistication, we can modify, pan, zoom and annotate graphics to the nth degree (with an extensive array of drawing tools). With the new fly-through feature, the animation of graphics is now added as a further aid to deciphering complex mathematics. The action of changing variables is now instantly visualized and can be replayed to demonstrate physical phenomena to students and colleagues. Many optimizations and improvements in resource allocations will be obvious in the speed of generation, as well as fine detail. The examples in Figure 3, from a Maple Tour, give some idea of the breadth and depth. The 3-D structure in the lower right pane can be panned to any angle and takes the axes along with the orientation.

**Summary**

I have often admitted in these reviews to my predilection for paper documentation. Although I still prefer these manuals, the e-documentation that comes with most modern software is getting better. We have the entire manual set under the Help menu and the search functions are improving somewhat (incrementally rather than a full Google engine). There are still shortcomings in many of the explanations under the help functions, as examples are given with code rather than menu-driven. This is not deadly, as most of the code is fairly straightforward.

Many of the functions are at an intuitive level, such that the beginner can guess at many steps or correctly use them after a few tries. The frustration level that one would expect with programs this sophisticated gets lower with each version. With a high degree of both ease-of-use and power-of-computation, it’s a pity that some academicians feel the need for free software. With the low price for student editions and upgrades, modern mathematical software is now within the reach of many.

**Availability**

• $1,895 single license, commercial

• student, academic, government and upgrade pricing available

*John Wass is a statistician based in Chicago, IL. He may be reached at* *editor@ScientificComputing.com**.*