Givaro
Public Member Functions
IntNumTheoDom< MyRandIter > Class Template Referenceabstract

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. 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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<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.
 
Rep & probable_prim_root (Rep &, double &, const Rep &n, const uint64_t L=10000000_ui64) 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.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
bool set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
 Factors with primes.
 
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
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
Rep & Erathostene (Rep &, const Rep &p) const
 returns a small factor
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isUnit (const Rep &x) const
 isUnit
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 
bool isDivisor (const Element &a, const Element &b) const
 isDivisor (a, b) Test if b | a.
 

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() [1/41]

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() [1/41]

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 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

◆ probable_prim_root() [2/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [2/41]

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.

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

◆ probable_prim_root() [3/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [3/41]

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.

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

◆ probable_prim_root() [4/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [4/41]

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.

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

◆ probable_prim_root() [5/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [5/41]

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.

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

◆ probable_prim_root() [6/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [6/41]

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.

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

◆ probable_prim_root() [7/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [7/41]

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.

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

◆ probable_prim_root() [8/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [8/41]

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.

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

◆ probable_prim_root() [9/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [9/41]

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.

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

◆ probable_prim_root() [10/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [10/41]

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.

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

◆ probable_prim_root() [11/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [11/41]

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.

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

◆ probable_prim_root() [12/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [12/41]

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.

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

◆ probable_prim_root() [13/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [13/41]

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.

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

◆ probable_prim_root() [14/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [14/41]

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.

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

◆ probable_prim_root() [15/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [15/41]

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.

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

◆ probable_prim_root() [16/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [16/41]

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.

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

◆ probable_prim_root() [17/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [17/41]

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.

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

◆ probable_prim_root() [18/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [18/41]

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.

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

◆ probable_prim_root() [19/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [19/41]

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.

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

◆ probable_prim_root() [20/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [20/41]

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.

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

◆ probable_prim_root() [21/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [21/41]

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.

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

◆ probable_prim_root() [22/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [22/41]

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.

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

◆ probable_prim_root() [23/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [23/41]

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.

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

◆ probable_prim_root() [24/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [24/41]

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.

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

◆ probable_prim_root() [25/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [25/41]

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.

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

◆ probable_prim_root() [26/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [26/41]

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.

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

◆ probable_prim_root() [27/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [27/41]

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.

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

◆ probable_prim_root() [28/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [28/41]

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.

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

◆ probable_prim_root() [29/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [29/41]

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.

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

◆ probable_prim_root() [30/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [30/41]

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.

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

◆ probable_prim_root() [31/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [31/41]

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.

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

◆ probable_prim_root() [32/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [32/41]

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.

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

◆ probable_prim_root() [33/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [33/41]

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.

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

◆ probable_prim_root() [34/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [34/41]

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.

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

◆ probable_prim_root() [35/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [35/41]

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.

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

◆ probable_prim_root() [36/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [36/41]

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.

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

◆ probable_prim_root() [37/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [37/41]

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.

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

◆ probable_prim_root() [38/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [38/41]

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.

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

◆ probable_prim_root() [39/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [39/41]

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.

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

◆ probable_prim_root() [40/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [40/41]

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.

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

◆ probable_prim_root() [41/41]

Rep & probable_prim_root ( Rep &  ,
double &  ,
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() [41/41]

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.

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


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