Using the Exploration Assistant
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Introduction


The Exploration Assistant allows users to instantly create interactive miniapplications, which can be used to explore the parameters of any arbitrary Maple expression, such as a plot, mathematical equation, or command. With these applications, you can use sliders to change the values of the parameters and see instant results.
How To Do It
There are two ways you can use the Exploration Assistant; either through the context panel for an expression, or by calling the Explore command.

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Exploration of a 3D Plot











Using the Context Panel


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1.

Enter the expression $\mathrm{factor}\left({x}^{n}\+1\right)$

2.

Click the expression and select Explore from the context panel. A new dialog box will appear. From here, you can set the range of values you want to explore, as well as specify any variables to skip. When you select skip, that parameter remains as a symbolic unknown in the expression; no slider will be created to control that value.

3.

Enter 0 for the lower value of n and 10 for the upper value. Next to the variable x, check the skip box. When you are done, click Explore.





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A new Exploration table is generated in the worksheet, inline, below the expression. The table is comprised of embedded components; a slider is used to manipulate the value of the indeterminate n, and a math container to display the expression and associated solution. Move the slider back and forth to see how it changes the solution.

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You can now save this table for future use by going to File>Save.



Using the Explore Command


You can just as easily use the Exploration Assistant by using the Explore command, which takes as its argument the Maple expression to be explored.
1.

Enter the expression $\mathrm{Explore}\left(\mathrm{expand}\left({\left({x}^{\frac{2}{3}}5{y}^{7}\right)}^{n}\right)\right)$ and press Enter.

4.

In the dialog that appears, enter 1 for the lower limit of n. Next to the variables x and y check the skip box on the right. This will keep these variables in the solution. When you are finished, click Explore.

5.

A new table is generated inline with the expression inside a math container and a slider component for n. Move the slider back and forth to see how it changes the expansion.

Tip: You can opt to have the exploration table appear in a new worksheet instead of in the current worksheet. To do this, add the option newsheet to the Explore command:
$\mathrm{Explore}\left(\mathrm{expand}\left({\left({x}^{\frac{2}{3}}5{y}^{7}\right)}^{n}\right)comma;\mathrm{newsheet}\right)$



More Examples



Exploring a Series Expansion


1.

Enter the expression $\sum _{k\=0}^{n}\frac{k}{{\left(k\+2\right)}^{2}}\cdot {\left(x4\right)}^{k}$

2.

Click the expression and select Explore from the context panel.

3.

When the input screen appears, enter 1 for the lower limit of n. Next to the variable x check the skip box on the right. This will keep the variable x in the solution. When you are finished, click Explore.

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A new table is generated inline with the expression inside a math container and a slider component for n. Move the slider back and forth to see its effect on the expression.

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Tip: When you are entering value ranges for the variables you want to explore, make sure they are mathematically acceptable (for example, avoid causing a value of zero in the denominator).


Exploring an Integral Numerically


1.

Enter the expression ${\int}_{0}^{\mathrm{\π}}a\cdot \mathrm{sin}\left(b\cdot x\right)DifferentialD;x$.

2.

Click the expression and select Explore from the context panel.

3.

Use the default ranges for a and b. To see numerical (rather than symbolic) results, select the numeric check box. When you are finished, click Explore.

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A new table is generated inline with the expression inside a math container and slider components for a and b. Move the sliders back and forth to see the effect on the computation.

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Tip: You can control whether the sliders vary through decimal values or only integer values. When you are entering value ranges for the variables you want to explore, if you enter the endpoints using decimals (such as 10.0 instead of 10), then the corresponding slider will explore decimal values.
For more details on numerical computation and the other options for Explore, see the Explore help page.


Exploring a 2D Plot


1.

Enter the command $\mathrm{plot}\left(\mathrm{cos}\left(a\cdot x\right)\cdot \mathrm{sin}\left(b\cdot x\right)comma;xequals;2\cdot \mathrm{pi;}..2\cdot \mathrm{pi;}\right)$

2.

Rightclick the expression and select Explore. A new window will appear.

3.

Enter 1 for the lower limits of a and b. When you are done, click Explore.

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A new table is generated inline with a plot area and sliders for a and b. Move the sliders back and forth to see their effects on the plot.

Tip: If you are going to explore a 2D plot it is not necessary to define the range for x . However, if you do not define a range for x then you must select skip for x in the dialog . Default values will then be used for the range.


Exploration of a 2D Plot








Exploring a 3D Plot


1.

Enter the command $\mathrm{plot3d}\left(\frac{x\cdot \mathrm{cos}\left(a\cdot \sqrt{{x}^{2}plus;{y}^{2}}\right)}{{\mathrm{\pi}}^{2}}comma;xequals;\mathrm{pi;}..\mathrm{pi;}comma;yequals;\mathrm{pi;}..\mathrm{pi;}\right)$

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2.

Click the expression and select Explore from the context panel. A new window will appear.

3.

Enter 5 for the lower limit of a, and 5 for the upper limit. When you are done, click Explore.

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A new table is generated inline with a plot area and slider for a. Move the slider back and forth to see its effect on the plot.



Exploration of a 3D Plot









Example Worksheet


The Explore example worksheet provides many more examples, including how to control the layout, creating explorations using animations, and more.

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