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It will be true only for an element whose value is greater than zero This expression will be evaluated for every n in nums when the query executes Only those values that satisfy this condition will be obtained In other words, a where clause acts as a filter on the data source, allowing only certain items through All queries end with either a select clause or a group clause This example employs the select clause It specifies precisely what is obtained by the query For simple queries, such as the one in this example, the range value is selected Therefore, it returns those integers from nums that satisfy the where clause In more sophisticated situations, it is possible to finely tune what is selected For example, when querying a mailing list, you might return just the last name of each recipient, rather than the entire address Notice that the select clause ends with a semicolon Because select ends a query, it ends the statement and requires a semicolon Notice, however, that the other clauses in the query do not end with a semicolon At this point, a query variable called posNums has been created, but no results have been obtained It is important to understand that a query simply defines a set of rules It is not until the query is executed that results are obtained Furthermore, the same query can be executed two or more times, with the possibility of differing results if the underlying data source changes between executions Therefore, simply declaring the query posNums does not mean that it contains the results of the query To execute the query, the program uses the foreach loop shown here:

the set P a partition Sometimes, to be more speci c, we call it a uniform partition (to indicate that all the subintervals have the same length) Refer to Fig 43

foreach(int i in posNums) ConsoleWriteLine(i + " ");

( 7, Geometry of Planar Cam Pro les)

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Notice that posNums is specified as the collection being iterated over When the foreach executes, the rules defined by the query specified by posNums are executed With each pass through the loop, the next element returned by the query is obtained The process ends when there are no more elements to retrieve In this case, the type of the iteration variable i is explicitly specified as int because this is the type of the elements retrieved by the query Explicitly specifying the type of the iteration variable is fine in this situation, since it is easy to know the type of the value selected by the query However, in more complicated situations, it will be easier (or in some cases, necessary) to implicitly specify the type of the iteration variable by using var

Because a query defines a set of rules that are used to retrieve data, but does not, itself, produce results, the same query can be run multiple times If the data source changes between runs, then the results of the query may differ Therefore, once you define a query, executing it will always produce the most current results Here is an example In the following version of the preceding program, the contents of the nums array are changed between two executions of posNums:

This appendix contains the polynomial coef cients appearing in the formulas derived in Chap 7, Sec 74 for the computation of the geometric properties of cams For ease of presentation, the subscript i of the spline coef cient, Axi, , Dyi is omitted throughout

The idea is to build an approximation to the area A by erecting rectangles over the segments determined by the partition The rst rectangle R1 will have as base the interval [x0 , x1 ] and height chosen so that the rectangle touches the curve at its upper right hand corner; this means that the height of the rectangle is f (x1 ) The second rectangle R2 has as base the interval [x1 , x2 ] and height f (x2 ) Refer to Fig 44

// Create a simple query using System; using SystemLinq; using SystemCollectionsGeneric;

19:

TABLE C1 aij ai1 ai2 ai3 ai4 ai5 Expression 1 (Cy Dx - Cx Dy ) 2 1 ( By Dx - Bx Dy ) 2 1 (3 Ay Dx - 3 Ax Dy + By Cx - Bx Cy ) 6 1 ( Ay Cx - Ax Cy ) 4 1 ( Ay Bx - Ax By ) 10

class SimpQuery { static void Main() {

y = f (x)

{ 1, -2, 3, 0, -4, 5 };

TABLE C2 qxij qxi1 qxi2 qxi3 qxi4 qxi5 qxi6 qxi7 qxi8 qxi9 Expression CyT7 CyT6 + ByT7 1 (Cy T4 + By T5 + 3 Ay T6 ) 2 1 (Cy T5 + 4 By T6 + 3 Ay T7 ) 3 1 (Cy T3 + 4 By T4 + 3 Ay T5 ) 5 1 (Cy T2 + By T3 + 3 Ay T4 ) 3 1 (Cy T1 + 4 By T2 + 3 Ay T3 ) 7 1 ( By T1 + 3 Ay T2 ) 4 1 Ay T1 3

// Create a query that obtains only positive numbers var posNums = from n in nums where n > 0 select n; ConsoleWrite("The positive values in nums: "); // Execute the query and display the results foreach(int i in posNums) ConsoleWrite(i + " "); ConsoleWriteLine(); // Change nums ConsoleWriteLine("\nSetting nums[1] to 99"); nums[1] = 99; ConsoleWrite("The positive values in nums after change: "); // Execute the query a second time foreach(int i in posNums) ConsoleWrite(i + " "); ConsoleWriteLine(); } }

The following output is produced:

TABLE C3 Ti T1 T2 T3 T4 T5 T6 T7 TABLE C4 h(1) i h(1) 1 h(1) 2 h(1) 3 h(1) 4 h(1) 5 h(1) 6 h(1) 7 h h h h

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