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Point object (see Problem 8.17) into a
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9.63 Overload the bitwise NOT operator -
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9.64 Implement a conversion operator that converts a
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Complex
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object (see Problem 8.59).
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CHAP. 91
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OVERLOADING
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OPERATORS
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9.65 Implement a conversion operator that converts a Complex object (see Problem 8.53) into a Point object (see Problem 8.17). 9.66 Implement the overloaded division operator / for the Complex
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class (see Problem 8.54) using the norm operator ! (see Problem 9.62) and the conjugate operator - (see Problem 9.62). The quotient of two complex numbers is computed by the formula
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U u-v -=V IV I
where v is the conjugate of v and IVI is the norm of v.
9.67 Implement an overloaded assignment operator =
for the Quaternion class (see Problem and stream extraction operator >> for
!= for the Quaternion class (see
8.59).
9.68 Implement overloaded stream insertion operator < < the Quaternion class (see Problem 8.59).
9.69 Implement overloaded comparison operators = = and
Problem 8.59).
9.70 Implement overloaded addition operator + and subtraction operator - for the Quaternion
class (see Problem 8.59).
9.71 Overload the NOT operator ! to return the norm for the Quaternion class (see Problem
8.59). The norm of a quaternion is the square root of the sum of the sauares of its real and imaginary parts. So if z represents the qu atemion 3 - 4i +12k, then ! z bould return 13. Note thit this is a unary operator.
9.72 Overload the bitwise NOT operator - to return the conjugate for the Quaternion class (see
Problem 8.59). The conjugate of a quatemion is the same quatemion except with the sign of its . . imaginary parts reversea. So II z represents 1 complex number 3 - 4i + 12k, then - z would me return the Quatekion object that represents 3 + 4i -12k. Note that this is a unary operator.
1 ri .P Al
9.73 Implement the overloaded division operator / for the Quaternion class (see Problem 8.59)
using the norm operator ! (see Problem 9.62) and the conjugate operator - (see Problem 9.72). The quotient of two quatemions is computed by the formula u u*v -=V IV I
where v is the conjugate of v and IVI is the norm of v.
9.74 Implement a conversion operator that converts a Point object (see Problem 8.17) into a Quaternion object (see Problem 8.59). 9.75 Implement a conversion operator that converts a Quaternion object (see Problem 8.59) into a Point object (see Problem 8.17). 9.76 Implement a conversion operator that converts a Complex Quaternion object (see Problem 8.59).
object (see Problem 8.53) into a
9.77 Implement a constructor that converts a Complex object (see Problem 8.53) into a Quaternion object (see Problem 8.59).
OVERLOADING
OPERATORS
[CHAP. 9
Answers to Review Questions
9.1 9.2 The operator keyword is used to form the name of a function that overloads an operator. For example, the name of the function that overloads the assignment operator = is operator =". The keyword thi s is a pointer to the object that owns the call of the member function in which the expression appears.
9.3 The expression * thi s always refers to the object that owns the call of the member function in which the expression appears. Therefore, it can only be used within member function. 9.4 9.5 The overloaded assignment operator should return * this so that the operator can be used in a cascade of calls, like this: w = x = y = z ; The declaration Rat ional y ( x) ; calls the default constructor; the declaration Rational calls the copy constructor. y = x
9.6 The declaration Rational y = x ; calls the copy constructor. The code Rational y ; y = x ; calls the default constructor and then the assignment operator. 9.7 9.8 The symbol * * cannot be overloaded as an operator because it is not a C++ operator. The stream operators c < and > > should be overloaded as friend functions because their left operands should be stream objects. If an overloaded operator is a member function, then its left operand is * this, which is an object of the class to which the function is a member.
9.9 The arithmetic operators +, -, *, and / should be overloaded as friend functions so that their left operands can be declared as cons t. This allows, for example, the use of an expression like 2 2 + x. If an overloaded operator is a member function, then its left operand is * thi s, which is not cons t . 9.10 The overloaded pre-increment operator has no arguments. The overloaded post-increment operator h a s one (dummy) argument, of type int. 9.11 The int argument in the implementation of the post-increment operator is left unnamed because it is not used. It is a dummy argument. 9.12 By returning a reference, the overloaded subscript operator [ ] can be used on the left side of an assignment statement, like this: v [ 2 ] = 2 2. This is because, as a reference, v [ 2 ] is an lvalue.
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