IntNumTheoDom< MyRandIter > Class Template Reference

Num theory Domain. More...

#include <givintnumtheo.h>

Inheritance diagram for IntNumTheoDom< MyRandIter >:

Collaboration diagram for IntNumTheoDom< MyRandIter >:

Public Member Functions
template<template< class, class > class Container, template< class > class Alloc>
Rep &	phi (Rep &res, const Container< Rep, Alloc< Rep > > &Lf, const Rep &n) const
	Euler's phi function.
Rep &	prim_root (Rep &, const Rep &) const
	Primitive Root.
template<class Array>
Rep &	prim_root_of_prime (Rep &A, const Array &Lf, const Rep &phin, const Rep &n) const
	Add Jacobi for quadratic nonresidue.
Rep &	probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) const
	Polynomial-time generation of primitive roots.
Rep &	probable_prim_root (Rep &, double &, const Rep &n, const double epsilon) const
	Here L is computed so that the error is close to epsilon.
Rep &	prim_inv (Rep &, const Rep &) const
	Generalization of primitive roots for any modulus Primitive means maximal order Primitive Element, Primitive invertible Both functions coincide except for m=8.
template<template< class, class > class Container, template< class > class Alloc>
short	mobius (const Container< Rep, Alloc< Rep > > &lpow) const
	Möbius function.
short	mobius (const Rep &a) const
	Möbius function.
bool	set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
	Factors with primes.
bool	isUnit (const Rep &x) const
	isUnit
bool	isDivisor (const Element &a, const Element &b) const
	isDivisor (a, b) Test if b | a.
Input/Output Operations
std::ostream &	write (std::ostream &os, const Element &x) const
	Print field element.
std::istream &	read (std::istream &is) const
	Read field.
virtual std::istream &	read (std::istream &is, Element &x) const
	Read field element.
Data Object Management.
first argument is set and the value is also returned.

Detailed Description

template<class MyRandIter = GivRandom>
class Givaro::IntNumTheoDom< MyRandIter >

Num theory Domain.

Examples

examples/Integer/isproot.C, examples/Integer/lambda.C, examples/Integer/lambda_inv.C, examples/Integer/order.C, examples/Integer/phi.C, examples/Integer/primitiveelement.C, examples/Integer/primitiveroot.C, and examples/Integer/probable_primroot.C.

Member Function Documentation

probable_prim_root()

template<class MyRandIter>

IntNumTheoDom< MyRandIter >::Rep & probable_prim_root	(	Rep &	primroot,
		double &	error,
		const Rep &	n,
		const uint64_t	L = 10000000_ui64 ) const

Polynomial-time generation of primitive roots.

L is number of loops of Pollard partial factorization of n-1 10,000,000 gives at least 1-2^{-40} probability of success [Dubrois & Dumas, Industrial-strength primitive roots] Returns the probable primitive root and the probability of error.

prim_inv()

template<class MyRandIter>

IntNumTheoDom< MyRandIter >::Rep & prim_inv	(	Rep &	A,
		const Rep &	n ) const

Generalization of primitive roots for any modulus Primitive means maximal order Primitive Element, Primitive invertible Both functions coincide except for m=8.

Lambda Function : maximal orbit size lambda : Order of a primitive Element lambda_inv : Order of an invertible primitive Element Both functions coincide except for m=8

write() [1/2]

std::ostream & write ( std::ostream & os, std::string F ) const

inlineinherited

Read field.

Returns

input stream from which field is read.

Parameters

is	input stream from which field is read.

write() [2/2]

std::ostream & write ( std::ostream & os, const Element & x ) const

inlineinherited

Print field element.

Returns

output stream to which field element is written.

Parameters

os	output stream to which field element is written.
x	field element.

read() [1/2]

std::istream & read ( std::istream & is ) const

inlineinherited

Read field.

Returns

input stream from which field is read.

Parameters

is	input stream from which field is read.

read() [2/2]

virtual std::istream & read ( std::istream & is, Element & x ) const

inlinevirtualinherited

Read field element.

Returns

input stream from which field element is read.

Parameters

is	input stream from which field element is read.
x	field element.

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The documentation for this class was generated from the following files:

• givintnumtheo.h
• givintnumtheo.inl