Plotting a function
(Excerpt from "The MathML Handbook" by Pavi Sandhu)
The following example shows an MSP for plotting functions. A user can enter a function along with a range, and then click a button to see a plot of the function over the specified range (see the following figure).
Example: An HTML document for plotting a function using webMathematica.
<html>
<head><title>Plot</title></head>
<body bgcolor="white" >
<h1>Plot a Function</h1>
<form method="post">
<p>Enter a function of one variable: <input type="text" name="f" size="20" value="<%Mathlet MSPValue[ $$f, "Sin[x^2]"] %>" /> </p>
<p>Enter the start of the range: <input type="text" name="x1" size="10" value="<%Mathlet MSPValue[ $$x1, "0"] %>" /> </p>
<p> Enter the end of the range: <input type="text" name="x2" size="10" value="<%Mathlet MSPValue[ $$x2, "5"] %>" /> </p>
<p><input type="submit" name="inputButton" value="Plot" /> </p>
<%Mathlet MSPBlock[ {$$f, $$x1, $$x2},MSPShow[ Plot[$$f, {x,$$x1,$$x2}]]] %>
</form>
</body>
</html>
Figure: A Web page for plotting functions using Mathematica.
This page is a straightforward generalization of the page shown in the example An HTML document for calculating the integral of a function using webMathematica. It contains a form element that contains four different controls: three text boxes and one button. Notice that each text box has its value attribute set to a Mathlet tag that contains the command MSPValue[$$name,value]. This command displays the variable contained in the first argument if that variable has been assigned a value. Otherwise, it displays the second argument. Specifying a second argument is thus a way to include a default value in the text box when the Web page is first displayed. When the page is first loaded, a default value of the function as well as the starting and ending values of the range are displayed in the corresponding text boxes.
The page also contains a fourth Mathlet tag, which encloses the command for generating the plot, as shown here:
MSPBlock[{$$f, $$x1, $$x2},
MSPShow[Plot[$$f, {x, $$x1, $$x2}]
The MSPBlock command, as in the example An HTML document for calculating the integral of a function using webMathematica, first checks to see that all three variables ($$f, $$x1, and $$x2) have valid values. Then, it executes its second argument, Plot[f, {x,a,b}]. This is the Mathematica command for plotting a function of x in the range from a and b. The MSPShow command saves an image of the resulting graphic on the server and returns a link to that image for insertion into the Web page.
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