CGAL::Zp< p, T, IsPrime > Class Template Reference

#include <CGAL/Zp.h>

Definition

template<size_t p, typename T = unsigned int, bool IsPrime = true>
class CGAL::Zp< p, T, IsPrime >

The class Zp implements the concept IntegralDomainWithoutDivision with the ring \(\mathbb Z/p\mathbb Z\) (which is a field when pis prime).

This is a "lightweight" implementation which aims at providing fast operations and constructors.

According to the value of p, users can chose the size of the representation used to store values (default size: int).

Warning

For \(\mathbb Z/2\mathbb Z\), prefer the class Z2 which is optimized.

Is model of

IntegralDomainWithoutDivision

Template Parameters

p	a positive integer.
T	a type used for the inner storage of the values (default: int).
IsPrime	a bool encoding wether p is a prime number or not.

Public Member Functions
	Zp (T i=0)
	Constructor from a value.
	Zp (const Zp &a)
bool	is_zero () const
	Tests if the element is 0.
Zp &	operator= (const Zp &a)
	Operator=.
Zp &	operator+= (const Zp &a)
	Operator+=.
Zp &	operator-= (const Zp &a)
	Operator-=.
Zp &	operator*= (const Zp &a)
	Operator*=.
Zp &	operator/= (const Zp &a)
	Operator/=.
bool	is_invertible ()
	Returns the invertibility of the element.

Static Public Member Functions
static T	operator() ()
	Returns the value of p.

Friends
Zp	operator+ (const Zp &a)
	Unary operator+.
Zp	operator- (const Zp &a)
	Unary operator-.
Zp	operator+ (const Zp &a, const Zp &b)
	Operator+.
Zp	operator- (const Zp &a, const Zp &b)
	Operator-.
Zp	operator* (const Zp &a, const Zp &b)
	Operator*.
Zp	operator/ (const Zp &a, const Zp &b)
	Operator/.
bool	operator== (const Zp &a, const Zp &b)
	Operator==.
bool	operator!= (const Zp &a, const Zp &b)
	Operator!=.
Zp	abs (const Zp &a)
	Absolute value.
std::ostream &	operator<< (std::ostream &out, const Zp &a)
	Operator<<.
std::istream &	operator>> (std::istream &in, Zp &a)
	Operator>>.