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First, the results of the group clause are stored (creating a temporary result) and a new query begins that operates on the stored results The range variable of the new query is ws At this point, ws will range over each group returned by the first query (It ranges over groups because the first query results in a sequence of groups) Next, the where clause filters the query so the final result contains only those groups that contain more than two members This determination is made by calling Count( ), which is an extension method that is implemented for all IEnumerable objects It returns the number of elements in a sequence (You ll learn more about extension methods later in this chapter) The resulting sequence of groups is returned by the select clause

19:

FOLLOWER ANGLE (DEGREES)

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In a query, you will sometimes want to retain a value temporarily For example, you might want to create an enumerable variable that can, itself, be queried Or, you might want to store a value that will be used later on in a where clause Whatever the purpose, these types of actions can be accomplished through the use of let The let clause has this general form: let name = expression Here, name is an identifier that is assigned the value of expression The type of name is inferred from the type of the expression Here is an example that shows how let can be used to create another enumerable data source The query takes as input an array of strings It then converts those strings into char arrays This is accomplished by use of another string method called ToCharArray( ), which returns an array containing the characters in the string The result is assigned to a variable called chrArray, which is then used by a nested from clause to obtain the individual characters in the array The query then sorts the characters and returns the resulting sequence

Without saying so explicitly, we have implicitly assumed in our discussion of area in the last section that our function f is positive, that is its graph lies about the x-axis But of course many functions do not share that property We nevertheless would like to be able to calculate areas determined by such functions, and to calculate the corresponding integrals This turns out to be simple to do Consider the function y = f (x) shown in Fig 411 It is negative on the interval [a, b] and positive on the interval [b, c]

// Use a let clause and a nested from clause using System; using SystemLinq; class LetDemo { static void Main() { string[] strs = { "alpha", "beta", "gamma" }; // Create a query that obtains the characters in the // strings, returned in sorted order Notice the use // of a nested from clause var chrs = from str in strs let chrArray = strToCharArray() from ch in chrArray orderby ch select ch; ConsoleWriteLine("The individual characters in sorted order:"); // Execute the query and display the results foreach(char c in chrs) ConsoleWrite(c + " "); ConsoleWriteLine(); } }

CAMCO B-12345 (SAMPLE) FOLLOWER RADIUS FOLLOWER VELOC FOLLOWER ACCEL (INCHES) (INCHES/SEC) (INCH/SEC/SEC)

The output is shown here:

Part I:

Suppose that we wish to calculate the shaded area as in Fig 412 We can do so by breaking the problem into pieces

RADIUS OF CURV (INCHES) 17909 17596 17297 17010 16735 16470 16215 15969 15732 15503 15283 15071 14868 14673 14486 14309 14141 13982 13833 13694 13565 13447 13339 13243 13159 13087 13027 12979 12944 12922 12913

In the program, notice how the let clause assigns to chrArray a reference to the array returned by strToCharArray( ):

let chrArray = strToCharArray()

930000 940000 950000 960000 970000 980000 990000 1000000 1010000 1020000 1030000 1040000 1050000 1060000 1070000 1080000 1090000 1100000 1110000 1120000 1130000 1140000 1150000 1160000 1170000 1180000 1190000 1200000 1210000 1220000 1230000

After the let clause, other clauses can make use of chrArray Furthermore, because all arrays in C# are convertible to IEnumerable<T>, chrArray can be used as a data source for a second, nested from clause This is what happens in the example It uses the nested from to enumerate the individual characters in the array, sorting them into ascending sequence and returning the result You can also use a let clause to hold a non-enumerable value For example, the following is a more efficient way to write the query used in the IntoDemo program shown in the preceding section

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