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As explained in 8, members of a class are often declared private to prevent their unauthorized use or tampering Inheriting a class does not overrule the private access restriction Thus, even though a derived class includes all of the members of its base class, it cannot access those members of the base class that are private For example, if, as shown here, Width and Height are made private in TwoDShape, then Triangle will not be able to access them:

q = 1, y = 0350, y = 0, y = 0, y = 0 The general polynomial equation is of the form y = C0q 2 + Cpq p + Cqq q + Crq r + Cwq w , where the exponents p, q, r, and w may have values such that 8 p < q < r < s 50

// Access to private members is not inherited // This example will not compile using System; // A class for two-dimensional objects class TwoDShape {

11:

Now let us indicate some polynomial curves that have been developed The following are four curves with excellent dynamic characteristics

Sketch the set of points {(x, y): x = 4}

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public void ShowDim() { ConsoleWriteLine("Width and height are " + Width + " and " + Height); } } // Triangle is derived from TwoDShape class Triangle : TwoDShape { public string Style; // style of triangle // Return area of triangle public double Area() { return Width * Height / 2; // Error, can't access private member } // Display a triangle's style public void ShowStyle() { ConsoleWriteLine("Triangle is " + Style); } }

The Triangle class will not compile because the use of Width and Height inside the Area( ) method is illegal Since Width and Height are now private, they are accessible only to other members of their own class Derived classes have no access to them

3-4-5

outside its class, including derived classes At first, you might think that it is a serious restriction that derived classes do not have access to the private members of base classes because it would prevent the use of private members in many situations However, this is not true; C# provides various solutions One is to use protected members, which is described in the next section A second is to use public properties to provide access to private data As explained in the previous chapter, a property allows you to manage access to an instance variable For example, you can enforce constraints on its values, or you can make the variable read-only By making a property public, but declaring its underlying variable private, a derived class can still use the property, but it cannot directly access the underlying private variable Here is a rewrite of the TwoDShape class that makes Width and Height into properties In the process, it ensures that the values of Width and Height will be positive This would allow you, for example, to specify the Width and Height using the coordinates of the shape in any quadrant of the Cartesian plane without having to first obtain their absolute values

// Use public properties to set and get private members using System; // A class for two-dimensional objects

SOLUTION The set consists of all points with y-coordinate equal to 3 This is the set of all points that lie 3 units above the x-axis We exhibit in Fig 19 It is a horizontal line

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Part I:

21:

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Method public static bool IsPositiveInfinity(float v) public static bool IsNegativeInfinity(float v) public static float Parse(string str)

The set k consists of all points with x-coordinate equal to 4 This is the set of all points that lie 4 units to the left of the y-axis We exhibit k in Fig 110 It is a vertical line EXAMPLE 17

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4-6-8-10 4-5-6-7

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