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In high-school math courses, you were probably taught that you can view complex numbers in two ways: as rectangular coordinates x + yi or as polar coordinates of a phase r and magnitude . In most computer systems, complex numbers are stored in the first format, although often the second format is more useful. Wouldn t it be nice if you could look at complex numbers through either lens You could do this by explicitly converting from one form to another when needed, but it would be better to have your programming language look after the transformations needed to do this for you. Active patterns let you do exactly that. First, here is a standard definition of complex numbers: [<Struct>] type Complex(r: float, i: float) = static member Polar(mag,phase) = Complex(mag * cos phase, mag * sin phase) member x.Magnitude = sqrt(r*r + i*i) member x.Phase = atan2 i r member x.RealPart = r member x.ImaginaryPart = i Here is a pattern that lets you view complex numbers as rectangular coordinates: let (|Rect|) (x:Complex) = (x.RealPart, x.ImaginaryPart) And here is an active pattern to help you view complex numbers in polar coordinates: let (|Polar|) (x:Complex) = (x.Magnitude, x.Phase) The key thing to note is that these definitions let you use Rect and Polar as tags in pattern matching. For example, you can now write the following to define addition and multiplication over complex numbers: let addViaRect a b = match a, b with | Rect (ar, ai), Rect (br, bi) -> Complex (ar+br, ai+bi) let mulViaRect a b = match a, b with | Rect (ar, ai), Rect (br, bi) -> Complex (ar*br - ai*bi, ai*br + bi*ar)

In this chapter you have seen how to use the .NET Framework class library to measure small amounts of time, represent periods of time, and represent moments in time. These are features that most programmers use frequently. One of the features I like most in the way that .NET and C# represent times and dates is the custom operators, which make comparing and combining dates and periods simple and elegant.

Recollect that earlier we created two web methods PutNameInSession() and GetNameFromSession() that deal with session storage. Let s see how you can call these methods in the client application. To see how this works, you need to create an application like the one shown shown in Figure 9-13.

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The General tab also lets you select whether the power icon is visible in the notification area. If you re using a notebook, you can display the icon only when the battery is nearly drained, when your battery is charging or discharging, or regardless of the battery state. Desktop PC users can choose not to display the power icon, which makes sense. The most fuss-free option is perhaps Only Display an Icon When Charging or Discharging, which is selected by default. Finally, there s also an extra option you can check to play sounds when error events occur.

The code loads the new Employees.xml file in the XmlDocument instance we created earlier by using its Load() method. A foreach loop then iterates over all the <employee> nodes. With each iteration, the employeeid attribute of the <employee> node is retrieved using the Attributes collection of the XmlNode class. The attribute value is added to the combo box. When the user selects a particular ID, the details of that employee are displayed. This is accomplished in the Click event handler of the Show Details button. The code inside the Click event handler is shown in Listing 2-8. Listing 2-8. Calling the GetElementById() Method private void button1_Click(object sender, EventArgs e) { XmlElement ele= doc.GetElementById(comboBox1.SelectedItem.ToString()); label6.Text = ele.ChildNodes[0].InnerText; label7.Text = ele.ChildNodes[1].InnerText; label8.Text = ele.ChildNodes[2].InnerText; label9.Text = ele.ChildNodes[3].InnerText; } The code calls the GetElementById() method of the XmlDocument class and passes the employee ID to look for. The GetElementById() method returns the matching element as an object of type XmlElement. Because the XmlElement class inherits from the XmlNode class, the ChildNodes collection is available to the XmlElement class also. To retrieve the values of the <firstname>, <lastname>, <homephone>, and <notes> nodes, the ChildNodes collection is accessed by using the index of the corresponding element. Finally, the InnerText property of each XmlNode gives the text inside the appropriate node.

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