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Applying symbolic differentiation is a straightforward translation of the mathematical rules of differentiation into code. You could use local functions that act as constructors and perform local simplifications, but with the simplification function described earlier, this isn t needed. Listing 12-7 shows the implementation of symbolic differentiation for the Expr type. Note how beautifully and succinctly the code follows the math behind it: the essence of the symbolic processing is merely 20 lines of code! Listing 12-7. ExprUtil.fs (continued): Symbolic Differentiation for Algebraic Expressions let Differentiate v e = let rec diff v = function | Num num -> Num 0M | Var v' when v'=v -> Num 1M | Var v' -> Num 0M | Neg e -> diff v (Prod ((Num -1M), e)) | Add exprs -> Add (List.map (diff v) exprs) | Sub (e1, exprs) -> Sub (diff v e1, List.map (diff v) exprs) | Prod (e1, e2) -> Add [Prod (diff v e1, e2); Prod (e1, diff v e2)] | Frac (e1, e2) -> Frac (Sub (Prod (diff v e1, e2), [Prod (e1, diff v e2)]), Pow (e2, 2N)) | Pow (e1, num) -> Prod (Prod(Num num, Pow (e1, num - 1M)), diff v e1) | Sin e -> Prod (Cos e, diff v e)

8. Finally, build and run the web project to see the results of your work. Click on the hyperlinks at the top of the page to navigate throughout the content pages you created (Figures 5-9, 5-10, and 5-11).

Listing 5-7. Formatting Numeric Strings // string_numerical_formatting.cpp using namespace System; int main() { String^ str; int i = -73000; double dbl = 1005.01; // Formats for floating-point types: str = String::Format("Currency format: {0:c2}", dbl); Console::WriteLine(str); str = String::Format("Scientific format: {0:e6}", dbl); Console::WriteLine(str); str = String::Format("Fixed-point format: {0:f6}", dbl); Console::WriteLine(str); str = String::Format("General format: {0:g6}", dbl); Console::WriteLine(str); str = String::Format("Number format: {0:n6}", dbl); Console::WriteLine(str); str = String::Format("Percent format: {0:p6}", dbl); Console::WriteLine(str); str = String::Format("Round-trip format: {0:r6}", dbl); Console::WriteLine(str); // Formats for integral types: str = String::Format("Decimal format: {0:d6}", i); Console::WriteLine(str); str = String::Format("General format: {0:g6}", i); Console::WriteLine(str); str = String::Format("Number format: {0:n0}", i); Console::WriteLine(str); str = String::Format("Hexadecimal format: {0:x8}", i); Console::WriteLine(str); }

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You can display a search box on your site in three ways: Most themes have a global search form built in, which you can toggle on or off from the global theme settings page (admin/themes/settings) or from your theme s specific configuration page. You can show the search form within a block by enabling and configuring the Search Form block. You do this in the normal fashion from the block administration page (admin/block). You can access a dedicated search page by using the Drupal path search. This page corresponds to a menu item in the main navigation menu. The menu item is disabled by default, so you will need to use the Menu module to turn it on. You can search on either content or users. Searching for content is done from the path search/node and returns a page of links to content that contains the search term(s). The search box displayed by the theme and the search box in the block both search for content by default. Searching for users is done from the path search/user and returns a result set of links to users whose profiles or usernames contain the search strings.

If all you re doing is changing ownership, you can omit the :group [the colon followed by the actual value for group]. Alternatively, you can use the chgrp command, which has similar syntax, if you merely want to change group ownership. To change ownership, you must either have granted the chown ACL right, or you must be running as root. You can use chmod to manage both POSIX and ACL permissions. Realize, however, that managing ACL s from the command line can be a bit hairy----it s not for the faint of heart. In any case, first though, the basics. As demonstrated earlier, you can use chmod to modify POSIX permissions. The syntax is:

void raise(String^ eventString) { Console::WriteLine(" Firing Exit event. "); if (_exit) _exit->Invoke(eventString); } } // function calls to raise the events from outside the class void RaiseStartEvent(String^ eventString) { Start(eventString); } void RaiseExitEvent(String^ eventString) { Exit(eventString); } // event handler for Start event void OnStart(String^ eventString) { Console::WriteLine("Starting: " + eventString); } // event handler for Exit event void OnExit(String^ eventString) { Console::WriteLine("Exiting: " + eventString); } }; void f(Events^ e) { // Raise event for starting this function. e->RaiseStartEvent("Start event occurred!"); Console::WriteLine("Doing something."); // Raise event for exiting this function. e->RaiseExitEvent("Exit event occurred."); }

cation infrastructure, it s a good idea to start thinking about it in terms of workflow and if complex systems and interactions can be designed as a workflow, you may save yourself and your company a lot of time and money by implementing it in WF. As such, WF, as one of the foundations of .NET 3.0, has a well-deserved place in the architecture of the future Web, and is a resource well worth learning and understanding. The simple applications that you learned in this chapter are but a taste of what is possible with WF. If you want to learn more about WF, a terrific resource to begin with is Microsoft Windows Workflow Foundation Step by Step, by Kenn Scribner (Microsoft Press, 2007).

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