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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, though often the second format is more useful. Now, 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. Here is the definition of a pattern that lets you view complex numbers as rectangular coordinates: open Microsoft.FSharp.Math 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.mkRect(ar+br, ai+bi) let mulViaRect a b = match a, b with | Rect(ar,ai), Rect(br,bi) -> Complex.mkRect(ar*br - ai*bi, ai*br + bi*ar) As it happens, multiplication on complex numbers is easier to express using polar coordinates, implemented as follows: let mulViaPolar a b = match a, b with | Polar(m,p), Polar(n,q) -> Complex.mkPolar(m*n, (p+q)) Here is an example of using the (|Rect|) and (|Polar|) active patterns directly on some complex numbers via the pattern tags Rect and Polar. We first make the complex number 3+4i using Complex.mkRect:

AddBusinessRules() must also be called when the business object is deserialized This will happen after a clone operation or when the object moves across the network via the data portal It is not efficient to try to maintain the list of rule delegates for each property during serialization and deserialization Instead, when the object is deserialized, it can simply call AddBusinessRules() to reestablish the rule references: [OnDeserialized()] private void OnDeserializedHandler(StreamingContext context) { ValidationRulesSetTarget(this); AddBusinessRules(); OnDeserialized(context); } [EditorBrowsable(EditorBrowsableStateAdvanced)] protected virtual void OnDeserialized(StreamingContext context) { // do nothing - this is here so a subclass // could override if needed } The [OnDeserialized()] attribute is used to tell the NET serialization infrastructure to call this method once deserialization is complete This attribute comes from the SystemRuntime Serialization namespace, and is one of a set of attributes you can use to decorate methods that are to be called by the .

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These methods are all part of the DOM Core. They aren t specific to JavaScript, and they can be used by any programming language with DOM support. They aren t just for web pages, either. These methods can be used on documents written in any markup language (XML, for instance). When you are using JavaScript and the DOM with HTML files, you have many more properties at your disposal. For example, I've actually used one of these properties, onclick, for event management in the image gallery. These properties belong to the HTML-DOM, which has been around longer than the DOM Core. For instance, the HTML-DOM provides a forms object. That means that instead of writing document.getElementsByTagName("form") you can use document.forms

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