In addition to providing access to powerful tools for mathematical computation, Maple has been designed to help you work quickly and efficiently. Here are 10 useful short-cuts when working with Maple:

1. Use F5 to switch between Text and 2D Math input modes in Maple.

2. Use F2 (Control+? for Macintosh) to quickly bring up Maple Help information for anything that you have typed in your document.

3.  Automatic Command Completion can be used when you don't want to type in the full name of a Maple command. To use, begin typing the first few letters of the command name, and press CTRL+Space (Esc or Command+Shift+Space for Macintosh, CTRL+Shift+Space for Linux).  A list of possible completions will display; click the one you want.

4. The Shift+Enter key combination lets you continue entering math or commands on a new line without executing that line. 

5. If you want more than a single command to be executed at once, you must separate them with a semi-colon or colon.

6. When you click inside a set of commands in Math mode, the dash line indicates the boundaries of the input region; all commands in this region will execute together in sequence.

7. To increase the size of a piecewise function, add a new row.  Place the cursor on the last row, and press CTRL+Shift+R (Command+Shift+R for Macintosh). These shortcut keys also work to add rows to matrices.

8. An easy way to insert a Greek letter is to first press CTRL+Shift+G (Command+Shift+G for the Macintosh). The next letter typed will appear in Greek.

9. Sometimes you may want to insert symbols above or below another character, for example, to enter a vector arrow. To insert a symbol above (called "overscript"), press CTRL+Shift+["] (Command+Shift+["] for Macintosh) and then type in your symbol (or insert it from a palette).

For example, typing "x" then holding down CTRL+Shift and pressing ["] allows you to insert a symbol above the x, such as 

10. Compute or recompute the entire Maple worksheet when you have changed expressions that affect subsequent Maple commands.  Press Ctrl + Shift + Enter (Command + Shift + Enter in Macintosh) or click the execute worksheet icon. 

Are there any short-cuts that you would add to this list?

The new Import and Export commands introduced in Maple 2015 provide a unified approach to all data import and export activities, replacing the need to use different commands in different situations. They can be used with many of the wide variety of file types supported by Maple, including 3-D graphics data, numeric and tabular data, images, audio files, special-purpose formats for mathematical objects such as graphs, and much more.

In the following example, you can see how to use these commands in order to bring 3-D models from the popular website Thingiverse and to export 3-D plots to a format suitable for 3-D printing.

Tips and Techniques: 3-D Model Import/Export and Printing

Naive simplification of  to results in a pair of functions that agree on only part of the complex plane. In this application, the enhanced ability of Maple 18 to find and display branch cuts of composite functions is used to explore the branch cuts and regions of agreement/disagreement of f and F.

The algorithm by which Maple calculates branch cuts for square-root functions involves squaring, to remove the square root, and solving appropriate equations and inequalities. Unfortunately, this process is inherently prone to introducing spurious solutions, in which case the returned branch cut is not correct. One such instance in which a spurious solution arises is in the calculation of the branch cut for f; a best suggestion for dealing with such errors is found in the application.

Application: Branch Cuts for a Product of Two Square Roots

For those interested in learning more, the design for the new branch-cut facility in Maple 18 is inspired by the following paper:

England, M., Bradford, R., Davenport, J. H., and Wilson, D. 2013.  Understanding branch cuts of expressions. In: Carette, J., Aspinall, D., Lange, C., Sojka, P. and Windsteiger, W., eds.  Intelligent Computer Mathematics. Berlin: Springer, pp. 136-151. (Lecture Notes in Computer Science; 7961)

Recently I was skimming on the Internet for algorithms for alignment of biological sequences (e.g. DNA sequences, protein sequences). The usual purpose of such comparisons is to determine the evolutionary genetic history of two sequences, which in the case of DNA you can think of as strings over the alphabet {A,G,C,T} (the nucleobases). Differences between sequences can arise though substitutions (A → G, G → A, C → T, or T → C), insertions, or deletions. In the last two cases, the resulting string differs in length from the original, and dealing with these size differences is the chief problem that alignment algorithms face. The Needleman-Wunsch algorithm is a very straightforward global sequence alignment algorithm, first proposed in 1970. It's a good example of the applicability of dynamic programming towards biological problems. Following is a Maple implementation based on this Ruby implementation. The algorithm depends on a similarity matrix which measures the "mutational distance" between two nucleobases. It takes two input strings, and returns two strings with dashes ("-") inserted to indicate insertion or deletion events between the sequences.