IntNumTheoDom< RandIter > Class Template Reference

Num theory Domain. More...

#include <givintnumtheo.h>

Inheritance diagram for IntNumTheoDom< RandIter >:

Collaboration diagram for IntNumTheoDom< RandIter >:

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 unsigned long L=10000000) const
	Polynomial-time generation of primitive roots. More...
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 coïncides except for m=8. More...
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.
template<class Container1 , class Container2 >
bool	set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
	Factors with primes.
Rep &	Erathostene (Rep &, const Rep &p) const
	returns a small factor

Detailed Description

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

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

IntNumTheoDom< RandIter >::Rep & probable_prim_root	(	Rep &	primroot,
		double &	error,
		const Rep &	n,
		const unsigned long	L = 10000000
	)		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.

IntNumTheoDom< RandIter >::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 coïncides 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 coïncides except for m=8

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

• givintnumtheo.h
• givintnumtheo.inl