12.1 Mathematical classes

12.1.1 Class Complex

Class Complex is a simple subset of functions provided in the Gnu and AT&T complex classes. The standard arithmetic operators are implemented, as are the assignment arithmetic operators +=, -=, *=, and /=, and equality and inequality operators == and !=. There is also real() and imag() methods for accessing real and imaginary parts. It was originally written when libg++ was subject to the GPL. The current licensing for libg++ does not prevent us from using it and still distributing Ptolemy the way we want, but having it makes ports to other compilers (e.g. cfront) easier. The following non-member functions take Complex arguments:

Complex conj(const Complex& arg); 
double real(const Complex& arg); 
double imag(const Complex& arg);
double abs(const Complex& arg);

Return the conjugate, real part, imaginary part, or absolute value, respectively.

double arg(const Complex& arg);

Return the angle between the X axis and the vector made by the argument. The expression

abs(z)*exp(Complex(0.,1.)*arg(z))

is in theory always equal to z.

double norm(const Complex& arg);

return the absolute value squared.

Complex sin(const Complex& arg);
Complex cos(const Complex& arg); 
Complex exp(const Complex& arg);
Complex log(const Complex& arg); 
Complex sqrt(const Complex& arg);

Standard mathematical functions. log returns the principal logarithm.

Complex pow(double base,const Complex& expon); 
xpon);

Raise base to expon power. There is also an operator to print a Complex on an ostream.

12.1.2 class Fraction

Class Fraction represents fractions. The header Fraction.h also provides declarations for the lcm (least common multiple) and gcd (greatest common divisor) functions, as these functions are needed for Fraction but are generally useful.

Fraction (); 
Fraction (int num, int den=1);

The default constructor produces a fraction with numerator 0 and denominator 1. The other constructor allows the numerator and denominator to be specified arbitrarily.

int num() const; 
int den() const;

Return the numerator or denominator.

operator double() const;

Return the value of the fraction as a double. Class Fraction implements the basic binary math operators +, -, *, /; the assignment operators =, +=, -=, *=, and /=, and the equality test operators == and !=. The method

Fraction& simplify();

reduces the fraction to lowest terms, and returns a reference to the fraction. There is also an operator to print a Fraction on an ostream.