Clickable Math: Smart Popups and Drag-to-SolveTM - Maple Programming Help

Clickable Math: Smart Popups and Drag-to-SolveTM

 Maple provides two features for step-by-step, interactive mathematical problem-solving; Smart Popups and Drag-to-Solve.
 This document provides information on each feature as well as examples on how to use them for step-by-step mathematical problem-solving.

Smart Popups

Description:

Smart Popups are interactive popup menus that are automatically displayed when you select an expression or individual terms in an expression. They provide a choice of options for manipulating your selection, such as plotting, expanding, factoring, substituting trigonometric expressions, etc. Smart Popups work only on the output of a Maple expression or equation.

Using the Smart Popups feature:

The general procedure for using Smart Popups is as follows.

 1 Click on your Maple input, then press Enter to generate output for the expression or equation you want to investigate.
 2 Select the expression or subexpression that you want to manipulate from the generated output. At this point, the Smart Popup window is automatically invoked.
 3 The Smart Popup window displays a choice of applicable operations. The results of selecting each operation are previewed in the Smart Popup window. To select an operation, click on the corresponding preview.

Note: To close the smart popup, click outside the popup window.

 4 Repeat steps 2 and 3 until you have your desired result.

Note: Smart popups are enabled by default in Maple. To disable this feature, from the View menu, clear the Clickable Math check box.

Drag-to-Solve

Description

The Drag-to-Solve feature enables you to drag individual terms in an output equation from one side of the equal sign to the other. This action invokes the Smart Popup feature which displays your available options.

Using the Drag-to-Solve feature allows you to direct what will happen interactively.

Using the Drag-to-Solve feature:

The general procedure for using Drag-to-Solve is as follows:

 1 Click on your Maple input, then press Enter to generate output for the equation you want to solve.
 2 Select a term in the output equation and drag it to the other side of the equality. A Smart Popup window is displayed, previewing the results of your manipulation.
 3 Click on the Smart Popup window to confirm the manipulation.
 4 Repeat steps 2 and 3 until you have your desired result.

Examples

Example 1: Solve a trigonometric identity using Smart Popups:

 Input the following expression, then press Enter to produce the required output: $-\frac{1}{2}\mathrm{cos}\left(x\right)+\frac{1}{2}=\mathrm{sin}{\left(\frac{1}{2}x\right)}^{2}$  Select the expression, from the generated output. The Smart Popup window is automatically displayed. From the previewed choice of operations, select Trig Identities  , then select the appropriate Trigonometric Identity. The results are returned to the worksheet.

Example 2: Produce a 3-D plot for an expression using Smart Popups:

 Input the following expression, then press Enter to produce the required output: $\mathrm{cos}\left(\frac{1}{10}x\cdot y\right)$ Select the entire output expression. The Smart Popup menu is automatically displayed. Select 3D Plot from the available choices. A preview of the 3-D plot is displayed. Click on the 3-D plot. The results are displayed in the worksheet.

Example 3: Complete the square using Smart Popups:

 Input the following expression, then press Enter to produce the required output: $\mathrm{expand}\left({\left(A+B+C\right)}^{2}\right)$  Select the entire output expression. The Smart Popup menu is automatically displayed. For this example, select the Complete the square in [A,C] menu option.  The results are displayed in the worksheet.

Example 4: Solving a linear equation using Drag-to-Solve:

 Input the following expression, then press Enter to produce the required output: $5\cdot x-7=3\cdot x+2$ Drag  $3x$ from the right side of the equal sign to the left side. A Smart Popup window is displayed, previewing the results of this manipulation. Click on the Smart Popup window to confirm this operation. Next, in the resulting output equation, drag -7 from the left side of the equation to the right side. Click on the Smart Popup window to confirm this operation. Drag and drop the factor of $2$, in front of $x$, to the right side of the equal sign. Click on the Smart Popup window to confirm this operation.

Note: Currently, the functionality for these features is restricted to arithmetic manipulations and plotting.