New Features in Maple 17: Clickable Math

Next Feature

Maple 17 continues the tradition of providing Clickable Math techniques to make it easy to learn, teach, and do mathematics.  Maple 17 builds on the Smart Popups and Drag-to-Solve technology first introduced in Maple 16, which offer new ways to explore math with only your mouse. Drag-to-Solve lets you solve your equations step-by-step simply by dragging terms to where you want them to be, while  Smart Popups suggest common operations that can be applied to the entire expression or just part of it, and let you preview the result before going ahead. You can use Smart Popups to easily determine if your subexpression can be factored, what its plot looks like, what mathematical identities could be applied, and more.

In Maple 17, the Smart Popups menus have been expanded, offering new choices for completion of the square and simplification options based on expression size. Other improvements have been made to the generation and display of the menus for Smart Popups and Drag-to-Solve, including visual improvements, internationalization, and display time.

In addition, a displayed suggested result of applying the simplify command will now visually match the result of applying the current binding of simplify. For example, if the RealDomain package has been loaded then a suggested result due to applying simplify will now match the result that RealDomain:-simplify would produce.

Complete the square

> expand(`*`(`^`(`+`(A, B, C), 2)))

`+`(`*`(`^`(A, 2)), `*`(2, `*`(A, `*`(B))), `*`(2, `*`(A, `*`(C))), `*`(`^`(B, 2)), `*`(2, `*`(B, `*`(C))), `*`(`^`(C, 2)))

Selecting the output expression above produces the Smart Pop-up menu after a brief pause. Completing the square on the given example may be done in terms of one or several of the variables. If the mouse pointer hovers over the appropriate item then the relevant submenu appears. For individual action items (choices within that submenu) a tooltip will further describe the suggested operation.

Below is a screenshot of the Smart Pop-up menu produced for the previous output.



For some expressions the concept of simplification may depend on context or preference. Simplification in a mathematical sense may not naturally be the same as simplification according to expression length. The menu suggestions will offer the results from the simplify command both with and without its size option.

If multiple mechanisms would normally compute the same result then the menu suggestions attempt to show the action which would usually be more efficient. For example, a suggestion to apply the normal command would take precedence over a suggestion to apply the simplify command.

Trigonometric identities

The Smart Pop-up menus provide an easy way for students to prove trigonometric identities in a self-documenting step-by-step manner.

The following operations are all achieved by suggestions in the Smart Pop-up menus. This example was executed in a Standard Maple Document, using default 2-D Math input and the self-documenting feature of context-sensitive menu actions.

sin(`+`(`*`(3, `*`(a)))) = `+`(`*`(3, `*`(sin(a))), `-`(`*`(4, `*`(`^`(sin(a), 3)))))

sin(`+`(`*`(3, `*`(a)))) = `+`(`*`(3, `*`(sin(a))), `-`(`*`(4, `*`(`^`(sin(a), 3)))))

`+`(`*`(2, `*`(cos(a), `*`(sin(`+`(`*`(2, `*`(a))))))), `-`(sin(a))) = `+`(`*`(3, `*`(sin(a))), `-`(`*`(4, `*`(`^`(sin(a), 3)))))

`+`(`*`(4, `*`(`^`(cos(a), 2), `*`(sin(a)))), `-`(sin(a))) = `+`(`*`(3, `*`(sin(a))), `-`(`*`(4, `*`(`^`(sin(a), 3)))))

`+`(`*`(4, `*`(`^`(cos(a), 2), `*`(sin(a))))) = `+`(`*`(4, `*`(sin(a))), `-`(`*`(4, `*`(`^`(sin(a), 3)))))

`+`(`*`(4, `*`(`^`(cos(a), 2)))) = `/`(`*`(`+`(`*`(4, `*`(sin(a))), `-`(`*`(4, `*`(`^`(sin(a), 3)))))), `*`(sin(a)))

`+`(`*`(4, `*`(`^`(cos(a), 2)))) = `+`(4, `-`(`*`(4, `*`(`^`(sin(a), 2)))))

`*`(`^`(cos(a), 2)) = `+`(1, `-`(`*`(`^`(sin(a), 2))))

`+`(1, `-`(`*`(`^`(sin(a), 2)))) = `+`(1, `-`(`*`(`^`(sin(a), 2))))